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TEXT-BOOK  OF  ELECTROCHEMISTRY 


THE  KINETIC  THEORY  OF  GASES.  Elementary  Treatise, 
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PRACTICAL  ELECTRICAL  TESTING  IN  PHYSICS  AND 
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AN  ELEMENTARY  TREATISE  ON  ALTERNATING 
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A  SHORT  HISTORY  OF  THE  PROGRESS  OF  SCIEN- 
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INTRODUCTION  TO  THE  STUDY  OF  CHEMICAL 
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LONGMANS,    GREEN,    AND    CO. 

LONDON,   NEW   YORK,  AND  BOMBAY 


RT741V* 

TEXT-BOOK    OF  ^ 

ELECTROCHEMISTRY 


BY 

SVANTE    ARRHENIUS 

PROFESSOR      AT      THE      UNIVERSITY      OF      STOCKHOLM 

TRANSLATED  BY  JOHN  McCRAE,  PH.D. 


WITH  NUMEROUS    DIAGRAMS 


LONGMANS,    GREEN,    AND    CO. 

39    PATERNOSTER    ROW,    LONDON 

NEW  YORK   AND   BOMBAY 

1902 

All  rights  reserved 


PREFACE 

THE  basis  of  this  book  is  a  series  of  lectures  delivered  by 
me  at  the  University  of  Stockholm  in  the  autumn  of  1897. 

The  English  translation  has  been  made  from  the  German 
edition. 

In  the  German  translation,  made  by  Dr.  H.  Euler, 
many  improvements  and  additions  to  the  original  Swedish 
edition  were  introduced  with  reference  to  the  literature  up 
till  1901.  Only  few  alterations  have  been  made  in  the 
present  edition,  and  these  refer  mainly  to  typographical 
errors.  By  the  list  of  literature-references  collected  by 
Dr.  McCrae  considerable  value  has  been  added  to  the 
book. 

THE  AUTHOR 

STOCKHOLM, 

June,  1902. 


CONTENTS 

CHAPTER   I. 
Fundamental  Physical  and  Chemical  Conceptions. 

Polarisation,!.  Cause  of  polarisation,  2.  The  electrolytic  decomposition  of 
water,  2.  Electrolysis  of  salts  of  th'e  heavy  metals,  3.  Primary  and 
secondary  electrolysis,  3.  Ions,  4.  Coulomb,  4.  Ampere,  4.  Ohm,  4. 
Unit  of  conductivity,  4.  The  absolute  systems,  4.  Ohm's  law,  Volt,  5. 
Potential,  5.  Fall  of  potential,  6.  Current  density,  7.  Electrochemical 
equivalents,  7.  Atomic  weight,  8.  Gram-equivalent,  9.  Gram-mole- 
cule, 9.  Concentration,  10.  Temperature,  10.  Mechanical  work,  11. 
Effect,  11.  Work  done  by  change  of  volume,  12.  Work  done  by 
evolution  of  a  gas  under  constant  pressure,  12.  Expansion  of  gases 
by  heat  at  constant  pressure,  14.  Expansion  of  gases  at  constant 
temperature,  14. 

CHAPTER   II. 
Older  Electrochemical  Views. 

The  first  electrochemical  investigations,  16.  Galvani  and  Volta,  17. 
Berzelius's  investigations,  18.  Davy's  electrochemical  theory,  18. 
Berzelius's  theory,  19.  The  Grotthuss  chain,  21.  Ampere's  theory,  21. 
Faraday's  law,  22.  Hittorf s  investigation,  22.  Helmholtz's  Faraday 
lecture,  22. 

CHAPTER    III. 
The  Laws  of  Avogadro  and  van't  Hoff. 

Boyle's  law,  25.  Gay-Lussac's  law,  25.  Avogadro's  law,  25.  Law  of  van 
der  Waals,-26.  Isotonic  solutions,  27.  Semi-permeable  membranes,  28. 
Osmotic  pressure,  28.  Osmotic  pressure  of  gases,  31.  Osmotic  experi- 
ments with  liquids,  32.  Nature  of  osmotic  pressure,  33.  Physiological 


viii  CONTENTS. 

measurement  of  the  relative  osmotic  pressures  in  different  solutions,  35. 
Tammann's  measurements,  37.  Further  experiments  on  osmotic 
pressure,  38. 

CHAPTER   IV. 

Vapour  Pressure  of  Solutions. 

Vapour  pressure  of  a  solution,  39.  Connection  between  vapour  pressure  and 
osmotic  pressure,  39.  Relative  lowering  of  vapour  pressure,  41.  Vapour 
pressure  of  solutions  in  ether,  43.  Higher  concentrations,  44.  Aqueous 
solutions,  45. 

CHAPTER   V. 

Boiling  Point  and  Freezing  Point  of  Solutions. 

Calculation  of  the  boiling  point  of  a  solution,  47.  Freezing  point  of  solutions, 
49.  Experimental  determination  of  the  freezing  point,  51.  Experi- 
mental determination  of  the  boiling  point,  52.  Advantages  of  the 
freezing  point  method,  53.  Connection  between  depression  of  vapour 
pressure  and  depression  of  freezing  point,  54.  Connection  between 
osmotic  pressure  of  a  solution  and  its  freezing  point  and  vapour  pressure, 
55.  Molecular  lowering  of  the  freezing  point,  56.  Molecule  complexes, 
58.  Dissociation  of  electrolytes,  59.  Range  of  validity  of  van't  HofFs 
law,  60.  Alloys,  61.  Solid  solutions,  63.  Experimental  results  on  the 
rise  of  boiling  point,  63.  Comparison  between  the  various  methods 
for  determining  the  molecular  weight,  65.  Review  of  the  results 
obtained,  66. 

CHAPTER   VI. 
General  Conditions  of  Equilibrium. 

Chemical  reactions,  69.  Chemical  equilibrium,  70.  The  phase  rule  of  Gribbs, 
73.  Osmotic  work,  75.  Henry's  law,  77.  Distribution  law,  80. 
Kinetic  considerations,  82.  Depression  of  solubility,  83.  Homogeneous 
equilibrium,  84.  Clapeyron's  formula,  90.  Change  of  solubility  with 
temperature,  91.  Change  of  homogeneous  equilibrium  with  temperature, 
93.  Maxima  and  minima  in  equilibria,  96.  Influence  of  pressure,  98. 


CHAPTER     VII. 
Velocity  of  Reaction. 

Formation  of  the  state  of  equilibrium,  100.  Inversion  of  cane  sugar,  100. 
Saponificatiou  of  an  ester,  102.  Velocity  in  heterogeneous  systems,  103. 
Influence  of  temperature,  104.  Velocity  of  reaction  and  osmotic 
pressure,  107.  Action  of  neutral  salts,  109. 


CONTENTS.  ix 

CHAPTER   VIII. 
Electrolytes.     Electrolytic  dissociation. 

Deviations  shown  by  electrolytes  from  van't  Hoffs  law,  110.  Faraday's 
experiments,  110.  The  ions,  113.  Charging  current,  116.  Faraday's 
laws,  117.  Composition  of  the  ions,  118.  Application  of  Ohm's  law 
to  solutions,  120.  Standard  units  for  resistance  and  electromotive 
force,  122. 

CHAPTER    IX. 

Conductivity  of  Electrolytes. 

Horsford's  method  of  determining  the  resistance,  125.  Change  of  con- 
ductivity with  dilution,  126.  Specific  and  molecular  conductivity,  127. 
The  Wheatstone  bridge,  129.  Determination  of  the  resistance  of 
electrolytes,  129.  Experimental  results,  133.  Calculation  of  the  degree 
of  dissociation  in  electrolytic  solutions,  137.  Transport  number,  138. 
Kohlrausch's  law,  140.  Transport  numbers  and  ionic  mobilities,  141. 
Abnormal  transport  numbers,  143.  Mobilities  of  organic  ions,  144. 
Migration  of  ions  in  mixed  solutions,  145.  Complex  ions,  146.  Ionic 
migration  and  the  theory  of  dissociation,  146.  Calculation  of  A^  for 
slightly  dissociated  electrolytes,  147.  Absolute  velocity  of  the  ions,  147. 
Diffusion,  152. 

CHAPTER   X. 

Degree  of  Dissociation  and  Dissociation  Constant. 

Strong  and  weak  electrolytes,  157.  Degree  of  dissociation  of  some  typical 
electrolytes,  157.  Comparison  between  the  results  of  the  osmotic  and 
the  electric  determinations  of  the  degree  of  dissociation,  159.  Dis- 
sociation equilibrium  of  weak  electrolytes,  162.  Dissociation  equilibrium 
of  strong  electrolytes,  164.  Divalent  acids,  166.  Influence  of  substitu- 
tion on  the  dissociation  of  acids,  166. 


CHAPTER   XI. 

Conclusions  from  the  Dissociation  Theory.     Additive  Properties  of 

Solutions. 

General  remarks,  168.  Specific  gravity  of  electrolytic  solutions,  169.  Com- 
pressibility, capillarity,  and  internal  friction  of  solutions,  172.  Refrac- 
tive index  of  solutions,  173.  Magnetic  rotation  of  solutions,  174. 
Molecular  magnetism,  175.  Natural  rotatory  power  in  solution,  176. 
Light  absorption  of  solutions,  177.  Chemical  properties  of  the  ions, 
178.  Physiological  action  of  the  ions,  180.  Catalytic  action  of 
hydrogen  and  hydroxyl  ions,  182.  Objections  to  the  assumption  of 
electrolytic  dissociation,  184. 


x  CONTENTS. 

CHAPTER   XII. 
Equilibrium  between  Several  Electrolytes. 

Isohydric  solutions,  188.  Precipitation,  189.  Distribution  of  a  base  between 
two  acids  (avidity),  191.  Strength  of  acids  and  bases,  192.  The  dis- 
sociation of  water,  193.  Heat  of  dissociation  of  water,  194.  Heat  of 
neutralisation,  196.  Electrolytes  with  a  negative  temperature  co- 
efficient for  the  conductivity,  198.  Neutralisation  volume.  198. 

CHAPTER   XIII. 
Calculation  of  Electromotive  Forces. 

Introduction,  201.  Galvanic  elements,  202.  Transformation  of  chemical 
into  electrical  energy  in  a  Daniell  cell  —  Thomson's  rule,  203.  Criticism 
of  Thomson's  rule,  205.  Helmholtz's  calculation,  207.  Free  and  bound 
energy,  209.  Meyer's  concentration  element,  210.  Helmholtz's  concen- 
tration element,  212.  Nernst's  calculation  of  the  electromotive  force  at 
the  surface  of  separation  of  two  solutions  of  the  same  salt,  218.  Nernst's 
calculation  of  the  electromotive  forces  of  concentration  elements,  220. 
Experimental  confirmation  of  the  theory,  223.  Solution  pressure  of 
metals.  225.  Planck's  formula,  227. 


CHAPTER   XIV. 
Potential  Difference  between  Two  Bodies. 

Electrical  double-layer,  230.  Potential  difference  between  a  metal  and  a 
liquid,  231.  Capillary  electrometer,  232.  Dropping  electrodes,  233. 
The  Volta  effect,  235.  Peltat's  method,  236.  Kesults  of  experimental 
determinations,  237.  Heat  of  ionisation,  238.  Seat  of  the  electro- 
motive force  in  a  Daniell  element,  240.  Very  small  ionic  concentra- 
tions, 242. 

CHAPTER   XV. 

Oxidation  and  Reduction  Elements.     Secondary  Elements. 

Hccquerel's  experiments,  244.  Neutralisation  element,  247.  Irreversible 
elements,  248.  Normal  elements,  251.  Secondary  elements,  253. 
Polarisation  current,  253.  Smale's  experiments,  253.  Helniholtz's 
investigation  on  the  influence  of  pressure,  254.  Strength  of  the  polari- 
sation current,  256.  Le  Blanc's  investigations,  257.  Maximum  polari- 
sation, 259.  Polarisation  by  deposition  of  solid  substances,  259.  Grove's 
investigations,  260.  Cathodic  and  anodic  polarisation,  260.  Accumu- 
lators, 261. 


CONTENTS.  xi 

CHAPTER   XVI. 
Electro-analysis. 

Determination  of  the  quantity  of  salt  in  a  solution  by  measuring  the  con- 
ductivity, 268.  Application  of  the  electrometer  as  an  indicator,  260. 
Analysis  by  metal  deposition,  270.  Peroxide  precipitates,  274.  Reduc- 
tion of  nitric  acid  to  ammonia,  275.  Copper  refining,  276.  Precipitation 
of  a  metal  from  a  solution  containing  two  metal  salts,  279.  Position 
of  hydrogen  in  deposition,  280.  Analytical  separation  of  the  metals, 
281.  Primary  and  secondary  deposition  of  metal,  282.  Difference  of 
the  temperature  influence  in  primary  and  secondary  processes,  284. 
Voltameter,  286. 

CHAPTER   XVII. 
Development  of  Heat  by  the  Electric  Current. 

Review,  288.  Arc  light,  289.  Influence  of  temperature  on  chemical 
reactions,  291.  Fused  electrolytes — Heroult's  furnace,  295.  Xon- 
electrolytic  processes  with  electrical  heating — Cowles'  furnace,  297. 
Resistance  furnaces — The  carborundum  process,  299.  Arc  light  fur- 
naces, 301.  Production  of  calcium  carbide,  303.  Silent  electrical 
discharges,  305.  Electrothermic  and  electrochemical  actions,  307. 
Production  of  ozone,  309. 


ELECTROCHEMISTRY 


CHAPTER   I. 

INTRODUCTION. 

Fundamental  Physical  and  Chemical  Conceptions. 

Polarisation. — Suppose   two  plates  of  platinum,  one  (Pi) 

connected  with  the   positive  and   the  other  (P2)  with  the 

negative  pole  of  a  galvanic  battery  (B),  dipped  into  a  solution 

(L)  of  sodium   sulphate   (Fig.  1).      Two   phenomena  may 

present  themselves :  (a)  when  the  electromotive  force  of  the 

battery  is  less  than  about  2*2  volts,  no 

bubbles  of  gas  appear  on  the  platinum  B 

plates,  or  (b)  when  the  electromotive  +A  '  I  \~      sQ) 

force  of  the  battery  is  sufficiently  great        f  /^ 

(over  2 '2  volts),  gas  is  evolved  at  each 

of    the    plates — oxygen    at    Plt     and 

hydrogen   at   P2.      In   both    cases,    a 


current  passes  through  the  salt  solu-  FIG.  i. 

tion  (in  case  (a)  the  current  is  very 
weak),  and  this  can  be  recognised  by  the  deflection  of  the 
needle  of  a  galvanometer  (G)  interposed  in  the  circuit  indi- 
cating that  the  current  is  passing  in  the  direction  from  PI 
to  P2.  Suppose,  now,  that  B  be  eliminated  from  the  circuit 
by  connecting  Px  directly  to  the  galvanometer  by  means  of  a 
wire ;  it  will  then  be  found  that  the  needle  of  the  galva- 
nometer is  deflected  in  the  opposite  direction,  showing  that 
a  current  is  passing  through  the  salt  solution  from  P2  to  PI. 
This  current  is  due  to  the  so-called  polarisation.  If  whilst  B 

B 


2  INTRODUCTION.  CHAP. 

was  in  the  circuit  gas  evolution  had  actually  taken  place,  the 
polarisation  current  would  be  stronger,  and  would  last  longer 
than  in  the  case  where  no  bubbles  of  gas  had  been  produced. 
Cause  of  Polarisation.— Let  us  assume  that  gas  had 
been  evolved  at  the  plates.  After  the  battery  has  been  in 
action  for  some  time  plate  PI  has  become  covered  with  a  film 
of  oxygen  and  plate  P2  has  a  similar  envelope  of  hydrogen. 
The  plates,  originally  quite  similar,  after  the  passage  of  the 
current  behave  like  two  different  metals.  In  the  same  way 
that  a  current  can  be  obtained  between  a  copper  plate  and  a 
zinc  plate  immersed  in  sodium  sulphate  solution,  the  current 
is  now  obtained  when  the  platinum  plate  covered  with  oxygen 
is  connected  by  means  of  a  conducting-wire  with  the  plate 
covered  with  hydrogen,  both  being  immersed  in  the  solution. 
The  gases  which  cling  to,  or  have  penetrated  into,  the  plates 
are  used  up  in  giving  rise  to  the  current  which,  consequently, 
soon  stops. 

Even  in  the  case  where  no  apparent  evolution  of  gas  has 
taken  place  when  current  has  been  drawn  from  the  battery 
the  plates  behave  in  the  same  manner.  It  is,  therefore, 
assumed  that  here  too  the  gases  are  really  separated,  but  in 
such  small  quantity  as  not  to  make  themselves  evident,  and 
this  assumption  is  supported  by  various  considerations. 

The  polarisation  of  the  plates  presents  itself,  therefore,  in 
the  property  which  these  have  of  behaving  like  two  different 
metals  which  exert  an  opposing  electromotive  force  against 
the  electromotive  force  of  the  battery.  Plate  PI  is  said  to  be 
"  polarised  "  with  oxygen,  plate  P2  with  hydrogen. 

The  Electrolytic  Decomposition  of  Water.— Other 
changes,  besides  the  separation  of  gases,  take  place  at  the 
plates  PI  and  P2,  which  also  are  of  importance  for  the 
polarisation.  If  a  few  drops  of  litmus  solution  be  added  to 
the  salt  solution  it  is  found  that  the  liquid  in  the  neigh- 
bourhood of  plate  PI  becomes  red,  whilst  that  near  plate  P2 
remains  (or  becomes)  blue,  indicating  that  the  salt  solution, 
originally  neutral,  has  altered  near  the  electrodes,  and  has 
become  acid  at  PI  and  basic  at  P2. 


i.  ELECTROLYSIS.  3 

This  process  of  passing  a  current  through  a  salt  solution 
is  termed  electrolysis.  The  result  of  the  electrolysis  here 
considered  consists  partly  in  the  evolution  of  oxygen  at  P\ 
and  hydrogen  at  P2,  and  partly  therein  that  the  solution  near 
PI  contains  free  acid,  and  that  near  P2  free  alkali.  These 
phenomena  are  typical  for  electrolysis  in  aqueous  solution  of 
oxygen  salts  of  the  alkali  and  alkaline  earth  metals. 

Electrolysis  of  Salts  of  the  Heavy  Metals.— When 
the  solution  of  a  salt  of  a  heavy  metal,  such  as  silver  or 
copper,  is  electrolysed,  the  phenomenon  is  somewhat  different. 
Let  the  plates  2\  and  P2  be  of  the  same  metal  as  that 
contained  in  the  salt,  e.g.  silver  electrodes  in  a  solution  of 
silver  nitrate.  In  this  case  there  is  no  evolution  of  gas,  nor 
any  change  in  the  neutrality,  and  polarisation  does  not  take 
place  to  an  appreciable  extent.  The  action  of  the  current 
passing  from  PI  to  P2  consists  in  the  dissolving  of  some  of 
the  silver  of  the  electrode  PI  and  deposition  of  the  same 
amount  of  silver  on  P2,  and  further,  the  solution  near  PI 
becomes  more  concentrated,  whilst  that  near  P2  becomes  more 
dilute.  This  concentration  change  gives  rise  to  a  weak 
electromotive  force  which  corresponds,  in  a  certain  respect, 
to  the  above-mentioned  polarisation  electromotive  force. 

Primary  and  Secondary  Electrolysis. — It  may  possibly 
appear  strange  that  the  salts  of  the  heavy  metals  behave 
differently  from  the  alkali  salts  on  electrolysis.  However,  if 
these  latter  be  electrolysed  in  the  fused  condition,  the  metal 
is  separated  at  the  negative  electrode  ;  and  even  from  aqueous 
solution  the  alkali  metal  may  be  separated  electrolytically 
if  mercury  be  used  as  the  negative  pole.  The  formation 
of  alkali  at  the  negative  pole  in  the  previous  example 
is  not  a  direct  consequence  of  the  electrolysis,  but  is  due 
to  the  chemical  action  of  the  water  on  the  primarily 
separated  metal.  The  alkali  metal  is  deposited  by 
"primary  electrolysis,"  and  the  secondary  formation  of 
alkali  is  termed  "  secondary  electrolysis."  When  a  chloride, 
e.g.  sodium  chloride,  is  electrolysed  between  platinum  plates, 
chlorine  is  primarily  separated  at  the  positive  pole,  and  this 


4  INTRODUCTION.  CHAP. 

partially  reacts  "  secondarily  "  with  the  water  present  to  form 
oxygen  and  hydrochloric  acid. 

Ions. — During  the  course  of  the  electrolysis  certain 
substances,  whose  nature  is  determined  by  chemical  analysis, 
are  removed  from  the  solution  to  each  pole.  Those  substances 
which  "  migrate  "  to  the  positive  electrode  (Pi),  or  anode, 
are  called  anions,  those  which  migrate  to  the  negative  electrode 
(P2),  or  cathode,  are  called  cations  (see  Chap.  VIII.),  this  being 
the  nomenclature  introduced  by  Faraday. 

Coulomb. — According  to  the  law  discovered  by  Faraday 
in  1834,  the  quantity  of  gas  and  the  quantity  of  silver  which 
separate  at  P2  in  the  examples  given  above  are  exactly 
proportional  to  the  quantity  of  electricity  which  passes 
through  the  solution  during  the  electrolysis.  The  mass  of 
the  deposited  material,  therefore,  is  a  convenient  measure  of  the 
quantity  of  electricity  which  passed  through  the  electrolyte. 
The  coulomb,  our  unit  for  the  quantity  of  electricity,  is  that 
quantity  required  for  the  separation  of  1*118  milligrams  of 
silver  (the  equivalent  quantity  of  copper,  0'3284  mgms.,  or 
of  hydrogen,  0'0104  mgms.,  according  to  Faraday's  law). 

Ampere. — The  current  strength  is  determined  by  the 
quantity  of  electricity  which  passes  through  a  circuit  in  a 
specified  time.  As  unit,  we  use  the  ampere  (amp.),  which  is 
obtained  when  1  coulomb  passes  through  the  circuit  in 
one  second. 

Ohm. — The  unit  of  electrical  resistance  is  that  resistance 
offered  at  0°  by  a  column  of  pure  mercury  106' 30  cm.  long 
with  a  section  of  one  square  millimetre.  This  is  the  inter- 
national ohm,  and  is  equal  to  1*063  Siemens'  units. 

Unit  for  Conductivity. — The  electrical  conductivity  of 
a  substance  is  the  reciprocal  of  the  value  of  its  resistance. 
As  unit,  the  conductivity  of  a  substance  is  used,  a  column 
of  which  1  cm.  long  and  of  1  sq.  cm.  section  possesses  the 
resistance  of  1  ohm.  The  best  conducting  solutions  of 
acids  have  nearly  this  conductivity  at  about  40°. 

The  Absolute  Systems. — In  scientific  work  it  is 
frequently  necessary  to  calculate  the  above  "  practical '" 


I.  OHM'S   LAW.  5 

units  into  those  of  the  "absolute  system  of  measurement," 
and  the  electrical  units  have  to  be  measured  either  in  electro- 
static or  electro-dynamic  units.  The  following  table  shows 
the  relationship  between  the  values  referred  to  : — 

Practical.  Electrostatic  (C.G.S.).         Electromagnetic. 

1  coulomb  300  x  107  10"  ( 

1  ampere  300  x  107  10  ~* 

lohm  T^xlO'9  10° 

1  volt  i  x  10~2  10* 

Ohm's  Law.  Volt. — If  the  terminals  of  a  galvanic 
battery  of  electromotive  force  E  be  connected  by  means  of 
a  conducting- wire  so  that  a  current  passes,  then  the  electro- 
motive force,  the  current  strength  (/),  and  the  resistance 
(R)  are  connected  by  the  following  relationship  :— 

~~  k 

This  is  termed  Ohm's  law,  after  its  discoverer.  That 
electromotive  force  which  in  a  circuit  of  resistance  1  ohm 
produces  a  current  strength  of  1  ampere  is  taken  as  unit, 
and  is  called  a  volt.  Formerly,  electromotive  forces  were 
referred  to  the  tension  (potential  difference)  between  the 
poles  of  a  Daniell  element  (zinc  pole  in  10  per  cent,  sulphuric 
acid,  copper  pole  in  saturated  copper  sulphate  solution)  at 
the  ordinary  temperature.  This  electromotive  force,  called 
a  "daniell,"  is  equal  to  about  1/10  volts  (compare  Chap. XI.). 
The  electromotive  force  of  a  Clark  element  functioning  at 
15°  is  now  generally  used  as  standard  (1/433  volts). 

Potential. — The  term  "potential  difference"  is  frequently 
used  in  place  of  electromotive  force.  Positive  electricity  tends 
always  to  pass  from  places  of  higher  potential  to  those  of 
lower  potential ;  and  this  is  an  essential  property  or  character- 
istic of  the  potential.  In  the  subject  of  electricity  the  potential 
plays  nearly  the  same  part  that  the  temperature  does  in  the 
subject  of  heat,  for  heat  always  tends  to  pass  from  places 
of  higher  to  those  of  lower  temperature.  In  the  subjects  of 
electricity  and  heat,  however,  there  is  this  difference,  'that 


6  INTRODUCTION.  CHAP. 

we  differentiate  between  two  kinds  of  electricity,  whilst  we 
recognise  only  one  kind  of  heat  (although  formerly  cold  was 
often  regarded  as  negative  heat).  For  negative  electricity 
the  opposite  to  that  which  holds  good  for  positive  electricity 
obtains,  i.e.  negative  electricity  tends  to  pass  from  places  at 
lower  to  those  at  higher  potentials. 

The  cause  of  that  displacement  of  the  position  of 
electricity  which  takes  place  without  the  expenditure  of 
external  work  is  therefore  the  inequality  of  the  electric 
potentials  at  the  different  places.  The  difference  of  the 
potentials  at  two  points  is  called  the  potential  difference  or 
electromotive  force,  and  is  that  force  which  tends  to  make 
the  electricity  pass  from  one  point  to  the  other.  In  the 
example  mentioned  on  p.  1  the  positive  electricity  passes 
from  electrode  PI  to  electrode  P2  because  the  positive  pole 
PI  has  a  higher  potential  than  the  negative  pole  P2. 

Fall  of  Potential. — In  the  example  quoted  it  is 
customary  to  speak  of  a  fall  of  potential *  between  the  poles 
PI  and  P2  in  the  solution. 

If  the  potential  difference  between  PI  and  P2  amounts  to 
V  volts,  and  the  distance  between  the  plates  is  a  cm.,  then 

the  fall  of  potential  is  —  volts  (mean  value)  per  cm. 

If,  however,  the  cross-section  of  the  solution  is  not  the 
same  throughout,  then  the  fall  of  potential  per  centimetre 
will  be  greater  where  the  section  is  smaller.  In  any  case, 
the  fall  of  potential  per  centimetre  has  a  definite  value  at 
each  point,  and  this  is  the  force  (where  107  dynes  =  10'2 
kilograms  is  the  unit)  with  which,  at  this  point,  1  coulomb  of 
positive  electricity  is  driven  from  the  higher  to  the  lower 
potential. 

The  potential  corresponds,  in  a  certain  sense,  to  work. 
Thus  if  the  potential  difference  between  two  points,  PI  and 

1  In  an  analogous  manner  we  speak  of  a  fall  of  temperature.  If  the 
temperature  at  a  point  P:  is  t^  and  at  a  point  P2  a  cm.  distant  it  is 
t2  «^)>  tnen  between  the  two  points  there  is  a  fall  of  temperature  of 

(*i  -  *8)  ^ 

-*£  degrees  per  cm. 


i.  CURRENT   DENSITY.  7 

P2,  which  are  a  cm.  apart,  is  V  volts,  then  at  each  point  a 
y 

force  —  is  acting  against  the  displacement  of  1  coulomb  of 
ct 

positive  electricity  from  the  lower  to  the  higher  potential. 
The  total  work  which  is  done  in  moving  1  positive  coulomb 

Y 

from  P2  to  PI  is,  therefore,  —  X  a  =  F,  expressed  in  10 -2 

ct 

kilogram-centimetres  as  unit.  Usage  has  led  to  the  adoption 
of  electromotive  force  as  synonymous  with  potential  difference, 
although  the  former  expression  is  not  quite  exact. 

Current  Density. — The  processes  which  take  place  at 
the  poles  PI  and  P2  depend  to  a  great  extent  on  how  much 
gas,  or  substance  in  general,  is  deposited  on  each  square 
centimetre  of  the  plates  per  second.  If  the  current  strength 
is  A  amperes,  and  if  plate  PI  has  an  area  of  y  sq.  cms.,  then 

the  quantity  deposited  on  1  sq.  cm.  per  second  is  given  by 

^ 

—     The  value   of  this  expression   is  termed  the  "  current 

density,"  which  obviously  is  measured  in  amperes  per  square 

^ 
centimetre.     In  the  above  example,  —  must  only  be  regarded 

u 

as  an  average  value  of  the  current  density ;  but  in  those  cases 
where  the  fall  of  potential  in  the  solution  is  the  same  through- 
out, the  current  density  has  the  same  value  at  all  parts  of  the 
plate. 

Electrochemical  Equivalents. — It  has  already  been 
mentioned  that  1  coulomb  can  bring  about  the  deposition 
of  1118  mgram.  of  silver,  0*3284  mgram.  of  copper,  or 
0'0104  mgram.  of  hydrogen.  On  this  account,  therefore,  we 
say  that  1118  mgram.  of  silver,  0'3284  mgram.  of  copper,  and 
0'0104  mgram.  of  hydrogen  are  electrochemically  equivalent. 

The  electrochemical  equivalents  correspond  exactly  with 
the  chemical  equivalents,  which  represent  the  weights  of  two 
substances  capable  of  replacing  each  other  in  chemical  com- 
pounds (Faraday's  law).  Thus,  for  instance,  31*8  grams  of 
copper  can  replace  1  gram  of  hydrogen  from  49  grams  of 
sulphuric  acid,  and  produce  79 '8  grams  of  copper  sulphate. 


INTRODUCTION. 


CHAP. 


Setting  the  equivalent  of  oxygen  equal  to  8,  the  following 
numbers  are  obtained  for  other,  elements  : — 


27-1 

Aluminium,  Al,  —  — 

Barium,  Ba,  — 
2 

Bromine,  Br,  79'96 

112*4 
Cadmium,  Cd, 


Calcium,  Ca, 


Chlorine,  Cl,  35*45  . 

52*1 

Chromium,  Cr;  - 

+ 
Copper,  Cu,  63*6      . 

+  +  63-6 
Copper,  Cu,—  2-      . 

Fluorine,  F,  19  -0     . 

197-2 
Gold,  An,  -^~ 

Hydrogen,  H,  1-008 
Iodine,  I,  126-85      . 

±  +  55-9 
Iron,  le  —     .    . 

+  +  +55-9 
Iron,  Fe,  —      .     . 


9-03 

Lead  Pb   2°6'9 

.  103-45 

.Lead,  ro,                   .     . 

Lithium,  Li,  7-03  .     .     . 

.      7-03 

68-7 

24-36 

79-96 

.     12-18 

Magnesium,  Mg, 

+  +55 

56-2 

Manganese,  Mn,  —   .     . 

.    27-5 

20-05 

Mercury,  fig,  200-3  .     . 

.  200-3 

+  +  200-3 

35-45 

.  100-15 

Mercury,  Hg,             .     . 

26-05 

Fjo.n 

Nickel,  Ni,  —     .     .     . 

.'    29-35 

63-6 

16 

Oxygen,  0,  -         .     .     . 

.      8-00 

31-8 

2 

Potassium,  K,  39-15  .     . 

.    39-15 

19-0 

Silver,  Ag,  107*93     .     . 

.  107-93 

65-73 

Sodium,  Na,  23-05     .    . 

.    23-05 

87-6 

1-008 

Strontium,  Sr,  —  —  .     . 

.    43-8 

126-85 

65-4 

Zinc,  Zn,  -            ... 

.    32-7 

27-95 

,       2 

18-63 

Atomic  Weight. — The  atomic  weights  of  the  elements 
are  whole  multiples  of  the  equivalent  weights.  The  simplest 
relationship  exists  in  the  case  of  the  so-called  monovalent 
elements,  like  hydrogen,  potassium,  chlorine,  etc.,  for  which 
the  atomic  and  equivalent  weights  are  the  same.  The  atomic 
weight  of  divalent  elements,  such  as  zinc,  magnesium, 
calcium,  iron  (in  ferrous  compounds),  mercury  (in  mercuric 
compounds),  is  double  the  equivalent  weight ;  whilst  in  the 
case  of  trivalent  elements  like  aluminium  and  iron  (in  ferric 
compounds),  the  atomic  weight  is  three  times  the  equivalent 
weight.  In  the  above  table  the  equivalent  weights  are  given 
as  fractions  of  the  corresponding  atomic  weights. 


i.  GRAM-EQUIVALENT.  9 

Gram-equivalent. — In  electrochemistry  the  equivalent 
weights  of  the  various  substances  play  an  important  part ; 
and  on  this  account  we  find  the  term  "  gram-equivalent "  very 
often  applied.  By  a  gram-equivalent  of  zinc  we  mean  32*7 
grams  of  this  metal ;  a  gram-equivalent  of  a  substance 
whose  equivalent  weight  is  E,  is  E  grams.  The  idea  of  an 
equivalent  (and  consequently  also  equivalent  weight)  can  be 
applied  not  only  to  chemical  elements  and  those  substances 
which  occur  as  ions,  i.e.  can  be  separated  at  the  electrodes, 
but  also  to  all  compounds  which  can  react  chemically  with 
these.  By  a  gram- equivalent  of  carbon  dioxide  is  meant  that 
quantity  which  unites  with  a  gram-equivalent  of  lime  to 
form  a  gram-equivalent  of  calcium  carbonate. 

Gram -molecule. — Even  more  important  in  chemistry 
than  the  equivalent  weight  is  the  molecular  weight.  The 
methods  for  the  determination  of  the  molecular  weight 
of  dissolved  substances,  which  plays  a  most  important 
part  in  all  branches  of  chemistry,  will  be  described  later; 
molecular  weights  are  only  relative  values  being  referred 
to  that  of  hydrogen  as  equal  to  2  (or,  more  exactly,  2*016), 
or  to  that  of  oxygen  as  32.  Here  we  make  use  of  the  term 
" molecular  weight"  in  the  sense  in  which  it  is  always 
applied  in  chemistry.  Thus,  for  example,  the  molecular 
weight  of  hydrochloric  acid  is  3  6 '46,  and  consequently 
1  gram-molecule  of  this  (HC1)  is  3646  grams,  that  is,  the 
equivalent  weight  in  grams ;  a  gram-molecule  of  sulphuric 
acid  is  98  grams,  i.e.  twice  the  gram-equivalent. 

A  gram-molecule  of  aluminium  chloride  (A1C13)  is  133'5 
grams,  and  one  of  ferric  chloride  (FeCl3)  is  162*3  grams ; 
these,  therefore,  are  three  times  the  corresponding  equivalent 
weights.  Eecently  the  term  "  mol "  has  been  introduced  for 
gram-rnolecule. 

Just  as  we  speak  of  a  gram-molecule,  so  may  we  also 
speak  of  a  gram-ion.  One  gram-ion  of  chlorine  signifies 
3 5 '45  grams  of  chlorine  in  the  ionic  condition  (Cl)  ;  a  gram- 
ion  of  SO4  weighs  96  grams  (96  being  the  sum  of  the  atomic 
weights).  In  the  same  way  a  gram- atom  of  an  element  is 


io  INTRODUCTION.  CHAP. 

its  atomic  weight  expressed  in  grams  (1  gram-atom  of 
chlorine  (01)  is  3  5 '45  grams). 

Concentration. — In  theoretical  chemistry  it  is  con- 
venient to  express  the  composition  of  a  solution,  not  by  the 
absolute  weight  of  the  dissolved  substance,  but  by  the 
number  of  dissolved  gram-molecules.  The  concentration  is 
then  expressed  by  the  number  of  gram-molecules  per  unit  of 
volume  (the  litre),  and  a  solution  which  contains  1  gram- 
molecule  in  the  litre  is  said  to  be  "  1  normal  "  (In)  or  simply 
"normal."  A  O'l  normal  solution  of,  for  instance,  hydro- 
chloric acid,  contains  only  O'l  gram  molecule,  or  3*645  grams 
per  litre :  in  a  litre  of  normal  sulphuric  acid  there  are 
98  grams  of  H2S04.  Use  is  frequently  made  of  equivalent- 
normal  solutions,  that  is  solutions  containing  1  gram-equi- 
valent per  litre.  Thus  an  equivalent-normal  solution  of 
sulphuric  acid  contains  49  grams  of  sulphuric  acid  in  the 
litre.  In  order  to  avoid  confusion,  this  latter  solution  is 
denoted  as  n  JH2S04. 

By  "  normal "  is  generally  meant  molecular-normal.1 

Such  a  method  of  expressing  the  concentration  has  the  dis- 
advantage that  it  is  not  the  same  for  one  particular  solution 
at  all  temperatures  and  pressures,  since  the  volume  of  the 
solution  changes  slightly  with  variation  of  these  factors. 
On  this  account  the  expression  of  concentration  in  percentage 
by  weight  may  be  preferable.  However,  the  volume  changes 
caused  by  variation  of  temperature  and  pressure,  especially 
of  aqueous  solutions,  :are  very  inconsiderable.  In  practice 
the  normality  is  determined  at  the  ordinary  temperature 
(4-  18°  C.)  and  pressure  (1  atmo.),  and  the  value  so  obtained 
is  used  also  for  other  temperatures  and  pressures.  In  more 
accurate  work  it  is  necessary  to  correct  for  the  change  of 
volume. 

Temperature — In  scientific  work  all  temperatures  are 
registered  in  Celsius  (or  centigrade)  degrees.  In  many  cal- 
culations, particularly  those  used  in  the  mechanical  theory 
of  heat  and  its  applications,  it  is  advisable  to  take  as  zero- 

1  In  analytical  practice  "equivalent-normal  solutions  are  used. 


i.  MECHANICAL    WORK.  n 

point  of  the  scale,  not  the  melting  point  of  ice,  but  the 
"  absolute  zero,"  which  lies  273°  lower.  If  the  temperature 
of  a  body  is  t°  on  the  ordinary  scale,  then  it  is  T°  =  273°  +  t° 
on  the  absolute  scale.  T  is  called  the  "  absolute  temperature  " 
of  the  body. 

Mechanical  Work.— The  work  which  is  done  in  raising 
a  kilogram  through  1  metre  is  a  "kilogram-metre."  In 
scientific  measurements  the  unit  of  force  is  the  "  dyne,"  and 
is  that  force  which  the  earth  by  its  attraction  exerts  on 
gj-j-  gram.  Since  the  unit  of  length  chosen  is  the  centimetre 
=0'01  metre,  the  kilogram-metre  (kg.m.)  =  9*81  X  107  cm. 
dynes  =  9'81  X  107  ergs ;  1  erg  =  1  cm.  dyne,  is  the  unit  of 
work  in  the  C.G.S.  (centimetre,  gram,  second)  system.  Ex- 
perimentally it  has  been  determined  that  mechanical  work 
of  426  gram-metres,  or  0'426  kg.m.  is  required  to  produce  one 
(small)  calorie  of  heat.  Consequently— 

1  cal.  =  9-81  x  0-426  x  107  =  0-418  X  108  ergs. 

In  electricity  the  unity  of  work  is  the  volt-coulomb, 
i.e.  the  work,  which  1  coulomb  balances  over  a  fall  of 
potential  of  1  volt.  For  the  value  of  this  we  have — 

1  volt-colomb  =  — — ~kg.ni.  =  0'24  cal. 
y  O-L 

Work  done  :  Effect. — In  the  working  of  a  machine  we 
are  concerned  chiefly  with  the  absolute  value  of  the  work 
done  per  second. 

As  a  practical  unit  the  horse-power  has  been  chosen, 
which  corresponds  to  a  work  of  75  kilog.met.  per  second.  The 
electrical  unit  of  work  is  the  volt-ampere,  or  watt,  which 
is  equal  to  1  volt-coulomb  per  second  (since  1  amp.  = 
1  coulomb  per  second).  As  the  watt  is  much  too  small  a 
unit  for  measuring  the  work  done  in  a  dynamo,  use  is  made 
of  a  unit  1000  times  larger — the  "  kilowatt."  It  is  quite 
evident  that — 

1  kilowatt  =  -=p Q^J  =  T36  horse-power. 


12 


INTRODUCTION. 


CHAP. 


FIG.  2. 


Work  done  by  Change  of  Volume. — If  we  have  v  c.c. 
of  a  substance  in  the  liquid  condition  contained  in  a  vessel  of 
1  sq.  cm.  section,  then  its  height  in  the  vessel  will  be  v  cm. 
(Fig.  2).  On  the  surface  of  the  liquid  let  there  rest  a 
weighted  piston,  so  that  there  is  a  pressure  of  P  dynes 
opposing  the  expansion  of  the  liquid. 

If  the  liquid  be  now  warmed,  or  if  a  chemical  reaction 
take  place  in  it,  then  the  volume  changes  ;  let 
the  change  be  represented  by  an  expansion  of 
dv  c.c. 

In  order  that  this  expansion  may  take 
place,  the  weighted  piston  resting  on  the  sur- 
face must  be  raised  through  dv  cm.,  whereby 
the  work  Pdv  will  be  done. 

From  this  it  is  clear  that  when  any  sub- 
stance whatever  expands  by  dv  c.c.  the  work 
done  is  Pdv  ergs  if  the  pressure  P  is  expressed  in  dynes 
per  square  centimetre. 

In  Fig.  3  the  shaded  portion  K  represents  the  original 
volume  of  a  substance,  whilst  the  outer  contour  represents 
the  volume  after  expansion.  Let  us  con- 
sider the  small  element  of  surface  dA  sq. 
cm.  This  has  been  displaced  through  h  cm., 
and  the  work  done  by  it  is  P.dA.h  ergs, 
since  there  is  a  pressure  P.  dA  on  dA. 
If  we  denote  the  volume  h .  dA  by  dw, 
then  the  work  is  P.  dw  ergs ;  and  if  we 
calculate  for  the  whole  substance  we  must  take  the  sum 
of  all  the  products,  P.  dw.  Since  now  P  possesses  the  same 
value  for  all  parts  of  the  surface,  and  as  the  sum  of  all  the 
volumes  dw  is  evidently  equal  to  the  total  change  of  volume 
dv,  the  total  work  done  will  be  P.  dv  ergs  (as  given  above). 

Work  done  by  Evolution  of  a  Gas  under  Constant 
Pressure.-— We  can  now  calculate  the  work  done  when  a 
gas  is  formed  at  constant  pressure;  for  instance,  by  the 
boiling  of  water.  For  the  sake  of  simplicity,  let  us  take  a 
gram-molecule  (18  grams)  of  water  vaporising  at  a  pressure  of 


i.  WORK   DONE.  13 

760  mm.  (1  atmo.).  Since  this  pressure  is  that  of  a 
column  of  mercury  76  cm.  high  and  of  1  sq.  cm.  section 
=  76  x  13 !6  grams,  then  in  absolute  measurement : 

1  atmo.  =  76  x  13-6  x  981  =  1-014  X  106  dynes  per  sq.  cm. 

According  to  Avogadro's  hypothesis  (see  below),  a  gram- 
molecule  of  a  gas  at  0°  and  1  atmo.  pressure  occupies  the 
volume  22,400  c.c. ;  and  since,  according  to  Gay-Lussac's 
(Charles's)  law,  the  volume  of  a  gas  (at  constant  pressure)  is 
proportional  to  its  absolute  temperature,  the  volume  of  a 
gram-molecule  of  water  vapour  (or  any  other  gas)  at  100°  is— 

X  373  =  82  x373  c.c. 

and  at  any  other  temperature  T  (in  absolute  degrees) 
VT  =  82  Tc.c. 

The  work,  therefore,  which  has  to  be  done  to  bring  a 
gram-molecule  into  the  gaseous  state  is  — 

Pdv  =  1-014  x  82  x  106  X  T  ergs  =  83'2  megergs.1 

"We  have  already  seen  that  1  cal.  =  41*8  megergs,  con- 
sequently the  work  done  on  vaporising  a  gram-molecule, 
expressed  in  calories,  is  given  by — 

83-2 


41-8 


T  cal.  =  2T  cal.  (or  more  exactly  1/99T  cal.). 


The  external  work,  therefore,  which  is  done  on  evolving 
a  gram-molecule  of  a  gas  is,  when  expressed  in  calories,  twice 
the  absolute  temperature.  The  work  done  on  forming  a 
gram-molecule  of  steam  at  100°  is  equivalent  to  2  x  373  =  746 
calories. 

This  work  is  independent  of  the  value  of  the  external 
pressure.  For  if  the  pressure  in  the  preceding  example  be 
2  atmos.  instead  of  one,  then,  according  to  Boyle's  law,  the 

1  The  syllable  meg-  before  a  unit  6f  measurement  signifies  a  million. 
Thus  1  megerg  =  1  million  ergs,  1  megohm  =  1  million  ohms.  The 
prefix  micro-  denotes  a  millionth;  thus,  1  microvolt  =  10 ~  volt. 


1  4.  INTRODUCTION.  CHAP. 

volume  will  only  be  equal  to  half  its  former  value.  That  is 
to  say,  in  the  expression 

P  .  dv  =  A 

the  value  of  P  has  been  doubled,  whilst  the  value  of  dv  has 
been  halved  ;  consequently  the  product  remains  the  same. 
It  is  evident  that  the  law  is  valid  for  any  variation  of 
pressure  whatsoever. 

Expansion  of  Gases  by  Heat  at  Constant  Pressure.— 
In  an  analogous  manner  it  can  be  seen  that  for  a  gas  which 
is  heated  from  the  absolute  temperature  T  to  T  +  1  the 
volume  changes  from  vr  =  82  T  c.c.  to  vT+l  =  82  (T  -f  1) 
c.c.,  and  the  work  done  on  so  raising  the  temperature  of  a 
gram-molecule  of  a  gas  is  — 


Expansion  of  Gases  at  Constant  Temperature.—  Let 

us  consider  a  gram-molecule  at  the  temperature  T  and  under 
a  pressure  of  p  atmos.  ;  on  expansion  the  pressure  p  changes, 
and  the  change  is  inversely  proportional  to  the  change  of 
volume  v.  The  work  done  on  expanding  from  VQ  to  v\  is 
obtained  by  integrating  pdv  ;  that  is, 


fvi 

—  I      pdv. 
Jv0 


From  Boyle's  law,  pv  =  p0vQt  it  follows  for  a  gram-molecule 
of  .gas  that  if  p0  =  1  atmo.  =  1*014  megadynes  per  square 
centimetre,  and  if  VQ  =  82  T  c.c., 

Pov0=pv  =  1-99  Teal. 

If  we  introduce  this  result  into  the  above  expression  for 
A  we  obtain  — 


A  =  1-99T  /       ±  cal.  =  1-99T  In  ^  cal.  = 

V  VQ  pi 


i.  EXPANSION    OF   GAS.  15 

Since  the  final  expression  contains  only  the  ratio  between 
the  initial  and  final  volumes  or  pressures,  it  is  immaterial 
in  which  system  of  units  these  values  are  measured.  By 
replacing  the  natural  logarithms  by  the  ordinary  (Brigg's) 
logarithms  we  obtain — 

A  =  4-58T  log  ^  cal.  =  191'6riog  ^  megergs. 

In  order,  therefore,  to  expand  a  gram-molecule  of  a  gas 
at  0°  so  far  that  its  pressure  sinks  from  760  mm.  to  76  mm., 
a  work  of  191-6  x  273  =  52,300  megergs  =  1251  cal.  must 
be  done.  This  work  (or  quantity  of  heat)  is  taken  from  the 
expanding  gas,  and  since  the  temperature  is  kept  constant  at 
0°  during  the  process,  heat  must  be  introduced  from  outside 
in  order  that  no  cooling  may  take  place.  Expansion  at 
constant  temperature  is  called  isothermal. 

If  we  use  n  gram-molecules  instead  of  1,  then  the  work 
done  is  n  times  that  indicated  by  the  preceding  formula, 
but  there  is  no  other  change  in  the  result. 


CHAPTER   II. 
Older  Electrochemical  Views. 

The  First  Electrochemical  Investigations.— The  striking 
effects  brought  about  by  electricity  formed  the  subject  of  much 
study  about  the  middle  of  the  eighteenth  century.  At  that 
time  friction  electrical  machines  were  in  use,  and  in  order 
to  intensify  the  effects  produced,  very  large  machines  were 
constructed.  The  most  famous  of  these  is  still  to  be  seen 
in  the  Teyler  Museum  in  Haarlem.  Pater  Beccaria,  some 
one  hundred  and  thirty  years  ago,  by  using  such  machines 
found  that  metals  could  be  "  revivified  "  (i.e.  reduced)  from 
their  calces  (oxides)  when  the  electric  spark  was  passed 
between  two  pieces.  In  this  way  he  obtained  zinc  and 
mercury.  Some  time  later,  Priestley  investigated  the  action 
of  the  electric  spark  on  air  and  observed  that  an  acid  was 
produced ;  he  mistook  this  for  carbonic  acid,  until  Cavendish 
recognised  it  as  nitric  acid.  Van  Marum  studied  the  behaviour 
of  several  other  gases  in  the  path  of  the  electric  spark  [which 
led  him  to  notice  the  formation  of  ozone],  and  made  experi- 
ments also  by  passing  the  spark  through  liquids.  Before  him, 
Priestley  had  discovered  that  in  oil  and  efrher  the  electric 
spark  produces  gas,  and  proved  that  this  gas  contained 
hydrogen. 

The  first  actual  electrolysis  was  made  by  Deimann  and 
Paets  van  Troostwyk  in  Haarlem  in  1789,  in  which  they 
successfully  decomposed  water  into  hydrogen  and  oxygen. 
In  their  experiments  the  water  was  contained  in  a  cylindrical 
tube  closed  at  the  top,  and  having  a  metal  wire  sealed  into 
its  upper  end.  Another  metal  wire  was  introduced  into  the 


CHAP.  ii.  GALVANI   AND   VOLTA.  17 

lower  end  of  the  tube,  which  dipped  into  a  basin  of  water. 
When  the  sparks  struck  through  the  water,  bubbles  of  gas 
were  disengaged  from  the  metal  wires,  and,  rising  in  the 
tube,  gradually  displaced  the  water.  As  soon  as  the 
column  of  water  sank  below  the  upper  electrode,  the  gas, 
which  was  a  mixture  of  hydrogen  and  oxygen,  exploded. 
This  experiment  was  later  repeated  by  Eitter,  using  silver 
wires  and  a  solution  of  a  silver  salt,  and  he  observed  that 
the  negative  pole  became  coated  with  precipitated  silver. 
On  changing  the  poles,  silver  was  dissolved  from  one 
and  deposited  on  the  other  (now  the  negative  pole). 
In  Deimann's  experiment,  oxygen  and  hydrogen  were 
simultaneously  formed,  both  at  the  positive  and  at  the 
negative  poles,  so  that  the  process  was  not  a  true  electrolytic 
one  like  that  of  Eitter. 

Galvani  and  Volta. — The  whole  state  of  the  science  was 
changed  in  a  great  degree  by  the  discoveries  of  Galvani,  and 
particularly  by  those  of  Volta.  In  1795  Volta  arranged  the 
metals  in  a  series  according  to  their  behaviour  in  galvanic 
experiments,  and  in  1798  Eitter  showed  that  the  same  series 
is  obtained  when  the  properties  of  the  metals  to  separate 
other  metals  from  their  salt  solutions  are  compared. 

After  the  introduction  of  Volta's  pile  (in  1800)  the 
physiological  and  optical  phenomena  were  less  studied,  and 
more  attention  was  paid  to  the  chemical  actions.  As  opposed 
to  the  electrical  machines,  these  piles  gave  large  quantities 
of  electricity  at  a  comparatively  low  potential.  Nicholson 
and  Carlisle,  in  1800,  studied  the  evolution  of  oxygen  and 
hydrogen  in  salt  solutions  at  immersed  gold  electrodes  which 
were  connected  with  the  poles  of  a  Voltaic  pile,  and  observed 
that  litmus  in  the  neighbourhood  of  the  positive  pole  was 
turned  red  by  the  acid  produced  there. 

Some  years  later  Davy  made  his  brilliant  electrochemical 
discoveries.  He  succeeded  in  decomposing  the  oxides  of  the 
alkali  and  alkaline  earth  metals,  which  had  previously  been 
regarded  as  elementary  substances,  and  in  preparing  the  pure 
metals.  Further  progress  in  obtaining  the  more  difficultly 

c 


1 8  OLDER   ELECTROCHEMICAL   VIEWS.          CHAP. 

reducible  metals  in  this  way  was  later  made  by  Bimsen  and 
his  pupils. 

Berzelius's  Investigations. — In  1807,  J.  J.  Berzelius, 
in  conjunction  with  Baron  Hisinger,  published  his  first 
paper,  which  formed  the  foundation  of  his  subsequent  electro- 
chemical theory.  These  investigators  came  to  the  following 
conclusions : — 

Neutral  salts  are  decomposed  by  the  electric  current.  In 
general,  chemical  compounds  are  decomposed  by  the  current, 
and  the  constituents  collect  at  the  poles. 

Combustible  substances,  the  alkalis,  and  earths  migrate 
to  the  negative  pole;  oxygen,  the  acids,  and  oxidised  com- 
pounds migrate  to  the  positive  pole.  Thus,  for  example, 
nitrogen  in  ammonia  goes  to  the  negative  pole,  whilst  in  nitric 
acid  the  nitrogen  goes  with  the  oxygen  to  the  positive  pole. 

The  quantities  of  the  products  of  decomposition  are 
proportional  to  the  quantities  of  electricity,  and  these  are 
dependent  upon  the  area  of  contact  of  the  metals  in  the  pile 
and  on  the  moist  conductor.  Further,  the  quantities  of 
substance  decomposed  are  proportional  to  the  electrical 
conductivities  of  the  solutions. 

The  chemical  processes  taking  place  during  an  electrolysis 
are  determined :  firstly,  by  the  affinities  of  the  constituents 
to  the  metals  of  which  the  poles  are  constructed ;  secondly, 
by  the  reciprocal  affinities  of  the  constituents ;  and  thirdly, 
by  the  cohesion  (solubility)  of  the  new  compounds. 

It  was  on  these  and  similar  conclusions  drawn  from 
experiment  that  Berzelius,  as  well  as  his  precursor,  Davy, 
founded  their  electrochemical  theories. 

Davy's  Electrochemical  Theory. — Davy  proved  that 
acid  and  base  could  not  be  formed  from  pure  (free  from  salt) 
water,  as  had  been  erroneously  believed.  He  found  that 
by  using  pure  water  in  a  gold  vessel  no  acid  or  base  was 
produced,  but  where  the  vessel  was  one  of  gypsum,  fluorspar, 
heavy  spar,  basalt,  lava,  or  glass,  partial  solution  of  the 
material  of  which  this  was  made  took  place,  and  the  results 
formerly  found  could  be  explained. 


ii.  DAVY'S   THEORY.  19 

Chemical  affinity  depends  upon  the  electric  properties 
of  the  atoms,  and  their  attraction  is  due  to  their  electric 
charges.  According  to  Davy,  the  cause  of  the  charge  is  to 
be  found  in  the  contact  of  the  atoms,  since  Volta  believed 
that  he  had  proved  that  when  two  bodies  are  brought  into 
contact,  they  become  oppositely  charged  with  electricity. 
Electrolysis  consists  in  bringing  back  the  atoms  into  the 
condition  in  which  they  were  before  union.  The  sign  of  the 
pole  at  which  the  atoms  separate  defines  the  nature  of  their 
charge,  which  is  opposite  to  that  of  the  pole. 

Contrary  to  the  prevailing  view,  Davy  was  of  the  opinion 
that  electrolysis  is  principally  a  primary  action,  thatjs,  the 
current  decomposes  electrolytes  directly. 

Berzelius's  Theory  differed  essentially  in  one  point 
from  Davy's.  Berzelius  assumed  that  the  atoms  do  not  first 
become  electrified  by  touching  each  other,  but  that  they  are 
already  charged  before  coming  into  contact — a  conclusion 
at  which  Schweigger  had  previously  arrived,  without,  how- 
ever, following  it  up  further.  The  different  kinds  of  elec- 
tricity concentrated  at  the  various  points  of  the  atoms  do 
not  act  outwardly  with  the  same  force,  but  with  different 
strengths. 

The  two  quantities  of  electricity  do  not  require,  therefore, 
to  be  unequal ;  for  the  action  might  be  compared  with  that 
which  a  magnet  with  two  equally  strong  poles  exerts  on  an 
object  placed  near  one  of  these ;  in  this  case  the  action  of  the 
nearer  pole  preponderates. 

The  atoms  behave  similarly,  they  also  have  two  (electric) 
poles,  so  that  the  most  highly  charged  atoms  do  not  neces- 
sarily show  the  strongest  affinity.  According  as  the  action 
of  the  positive  or  negative  pole  preponderates,  the  body  shows 
positive  or  negative  properties,  that  is,  is  attracted  by  the 
negative  or  positive  pole  of  a  voltaic  pile. 

Since  in  all  compounds  the  oxygen  migrates  to  the 
positive  pole,  oxygen  was  regarded  as  the  most  negative  of 
all  substances.  For  a  similar  reason  potassium  (and  after- 
wards caesium)  was  held  to  be  the  most  positive  element. 


20  OLDER   ELECTROCHEMICAL   VIEWS.  CHAP. 

After  oxygen  followed  sulphur,  chlorine,  bromine,  iodine,  etc., 
which  are  all  separated  from  their  compounds  at  the  positive 
pole.  With  oxygen,  these  negative  substances  form  strong 
acids,  which  likewise  separate  at  the  positive  pole.  Close 
to  the  negative  substances  Berzelius  set  in  the  series  those 
elements  (all  positive  bodies)  which  could  form  acids  with 
oxygen,  and  the  stronger  the  acid  which  was  formed,  the 
nearer  did  these  elements  stand  to  the  negative  substances. 
Further,  he  placed  those  bodies  which  give  difficultly  reducible 
compounds  with  oxygen  at  the  positive  end  of  the  series, 
on  the  assumption  that  compounds  are  the  more  stable  the 
greater  the  charge  possessed  by  the  positive  component. 

Metals  capable  of  separating  others  from  their  compounds 
were  regarded  as  more  positive,  and  substances  with  similar 
chemical  properties  were  placed  together.  If  an  element  lay 
between  two  others  as  far  as  chemical  properties  were  con- 
cerned, it  was  placed  between  them  also  in  the  series — for 
example,  bromine  between  chlorine  and  iodine. 

In  this  way  Berzelius,  after  many  alterations,  set  up  the 
following  so-called  electrochemical  series,  beginning  with  the 
negative  elements : — 


Oxygen 

Boron 

Palladium 

Thorium 

Sulphur 

Carbon 

Silver 

Zirconium 

Selenium 

Antimony 

Copper 

Aluminium 

^Nitrogen 

Tellurium 

Uranium 

Yttrium 

Fluorine 

Tantalum 

Bismuth 

Beryllium 

Chlorine 

Titanium 

Tin 

Magnesium 

Bromine 

Silicon 

Lead 

Calcium 

Iodine 

Hydrogen 

Cadmium 

Strontium 

Phosphorus 

Gold 

Cobalt 

Barium 

Arsenic 

Osmium 

Nickel 

Lithium 

•Chromium 

Iridium 

Iron 

Sodium 

Vanadium 

Platinum 

Zinc 

Potassium 

Molybdenum 

Mercury 

Manganese 

Tungsten 

Rhodium 

Cerium 

From  what  has  been  said,  it  is  evident  that  this  series  was 
really  only  a  chemical  scheme,  and  that  it  is  incomplete  and 
arbitrary,  may  be  gathered  from  the  number  of  alterations 


ii.  GROTTHUSS   CHAIN.  21 

made  in  it.  Nevertheless,  it  has  played  an  extremely 
important  part  in  the  development  of  the  science,  and  has 
been  introduced  here,  as  it  has  to  a  certain  extent  an  orien- 
tating character.  It  is  hardly  connected  with  the  subject  of 
electricity,  but  must  rather  be  regarded  as  an  attempt  to 
represent  the  chief  facts  of  "  Berzelian  "  chemistry. 

The  Grotthuss  Chain. — It  became  necessary  to  explain 
why  the  ions  were  only  separated  at  the  poles  by  the  electric 
current.  It  was  at  first  believed  (Ritter)  that  hydrogen  was 
formed  by  the  union  of  water  with  negative  electricity,  and 
that  oxygen  resulted  from  the  combination  of  water  with 
positive  electricity.  In  1805,  Grotthuss  brought  forward  the 
view  that  the  molecules  of  an  electrolyte  arrange  themselves 
polarly  so  as  to  form  a  chain : 

according  to  this  hypothesis,  which  _|  ©0^00^0©  I  + 
gained  credence  for  a  long  time,  /£•££ 

all  the  dissolved  molecules  in  a  ^I0i  4. 

potassium  chloride  solution  take 

up  such  a  position  that  their  positively  charged  potassium 
sides  are  towards  the  negative  electrode,  and  the  chlorine 
sides  towards  the  positive  electrode  (see  Fig.  4). 

During  the  electrolysis  the  positive  potassium  atom  next 
the  negative  electrode,  and  the  negative  chlorine  atom  next 
the  positive  electrode,  are  separated.  The  chlorine  of  the 
first  molecule  combines  with  the  potassium  of  the  molecule 
next  it,  and  this  new  molecule  now  turns  so  as  to  take  up  a 
position  similar  to  that  of  the  original  molecule.  An  analogy 
drawn  by  Grotthuss,  as  well  as  by  Davy  and  Faraday,  con- 
ceived the  electrodes  as  doors  through  which  the  two  elec- 
tricities entered  into  the  liquid,  and  there  combined  with  the 
nearest  ions,  whereupon  the  other  ions  between  the  electrodes 
then  rearranged  themselves. 

The  Grotthuss  view,  however,  cannot  be  correct,  for  in  a 
cylindrical  column  of  liquid  the  electrical  force  acts  equally 
at  all  parts  (the  fall  of  potential  per  centimetre  drives  the 
charged  ions  ;  compare  p.  6). 

Ampere's  Theory. — Contrary  to   Davy  and  Berzelius, 


22  OLDER   ELECTROCHEMICAL   VIEWS.  CHAP. 

Ampere  (in  1821)  had  already  assumed  that  the  atoms  carry 
with  them  a  certain  invariable  quantity  of  electricity,  some 
carrying  a  positive  charge,  others  a  negative.  The  charge  on 
the  atoms  binds  an  equal  quantity  of  the  opposite  kind 
of  electricity  in  the  surrounding  medium.  If  a  positive 
and  a  negative  atom  collide,  the  bound  electricity  in  the 
neighbourhood  becomes  free,  the  charges  on  the  two  atoms 
bind  each  other,  and  a  union  of  the  ^,toms  takes  place  with 
formation  of  a  neutral  compound. 

On  the  other  hand,  according  to  Berzelius  the  atoms  are 

K        ci 
charged  polarly,  as  in  the  scheme :  (-"+)  (-~+).    When  they 

combine,   negative  electricity  from  potassium  and  positive 

K     ci 
from  chlorine  become  free,  and  there  is  formed  (+)  Q. 

By  this  process  heat  and  light  phenomena  were  supposed 
to  arise  during  a  reaction.  These  and  similar  speculations  on 
the  part  of  Fechner,  De  la  Rive,  Schonbein,  and.  Magnus,  were 
too  speculative  to  command  attention  for  any  length  of  time. 

Faraday's  Law. — Faraday  (7),1  in  1834,  discovered 
that  every  equivalent  binds  the  same  quantity  of  elec- 
tricity, so  that  a  zinc  atom  takes  up  twice  as  much,  and 
an  aluminium  atom  three  times  as  much,  as  a  hydrogen 
iitom  (see  p.  7).  Berzelius  strongly  questioned  this  law, 
as  it  was  not  in  agreement  with  the  views  which  he  had 
previously  expressed. 

Hittorf's  Investigation. — In  the  course  of  the  sixth 
decade  of  last  century,  Hittorf  (2)  performed  his  work  on 
the  migration  of  the  ions,  a  piece  of  work  of  fundamental 
importance,  to  which,  nevertheless,  little  attention  was  paid 
at  the  time.  We  return  later  to  this  subject. 

Helmholtz's  Faraday  Lecture  (3), — Helmholtz,  one 
of  the  most  brilliant  devotees  of  the  exact  sciences,  in  1881 
delivered  the  Faraday  lecture,  in  which  he  discussed  the  then 
modern  development  of  Faraday's  ideas  on  electricity.  The 

1  The  italic  numbers  enclosed  in  brackets  refer  to  the  literature 
references  at  the  end  of  the  book. 


ii.  FARADAY    LECTURE.  23 

following  abstract  of  the  address  may  serve  to  indicate  what 
were  the  best-founded  electrochemical  views  of  that  period  : — 

Since  the  quantity  of  electricity  on  any  atom  is  equal  to, 
or  is  a  whole  multiple  of,  that  on  a  hydrogen  atom,  Helm- 
holtz  proposed  a  unit  for  this — the  atomic  charge.  Electricity 
is  assumed  to  exist  in  matter  in  distinct  homogeneous  par- 
ticles which  correspond  to  the  atoms.  An  atom  can  occur 
charged  either  positively  or  negatively — for  example,  in 
hydrogen  sulphide  the  sulphur  is  negative,  in  sulphuric 
anhydride  (S03)  it  is  positive. 

According  to  Helmholtz,  all  substances  are  electrolytes, 
and  better  or  worse  conductors  of  electricity.  After  electro- 
lysing the  "  non-conductor  "  turpentine  for  twenty-four  hours, 
it  was  found  that  an  electrometer  placed  between  the  two  elec- 
trodes indicated  a  potential  difference— that  is,  polarisation  had 
taken  place,  proving  that  there  had  been  some  electrolysis 
(8  dll.  caused  a  polarisation  of  0'3  dll.  in  ether,  oil,  and 
turpentine,  and  of  0'8  dll.  in  benzene).  Similarly,  Helm- 
holtz found  a  potential  difference  between  metals,  such  as 
copper  and  zinc,  which  were  separated  by  the  best  known 
insulators — glass,  resin,  shellac,  paraffin,  or  sulphur — and 
proved  that  this  result  was  not  due  to  hygroscopic  moisture. 
He  called  attention  to  the  extraordinarily  high  values  of  the 
electric  forces  binding  hydrogen  and  oxygen  in  water,  which 
forces  are  able  to  completely  change  the  properties  of  these 
elements  on  combination. 

Helmholtz  explained  the  capability  of  one  element  of 
separating  another  from  its  compound  as  due  to  the  greater 
affinity  for  positive  electricity.  The  Berzelius  series  is  to  be 
understood  in  this  sense.  This,  too,  is  the  cause  of  the  Yolta 
effect. 

Each  valence  corresponds  with  a  single  charge,  con- 
sequently the  atoms  combine  in  multiple  proportions.  In  the 
case  of  unsaturated  compounds  with  two  free  valencies,  it  is 
to  be  assumed  that  one  of  these  corresponds  with  a  positive, 
the  other  with  a  negative  charge.  Unsaturated  compounds 
with  an  odd  number  of  free  valencies  were  assumed  to  exist 


24  OLDER   ELECTROCHEMICAL    VIEWS.    CHAP.  n. 

only  at  high  temperatures,  and  possessed  an  excess  (one  atomic 
charge)  of  one  kind  of  electricity.  Mtric  oxide  (NO),  which 
has  one  free  valence,  offered  a  great  difficulty  in  this  con- 
nection, for  it  is  stable  at  the  ordinary  temperature,  and  does 
not  conduct  the  current. 

In  concluding,   Helmholtz   remarked  on  the  great  im- 
portance of  electrochemistry. 


CHAPTEE   III. 
The  Laws  of  Avogadro  and  van't  Hoff. 

Boyle's  Law. — When  a  gas  is  contained  in  a  vessel  the 
volume  of  which  can  vary,  as,  for  instance,  in  a  cylinder  with 
a  movable  piston,  then,  if  the  volume  v  be  changed  by  moving 
the  piston,  the  pressure  p  changes  in  inverse  proportion ;  if  the 
volume  be  changed  to  half  what  it  originally  was,  the  pressure 
is  doubled.  This  law  is  expressed  by  the  general  formula : — 

pv  =  constant. 

Boyle  proved  this  for  pressures  greater  than  1  atmo., 
and  Mariotte  afterwards  proved  it  for  lower  pressures. 

Gay-Lussac's  (Charles's)  Law. — The  above  law  is  only 
applicable  when  the  temperature  of  the  gas  remains  constant. 
If  the  temperature  rises,  the  product  pv  increases,  as  Gay- 
Lussac  found,  by  ^73  of  its  value  at  0°  for  each  Celsius 
degree.  In  other  words,  the  product  pv  is  proportional  to  the 
absolute  temperature  T — 

pv  =  constant  x  T. 

Avogadro's  Law. — Avogadro  showed  that  the  constant 
in  this  formula  was  the  same  for  all  gases  if  a  gram-molecule 
of  the  gas  be  taken.  In  the  usual  form  of  the  equation — 

pv  =  ET 

R  =  84688  when^>  is  measured  in  grams  per  square  centimetre 
and  v  in  cubic  centimetres. 

This  is  found  by  considering  1  gram-molecule  of  oxygen, 


26      LAWS   OF   AVOGADRO   AND    VAN'T   HOFF.     CHAP. 

the  density  of  which  was  found  by  Kegnault  to  be  0'00143011 
at  0°  and  760  mm.  pressure;  under  these  conditions 
(T  =  273,  p  =  1033*6  grams  per  square  centimetre)  the 

volume  of  1  gram  is        fi  =  699*3   c.c.  and   that  of 

32  grams  is  32  x  699'3  c.c.  ;  consequently  — 

1,033-6  x  32  x  699-3  =  273J2 
R  =  84,688. 

If  the  pressure  is  measured  not  in  grams  per  square 
centimetre,  but  in  millimetres  of  mercury,  the  value  of  R 
is  1*36  times  smaller,  i.e.  R  =  62,265. 

"We  have  already  obtained  (see  p.  13)  another  expression 
of  Avogadro's  rule,  extremely  useful  for  calculations,  namely  — 


in  which  the  value  of  R  is  2  (or,  more  exactly,  T99). 

By  means  of  this  equation  we  can  ascertain  the  pressure, 
volume,  or  temperature  of  a  given  mass  of  gas  provided  we 
know  two  of  these  factors. 

It  might  be  required  to  find,  for  example,  how  many 
litres  of  saturated  water  vapour  are  evolved  from  1  litre  of 
water  at  0°.  The  vapour  tension  of  water  at  this  tem- 
perature is  4-  60  mm.  In  our  formula,  pv  =  R  T,  we  have  to 
set  p  =  4-6,  R  =  62,265,  and  T  =  273,  and  we  find  v  = 
3,612,000  c.c.,  a  value  which  applies  to  1  gram-molecule,  i.e.  18 
grams,  of  water.  A  litre  of  water  at  0°  weighs  9  99  '9  grams, 
and  contains,  therefore,  55*55  gram-molecules  ;  consequently, 
in  the  state  of  gas  it  occupies  a  volume  55  '55  times  as  great 
as  that  which  we  have  calculated  for  1  gram-molecule, 
55*55  X  3,612,000  c.c.  =  205,600  litres. 

Law  of  van  der  Waals.  —  The  relationship  pv  =  RT 
represents  a  limit  law  —  that  is  to  say,  it  only  becomes 
strictly  correct  at  very  great  dilution.  At  moderate  and 
high  pressures  the  forces  acting  between  the  molecules,  and 
the  volume  actually  occupied  by  the  molecules,  become 


in.  ISOTONIC    SOLUTIONS.  27 

appreciable.     Van  der  Waals,  correcting   the   pressure   and 
volume  for  these  circumstances,  arrived  at  the  formula — 


containing  two  new  constants,  a  and  b,  which  are  functions 
of  the  "  internal  pressure  "  and  of  the  molecular  volume. 
Experimental  results  show  a  high  degree  of  agreement  with 
this  formula. 

Isotonic  Solutions. — Certain  parts  of  plants,  when  in  a 
more  or  less  dehydrated  condition,  are  able  when  placed  in 
water  to  absorb  some  of  it  without  losing  any  of  the  cell- 
content — a  fact  which  has  long  been  known  to  physiologists. 
Further  experiments  with  salt  solutions  and  plant  cells 
showed  that  at  a  certain  concentration  of  the  solution  an 
equilibrium  is  established  between  it  and  the  cell-contents. 
If  the  solution  is  too  dilute,  water  passes  into  the  cell ;  if  too 
concentrated,  water  passes  out  from  the  cell.  Those  salt 
solutions  which  are  in  equilibrium  with  the  cell-sap  are  said 
to  be  isotonic  or  isosmotic  with  it. 

By  using  the  same  or  quite  similar  cells — cells  are  used 
which  lie  close  together  in  a  homogeneously  developed  part 
of  a  plant — these  could  be  compared  with  solutions  of 
different  substances,  and  the  concentrations  of  the  various 
dissolved  substances  in  solutions  which  are  isotonic  with 
the  cells  could  be  determined.  These  solutions  are,  of  course, 
isotonic  with  respect  to  each  other. 

De  Vries  (1)  found,  in  a  series  of  experiments  with 
Tradescantia  discolor  and  Begonia  manicata,  that  solutions 
which  contained  in  a  litre  equivalent  quantities  of  potassium 
nitrate,  sodium  nitrate,  and  potassium  chloride  were  isotonic 
with  each  other.  But  a  solution  containing  1  gram-molecule 
of  potassium  chloride  had  the  same  effect  as  a  solution  con- 
taining 1/7  gram-molecules  of  cane  sugar  or  glycerol. 

The  cell  preparations  in  the  salt  solution  to  be  investi- 
gated are  examined  under  the  microscope.  Each  cell  (Fig.  5  a) 
is  surrounded  by  a  solid  cell-membrane,  which  allows  both 


28      LAWS   OF   AVOGADRO   AND   VAN'T   HOFF.     CHAP. 


water  and  dissolved  substance  to  pass  through  its  pores. 
Inside  this  cell-wall  there  is  the  real  cell-content,  the 
protoplasm.  If  the  cell-content  parts  witli  water  to  the 
surrounding  medium,  it  contracts  and  separates  from  the  cell- 
wall  (plasmolysis),  at  first 
at  the  corners  as  repre- 
sented in  Fig.  5&.  If  much 
water  is  lost*  by  the  cell,  the 
protoplasm  aggregates  to  a 
mass  which  remains  con- 
nected with  the  cell-wall 
only  by  a  few  fine  threads 

(Fig.  5c).     The  cell-content  can  easily  be  distinguished  from 
the  cell-wall  by  staining  (methyl- violet,  etc.). 

Semi -permeable  Membranes. — Living  cells  have  the 
peculiar  property  of  allowing  water  but  not  dissolved  material 
to  pass  to  or  from  the  protoplasm. 

After  death  or  by  the  action  of  some  poisons,  the  cell 
loses  this  property.  An  artificial  cell  possessed  of  this 
property  is  naturally  of  great  value.  The  physiologist  Traube 
(2)  succeeded  in  preparing  such  a  cell  by  precipitating  a 
thin  colloidal  film  of  copper  ferrocyanide  within  the  walls  of 
a  porous  cylinder.  With  so-called  semi-permeable  membranes 
of  this  nature,  Pfeffer  (3)  carried  out  a  series  of  striking 
experiments. 

Osmotic  Pressure. — Pfeffer  filled  a  porous  cylinder,  A 
(Fig.  6),  with  copper  sulphate  solu- 
tion, and  immersed  it  in  a  solution 
of  potassium  ferrocyanide.  Some- 
where about  the  middle  of  the  cell- 
wall  the  two  solutions  met,  and 
there  a  fine  membrane  of  copper 
ferrocyanide  was  formed,  which 
gradually  grew  stronger.  The  cell 
A,  whose  wall  only  served  as  a  mechanical  support,  was 
washed  out,  and  filled  quite  full  with  a  solution  of  cane 
sugar.  A  cover,  L,  fitted  with  a  manometer,  Mt  was  luted 


FIG. 


in.  OSMOTIC    PRESSURp.  29 

on  to  the  cylinder,  and  the  whole  apparatus  was  placed  in 
a  water-bath  kept  at  a  constant  temperature.  The  water 
forced  itself  into  the  sugar  solution,  and  the  pressure  in  the 
cell  rose  to  a  maximum  value,  at  which  evidently  water 
neither  diffused  into  nor  out  of  the  cell.  The  equilibrium 
was  established  more  quickly  when  mercury  was  poured  into 
the  open  end  of  the  manometer.  If  the  pressure  was  in- 
creased beyond  this  maximum  value,  which  is  the  osmotic 
pressure  of  the  sugar  solution  in  question,  water  was  forced 
out  of  the  cell  into  the  outer  bath. 

Pfeffer  first  investigated  the  behaviour  of  solutions  of 
cane  sugar  of  different  concentrations,  and  found  the  following 
values : — 


Percentage  of  sugar 

1 

'2 

2-74 

4 

6 

Osmotic  pressure 

535 

101G 

1513 

2082 

3075  mm. 

Hg. 

Osmotic  pressure 

535 

508 

554 

521 

513 

Percentage  of  sugar 

The  numbers  in  the  last  line  are  very  nearly  equal,  and 
the  differences  are  easily  attributable  to  the  errors  of  experi- 
ment, which  are  fairly  appreciable.  The  osmotic  pressure  is, 
therefore,  proportional  to  the  quantity  of  substance  or  the  number 
of  molecules  in  unit  volume.  This  corresponds  exactly  with 
gas  pressure,  which,  according  to  the  law  of  Boyle,  is  inversely 
proportional  to  the  volume  taken  up  by  the  gas — that  is, 
directly  proportional  to  the  concentration  of  the  gas. 

Pfeffer  also  carried  out  experiments  with  other  solutions 
of  such  substances  as  gum,  dextrin,  potassium  sulphate, 
potassium  nitrate,  etc.  With  potassium  nitrate  he  obtained 
the  following  results  : — 

Percentage  of  potassium  nitrate       .  0'80          1*43  3'3 

Osmotic  pressure       .     .      .      .      .  1304        2185        4368  mm.  Hg. 

Osmotic  pressure 1330 

Percentage  01  KN03 

In  this  case  the  osmotic  pressure  is  not  exactly  pro- 
portional to  the  quantity  of  salt,  but  increases  more  slowly 
than  the  concentration.  The  cause  of  this  deviation  lies 
chietiy  in  the  fact,  which  Pfeffer  proved,  that  the  membrane, 


30      LAWS   OF   AVOGADRO   AND   VAN'T   HOFF.     CHAP. 

particularly  at  high  pressures,  is  not  quite  impermeable  for 
the  salt. 

Pfeffer  further  proved  that  the  osmotic  pressure 
increases  slowly  with  rise  of  temperature  as  the  following 
table  shows : — 


Temperature. 

Osmotic  pressure  in  cm.  Hg. 

Observed. 

Calculated. 

6-8° 
13-5° 
14-2° 
22-0° 

50-5 
52-1 
53-1 

54-8 

50-5 
51-7 
51-8 
532 

The  numbers  in  the  last  column  have  been  calculated  on 
the  assumption  that  the  osmotic  pressure,  just  as  the  gas 
pressure  according  to  the  law  of  Gay-Lussac,  increases  pro- 
portionally to  the  absolute  temperature,  and  it  will  be  shown 
later  that  this  must  be  the  case.  Pfeffer's  numbers  do  not 
justify  this  conclusion,  but  they  at  least  show  that  the  direction 
of  the  influence  of  temperature  is  in  agreement  with  the 
assumption. 

Lastly,  we  may  try  to  find  if  Avogadro's  law  also  obtains 
for  the  osmotic  pressure — that  is,  whether  for  dissolved  sub- 
stances the  constant  R  in  the  equation ^w  =  ET  has  the  same 
value  as  for  gases. 

At  the  absolute  temperature  2 79 '8°  cane  sugar  in  a 
1  per  cent,  solution  has  a  pressure  of  505  mm.  Hg.  As 
the  molecular  weight  of  sugar  is  342,  if  1  gram  is  contained 
in  100  c.c.  of  solution,  1  gram-molecule  is  contained  in 
34,200  c.c. 

From  the  equation— 

505  x  34,200  =  R  x  279*8 
E  =  61,720, 

instead  of  the  value  62,265  found  for  gases  (see  p.  26). 

This  calculation  was  first  made  by  van't  Hoff  (4),  who 


OSMOTIC    PRESSURE. 


called  attention  to  the  great  similarity  which  exists  between 
the  gas  pressure  and  the  osmotic  pressure  of  dissolved  sub- 
stances. He  expressed  this  by  saying  that  the  gas  laws  are 
also  applicable  to  dilute  solutions  if  the  gas  pressure  be 
replaced  by  osmotic  pressure.  The  law  of  Boyle,  applicable 
to  all  gases  at  constant  temperature,  followed  by  Gay- 
Lussac's  law  for  the  single  gases  at  all  temperatures, 
then  by  Avogadro's  law  for  all  gases  at  all  temperatures,  and 
finally,  by  van't  Hoffs  generalisation  for  all  finely  dispersed 
material  at  every  temperature,  together  form  one  of  the  most 
beautiful  series  of  development  in  science. 

Of  all  the  laws  of  matter  known  to  us,  that  of  van't  Hoff 
is  one  of  the  most  general. 

Osmotic  Pressure  of  Gases.— Experiments  with  semi- 
permeable  membranes  offer  as  a  rule  considerable  difficulties, 
since  the  pressure  equilibrium  is  only  slowly  established. 
The  best  results  are  obtained  by  working  with  gases. 
Eamsay  (5)  carried  out  the  following  experiment,  first 
suggested  .by  me  : — 

Two  vessels,  A  and  B  (Fig.  7),  each  provided  with  a 
manometer,  mi  and  m2,  are 
separated  by  a  palladium  wall, 
P.  A  is  filled  with  hydrogen 
and  B  with  nitrogen,  both  at 
atmospheric  pressure  and  ordi-  ,-, 
nary  temperature;  the  mano-  \rn,t 
meters  then  indicate  the  same  \^-Jj 
pressure  in  each  vessel.  The 
apparatus,  but  not  the  mano- 
meters, is  then  heated  to  600°.  Hot  palladium  has  the 
peculiar  property  of  taking  up  hydrogen  and  allowing  it, 
but  not  nitrogen,  to  pass  through.  Hydrogen,  therefore,  can 
pass  from  A  to  B  until  the  hydrogen  pressure  is  the  same 
on  both  sides  of  the  palladium  wall — J-  atmo.,  if  A  and  B 
are  of  equal  volume.  When  the  apparatus  is  now  brought 
back  to  the  ordinary  temperature,  there  will  be  found  in  B 
nitrogen  at  1  atmo.  pressure  and  hydrogen  at  J  atmo., 


B 


FIG.  7. 


32      LAWS    OF   AVOGADRO   AND   VAN'T   HOFF.     CHAP. 


whilst  in  A  there  is  only  hydrogen  at  -|  atmo.  pressure. 
The  excess  of  pressure  in  B  may  be  termed  the  osmotic 
pressure  of  nitrogen.  In  this  case  it  is  quite  clear  that  the 
osmotic  pressure  of  nitrogen  in  B  (according  to  Dalton's 
law)  is  equal  to  the  pressure  which  obtains  if  it  alone 
occupied  the  volume  B  in  the  state  of  gas. 

A  similar  experiment  may  be  carried  out  at  the  ordinary 
temperature  with  carbon  dioxide  and  hydrogen,  if  the  pal- 
ladium be  replaced  by  a  caoutchouc  membrane.  Carbon 
dioxide  is  much  more  soluble — about  60  times — than 
hydrogen  in  caoutchouc,  and  consequently  the  carbon  di- 
oxide passes  from  A  to  B  comparatively  quickly,  whilst  the 
hydrogen  almost  all  remains  in  B.  Complete  equilibrium  is 
established  in  this  case  when  the  carbon  dioxide  and  hydrogen 
have  distributed  themselves  equally  between  A  and  B.  But 
at  the  beginning  a  rapid  rise  is  noticed  at  the  manometer  ra2, 
which  then  sinks  slowly  after  some  time.  With  respect  to 

hydrogen   and  carbon   dioxide, 
caoutchouc  is,  therefore,  not  a 
perfect    semi-permeable   mem- 
/  V  brane ;    and   a   similar  imper- 

fection  is  to  be  found  in  all 
semi-permeable  membranes. 

The   above  experiment  can 
also  be  carried  out  in  the  fol- 
FlG  8     b  lowing  way :    The  wide  end  of 

a    funnel,     T    (Fig.     8a),    is 

covered  with  a  sheet  of  rubber.  The  funnel  is  then  filled 
with  carbon  dioxide,  and  the  narrow  end  dipped  into  water  or 
other  liquid,  V.  The  liquid  rises  against  the  external  pres- 
sure, because  the  carbon  dioxide  diffuses  more  quickly  out- 
wards through  K  than  air  diffuses  inwards. 

Osmotic  Experiments  with  Liquids. — Dutrochet  in 
1826  carried  out  a  similar  experiment  with  a  liquid.  He  closed 
a  funnel  with  an  animal  membrane,  H,  and  after  filling  the 
funnel  with  copper  sulphate  solution,  dipped  it  into  water. 
As  water  passes  through  the  membrane  more  quickly  than 


^ 

I\ 

T 
H 

\ 

V 

Water    +  K^  Cye  Fe 


in.  NATURE   OF   OSMOTIC   PRESSURE.  33 

the  copper  sulphate  solution,  the  liquid  rises  in  the  tube  r 
against  the  external  pressure  (Fig.  8&).  After  some  time, 
however,  the  level  of  the  liquid  in  the  tube  sinks  to 
that  of  the  liquid  outside,  because  the  membrane  H 
does  not  completely  prevent  the  diffusion  of  the  copper 
sulphate. 

The  Abbe  de  Nollet  in  1750  had  performed  the  same 
experiment,  using  alcohol  instead  of  copper  sulphate. 

The  so-called  "  chemical  garden  "  is  an  osmotic  pheno- 
menon from  which  much  may  be  learned.  If  a  crystal  of 
ferric  chloride  be  thrown  into  a  dilute  solution  of  potassium 
ferrocyanide,  it  sinks  and  becomes  enveloped  in  a  film  of 
Prussian  blue,  which  is  permeable  by  water  but  not  by  ferric 
chloride  or  potassium  ferrocyanide.  Consequently  water 
forces  its  way  into  this  semi-permeable 
cell  of  Prussian  blue  and  expands  it. 
Further  quantities  of  the  ferric  chloride 
will  be  dissolved  by  the  water  which 
has  entered,  so  that  the  osmotic  pressure 
is  always  kept  high.  If  the  inflowing  J 

water  bursts  the  membrane,  a  new 
precipitation  takes  place  at  the  same  spot,  and  so  the  cell 
at  once  closes.  The  small  air-bubbles  originally  attached  to 
the  ferric  chloride  crystal  exert  an  upward  pull  on  the  cell, 
and  a  more  or  less  tree-like  formation  is  noticed;  at  the 
higher  extremities  the  small  air-bubbles  are  frequently 
visible  (Fig.  9). 

Nature  of  Osmotic  Pressure. — Eamsay's  application  of 
palladium  as  a  semi-permeable  membrane  teaches  us  much. 
If  we  imagine  the  hydrogen  replaced  by  water,  the  nitrogen 
by  sugar,  and  the  sheet  of  palladium  by  a  film  of  copper 
ferrocyanide,  then  we  have  Pfeffer's  experiment. 

The  water  forces  its  way  into  E  (Fig.  7),  dissolves  the 
sugar  there,  and  fills  B  with  the  solution  until  the  manometer 
indicates  an  excess  of  pressure,  which  corresponds  with  the 
osmotic  pressure  of  the  sugar.  In  Eamsay's  experiment  the 
pressure  of  the  hydrogen  was  the  same  on  both  sides  of 

D 


34      LAWS   OF   AVOGADRO   AND   VAN'T   HOFF.     CHAP. 

the  palladium,  so  also  in  Pfeffer's  experiment  the  pressure 
of  the  water  is  the  same  in  A  and  B.  The  excess  of  pressure 
in  B  is  in  this  case  due  to  sugar,  just  as  in  the  former  case  it 
is  due  to  nitrogen.  We  generally  conceive  gas  pressure  as 
due  to  the  impact  of  the  molecules  against  the  walls  of  the 
containing  vessel ;  in  the  same  way  the  osmotic  pressure  of 
the  sugar  may  be  imagined  to  be  due  to  impacts  of  the 
sugar  molecules  against  the  membrane.  The  impacts  of  the 
molecules  of  a  substance  exert  the  same  action  whether 
the  substance  be  in  the  gaseous  or  dissolved  (liquid) 
state. 

It  is,  however,  quite  unnecessary  to  rely  on  the  kinetic 
view.  It  is  well  known  that  a  gas  tends  to  expand  so  as  to 
fill  the  volume  placed  at  its  disposal,  and  this  tendency 
evidences  itself  in  the  pressure. 

The  dissolved  sugar  has  a  similar  tendency  to  become 
evenly  distributed  over  the  solvent,  water,  and  the  measure 
of  this  is  the  osmotic  pressure.  This  expansion  tendency  of 
gaseous  and  dissolved  substances  at  the  same  temperature, 
and  with  the  same  number  of  molecules  in  unit  volume,  is 
the  same  for  all  substances;  it  increases  directly  with  the 
absolute  temperature  and  with  the  concentration. 

From  the  preceding  examples  it  will  be  seen  what  is 
meant  by  a  semi-permeable  membrane.  It  is  a  medium 
which  is  capable  of  taking  up  one  component  of  a  (gaseous 
or  liquid)  mixture  and  holding  the  other  back.  As  a  rule 
one  of  the  components  is  water,  the  other  a  dissolved 
substance.  The  envelopes  of  protoplasm,  copper  ferro- 
cyanide,  Prussian  blue,  etc.,  take  up  water,  but  not  substances 
dissolved  therein ;  palladium  dissolves  hydrogen,  but  not 
nitrogen;  caoutchouc  dissolves  carbon  dioxide,  but  not  (in 
appreciable  amount)  hydrogen. 

The  above  definition  of  a  semi- permeable  wall  corresponds 
with  two  cases,  the  meaning  of  which  we  now  come  to.  One 
case  is  the  vacuum  or  a  gas :  the  water  may  be  taken  out  of  a 
sugar  solution  in  the  form  of  vapour,  but  the  sugar  remains, 
being  practically  non- volatile.  The  other  case  is  ice.  If  water 


in.  RELATIVE   OSMOTIC    PRESSURES.  35 

be  allowed  to  freeze  out  of  a  sugar  solution,  it  is  found  that 
only  ice  (i.e.  water)  separates,  and  the  sugar  remains  entirely 
dissolved. 

If  a  vessel,  A,  containing  water,  and  another,  B,  containing 
an  aqueous  solution,  be  placed  under  a  glass  globe  (Fig.  10), 
water  will  pass  from  A  to  B,  the  air  acting  as  semi-permeable 
wall. 

If  in  a  vessel,  KK  (Fig.  11),  one  half,  A,  be  filled  with 


K 


M 


K 


FIG.  10.  Fia.  11. 

water  and  the  other  half,  B,  with  a  sugar  solution,  and 
if  these  be  separated  by  a  sheet  of  ice,  water  can  pass 
from  A  to  B  by  the  thawing  of  the  ice  on  the  side  next  to 
the  sugar  solution  and  the  freezing  of  the  same  quantity  of 
water  on  the  other  side. 

Physiological  Measurement  of  the  Relative  Osmotic 
Pressures  in  Different  Solutions.— Physiological  experi- 
ments have  been  made  with  isotonic  solutions,  and  these  will 
be  discussed  in  this  section.  Donders  and  Hamburger  (6) 
found  that  two  solutions  which  were  isotonic  at  0°  were 
isotonic  also  at  34°.  This  corresponds  with  the  fact  that  the 
pressure  varies  with  the  temperature  in  the  same  way  for  all 
gases  (at  constant  volume),  so  that  they  will  have  nearly 
the  same  pressure  at  any  temperature  whatever,  if  at  one 
particular  temperature  their  pressures  are  equal. 

De  Vries  (1)  showed  by  means  of  plant  cells  that 
equimolecular  solutions  of  non-electrolytes — that  is,  solutions 
containing  the  same  number  of  molecules  in  the  litre — 
are  isotonic,  as  exhibited  in  the  following  table.  For  salts 
this  same  relationship  does  not  hold  good.  The  table  gives 
the  so-called  isotonic  coefficients,  that  of  potassium  nitrate 
being  taken  as  3.  T78  for  glycerol  indicates,  therefore,  that 


36      LAWS   OF   AVOGADRO   AND   VAN'T   HOFF.     CHAP. 

a  solution  which  contains  3  gram-molecules  of  glycerol  in 
the  litre  is  isotonic  with  a  solution  of  potassium  nitrate 
containing  178  gram-molecules  in  the  litre. 

Glycerol 1*78  i  Potassium  iodide     ....  3-04 

Glucose 1'88      Sodium  nitrate 3 

Cane  sugar 1*81      Sodium  iodide 2-90 

Malic  acid 1-98  :   Sodium  bromide     ....  3-05 

Tartaric  acid 2-02  Potassium  acetate  ....  2-85 

Citric  acid 2-02  Potassium  bromide      .     .     .  3-05 

Magnesium  sulphate    .     .     .  1'96  |  Potassium  sulphate     ...  3*9 

Potassium  nitrate    ....  3  i  Calcium  chloride     ....  4-05 

Potassium  chloride ....  3  I  Potassium  citrate   ....  4-74 

Sodium  chloride      ....  3 

Bonders,  Hamburger,  and  Hedin  (7)  have  obtained 
analogous  results  using  blood  corpuscles.  When  the  red 
corpuscles  are  introduced  into  a  solution,  which  is  so  con- 
centrated that  it  abstracts  water  from  them,  the  corpuscles 
sink.  If,  on  the  other  hand,  the  corpuscles  absorb  water 
from  the  solution,  they  at  the  same  time  lose  part  of  their 
colouring  matter,  and  the  solution  becomes  red.  In  this  way 
it  is  easy  to  determine  the  concentration  of  a  solution  which 
is  isotonic  with  the  corpuscles. 

Bonders  and  Hamburger  investigated  blood  corpuscles 
from  the  various  vertebrates,  from  the  frog  to  the  ox,  and 
always  obtained  the  same  results,  which,  moreover,  agreed 
with  those  arrived  at  by  De  Vries. 

Experiments  in  which  living  cells  are  used  have  the 
disadvantage  that  isotonic  can  only  be  proved  between  such 
solutions  as  have  the  same  osmotic  pressure  as  the  cell.  The 
osmotic  pressure  of  the  cells,  however,  does  not  vary  very 
much,  for  most  of  the  cells  available  for  investigation  show 
a  pressure  of  about  4  atmos.  Young  cells  have  a  higher 
pressure  than  older  ones,  on  which  fact  their  power  of 
development  depends. 

In  certain  species  of  bacteria  the  osmotic  pressure  rises 
to  as  much  as  10  atmos.,  which  high  pressure  is  closely 
connected  with  their  power  of  destroying  other  organisms  of 


in.  TAMMANN'S   MEASUREMENTS.  37 

lower  osmotic  pressure.  Sea-weed  has,  as  a  rule,  an  osmotic 
pressure  greater  by  about  4  atmos.  than  the  water  sur- 
rounding it. 

Tammann's  Measurements. — The  method  devised  by 
Tammann  (8)  is  capable  of  more  general  application.  The 
method  consists  in  observing  the  diffusion  currents  in  Topler's 
apparatus.  If  in  a  liquid  the  density  is  greater  or  less  at 
any  one  point  than  in  the  neighbourhood,  then  at  this  point 
the  liquid  either  falls  or  rises,  and  this  is  easily  seen  on  account 
of  the  different  refractive  indices  of  the  solutions  of  different 
densities.  Thereby  the  well-known  phenomenon  of  streaking 
is  produced,  a  phenomenon  which  is  often  to  be  noticed  when 
the  sun  shines  on  a  wall,  producing  a  slow  upward  current 
of  air. 

Tammann  uses  as  bath  a  solution  of  potassium  ferro- 
cyanide.  Into  this  is  introduced  a  drop  of  a  solution  of  a 
copper  or  zinc  salt  hanging  from  the  end  of  a  glass  point ; 
the  drop  at  once  becomes  covered  with  a  semi-permeable 
membrane  of  copper  or  zinc  ferrocyanide.  If  the  drop  is 
isotonic  with  the  solution  in  the  bath,  no  change  of  concen- 
tration takes  place  in  its  neighbourhood,  and  no  streaking  is 
formed.  If  the  drop  is  more  concentrated  than  the  ferro- 
cyanide solution,  it  absorbs  water  from  the  solution  in 
immediate  contact  with  it,  thus  making  part  of  the  solution 
specifically  heavier  than  the  mass  of  liquid  in  the  bath,  and 
it  sinks,  producing  a  streakiness  along  its  course.  The 
opposite  action  takes  place  when  the  solution  within  the 
membrane  is  too  dilute. 

In  Tammann's  experiments,  the  drops  contained  in  some 
cases  other  substances,  such  as  ethyl  alcohol,  cane  sugar,  etc., 
besides  the  copper  salt.  The  osmotic  pressure  of  the  sub- 
stances was  calculated  on  the  assumption  that  the  total 
osmotic  pressure  is  the  sum  of  the  osmotic  pressure  of  the 
copper  salt  and  that  of  the  substance  added. 

The  following  table,  which  contains  the  chief  results 
obtained  by  Tammann,  gives  the  isotonic  coefficients  of  those 
solutions  which  correspond  with  O'l  n  and  0*3  n  solutions  of 


38       LAWS  OF  AVOGADRO  AND  VAN'T  HOFF.     CHAP.  in. 

potassium  ferrocyanide,  the  coefficients  of  these  latter  solutions 
being  set  equal  to  1 : — 

n  =  0-l   n  =  0-3  I  n  =  0-l   n  =  0-3 

Potassium  ferrocyanide  1  1  ]  Cane  sugar   ....  0-40     0'40 

Ammonium  sulphate  .  0*75  O80      Salicin 0*42      — 

Cupric  nitrate    .     .     .  O82  0-93  Chloral  hydrate      .     .  0-46    O45 

Copper  acetate  .     .     .  O69  0-66  j  Ether Q-45 

Copper  chloride      .     .  0-90  1-00  !  Urea 0-50 

Magnesium  sulphate   .  O33  0-37  ,  Propyl  alcohol  .     .     .  0-45 

Zinc  sulphate     .     .     .  O40    0-34  ]  Isobutyl  alcohol     .     .  0-45     — 

Copper  sulphate     .     .  0'41  0'36  !  Ethyl  acetate     .     .     .  0-45 

Ethyl  alcohol    .     .     .  0-45  0-45  i 

Further  Experiments  on  Osmotic  Pressure. — Adie 
(9)  has  in  a  large  measure  overcome  the  technical  difficulties 
in  connection  with  osmotic  experiments ;  he  has  determined 
the  osmotic  pressure  of  salt  solutions,  and  obtained  results 
which  agree  remarkably  well  with  the  requirements  of  the 
theory,  so  long  as  dilute  solutions  are  used.  For  concentrated 
solutions,  however,  it  has  not  yet  been  possible  to  prepare 
perfect  semi-permeable  membranes. 

In  this  respect  the  experiments  of  G-.  Hedin  (7)  and 
Koppe  (10)  are  interesting.  A  certain  quantity  of  blood 
was  added  to  equal  quantities  of  various  salt  solutions  placed 
in  tubes  in  a  centrifugal  machine.  The  blood  corpuscles 
collected  together  in  the  end  of  the  tube  in  a  cylindrical 
mass  from  the  height  of  which  the  total  volume  of  corpuscles 
added  to  the  salt  solution  could  be  estimated.  This  volume 
was  found  to  be  the  smaller  the  higher  the  osmotic  pressure 
of  the  salt  solution.  Hedin  and  Koppe  obtained  results  for 
the  osmotic  pressure  of  different  solutions  which  were  in 
close  agreement  with  theory. 


CHAPTER  IV. 
Vapour  Pressure  of  Solutions. 

The  Vapour  Pressure  of  a  Solution  is  lower  than  that 
of  the  Pure  Solvent. — It  has  been  well  known  for  a  long 
time  that  a  solution  in  water  of  a  substance  which  has  no 
appreciable  vapour  pressure  has  a  lower  vapour  tension 
than  water.  Thus,  for  instance,  the  vapour  tension  of  water 
can  be  reduced  by  the  addition  of  sulphuric  acid,  and  such 
solutions  are,  therefore,  used  to  extract  the  moisture  from 
the  air.  If  the  vapour  tension  is  lowered,  the  boiling  point 
must  be  raised,  because  when  a  liquid  boils,  its  vapour 
pressure  amounts  to  1  atmo.,  and  consequently,  when 
the  vapour  pressure  is  diminished  by  the  addition  of  some 
foreign  substance,  the  temperature  must  be  raised  in  order 
that  the  pressure  may  reach  the  value  of  1  atmo. 

This  corollary  has  also  been  known  for  a  long  time ;  for 
instance,  if  a  salt  be  dissolved  in  water,  the  boiling  point  of 
the  solution  (at  760  mm.  Hg)  is  higher  than  100°,  and  the 
more  salt  is  added  the  higher  is  the  boiling  point.  (Faraday, 
1822;  Legrand,  1833.) 

Connection  between  Vapour  Pressure  and  Osmotic 
Pressure  of  a  Solution. — In  the  very  first  investigation 
made  on  osmotic  pressure,  it  was  found  that  the  depression 
of  the  vapour  pressure  of  a  solution  was  almost  exactly  pro- 
portional to  the  osmotic  pressure.  A  conclusive  proof  of  this 
proportionality,  based  on  the  mechanical  theory  of  heat,  was 
first  deduced  by  van't  Hoff  (1)  in  a  paper  to  the  Swedish 
Academy  (1886).  I  (#)  have  later  deduced  the  same 


VAPOUR  PRESSURE   OF   SOLUTIONS.         CHAP. 


thing  in  a  simpler  way,  and  this  development  may  fitly  be 

introduced  here. 

A  basin,  S,  containing  a  liquid,  is  placed  under  a  glass 

globe,  A,  from  which  the  air  can  be  pumped  out  (Fig.  12). 

The  wide  end  of  a  funnel  which  is  closed  by  a  semi-permeable 

membrane,  M,  dips  into  the  liquid  in  the  basin  ;  the  funnel 

is  provided  with  a  long  stem,  r. 
The  funnel  contains  a  solution,  the 
solvent  being  the  same  as  the  liquid 
in  S,  and  the  dissolved  substance 
being  non-volatile. 

The  liquid  in  $  passes  through 
the  semi-permeable  membrane  and 
rises  in  r,  until  there  is  a  hydro- 
static pressure  on  M,  equal  to  the 
osmotic  pressure  of  the  solution  L. 

In  this  case  we  have  two  semi- 
permeable  media,  namely,  the  mem- 
brane M  and  the  vacuous  space 
between  the  surfaces  of  the  liquids 
in  r  and  £  Suppose  that  the  so- 
lution L  contains  N  molecules  of 
solvent  of  molecular  weight  M  for  1 
molecule  of  dissolved  substance,  N 


11 


v\ 


FlG-  12- 
being  large  —  that  is,  the  solution  a  dilute  one. 

The  osmotic  pressure,  and  from  this  the  height  of  the 
column  of  liquid  in  the  tube  r,  can  be  calculated.  The 
equation  pv  =  RT  gives  us  pt  when  v  and  T  are  known. 
v  is  the  volume  which  contains  1  gram-molecule  of  dis- 
solved substance.  In  this  volume  there  are,  according  to  the 
above  assumption,  N  gram-molecules  of  solvent  of  molecular 
weight  M  —  that  is,  NM  grams  of  solvent,  the  specific  gravity 
of  which  may  be  s.  Therefore  — 

MN 


and  consequently — 


»  = • 

1          MN 


iv.  LOWERING   OF   VAPOUR    PRESSURE.  41 

The  height  li  of  the  column  in  r,  since  the  pressure  per 
square  centimetre  must  be^>  grams,  is  given  by  — 


. 

~  s      MN 

The  vapour  pressure  over  the  solution  in  r  has  now  to  be 
found.  The  decrease  of  pressure  from  the  surface  of  the 
liquid  in  S  to  that  in  r  is  equal  to  the  weight  of  a  column  of 
vapour  h  cm.  high  and  of  1  sq.  cm.  cross-section.  If  p  be 
the  vapour  pressure  at  the  lower  and  p'  that  at  the  higher 
surface,  this  weight  is  equal  to  p  —  p'. 

Now  we  know  that  the  weight  M  of  a  gram-molecule  of 


a  gas  at  pressure  p  is  contained  in  the  volume  v  =  -—.  M 
grams  occupy  v  c.c.,  and  consequently  1  c.c.  weighs  -M  grams, 

and  h  c.c.  weigh  -M  grams.  The  weight  of  a  column  of 
vapour  of  1  sq.  cm.  section  between  the  two  liquid  surfaces 
is,  therefore,  equal  to  p  -  p'  and  to  -M. 

If  we  now  substitute  the  values  found  above  for  h  and  v, 
we  obtain  — 

hj,,     H..RT  .  RT     p 

p  —  p  =     M  =  M  ~  -—-7  —  -  =  1- 

v  MN        p        N 


or- 


p          N 


The  Relative  Lowering  of  Vapour  Pressure.—  The 

relationship  just  deduced  may  be  brought  into  a  very  simple 

form.      P  ~  P    js   caiied    the   relative   lowering   of  vapour 

P 

pressure,  and  it  obviously  gives  the  difference  between  the 
vapour  pressure  of  solvent  and  that  of  the  solution  referred  to 
the  vapour  pressure  of  the  solvent.  It  is  independent  of  the 
temperature,  of  the  nature  of  the  solvent,  and  of  the  nature 


42  VAPOUR  PRESSURE   OF   SOLUTIONS.          CHAP. 

of  the  dissolved  substance,  and  is  conditioned  solely  by  the 
number  of  dissolved  and  solvent  molecules. 

This  law  was  first  established  by  Eaoult  (3)  from  purely 
experimental  results ;  the  connection  with  osmotic  pressure 
was  later  shown  by  van't  Hoff  (4). 

If  one  gram-molecule  of  a  substance  be  dissolved  in  100 
gram-molecules  of  a  solvent,  the  relative  lowering  of  the 
vapour  pressure  should  amount  to  yj^.  Eaoult  carried  out  a 
large  number  of  experiments  on  this  subject. 

The  following  table  gives  the  mean  values  for  a  series 
of  solvents  from  results  obtained  with  various  dissolved 
substances  : — 

Water 0*0102  I  Methyl  iodide      ....    0-0105 

Phosphorus  trichloride  .  .  0-0108  Methyl  bromide  ....  0-0109 
Carbon  disulphide  .  .  .  0-0105  Ether 0-0096 


Carbon  tetrachloride     .     .  0*0105 

Chloroform 0-0109 

Amylene 0-0106 

Benzene  .  0-0106 


Acetone 0-0101 

Methyl  alcohol     ....  0-0103 

Ethyl  alcohol 0-0101 

Acetic  acid .  .  0-0163 


It  has  occasionally  been  assumed  that  by  means  of  the 
above  formula  the  molecular  weight  of  the  solvent  could  be 
calculated  as  that  of  the  dissolved  substance  can  be,  since  the 
relationship  between  the  number  of  molecules  of  dissolved 
substance  and  of  the'  solvent  apparently  occurs  in  the 
equation.  If  we  regard  the  deduction  more  closely,  however, 
we  see  that  we  have  assumed  the  same  molecular  weight  for 
the  solvent  in  the  liquid  and  in  the  vapour  state.  The 
molecular  weight  for  the  solvent  in  the  vapour  state  must  be 
that  deduced  from  the  vapour  density,  for  otherwise  A  vogadro's 
law,  which  is  used  in  developing  the  formula,  would  not  be 
applicable.  When  Eaoult  experimented  with  acetic  acid,  the 
molecular  weight  of  which,  according  to  the  chemical  formula, 
is  60,  but  from  the  vapour  density  is  97*2  (=  1/62  x  60),  he 
obtained  for  the  relative  lowering  of  the  vapour  pressure  a 
number  which  was  nearly  1/62  (exactly  1*63)  times  greater  than 
that  calculated,  assuming  60  for  the  molecular  weight.  This  ap- 
parent deviation  is,  therefore,  in  complete  accord  with  the  law. 


iv.      VAPOUR  PRESSURE  OF  SOLUTIONS  IN  ETHER.     43 

It  should  be  mentioned  that  here  also  salts  seem  to 
behave  anomalously.  Eaoult  only  investigated  few  of  these. 
We  return  later  to  a  consideration  of  their  behaviour. 

Vapour  Pressure  of    Solutions   in  Ether.— Eaoult 
proved  that  for  solutions  in  ethyl  ether  the  relative  lowering 
of  vapour  pressure  is  independent  of  the          c     B     A 
temperature.  He  used  the  ordinary  method 
for    determining     the     vapour    pressure, 
namely  allowing  the  liquid  to  evaporate  in 
a    barometer    vacuum.      The    barometric 
height  h  was  read  off  on  the  barometer  A 
(Fig.  13)  ;  into  another  barometer,  B,  ether 
was  introduced,  and  the  mercury  meniscus 
sank  to  hi.     The  vapour  pressure  p  of  the 
ether  is   given   by  h  —  hi.     Into  a  third 
barometer,  C,  was  introduced  a  solution,  e.g. 
of  1  gram-molecule  (136  grams)  of  turpentine  in  1000  grams, 
that  is,  J-92—  gram-molecules,  of  ether. 

For  this  solution  Eaoult  found  the  vapour  pressure  p'. 
The  calculation  leads  to — 


FIG.  13. 


P  ~  P 

P 


=  0-074. 


whilst  the  experiment  gave  0'071. 

The  experiments  were  carried  out  in  a  room  in  which  the 
temperature  varied  between  0°  and  20°,  but  the  same  lowering, 

? ±-  =  P,  was  always  obtained,  although  p  varied  over  a 

P 
tolerably  wide  range  (from  185  to  442  mm.). 

Other  substances  besides  turpentine  were  examined,  in 
all  cases  1  gram-molecule  in  1000  grams  of  ether  being 
taken.  The  values  obtained,  which  are  given  in  the  follow- 
ing table,  all  agree,  within  the  limits  of  experimental  error, 
with  the  result  found  for  turpentine  O'OTl  and  the  theoretical 
value  0-074. 


4-4  VAPOUR  PRESSURE   OF   SOLUTIONS.          CHAP. 


Perchloro-ethylene    .  237      0-071 

Methyl  salicylate .     .  152     0-071 

Methyl  azocuminate .  382     0-068 

Cyanic  acid     ...  43     0-070 

Benzoicacid    ...  122      0'071 

Trichloracetic  acid    .  163'5  0-071 


M          P      i  M          P 


Benzaldehyde  ...  106     0-072 

Capryl  alcohol      .     .  130     0-073 

Cyanamide.     ...  42     0-074 

Aniline 93     0-071 

Mercury  diethyl   .     .  258     0-069 

Antimony  trichloride  228*5  0'067 


Higher  Concentrations.— The  formula  no  longer 
applies  when  the  solution  is  concentrated,  for  when  N  =  1— 
that  is,  when  the  number  of  molecules  of  solvent  is  the  same 
as  the  number  of  molecules  of  dissolved  substance,  then 

- — —  should  be  equal   to    1,   or,  in    other  words,  p  =  0, 

* 

which   would  indicate   that    the    solution    has    no    vapour 

pressure.  Experience  teaches  that  this  is  incorrect,  and,  as 
Eaoult  has  shown,  the  results  are  in  agreement  with  the 
formula — 

p  -  p  _      1 

p       ~l  +  N 

which  coincides  with  the  former  one  when  N  becomes  great 
in  comparison  with  1. 

Good  results,  can  also  be  obtained  for  concentrated 
solutions  if  we  assume  that  the  relative  lowering  of  the 
vapour  pressure  increases  proportionally  with  the  concentra- 
tion of  the  solution,  provided  this  is  measured  in  gram- 
molecules  per  litre.  If  d  is  the  specific  gravity  of  the  solvent, 

then  the  weight  of  a  litre  is  lOOOd  grams,  or  — — —  gram- 
molecules  are  contained  in  a  litre.  The  vapour  tension  of 
a  solution  which  contains  1  gram-molecule  of  a  dissolved 
substance  in  100  litres  can,  therefore,  be  found  from — 


P^_P_  = 
P 


because  at  such  great  dilution  we  may  set  the  volume  of  the 


IV. 


AQUEOUS   SOLUTIONS. 


45 


solvent  equal  to  that  of  the  solution.    If  the  solution  contains 
ni  gram-molecules  of  dissolved  substance  per  litre,  then  — 


p  —  p  _ 
~ 


This  formula  has  been  tested  with  the  data  accumulated 
by  Eaoult  for  concentrated  solutions,  and  a  very  perfect 
agreement  has  been  found. 

Aqueous  Solutions. — In  one  investigation  Tammann 
{o)  measured  the  external  pressure  under  which  aqueous 
solutions  boil  at  100°,  and  in  this  way  found  the  vapour 
pressures  of  the  solutions  at  this  particular  temperature. 
From  the  last  formula  of  the  preceding  section  we  find  for  a 
normal  solution  in  water  (since  ^>  =  760  mm.,  n  =  1,  M  =  18, 
andd  =  0-959) 

i          *-rpr\  ^1   18 

p  -  p  =  760 


1000  x  0-959 


14-3  mm.  Hg. 


One  hundred  and  eighty  substances  were  examined  at 
various  dilutions.  In  the  following  table,  which  contains 
some  of  Tammann' s  results,  the  concentration  is  expressed 
in  gram-molecules  dissolved  in  1000  grams  of  water.  A 
dilute  solution  containing  n  mols  dissolved  in  1000  grams 
•of  water  corresponds  at  4°  almost  exactly  with  an  ^-normal 
solution ;  at  100°  it  corresponds  with  a  0-959  n  -normal 
solution. 


w,  = 

0-5 

1 

2 

3 

4 

5 

6 

•Calculated  value     .     .     . 

6-8 

13-7 

27-4 

41-0 

54-7 

68-4 

75-2 

Potassium  chloride,  KC1   . 

12-2 

24-4      48  8 

74-1 

100-9 

1285 

152-2 

•Sodium  chloride,  NaCl 

12-3 

25-2  !    52-1 

800 

111  0 

143-0 

176-5 

Potassium  hydroxide,  KOH 

15-0 

29-5 

64-0 

99-2 

1400 

181-8 

223-0 

Aluminium  chloride,  A1CI3 

225 

61-0 

179-0 

3180 

— 

— 

— 

Calcium  chloride,  CaCl2    . 

17-0 

39-8 

95-3 

1666 

241-5 

3195 

— 

•Sodium  sulphate,  Na2SO4  . 
Succinic  acid,  C4H6O4  .     . 

12-6 
6-2 

25-0 
12-4 

48-9 
24-8 

74-2 
36-7 

48-5 

59-7 

71-2 

•Citric  acid,  C6H8O7       .      . 
Lactic  acid,  C3H6O3      .      . 
Boric  acid,  B(OH)3      .      . 

7-9 
6-5 
6-0 

15-0 
12-4 
12-3 

31-8      50-0 
24  0      34-3 
25-1      38-0 

71-1 
44-7 
51-0 

92-8 
55-8 

65-6 

•Sulphuric  acid,  H2SO4 

12-9 

26-5  i    62  8    10H) 

1480 

198-4 

247-0 

46  VAPOUR   PRESSURE   OF   SOLUTIONS.      CHAP.  iv. 

It  is  clear  that  in  the  case  of  the  not  too  concentrated 
solutions  of  the  four  weak  acids — succinic,  citric,  lactic,  and 
boric — the  agreement  between  the  calculated  and  the  experi- 
mental values  is  satisfactory,  and  would  be  better  if  a  correc- 
tion were  introduced  for  the  increase  of  volume  which  takes 
place  on  dissolving  the  substance.  On  the  other  hand,  the 
strong  acids  and  bases  (H2S04  and  KOH)  and  all  the  salts  give 
results  which  are  not  at  all  in  agreement  with  the  values 
calculated.  The  solutions  giving  apparently  anomalous 
results  are  all  good  conductors  of  electricity,  and  it  may  be 
noticed  that  the  deviation  between  calculated  and  experi- 
mental value  is  greater  the  more  radicles  (ions)  the  dissolved 
substance  contains,  just  as  was  found  to  be  the  case  with  the 
osmotic  pressure. 

We  return  later  to  this  behaviour  of  strong  electrolytes. 

For  very  concentrated  solutions  enormous  differences  are 
found  between  the  theoretical  and  the  experimental  results. 
Particularly  is  this  the  case  with  very  hygroscopic  substances 
such  as  caustic  potash,  calcium  chloride,  and  sulphuric  acid, 
and  the  application  of  these  as  drying  agents  depends  on  the 
fact  that  the  vapour  pressure  of  their  solutions  is  small,  and 
consequently  water  passes  to  them  from  places  of  higher 
pressure. 


CHAPTER    V. 


dT 


Boiling  Point  and  Freezing  Point  of  Solutions. 

Calculation  of  the  Boiling  Point  of  a  Solution. — The 

curve  pp  (Fig.  14)  represents  the  change  of  vapour  pressure 
of  water  (or  other  solvent)  with  temperature  near  the  boiling 
point  (at  760  mm.) ;  the  curve  p'p'  represents  in  the  same 
way  the  vapour  pressure  of  a  solution  in  the  same  solvent, 
which,  according  to  what  has 
been  stated  above,  must  be 
lower  than  that  of  the  pure 
solvent.  The  boiling  point  of 
the  solution  (at  760  mm.)  is 
found  by  drawing  through  A, 
which  lies  on  pp  directly  above 
T,  a  line  parallel  to  the  ab- 
scissa-axis. This  horizontal  line 
corresponds  with  a  pressure  of 
760  mm.,  and  cuts  the  curve  p'p' 
at  B.  A  line  is  then  dropped 
perpendicularly  from  B,  cutting 
the  abscissa-axis  at  E,  or  T  +  dT.  The  perpendicular  cuts  pp 
at  C,  which  corresponds  with  a  pressure  of  760  mm.  +  dp.  If 
the  inclination  a  of  the  curve  at  A  is  known,  we  can  find 
_  dp 

The  part  AC  of  the  curve  may  be  regarded  as  a  straight 
line,  and  we  then  have — 

/  j~*  \ 

=  dT  tan  a. 


__L_  T 


T 
FIG.  14. 


GB  =  p  -  p  = 


48  BOILING   AND   FREEZING    POINT.  CHAP. 

If,  then,  by  experiment  the  vapour  pressure  of  the  solvent 
has  been  determined  for  all  temperatures,  and  thereby  tan  a 
has  been  found,  we  can  calculate  the  rise  of  boiling  point  dT, 
knowing  the  value  ot  p  -  p't  which  is  the  relative  lowering 
of  the  vapour  pressure  referred  to  in  the  preceding  chapter. 

The  mechanical  theory  of  heat  gives  us  the  following 

formula  (Clapeyron's  equation)  for  —,  or  for  tan  a— 

dp  =         X 
dT      (v  -Vi)T' 

where  T  is  the  absolute  temperature  at  which  the  vapour 
pressure  is  p,  \  is  the  heat  of  vaporisation  of  1  gram- 
molecule  of  the  solvent,  and  v  and  vi  are  the  volumes  of  the 
gram-molecule  in  the  gaseous  and  liquid  states.  Compared 
with  v,  vi  is  so  small  that  without  introducing  an  appreciable 
error  it  may  be  entirely  omitted. 

Further,  we  have  the  relationship  — 

pv  =  RT 

(where  p  and  v  denote  the  pressure  and  volume  of  the 
gaseous  solvent);  and  if  this  be  introduced  into  the  above 
equation,  we  obtain  — 


- 

p          A 


Since  X  is  not  measured  in  mechanical  units  but  in 
calories,  R  also  must  be  expressed  in  calories.  The  value  of 
R  in  calories  has  already  been  shown  (see  pp.  13  and  26)  to 
be  equal  to  T99,  for  which,  with  a  sufficiently  close  approxi- 
mation, we  may  set  2.  For  a  solution  which  contains  n 
dissolved  molecules  per  100  molecules  of  solvent,  we  know 

/iy     -  -     /yi  fYi 

that  £        -  =  -—  .  ,  and   for   a   solution  which   contains  n\ 
gram-molecules  of  dissolved   substance  per  litre,  we   have 


v.  FREEZING    POINT   OF   SOLUTIONS.  49 

p  —  p'        n\M 

--  i  c\(\c\j  (see  P-  45).     From  this  it  follows  that  for 
p  1000^  v 

the  rise  of  boiling  point  dT  — 

»      22"* 

aJ.  =  -  -  .  -    —  and  dT  = 


100       A  lOOO^X 

It  should  be  carefully  noticed  that  T  denotes  the  absolute 
temperature  of  the  boiling  point  of  the  solvent,  and  X  is  the 
heat  of  vaporisation  of  a  gram-molecule  of  it  at  the  same 
temperature  (compare  p.  56). 

Freezing  Point  of  Solutions.  —  In  the  same  way  we 
can  calculate  the  freezing  point  of  a  solution,  as  has  been 
shown  by  Guldberg  (7)  and 
van't  Hoff  (2).  Let  us  consider 
a  solvent  —  water,  for  example 
—which  freezes  at  the  tempera- 
ture A  (Fig.  15).  The  vapour 
pressure  of  the  liquid  solvent  is 
represented  by  pp,  the  tempera- 
ture being  marked  off  as  abscissa 
and  the  pressure  as  ordinate.  At 
0°  (temperature  A)  the  tension 

of  water  vapour,  represented  by  the  point  P,  is  4'61  mm.  ; 
at  lower  temperatures   the    tension   is   smaller,   and   exact 
measurements    of    this    have   been    made    by    Juhlin   (3). 
Water  in  the   solid  form,  ice,  also   has  a  vapour  pressure 
represented  by   PP,  which   at   the  same   tem- 
perature is  lower  than   that  for  liquid  water; 
at  the  freezing  point,  water  and  ice  must  have 
the   same  vapour  pressure.     In  order  to  prove       FlG  16 
this,  suppose  that  we  have  a  closed  vessel  con- 
taining ice,  water,  and  water  vapour  at  0°  (Fig.  16).     If  the 
vapour  tension  over  the   ice  were   smaller  than   that   over 
the   liquid,    the   water   would   distil   over   to  the  ice  until 
it    was    all    converted    into    ice.      And,     on     the     other 
hand,  if  the  tension  over  the  water  were  lower  than  that 
over  the    ice,   then    this    latter  would    by   distillation    be 

E 


50  BOILING   AND   FREEZING   POINT.  CHAP. 

transformed  into  water.  But  since  the  freezing  point  is  the 
point  at  which  there  is  an  equilibrium  between  ice  and  water, 
it  necessarily  follows  that  at  this  temperature  they  must 
have  the  same  vapour  pressure.  Similarly,  the  solution  whose 
vapour  pressure  is  represented  by  p'pf  must  at  its  freezing 
point  have  the  same  vapour  pressure  as  the  pure  ice  which 
freezes  out.  This  point  falls,  therefore,  exactly  where  the 
curves  PP  and  p'p'  cut  each  other. 

(It  follows  from  the  above  that  neither  water  nor  solution 
can  exist  below  the  freezing  point  in  presence  of  ice;  the 
introduction  of  a  crystal  of  ice  causes  the  solidification  of  the 
supercooled  liquid.) 

If  now  a  line  parallel  to  the  abscissa-axis  be  drawn 
through  P,  and  through  M  a  line  perpendicular  to  this,  the 
two  cut  at  Q,  and  the  perpendicular  meets  pp  at  N  and  the 
abscissa-axis  at  R.  RA,  which  is  equal  to  PQ,  is  denoted  by 
dT,  and  represents  the  depression  of  the  freezing  point  —  that 
is,  the  difference  between  the  freezing  point  of  the  solvent 
and  that  of  the  solution.  We  then  obtain  — 

QM  =  PQ  tan  MPQ, 
and  QN  =  PQ  tan  NPQ. 

Further,  according  to  the  modified  formula  of  Claperyon 
(see  p.  48)— 

i  ~dP  -  (A 

LI 


In  this  formula,  (X  4-  u)  is  the  heat  of  vaporisation  of  ice, 
i.e.  the  sum  of  the  heat  of  vaporisation  X  of  the  water  at  0°, 
and  the  heat  of  fusion  u  of  the  ice  at  the  same  temperature. 

If  we  denote  the  vapour  pressure  of  ice  at  the  freezing 
point  R  of  the  solution  by  p'R,  and  the  corresponding  value  of 
water  by  pa,  then  — 


i-  , 

A  =  p.  -  p',,  = 


V. 


DETERMINATION   OF   FREEZING   POINT. 


since  at  the  freezing  point  of  the  solvent  the  vapour  pressure 
P  of  ice  and  that  p  of  the  liquid  must  be  the  same,  and  for 
this  we  may,  without  appreciable  error,  use  pR. 
If  we  introduce  the  values — 


PR  ~  P*  =    n 
~  100 


and  R  =  2,  we  find  for  (IT— 


100 


u 


WOOdn 

that  is,  the  same  formulae  as  were  found  for  the  rise  of  boil- 
ing point  with  the.  heat  of  vaporisation  A  replaced  by  the 
heat  of  fusion  u. 

Experimental  Determination  of  the  Freezing  Point. 
— The  depression  of  the  freezing  point  and 
the  rise  of  the  boiling  point  can  now  be 
determined  with  a  very  high  degree  of 
accuracy  by  the  methods  worked  out  by 
E.  Beckmann  (4)-  The  apparatus  devised 
by  him  for  the  determination  of  freezing 
points  is  shown  in  Fig.  17.  A  known 
weight  of  the  solvent  whose  freezing 
point  is  to  be  determined  is  introduced 
into  the  tube  A,  which  is  about  the  size 
of  an  ordinary  test-tube,  and  is  provided 
with  a  side  tube  B.  Through  a  rubber 
stopper  in  A  there  passes  a  platinum 
wire,  G-,  which  serves  as  a  stirrer,  and  a 
thermometer,  C,  graduated  into  hun- 
dredths  of  a  degree.  The  tube  A  is  sur- 
rounded by  an  air-mantle  by  inserting  it 
into  a  wider  tube,  D.  The  whole  appa- 
ratus is  placed  in  a  freezing  mixture  con- 
tained in  the  vessel  E,  which  is  provided  FIG.  17. 


52  BOILING   AND   FREEZING    POINT.  CHAP. 

with  a  cover  of  sheet  metal  and  the  stirrer  H.  The  ther- 
mometer scale  extends  only  over  five  or  six  degrees,  in  order 
not  to  require  to  be  of  inconvenient  length.  In  order,  how- 
ever, to  make  this  thermometer  available  for  the  registration 
of  temperature  over  a  large  interval,  the  capillary  is  bent  at 
the  top,  and  enters  a  reservoir,  as  shown  in  Fig.  18  (see 
also  Fig.  19).  When  the  bulb  of  the  thermometer 
is  warmed,  the  mercury  rises  in  the  capillary 
stem,  and  overflows  into  the  top  of  the  reservoir. 
By  adhesion  to  the  glass,  however,  the  mercury 
is  prevented  from  falling  off  into  the  bottom  of 
FIG.  18.  ^e  reservoir-  By  gently  tapping,  the  thread  can 
be  broken,  and  the  excess  of  mercury  drops  into 
the  reservoir.  In  this  way  the  quantity  of  mercury  in 
the  thermometer  can  be  varied  at  pleasure,  and  the  quantity 
is  so  arranged  that  at  the  freezing  point  of  the  solvent  the 
meniscus  will  stand  near  the  top  of  the  scale.  The  tem- 
perature of  the  freezing  mixture  should  be  only  very  little 
lower  than  the  freezing  point  to  be  determined,  and  all 
disturbances  due  to  radiation  should  be  avoided. 

After  the  freezing  point  of  the  solvent  has  been  determined, 
a  weighed  quantity  of  substance  is  introduced  through  B,  and 
dissolved  by  stirring  with  the  wire  G-.  The  temperature  is 
now  allowed  to  sink  a  little  below  the  freezing  point,  and  a 
small  crystal  of  the  solidified  solvent  is  dropped  in.  This 
causes  deposition  of  solid  from  the  super-cooled  solution,  and 
the  mixture  is  now  vigorously  stirred  when  the  temperature 
rises  to  a  maximum  (the  freezing  point)  and  remains  constant 
for  a  considerable  time,  then  falls  slowly  on  account  of  the 
solution  becoming  more  concentrated  because  of  the  separation 
of  ice,  whereby  the  freezing  point  is  continually  decreasing. 

Experimental  Determination  of  the  Boiling  Point— 
The  boiling  point  apparatus  devised  by  Beckmann  (o)  is  very 
similar  to  that  used  for  the  determination  of  the  freezing 
point.  The  inner  tube  A  (Fig.  19)  is  the  same  as  that 
described  above,  but  a  short  platinum  wire,  a,  is  sealed  into 
the  bottom  of  it. 


v.    ADVANTAGES   OF    FREEZING    POINT   METHOD.  53 


The  tube  contains,  besides  the  liquid  to  be  examined, 
the  thermometer  G-  and  a  column  of  glass  beads,  2  to 
3  cm.  high,  which  causes  the 
boiling  to  be  more  even. 
This  vessel  is  surrounded  by 
a  vapour-mantle,  D,  made 
of  glass,  porcelain,  or  metal, 
which  is  half  filled  with  the 
same  solvent  (or  solution) 
as  is  contained  in  A.  The 
tube  and  the  mantle  are 
separated  below  by  a  ring 
of  asbestos,  and  both  are 
provided  with  air-conden- 
sers, or,  if  the  solvent  be 
very  volatile,  with  small 
Liebig  condensers,  C  and  F. 
The  apparatus  rests  on  an 
asbestos  stand,  fitted  with 
funnels,  so  that  the  heat  can 
be  easily  regulated.  With 
this  arrangement  Beckmann 
has  succeeded  in  maintain- 
ing the  boiling  point  con-  pia  19 

stant   within   a    few   thou- 

sandths of  a  degree,  a  result  which  had  previously  never- 
been  expected. 

[Another  method  has  been  devised  by  Landsberger 
(Ber.,  1898,  31,  458),  and  modified  by  Walker  and  Lumsden 
(./.  Chem.  Soc.,  1898,  73,  502).] 

Advantages  of  the  Freezing  Point  Method.  —  The 
determination  of  the  boiling  point  or  the  vapour  pressure 
does  not  permit  of  the  calculation  of  the  molecular  weight  of 
such  dissolved  substances  as  have  themselves  an  appreciable 
vapour  tension.  The  method  of  the  freezing  point  is  free 
from  this  disadvantage,  for  it  is  only  the  vapour  pressure  of 
the  solvent  which  plays  any  part  in  it;  thus,  for  instance, 


54 


BOILING   AND   FREEZING   POINT. 


CHAP. 


it  gives  correct  values  for  a  solution  of  alcohol  in  water, 
although  the  alcohol  has  a  much  higher  vapour  tension  than 
the  water.  Furthermore,  the  freezing  point  method  gives 
much  more  exact  values  than  the  boiling  point  method. 
This  latter  is  consequently  chiefly  used  for  the  determination 
of  the  molecular  weight  in  cases  where  the  freezing  point  of 
the  solvent,  e.g.  alcohol,  ether,  carbon  disulphide,  can  only  .be 
reached  with  difficulty. 

Connection  between  Depression  of  Vapour  Pressure 
and  Depression  of  Freezing  Point. — In  1870,  Guldberg 
(1)  proved  theoretically  that  the  vapour  pressure  and  the 
freezing  point  stand  in  close  relationship,  so  that  the 
two  corresponding  depressions  run  parallel;  and  he  further 
showed  that  this  was  confirmed  by  experiment.  On  the 
basis  of  purely  experimental  data,  Eaoult,  in  1878,  again 
brought  forward  this  same  statement,  and  showed  that  it 
applied  to  one  per  cent,  salt  solutions.  As  the  numbers 
obtained  by  Eaoult  possess  a  certain  historical  interest, 
they  are  reproduced  in  the  following  table : — 


Salt. 

Lowei 
Freezing  point. 

ing  of  the 
Vapour  pressure 
in  mm.  Hg  at  100°. 

Mercuric  chloride  .... 
Mercuric  cyanide   .... 
Lead  nitrate     
Barium  nitrate  
Silver  nitrate    . 

Degree. 

0-048 
0-059 
0-104 
0-145 
0-146 
0-146 
0-200 
0-210 
0-215 
0-215 
0-245 
0-273 
0-295 
0-347 
0-378 
0-446 
0-660 
0-639 

0-058  x 
0-087     , 
0-110 
0-137 
0-160 
0-165 
0-213 
0-201 
0-225 
0-240 
0-280 
0-230 
0-310 
0-380 
0-361 
0-450 
0-604 
0-565 

7-6 

i 

Potassium  ferricyanide 
Potassium  chromate 
Potassium  sulphate 
Potassium  iodide   . 
Potassium  chlorate 
Potassium  nitrate  . 
Ammonium  sulphate 
Potassium  bromide 
Sodium  nitrate. 

•      • 

Ammonium  nitrate 
Potassium  chloride 
Sodium  chloride    . 
Ammonium  chloride 

•      • 

The  proportionality  is  not  so  good  as  perhaps  might  be 


V. 


OSMOTIC    PRESSURE   OF   A    SOLUTION. 


desired.  The  agreement  is  much  better  if  Tammann's 
results  be  compared  with  the  older  determinations  of  the 
freezing  point  by  Eiidorff  and  de  Coppet,  and  there  is  no 
doubt  that  fresh  and  more  accurate  determinations  would  lead 
to  a  much  better  result. 

Connection  between  the  Osmotic  Pressure  of  a 
Solution  and  its  Freezing  Point  and  Vapour  Pressure. 
— This  connection  was  first  shown  empirically  by  De  Vries 
in  1884.  Soon  after,  van't  Hoff  deduced  from  the  laws  of  the 
osmotic  pressure  both  Eaoult's  law  of  the  depression  of  the 
vapour  pressure  and  his  own  law  of  the  depression  of 
the  freezing  point ;  and  in  the  manner  given  by  van't  Hoff 
I  developed  the  formula  for  the  rise  of  boiling  point. 

It  may  be  here  noticed  that  Eaoult,  after  collecting  a 
very  large  number  of  data  on  the  freezing  points  of  solutions, 
empirically  found  a  connection  which  he  expressed  in  the 
following  formula : — 

dT  =  0-63  x  n. 

According  to  this  formula,  0*63  x  n  is  the  depression  of 
the  freezing  point  of  a  solution  which  contains  n  molecules 
in  100  molecules  of  solvent.  This  formula  only  agrees  with 
the  law  of  van't  Hoff  when  applied  to  formic  acid,  acetic 
acid,  and  benzene,  for  which  the  law  requires  the  values 
0-62,  0*65,  and  0'68.  On  the  other  hand,  the  value  for 
water  is  1*05,  and  Eaoult  takes  this  to  indicate  that  some 
of  the  water  molecules  have  condensed  to  complexes  2H2O 
and  3H20.  In  this  connection  Eykman  (6)  carried  out  an 
investigation,  in  which  he  obtained  the  following  results  : — 


Solvent. 

dT  (observed). 

dT  (calculated), 
van't  Hoff. 

d  recalculated). 
Raoult. 

Phenol       .      . 

74 

77 

58-3 

Naphthalene   . 

69 

69-4 

79-4 

^-Toluidine     . 

51 

49 

66-3 

Diphenylamine 

88 

98-6 

104-8 

Naphthy  lamin  e 

78 

102-5  (?) 

88-7 

Laurie  acid 

44 

45-2 

124 

Palmitic  acid  . 

44 

44-3 

158-7 

56  BOILING   AND   FREEZING   POINT.  CHAP. 

In  this  table  dT  represents  the  so-called  molecular 
lowering  of  the  freezing  point,  i.e.  that  lowering  produced 
by  dissolving  a  gram-molecule  in  100  grams  of  solvent. 

The  formula  — 


based  on  theory  and  confirmed  by  Eykman's  results,  gives 
the  lowering  of  the  freezing  point  caused  by  the  solution  of  a 
gram-molecule  in  100  gram-molecules  of  solvent.  As  above, 
u  denotes  the  heat  of  fusion  of  a  gram-molecule  of  the  solvent. 
If  the  gram-molecule  be  dissolved  in  100  grams  of  the  solvent 
(and  not  in  M10Q  grams),  the  concentration  will  be  M 
times  as  great,  and  the  lowering  of  the  freezing  point  will  be 
correspondingly  increased.  This  can  also  be  expressed  by 
the  above  formula,  if  we  understand  by  u  the  latent  heat  of 
fusion  of  a  gram  (not,  as  formerly,  a  gram-molecule)  of  the 
solvent  ;  for  since  the  value  of  the  denominator  becomes  M 
times  smaller,  that  of  dT  must  become  just  as  much  greater. 
And  the  same  applies  to  the  rise  of  boiling  point. 

From  what  has  been  said,  it  is  evident  that  the  value  of  n 
can  be  ascertained  either  from  the  depression  of  the  vapour 
pressure,  the  rise  of  the  boiling  point,  or  the  depression  of  the 
freezing  point,  n  being  the  number  of  dissolved  molecules  in 
the  liquid.  Since  the  quantity  of  dissolved  substance  is 
known,  if  we  know  n  we  can  calculate  the  weight  of  a  gram- 
molecule  of  the  dissolved  substance.  These  three  methods  of 
determining  the  molecular  weight,  particularly  the  method 
of  the  freezing  point,  on  account  of  their  simplicity  and  their 
general  applicability,  are  fast  displacing  the  older  methods 
in  which  the  gas  density  is  determined. 

Molecular  Lowering  of  the  Freezing  Point.  —  The 
following  tables  contain  some  data  on  the  molecular  lowering 
of  the  freezing  point,  taken  from  Kaoult's  (7)  results  with 
aqueous  solutions,  and  Beckmann's  (8)  extremely  exact  deter- 
minations with  solutions  in  benzene.  The  value  at  the  top  of 
each  table  is  that  calculated  by  means  of  van't  Hoff  's  formula. 


LOWERING   OF   THE   FREEZING   POINT. 


57 


SOLUTIONS  IN  WATER. 
(Calculated  Molecular  Lowering,  18' 6.) 


Methyl  alcohol 17-3 

Ethyl  alcohol 17-3 

Grlycerol 17-1 

Cane  sugar 18'5 

Formic  acid 19*3 

Phenol 15-5 

Acetic  acid 19-0 

Butyric  acid 18'7 

Ether 16*6 

Ammonia 19-9 

Aniline 15-3 

Oxalic  acid    .  22' 9 


Hydrochloric  acid  . 
Nitric  acid     .     . 
Sulphuric  acid    .     . 
Potassium  hydroxide 
Sodium  hydroxide  . 
Potassium  chloride . 
Sodium  chloride 
Calcium  chloride     . 
Barium  chloride 
Potassium  nitrate    . 
Magnesium  sulphate 
Copper  sulphate .     . 


39-1 
35-8 
38-2 
35-3 
36-2 
33-6 
35-1 
49-9 
48-6 
30-8 
19-2 
18-0 


SOLUTIONS  IN  BENZENE. 
(Calculated  Molecular  Lowering,  53.) 

Methyl  iodide 50'4 

Chloroform 51*1 

Carbon  disulphide  .     .     .     .     49  '1 
Ethylene  chloride   ....     48-6 

Nitro-benzene 48 '0 

Ether 49*7 

Chloral 50-3 

Nitro-glycerol 49  '9 


Aniline 46-3 

Formic  acid 23-2 

Acetic  acid 25*3 

Benzoic  acid 25*4 

Methyl  alcohol 25-3 

Ethyl  alcohol      .....  28'2 

Amyl  alcohol 39*7 

Phenol .  32-4 


From  the  results  given,  it  is  evident  that  in  the  majority 
of  cases  the  experimental  result  agrees  with  the  theoretical. 
There  are,  however,  a  number  of  exceptions.  In  benzene 
solution  many  substances  (alcohols,  phenol,  and  organic 
acids)  give  smaller  values  for  the  molecular  lowering  than 
would  be  expected;  thus,  e.g.,  a  gram-molecule  of  methyl 
alcohol  (CH3OH  =  32)  only  exerts  about  half  its  normal 
action. 

This  deviation  is  easily  explained  by  assuming  that  a 
gram -molecule  of  methyl  alcohol  in  benzene  solution  weighs 
64  grams,  or,  in  other  words,  the  chemical  formula  for  this 
alcohol  in  benzene  solution  is  (CH3OH)2;  the  molecular 
lowering  is  then  calculated  to  be  50*6.  Other  deviations 
between  experimental  and  theoretical  results  can  in  most 


58  BOILING   AND   FREEZING   POINT.  GHAP. 

cases  be  accounted  for  in  a  similar  manner,  leaving  for  the 
moment  aqueous  solutions  out  of  account. 

The  existence  of  such  double  molecules,  which,  of  course, 
are  mixed  with  simple  molecules  and  higher  complexes,  is  by 
no  means  improbable.  On  the  contrary,  such  relationships 
were  formerly  considered  as  the  normal,  and  the  difference 
between  the  liquid  and  gaseous  conditions  were  attributed  to 
them.  More  recent  researches  have,  however,  shown  that  at 
moderate  dilutions  it  is  only  in  exceptional  cases  that  double 
molecules  are  formed.  The  substances  which  most  easily 
form  these  double  molecules  belong  to  the  classes  already 
mentioned,  namely,  alcohols,  phenols,  and  organic  acids 
(particularly  the  fatty  acids). 

Molecule  Complexes.— The  formation  of  double,  triple, 
etc.,  molecules  of  dissolved  substances  depends  to  a  great 
extent  on  the  nature  of  the  solvent.  It  appears  to  take  place 
very  seldom  in  aqueous  solution,  although  it  does  so  in  the 
case  of  some  salts  of  cadmium  and  mercury,  and  with  the 
sulphates  of  magnesium,  zinc,  and  copper.  (This  matter  is 
discussed  in  more  detail  below.)  The  formation  of  these 
double  molecules  takes  place  more  frequently  when  the 
solvent  is  acetic  acid  or  formic  acid,  and  still  more  so  with 
benzene  or  other  hydrocarbon. 

The  dielectric  constant  of  the  solvent  has  a  great  influence 
on  the  complex  formation  taking  place  in  the  solution. 
Liquids  with  a  high  dielectric  constant  have  the  power  of 
decomposing  the  dissolved  substance  into  simple  molecules, 
and  this  power  increases  with  the  dielectric  constant.  These 
constants  vary  greatly  with  the  chemical  nature  of  the  media ; 
of  the  solvents  in  common  use  water  has  the  highest  dielectric 
constant  (DE),  namely,  80  ;  for  formic  acid  DE  =57,  for 
acetic  acid  DE  =  6'5,  for  ethyl  alcohol  DE  =  217,  and  for 
benzene  DE  =  2'2. 

As  we  shall  see  later,  the  same  holds  good  for  the  power 
of  a  solvent  to  dissociate  an  electrolyte  into  ions  (9). 

As  the  dilution  increases  the  complex  molecules  become 
broken  up  into  simpler  ones,  as  the  following  results  of 


V. 


DISSOCIATION   OF    ELECTROLYTES. 


59 


Beckmann  (10)  show.1  Thus,  for  instance,  if  the  concentra- 
tion of  ethyl  alcohol  be  increased  from  0'2  per  cent,  to  6  per 
cent.,  its  molecular  weight  in  benzene  increases  from  46  to  128, 
and  in  acetic  acid  from  47  to  54,  whilst  in  water  it  remains 
almost  constant. 


Ethyl  alcohol 
(C2H60  =  46) 
in  benzene. 

Cone.       Mol. 
%        weight. 

Ace  tic  acid 
(CH3COOH  =  60) 
in  benzene. 

Cone.       Mol. 
o/o        weight. 

Phenol 
(C6H5OH  =  94) 
in  benzene. 

Cone.       Mol. 
%        weight. 

Ethyl  alcohol 
(C2H60  =  46) 
in  acetic  acid. 

Cone.       Mol. 
°/o        weight. 

Ethyl  alcohol 
(C2H60  =  46) 
in  water. 

Cone.       Mol. 
%       weight. 

0-164          46 
0-494          50 
1-09            61 
2-29            82 
3'48          100 
5-81          128 
8-84          159 
14-63          208 
22-6            265 
32-5            318 

0-465      110 
1-2          115 
2-3          117 
4-5          122 
8-2          129 
15-2          141 
22-8          153 

0-34        144 
1-2          153 
2-5          161 
4-0          168 
8-0          188 
17-3          223 
26-8          252 

0-25          47 
1-08          50 
2-81          52 
6-2            54 
9-7            56 
14-2            58 

0-6          47 
1-4          46 
2-9          46 
5-7          44 

Dissociation  of  Electrolytes.— The  deviations  which 
have  been  found  for  electrolytes  in  aqueous  solution  must  be 
explained  otherwise  than  by  the  assumption  that  complex 
formation  takes  place.  Van't  Hoff  limited  himself  to  showing 
that  most  salts,  as  well  as  the  strong  acids  and  bases,  or, 
generally,  strong  electrolytes,  give  too  large  a  molecular 
lowering  of  the  freezing  point,  without  discussing  the  cause. 
Since  that  time  different  explanations  have  been  brought 
forward.  It  has  been  assumed  that  the  molecules  of  the 
solvent  can  combine  with  those  of  the  dissolved  substance,  or 
exert  an  attraction  on  them,  but  none  of  these  hypotheses 
has  been  able  to  withstand  full  investigation,  except  that  one 

1  In  the  gaseous  condition,  too,  the  fatty  acids  tend  to  form  double 
molecules  (see  p.  42).  In  a  less  degree  this  applies  also  to  alcohols. 
Also  for  the  gaseous  state  theory  predicts,  and  in  this  is  confirmed  by 
experiment,  that  fewer  molecules  combine1  to  complexes  the  lower  the 
concentration  is.  In  a  highly  concentrated  (or  liquid)  form  the  substances 
mentioned  aggregate  to  a  great  extent  to  molecular  complexes,  as  the 
results  obtained  in  connection  with  the  capillary  forces  and  at  the  critical 
point  prove. 


6o 


BOILING   AND   FREEZING   POINT. 


CHAP. 


which  appears  to  be  the  most  evident.  If  the  deviation  in 
benzene  solutions,  in  which  the  molecular  lowering  of  the 
freezing  point  is  too  small,  is  to  be  explained  by  assuming 
that  the  dissolved  molecules  are  greater  than  is  expressed  by 
the  chemical  formula,  then  the  deviation  in  aqueous  solutions, 
where  the  lowering  of  the  freezing  point  is  greater  than  that 
calculated,  may  be  assumed  to  be  due  to  the  dissolved 
molecules  being  smaller  than  indicated  by  the  chemical 
formula.  In  the  first  case  we  imagine  that  a  combination  of 
simple  molecules  to  a  molecular  complex  takes  place,  and  in 
the  second  case  we  have  to  assume  that  the  simple  molecules 
split  up  into  smaller  parts.  As  we  shall  see  later,  this 
assumption  is  quite  justified.  In  the  case  of  certain  salts, 
as,  for  instance,  sodium  chloride  (NaCl),  there  can  be  no 
doubt  what  the  parts  are  because  only  one  kind  of  split- 
ting seems  possible,  namely,  into  Na  and  Cl.  In  order 
to  receive  general  credence,  this  assumption  must  be  sup- 
ported by  other  experimental  evidence;  for  it  does  appear 
strange  at  first  sight  that  in  a  solution  of  salt  this  substance 
has  always  the  same  constant  composition,  although  the 
constituents  Na  and  Cl  in  the  solution  are  separated  from 
each  other. 

Range  of  Validity  of  van't  Hoff 's  Law.— The  following 
values  for  the  molecular  lowering  of  the  freezing  point, 
obtained  as  mean  values  from  experiments  with  a  large 
number  of  dissolved  substances,  were  used  by  van't  Hoff  in 
support  of  his  theory  : — 


Solvent. 

r. 

u. 

y2 

0-02  L. 

U 

dT  (calculated). 

Water      ..... 

273 

80 

18-6 

18-5 

Acetic  acid  .... 

290 

43-2 

38-8 

38-6 

Formic  acid  .     .     .     . 

281-5 

55-6 

28-4 

27-7 

Benzene   ... 

277-9 

29-1 

53-0 

50-0 

Nitro-benzene    .     .     . 

278-3 

22-3 

69-5 

70-7 

The  van't  Hoff  law  is  only  valid  for  dilute  solutions,  for 
in  more  concentrated  solutions  forces  come  into  play  which 


v.  ALLOYS.  6 1 

disturb  its  simplicity.     This  recalls  the  behaviour  of  gases 
which  at  high  pressure  deviate  from  Boyle's  law. 

It  is  well  known  that  van  der  Waals  has  sought  to  explain 
these  deviations  by  forces  of  attraction  which  act  between  the 
gas  molecules.  In  the  same  way  we  may  assume  that  in 
solution  there  is  an  attraction  between  the  dissolved  molecules, 
and  also  between  these  and  the  molecules  of  the  solvent.  The 
former  attraction  causes  a  diminution  in  the  molecular 
lowering  of  the  freezing  point  as  the  concentration  increases, 
and  the  latter  causes  a  rise.  Both  cases  occur  frequently, 
the  latter  particularly  in  aqueous  solutions,  and  the  former 
in  most  other  solutions.  Almost  the  greatest  deviation  which 
has  been  noticed  at  high  concentration  was  with  a  solution  of 
cane  sugar  in  water.  In  this  case  the  molecular  depression 
rises  (almost  proportionally  with  the  concentration)  from  the 
value  18*6  at  high  dilution  to  27*0  for  a  normal  solution. 
Consequently,  when  the  molecular  weight  of  a  dissolved 
substance  is  to  be  determined,  it  should  be  investigated  in 
very  dilute  solution,  or  it  should  be  examined  at  several 
concentrations,  and  from  the  results  the  value  at  concentration 
0  is  ascertained  by  extrapolation.  Eaoult  found  this  rule 
empirically. 

Alloys. — W.  Ramsay  (11)  investigated  the  vapour  pressure 
of  solutions  of  various  metals  in  mercury  in  the  following  way. 
A  U-tube,  closed  at  one  end,  was  filled  with  mercury,  and  a 
similar  tube  contained  the  amalgam  to  be  investigated. 
These  were  immersed  in  a  mercury  bath  at  high  temperature 
and  the  vapour  pressures  were  measured.  A  lowering  of  the 
vapour  pressure  was  always  observed  on  dissolving  foreign 
metals  in  the  mercury,  and  Eamsay  was  thus  able  to 
determine  the  molecular  weight  of  the  dissolved  metal ;  for 
most  metals,  namely,  Li,  Na,  Mg,  Zn,  Cd,  Ga,  Tl,  Sn,  Pb,  Mn, 
Ag,  and  Au,  he  obtained  results  which  agreed  with  the  atomic 
weights  within  the  experimental  error.  For  potassium, 
calcium,  and  barium  he  found  numbers  which  are  very 
appreciably  lower  (about  half)  than  the  atomic  weights,  a 
peculiar  phenomenon  which  has  not  yet  been  explained.  The 


62  BOILING   AND   FREEZING   POINT.  CHAP. 

molecular  weights  found  for  aluminium,  antimony,  and  bis- 
muth are  considerably  greater  than  the  atomic  weights  of 
these  elements,  indicating  that  their  molecules  consist  of 
several,  probably  two,  atoms.  On  the  whole,  the  results 
agree  remarkably  well  with  what  is  known  of  the  molecular 
weights  of  the  metals  in  the  gaseous  state. 

Eamsay's  observations  have  been  confirmed  by  the  ex- 
periments on  the  freezing  points  of  metal  alloys  made  by 
Tammann.  From  his  results,  Tammann  (12)  calculated 
the  molecular  weights  of  some  metals,  and  these,  along 
with  the  corresponding  atomic  weights,  are  contained  in  the 
following  table : — 

SOLUTIONS  IN  MERCURY  (TAMMANN). 
dT  (theoretical)  =  425. 


Metal.  Mol.  weight.     '   Atom,  weight. 


Potassium  .  .             40*5  30-1 

Sodium   .  .  .  22-8  23-0 

Thallium  .  .  181  204 

Zinc  .  59  65-4 


Hey  cock  and  Neville  (13)  made  similar  experiments, 
using  sodium,  and  afterwards  tin,  bismuth,  cadmium,  lead, 
thallium,  and  zinc,  as  solvent.  In  the  next  table  some  of 
their  results  are  reproduced;  the  numbers  given  are  the 
depressions  of  the  freezing  point  produced  by  the  solution 
of  a  gram-atom  of  the  metal  in  1880  grams  of  tin.  The 
theoretical  value  is  2*98. 

Nickel 2-94  ,  Lead 2-76 

Silver 2'93  j  Zinc 2-64 

Gold 2-93  Cadmium 2-43 

Copper      . 2-91  Mercury 2-39 


Thallium 2-8G 

Sodium  2-84 


Bismuth 2-40 

Calcium  2-40 


Palladium 2-78  !  Indium 1-8G 

Magnesium 2-76      Aluminium 1-25 


v.  SOLID   SOLUTIONS.  63 

The  experiments  of  Roberts-Austen  (14)  and  of  G.  Meyer 
(lo)  on  the  diffusion  of  metals  in  mercury  confirmed  the 
above  results. 

Solid  Solutions. — Van't  Hoff's  formula  for  the  calcula- 
tion of  the  molecular  weight  can  only  be  applied  provided 
that  the  solvent  separates  in  the  pure  form  when  the  solution 
freezes,  or  that  when  the  boiling  point  method  is  used  the 
dissolved  substance  does  not  volatilise.  These  conditions 
are  not  always  fulfilled,  and  this  is  particularly  the  case 
when  the  dissolved  substance  chemically  resembles  the 
solvent.  Thus  when  the  dissolved  substance  is  /3-naphthol 
and  the  solvent  is  naphthalene,  or  the  dissolved  substance 
is  antimony  and  the  solvent  tin,  it  is  found  that  the  two 
separate  out  in  union,  and  abnormally  low  depressions  of  the 
freezing  point  are  obtained  (16).  A  similar  behaviour  is 
sometimes  noticed,  e.g.  iodine  in  benzene,  when  the  substances 
are  in  no  way  chemically  related.  As  a  general  rule  the 
concentrations  of  the  dissolved  substance  in  the  liquid  and 
in  the  solid  (separated)  solvent  bear  a  constant  ratio  to  each 
other  (distribution  ratio). 

In  these  cases,  and  in  many  others,  a  solid  substance  acts 
as  a  solvent.  Van't  Hoff  (17)  has  shown  that  substances 
dissolved  by  solids  have  an  osmotic  pressure,  and  so  we  may 
speak  of  "  solid  solutions."  The  chief  result  with  respect  to 
the  determination  of  the  molecular  weight  in  solids  is,  as  the 
recent  investigations  of  Bruni  (18)  and  others  have  proved, 
that  apparently  the  solid  state  is  in  no  way  connected  with 
a  high  degree  of  polymerisation. 

Hydrogen,  which  possesses  many  metallic  properties,  is 
monatomic  when  dissolved  in  palladium  ;  as  Hoitsema  found, 
the  dissolved  molecule  has  the  formula  H  and  not  H2. 

Experimental  Results  on  the  Rise  of  Boiling  Point. 

ff'2 

— The  correctness   of  the  theoretical  formula  dT  =  0-02-^ 

A 

may  be  gathered  from  the  results  obtained  by  Beckrnann 
•(19)  contained  in  the  following  table  in  the  column  headed 
.dT  (observed) :— 


64  BOILING   AND   FREEZING    POINT.  CHAP. 


Solvent.  dr  (observed).         dT  (calculated). 


Water     .... 

4-5 

-    5-2 

Ethyl  alcohol      .     . 

.     10-12 

11-5 

Acetone  .... 

17  -  18 

16-7 

Ether      .... 

21  -  22 

21-1 

Carbon  disulphide    . 

22  -  24 

23-7 

Acetic  acid   . 

25 

25-3 

Ethyl  acetate     .      . 

25-26 

26-0 

Benzene  .... 

25  -  27 

26-7 

Chloroform    .     . 

35-36 

36-6 

The  following  numbers  show  that  in  some  cases  (denoted 
in  the  table  by  an  asterisk  *),  exceptional  results  are  obtained 
in  the  same  manner  as  for  the  lowering  of  the  freezing  point: — 

MOLECULAR   RISE   IN  BOILING   POINT   IN   BENZENE. 

d  !T(calcnlated)  =  26*7. 

Anthracene 26-2  ,  *Benzoic  acid 18*6 

Naphthalene 24-7  j  *  Salicylic  acid    ......  21-0 

Benzil 26-0  j  Phenyl  salicylate     ....  24  4 

Phenyl  benzoate     ....  26-1  '  Borneol 27-2 

Ethyl  benzoate 25-0  ;  Acetophenone  oxime   .     .     .  26*0 

Benzole  anhydride  ....  26  9  i  Acetanilide 25O 

MOLECULAR  RISE  IN  BOILING  POINT  IN  CHLOROFORM. 
dT  (calculated)  =  36-6. 

Naphthalene 36'2  <   *Benzoic  acid 24*5 

Camphor  .......     36'0  !   *Salicylic  acid 26-5 

Ethyl  benzoate 34-5 

MOLECULAR  RISE  IN  BOILING  POINT  IN  ETHYL  ALCOHOL. 
dT  (calculated)  =  11-5. 


Benzil 11-1 

Phenyl  benzoate      .     .     .     .     ll'l 

Ethyl  benzoate 10*3 

Benzoic  acid 11-3 

Salic vlic  acid  11 '5 


Tartaric  acid 11-1 

Borneol 11-4 

*Lithium  chloride   ....  13-2 

Mercuric  chloride    ....  11-8 

*Cadmium  iodide    ....  12*9 

*Potassium  acetate      .     .     .     14-5  I  *Sodium  iodide 16*8 

MOLECULAR  RISE  IN  BOILING  POINT  IN  GLACIAL  ACETIC  ACID. 
d  recalculated)  =  25*3. 

Anthracene 25'0       Benzoic  acid 25O 

Benzil.                                      24-7       *Sodium  acetate  30'8 


v.       DETERMINATION  OF  MOLECULAR  WEIGHT.     65 

MOLECULAR  RISE  IN  BOILING  POINT  IN  WATER. 
dT  (calculated)  =  5'2. 

Mannitol 5'0  '  Mercuric  chloride      .     .     .     .     5'0 

Cane  sugar 4'9      Cadmium  iodide 5'3 

Boric  acid 4-8  I  *Sodium  acetate 9-4 

Attention  may  here  be  called  to  the  following  results. 
The  dissimilar  colours  of  iodine  in  benzene,  ether,  and  acetic 
acid  (brown),  and  in  carbon  disulphide  (violet),  were  previously 
attributed  to  different  molecular  magnitudes  of  the  iodine. 
Beckmann's  results  (20),  however,  indicate  that  in  all 
these  solvents  the  molecular  weight  of  the  dissolved  iodine 
corresponds  with  the  formula  1%  (254),  and  is  the  same  as 
that  of  iodine  vapour  at  low  temperatures.  Phosphorus  has 
the  same  molecular  weight  (P4  =;  124)  when  dissolved  in 
carbon  disulphide  as  in  the  gaseous  state.  For  sulphur 
dissolved  in  carbon  disulphide,  Beckmann  found  the  molecular 
weight,  256,  corresponding  with  the  formula  Sg,  which  is  the 
same  as  that  obtained  by  Biltz  and  V.  Meyer  (21)  for  sulphur 
vapour. 

Comparison  between  the  Various  Methods  for  the 
Determination  of  Molecular  Weights. — It  must  now 
be  clear  that  the  several  methods  for  determining  the  mole- 
cular weight,  by  measurement  of  the  osmotic  pressure,  of  the 
depression  of  vapour  pressure  and  freezing  point,  and  of  the 
rise  of  boiling  point,  lead  to  the  same  result,  provided  that 
in  all  cases  the  temperature  is  the  same.  The  results  of 
Bonders  and  Hamburger  (22)  show  that  temperature  has 
only  a  small  influence  on  the  relative  values  of  the  osmotic 
pressure,  and  this  is  further  proved  by  a  comparison  of  the 
values  obtained  by  Tammann  for  the  lowering  of  the  vapour 
pressure  at  100°  with  those  found  by  Dieterici  (23)  at  0°. 
This  result  is  also  required  by  theory,  as  we  shall  see  later,  in 
those  cases  where  no  heat  change  takes  place  on  dilution  of 
the  solution,  a  condition  which  is  very  nearly  fulfilled  with 
dilute  solutions.  Consequently  we  may  assume  that  when 
results  are  obtained  which  are  at  variance  with  the  theory, 

F 


66  BOILING   AND   FREEZING    POINT.  CHAP. 

these  are  due  either  to  accident  or  to  the  characteristic  pecu- 
liarities possessed  by  every  method;  in  this  respect  the 
large  number  of  possible  methods  of  determining  the  mole- 
cular weight  is  of  great  importance. 

Review  of  the  Results  obtained. — These  various 
methods  opened  up  to  the  investigator  a  new  world  which 
was  formerly  regarded  as  quite  unattainable.  Up  till 
the  time  of  the  discovery  of  these  methods  the  molecular 
weight  was  only  known  for  a  limited  number  of  substances, 
namely,  those  which  could  be  gasified.  On  account  of  the 
great  theoretical  importance  of  the  molecular  weight,  a 
scheme  was  drawn  up  from  these  few  results  which  was 
supposed  to  cover  the  whole  field  of  chemistry.  The  funda- 
mental doctrine  of  this  was  that  free  valencies  of  the  atoms 
cannot  occur.  This  was  believed  to  be  a  reason  why  two 
hydrogen  atoms  always  combine  to  form  a  molecule ;  for 
if  the  molecule  of  hydrogen  consisted  of  a  single  atom  it 
would  possess  an  unsaturated  valency.  It  is  true  that 
the  gas  densities  of  mercury  and  cadmium  show  that  the 
molecules  of  these  elements  consist  of  single  atoms,  but  as 
they  are  divalent  the  difficulty  was  got  over  by  assuming 
that  the  two  valencies  of  an  atom  saturated  each  other.  It 
was,  however,  later  found  that  the  molecule  of  certain 
monatomic  metals  also  consisted  of  a  single  atom ;  and  the 
same  was-  found  to  be  true  for  bromine  and  iodine  at  high 
temperature.  It  was  then  considered  as  satisfactory  to  say 
that  at  high  temperature  the  doctrine  of  valency  lost  its 
validity,  and  little  importance  was  attached  to  the  so-called 
exceptions. 

By  the  newer  methods  of  determining  the  molecular 
weight  it  has  been  proved  that  also  at  low  temperature— 
for  instance,  at  the  melting  point  of  mercury — the  molecules 
of  the  metals,  monovalent  as  well  as  polyvalent,  are  as  a 
rule  monatomic.  It  has  already  been  pointed  out  that  the 
atoms  of  sulphur  and  phosphorus  form  molecules  of  the 
same  magnitude,  namely,  S8  and  P4,  both  in  the  gaseous  and 
in  the  dissolved  state.  It  would,  therefore,  seem  as  if  the 


v.  REVIEW   OF   THE    RESULTS   OBTAINED.  67 

molecules  of  the  elements  were  always  formed  by  a  certain 
number  of  atoms,  quite  independent  of  the  state  of  aggrega- 
tion in  which  they  exist. 

Compound  molecules  behave  in  the  same  way — that  is  to 
say,  the  molecular  weight  is  the  same  in  the  gaseous  and  in 
the  dissolved  condition.  In  so  far  as  the  composition  of  the 
dissolved  molecules  is  concerned,  there  frequently  exists  a 
slight  difference  between  two  solvents,  as,  for  instance, 
between  water  and  benzene,  in  the  same  way  as  there  is 
a  difference  between  these  liquids  and  a  vacuum,  which  may 
be  conceived  as  a  solvent  for  gases. 

A  further  conclusion  drawn  from  the  doctrine  that  no 

free  valencies  could  occur  in  molecules, 

PI 
was  that  the   valency  of  an   element          ^  .    ^ 

»     -^  \  ATI PI 

could  only  change  by  an  even  number.  \ 

Thus,   gold   could   be    monovalent   or 

Aurous  Auric 

trivalent ;    but    the    assumption    was       chloride.  chloride. 

made  that  gold  is  trivalent,  and  two  of 

the  valencies  may  saturate  each  other  ^ 

YQ (»1 

and  so  allow  the  gold  atom  to  appear       rj  ,  O^ 

monovalent.     Auric  and  aurous  chlo-     Fe— Cl 


rides  were  assumed  to  have  the  con-         \ 


Cl 


stitutions  shown.    Nevertheless,  several  Fe— < 

cases  were  known  in  which  the  number 

of    valencies   changes    by   an   uneven       c*®;jJde.  cSSfe. 

number,   as,   for    example,   in  ferrous 

chloride  (FeCl2)    and  ferric  chloride  (FeCl3).      In  order  to 

explain  this  anomaly  it  was  assumed  that  iron  is  di-  and 

tetra-valent  in  these  compounds  which  are  constituted  as 

shown  in  the  diagram  given. 

So  long  as  the  molecular  weights  of  these  substances  could 
not  be  determined  such  assumptions  appeared  quite  valid. 
But  it  is  much  more  difficult  to  explain  the  exceptions  formed 
by  the  series  of  nitrogen  oxides.  Nitrogen  is  pentavalent,  and 
accordingly  the  only  compounds  which  should  be  capable  of 
existence  are  N20,  N203,  and  N205.  Besides  these,  however, 
the  oxides  NO  and  N02  are  also  known,  and  their  gas  densities 


68  BOILING   AND   FREEZING   POINT.        CHAP,  v 

correspond  with  the  simple  formulae  given.  In  this  case  it  is 
evident  that  the  valency  changes  by  an  uneven  number. 
The  same  was  later  found  to  be  the  case  with  the  chlorides 
of  indium  (24).  Quite  the  greatest  difficulties  have  arisen 
from  the  results  of  recent  investigation,  whereby  it  has  been 
proved  that  in  a  solution  of  sodium  chloride  the  chlorine  and 
the  sodium  atoms  exist  for  the  most  part  as  molecules.  In 
its  old  form  the  doctrine  of  valency  is  no  longer  tenable. 


CHAPTEK  VI. 
General  Conditions  of  Equilibrium. 

Chemical  Reactions. — In  many  cases  when  two  substances 
which  react  chemically  upon  each  other  are  brought  into 
contact,  it  may  be  observed  that  the  reaction  proceeds 
gradually.  This  is  particularly  evident  when  there  is  a 
visible  surface  of  separation  between  the  two  reacting  bodies, 
as,  for  instance,  zinc  and  sulphuric  acid ;  that  is,  when  the 
system  is  heterogeneous.  On  the  other  hand,  if  there  is  no 
surface  of  separation  between  the  two  reacting  substances — 
that  is,  if  they  be  perfectly  mixed  or  dissolved  in  each  other, 
either  in  presence  or  absence  of  a  third  substance  (solvent) — 
physical  or  chemical  methods  must  be  applied  in  order  to 
detect  any  change  of  the  properties  of  the  solution  which 
depends  on  the  chemical  composition. 

The  typical  example  of  such  a  homogeneous  system  in 
which  a  physical  property,  easy  to  be  examined,  changes,  is 
a  solution  of  cane  sugar  in  water  to  which  some  acid  has 
been  added.  Such  a  solution  possesses  the  power  of  rotating 
the  plane  of  polarised  light  through  a  certain  angle;  this 
power  gradually  changes  as  the  dextro-rotatory  cane  sugar 
is  transformed  into  laevo-rotatory  invert  sugar  (a  mixture  of 
equal  parts  of  dextrose  and  levulose),  according  to  the 
equation — 

Ci2H22Oii  +  H20  (-J-  acid)  =  C6H1206  +  C6Hi206(+  acid). 

If  the  change  in  the  rotatory  power  of  the  solution  be 
followed  we  can  estimate  how  far  the  reaction  has  proceeded 
at  each  moment. 


7o     GENERAL   CONDITIONS   OF   EQUILIBRIUM.     CHAP. 

As  an  example  of  a  homogeneous  system  in  which  the 
change  can  be  conveniently  followed  by  chemical  investiga- 
tion, we  may  instance  a  solution  containing  sodium  hydroxide 
and  ethyl  acetate  which  decompose  according  to  the  equation — 

NaOH  +  CH3.COOC2H5  =  CH3.COONa  +  C2H5OH 

into  sodium  acetate  and  ethyl  alcohol. 

As  the  reaction  proceeds,  the  quantity  of  sodium  hydroxide 
in  the  solution  decreases,  and  the  amount  present  at  any 
moment  can  be  ascertained  by  titrating  a  portion  with  acid. 

The  amount  of  substance,  expressed  in  gram-molecules 
per  litre,  which  is  transformed  in  unit  of  time,  is  termed  the 
velocity  of  reaction  of  the  system. 

The  velocity  of  reaction  is  frequently  so  great  that  by  the 
methods  known  to  us  at  present  it  is  impossible  to  determine 
it.  Nevertheless  it  can  hardly  be  doubted  that  every  chemical 
reaction  requires  a  certain  time  in  which  to  take  place.  In 
heterogeneous  systems  this  time  is.  consider  able,  for  reaction 
can  only  take  place  at  the  surface  of  contact  of  the  reacting 
substances,  and  consequently  cannot  go  on  suddenly.  This 
is  expressed  in  the  old  dictum  :  corpora  non  agunt  nisi  soluta. 
In  a  heterogeneous  mixture,  however,  the  velocity  of  reaction 
may  be  very  high,  as  is  shown  by  the  explosive  power  of 
gunpowder,  in  which  all  the  reacting  substances  are  solid, 
and  by  that  of  flour-dust,  where  one  of  the  substances  is  solid 
and  the  other  (the  oxygen  of  the  air)  gaseous.  In  all  such 
cases  the  surface  of  contact  is  very  great,  either  on  account 
of  the  close  incorporation  or  on  account  of  the  fine  state  of 
division  of  the  reacting  substances. 

Chemical  Equilibrium. — If  ethyl  acetate  and  water  be 
mixed  in  molecular  proportions  and  a  little  acid  (e.g.  hydro- 
chloric acid)  added,  then  at  the  ordinary  temperature  a  slow 
change  takes  place,  the  ester  being  converted  into  ethyl 
alcohol  and  acetic  acid  by  taking  up  water — 

CH3.COOC2H5  +  H20  (+  acid)  =  C2H5OH  -f  CH3.COOH 

(+  acid). 


vi.  CHEMICAL   EQUILIBRIUM.  71 

A  chemical  action  of  this  sort  in  which  one  of  the 
substances  present,  although  essential  for  the  speed  of  the 
reaction,  does  not  suffer  any  change,  is  termed  catalysis  or 
a  catalytic  reaction.  The  decomposition  of  cane  sugar  into 
invert  sugar  is  a  similar  process. 

The  catalysis  of  ethyl  acetate  does  not  proceed,  as  might 
be  expected  from  the  chemical  equation,  so  that  the  whole 
quantity  of  ester  is  changed  into  alcohol  and  acetic  acid,  but 
the  reaction  approaches  a  limit,  the  so-called  limit  of  reaction. 
In  this  case  the  limit  is  reached  when  two-thirds  of  the  ethyl 
acetate  has  decomposed.  On  the  other  hand,  if  equimolecular 
quantities  of  alcohol  and  acetic  acid  be  mixed,  and  a  little 
hydrochloric  acid  added,  ethyl  acetate  and  water  are  gradu- 
ally formed  according  to  the  equation — 

C2H5OH  +  CH3.COOH  (+  acid)  =  CH3.COOC2H5  +  H20 

(+  acid), 

that  is  to  say,  a  reaction  opposed  to  the  above  catalysis  takes 
place.  This  reaction  also  approaches  a  limit  which  is  the 
same  as  that  already  mentioned,  and  is  reached  when  a  third 
of  the  alcohol  and  acetic  acid  have  formed  ester. 

In  order  to  express  that  a  measurable  equilibrium  is 
established,  the  reaction  is  written  in  the  following  way, 
according  to  the  suggestion  of  van't  Hoff — 

CH3.COOC2H5  +  H20  (+  acid)  $  C2H5OH  +  CH3.COOH 

(+  acid). 

The  double  arrow  sign  (^),  used  in  place  of  the  usual 
sign  of  equality  ( = ),  denotes  that  the  reaction  may  proceed 
in  one  direction  or  the  other,  depending  on  the  concentrations 
of  the  reacting  substances,  and  that  finally  an  equilibrium 
will  be  established  when  the  two  opposite  reactions  take 
place  at  the  same  speed. 

Besides  these  "  incomplete  "  reactions — i.e.  those  in  which 
the  extent  of  reaction  is  limited — there  are  other-  reactions 
in  which  practically  the  whole  of  the  substance  originally 
present  is  transformed;  the  inversion  of  cane  sugar  is  an 


72     GENERAL   CONDITIONS   OF   EQUILIBRIUM.     CHAP. 

example  of  a  reaction  of  this  type.  In  the  chemical  equations 
representing  reactions  belonging  to  this  class  the  ordinary 
sign  of  equality  is  used.  There  are  theoretical  reasons  for 
believing  that  reactions  in  a  homogeneous  system  never  take 
place  absolutely  completely.  According  to  the  theory  an 
equilibrium  is  always  established  ;  but  in  many  cases  the 
reaction  proceeds  so  nearly  to  completion  that  by  the 
chemical  or  physical  methods  at  present  available  it  is  im- 
possible to  detect  the  presence  of  the  substances  represented 
on  one  side  of  the  equation. 

Complete  reactions  occur  during  chemical  change  in  a 
heterogeneous  system.  The  simplest  case  of  such  a  trans- 
formation is  the  change  of  the  state  of  aggregation  of  a 
substance.  Water  under  normal  pressure  (760  mm.  Hg) 
passes  completely  into  ice  if  the  temperature  be  lower  than 
0°,  and  the  opposite  change  takes  place  completely  if  the 
temperature*  be  higher.  If  the  pressure  be  760  mm.  ice  and 
water  can  only  be  in  equilibrium  at  0°.  That  point  at  which 
an  equilibrium  may  exist  (temp.  =  0°,  press.  =  760  mm.)  is 
called  the  transition  point  of  the  system.  In  this  special 
case,  and  in  general  when  gases  do  not  take  part  in  the 
equilibrium,  and  when  the  pressure  exerts  but  little  influence, 
it  is  customary  to  state  that  the  transition  point  of  the  system, 
ice  ^  water  :  is  0°.  According  to  Eeicher's  determination 
(1)  the  transition  between  monoclinic  and  rhombic  sulphur 
takes  place  at  95*6°.  The  system  — 


HaO  $  Na2Mg(S04)2.4H20+13H2O 

Cryst.  Glauber  salt.  Cryst.  Epsom  salt.  Cryst.  astrakanite.  Water. 

has  a  transition  point  (determined  by  various  methods)  which 
lies  at  about  21  '5°.  If  crystals  of  Glauber  salt  be  mixed 
with  crystals  of  Epsom  salt  below  21*5°  no  change  takes 
place;  but  if  this  mixture  be  heated  to  above  21*5°  it  is 
transformed  into  astrakanite  and  water. 

Systems  in  which  no  gases  occur  (and  in  which  solu- 
tions play  only  an  unimportant  part)  are  termed  condensed 
systems  by  van't  Hoff,  who,  with  his  pupils,  has  studied  the 


vi.  THE    PHASE    RULE    OF   GIBBS.  73 

transition  points  of  many  of  these.  Condensed  systems  are 
characterised  by  having  a  surface  of  separation  between  the 
substances  on  the  two  sides  of  the  equilibrium  sign  (^)  in 
the  equation,  and  are  thus  necessarily  heterogeneous.  Thus, 
in  the  example  mentioned,  the  Glauber  salt  crystals  and  the 
Epsom  salts  crystals  are  separated  from  the  astrakanite 
crystals  and  the  water  by  well-defined  surfaces.  For  the 
liquid  part  of  the  system  formed  by  the  water  and  the  salts 
dissolved  therein,  the  law  of  condensed  systems  "that  the 
components  are  only  stable  in  presence  of  each  other  at  the 
transition  point,  21/5°,"  does  not  hold. 

In  so  far  as  the  quantitative  respect  is  concerned,  the  case 
is  somewhat  different  for  those  physical  and  chemical  changes 
in  which  a  gas  is  produced.  As  an  example  of  this  kind  we 
may  conveniently  take  the  system :  water  ^  steam  (or  water 
vapour).  At  20°  and  17'4  mm.  pressure  this  system  possesses 
a  transition  point,  for  at  this  pressure  water  is  only  stable 
under  20°  and  steam  only  above  20°,  but  at  20°  the  two 
forms  can  "  co-exist."  Here  it  is  evidently  necessary,  in 
distinction  to  condensed  systems,  to  give  the  (vapour)  pressure 
for  the  transition  point,  since  this  has  now  as  much  influence 
as  the  temperature. 

Formerly  it  was  supposed  that  all  chemical  reactions 
took  place  completely.  It  was  conceived  that  the  stronger 
affinity  caused  the  reaction  to  be  complete  at  the  expense  of 
the  weaker  affinity.  This  view  of  chemical  reactions  was 
first  systematised  by  Torbern  Bergman,  and  it  prevailed 
until  quite  recent  times.  Thermochemists,  more  particularly 
Berthelot,  have  striven  to  uphold  this  conception,  which  has 
no  strict  scientific  foundation. 

The  Phase  Rule  of  Gibbs. — A  state  of  equilibrium 
between  substances  in  a  homogeneous  system  is  usually 
termed  a  homogeneous  equilibrium.  The  corresponding  name 
for  equilibrium  in  a  heterogeneous  system  is  heterogeneous 
equilibrium.  W.  Gibbs  (2)  calls  the  homogeneous  parts  of 
a  heterogeneous  system  the  "phases"  of  the  system.  In 
the  equilibrium  between  ice,  water,  and  water  vapour  (at  0° 


74     GENERAL   CONDITIONS   OF    EQUILIBRIUM.     CHAP. 

and  4' 6  mm.  pressure)  there  are  three  phases — one  solid  (ice), 
one  liquid  (water),  and  one  gaseous  (water  vapour).  Gibbs 
has  deduced  a  law  for  the  number  of  these  phases  which  is 
known  as  "  Gibbs's  phase  rule."  This  law  may  be  stated  as 
follows:  n  bodies  (different  chemical  substances,  simple  or 
compound)  can  form  n  4-  2  phases,  and  these  co-exist  only  at 
a  single  point  (i.e.  all  the  external  conditions  of  the  system, 
pressure,  temperature,  and  composition  of  each  phase,  are 
given).  Let  us  consider  the  substance  water;  here  n  =  1. 
and  therefore  three  phases  of  the  substance,  the  solid,  the 
liquid,  and  the  gaseous,  may  co-exist,  but  only  at  one  point, 
namely,  at  0°  and  4'6  mm.  pressure.  The  composition  must 
be  the  same  throughout,  since  only  one  kind  of  molecule  is 
present.  If  the  system  consists  of  two  bodies,  e.g.  common 
salt  and  water,  then  n  =  2  and  the  number  of  phases  is 
n  -f  2  =  4.  These  phases  can  co-exist  at  about  —21°,  at 
which  temperature  by  loss  of  heat  a  so-called  cryohydrate 
(constant  mixture  of  ice  and  salt  crystals)  separates  from  the 
saturated  solution. 

At  this  temperature  (  —  21°,  the  corresponding  pressure 
being  0*73  mm.)  there  are  present  two  solid  phases  (ice  and 
salt),  a  liquid  (saturated  salt  solution,  which  contains  36 
grams  of  salt  to  100  grams  of  water),  and  a  gaseous  phase 
(water  vapour  at  073  mm.  pressure). 

When  the  number  of  phases  is  only  n  +  1,  one  of  the 
external  conditions  can  (within  certain  limits)  be  fixed  at 
pleasure;  thereby,  however,  the  other  conditions  are  also 
fixed.  Thus  if  we  take  water  (n  =  1)  in  the  liquid  and 
gaseous  states,  the  number  of  phases  is  n  -f  1  =  2.  At 
any  particular  temperature  we  may  happen  to  choose,  the 
pressure  at  which  the  two  phases  can  exist  in  presence  of 
each  other  can  only  have  one  value.  (Saturated  water 
vapour  at  20°  has  a  pressure  of  17 '4  mm.) 

Two  bodies,  such  as  salt  and  water  (n  =  2),  can  co-exist 
at  a  temperature  of,  say,  20°  in  n  4-  1  =  3  phases ;  these  are 
(1)  salt  crystals ;  (2)  saturated  solution,  containing  36  grams 
of  salt  to  100  grams  of  water;  and  (3)  water  vapour  of  pressure 


vi.  OSMOTIC   WORK.  75 

about  13*4  mm.  At  any  given  temperature  the  pressure  and 
composition  of  the  phases  are  fixed.  If  the  composition  of 
the  liquid  phase  were  given,  such  a  saturated  solution  could 
only  be  obtained  at  a  single  temperature  and  with  a  single 
pressure  of  water  vapour. 

If  the  number  of  co-existing  phases  is  the  same  as  the 
number  of  bodies  present  in  the  system,  then  two  of  the 
external  conditions  may  be  chosen  (e.g.  temperature  and 
pressure),  but  the  composition  of  the  phases  is  then  deter- 
mined. If,  therefore,  we  have  two  bodies,  salt  and  water,  in 
two  phases,  namely,  solution  and  vapour,  and  the  system  is 
to  have  a  particular  temperature  and  pressure,  the  composition 
of  the  solution  can  only  have  one  value.  In  other  words, 
there  is  only  one  concentration  of  the  solution  which  at  a 
given  temperature  possesses  a  particular  vapour  pressure. 

Osmotic  Work. — In  order  to  derive  the  various  con- 
ditions of  equilibria  it  is  necessary  to  know  how  much  work 
is  done  when  a  dissolved  substance  passes  from  one  concen- 
tration to  another  by  removal  of  the  solvent.  This  removal 
may  be  carried  out  in  different  ways,  as  by  evaporation,  by 
freezing  out,  or  by  forcing  solvent  out  from  the  solution  by 
means  of  a  semi-permeable  piston  which  does  not  allow  the 
dissolved  substance  to  pass  through.  In  our  derivation  we 
shall  make  use  of  this  last  method.  We  premise  that  a 
semi-permeable  membrane  can  be  found  for  every  substance 
which  will  allow  this  but  no  other  substance  present  in  the 
solution  to  pass  through.  In  reality  this  is  not  quite  the 
case,  but  in  general  an  arrangement  can  be  made  which 
closely  approximates  to  the  condition  of  semi-permeability. 

The  simplest  case  is  offered  by  a  solid  substance  which 
dissolves  in  a  liquid,  so  that  the  solution  in  contact  with  the 
solid  is  always  saturated.  Suppose  a  piston,  permeable  by 
the  solvent  but  not  by  the  dissolved  substance,  resting  on 
the  surface  of  the  solution,  and  suppose  further  that  there  is 
solvent  above  the  piston.  In  order  that  there  may  be  a 
condition  of  equilibrium  so  that  the  pure  solvent  does  not 
pass  into  the  solution,  the  piston,  according  to  our  previous 


76     GENERAL   CONDITIONS   OF   EQUILIBRIUM.     CHAP. 

calculations  (see  p.  29),  must  be  so  weighted  that  it  exerts  on 
the  solution  a  pressure  (P  per  square  centimetre)  equal  to  the 
osmotic  pressure.  By  raising  the  piston,  in  doing  which  work 
must  be  done,  a  volume  dv  of  the  solvent  is  caused  to  pass 
into  the  solution.  Since  solid  substance  is  present  in  contact 
with  the  solution,  the  concentration,  and  consequently  also 
the  osmotic  pressure,  remain  constant,  and  the  work  done 
during  the  solution  process  is,  like  that  done  by  evaporation 
of  a  liquid — 

dA  =  Pdv. 

When  a  gram-molecule  of  a  solid  substance  dissolves, 
the  work  done  is,  according  to  van't  Hoff  s  law,  the  same 
as  for  a  liquid  which  is  vaporised — 

A  =  PV  =  l-99rcal., 

where  V  is  the  volume  occupied  by  a  gram-molecule,  and  T 
denotes  the  absolute  temperature.  This  work,  like  that  done 
during  the  evaporation  of  a  liquid,  is  independent  of  the 
pressure  iinder  which  the  vaporisation  takes  place,  but  is 
proportional  to  the  absolute  temperature. 

This  does  not,  of  course,  apply  to  the  solution  of  those 
substances  (salts,  strong  acids  and  bases)  which  exert  an 
osmotic  pressure  greater  than  that  which  can  be  calculated 
by  van't  Hoff' s  law.  In  such  cases  a  correction  must  be 
introduced,  and  this  can  easily  be  done.  If  it  has  been 
ascertained  by  experiment  that  the  osmotic  pressure  of  the 
solution  in  question  is  i  times  greater  than  it  should  be 
according  to  van't  Hoff's  law,  we  must  multiply  by  this 
factor,  and  obtain — 

A  =  l-99ir  cal. 

Let  us  now  take  the  case  of  a  solution  containing  a  certain 
amount  of  a  dissolved  substance  and  no  solid  in  contact  with 
it.  As  before,  let  the  solution  be  contained  in  a  vessel  with 
a  piston  above  which  there  is  pure  solvent.  By  raising  the 
piston  we  allow  some  of  the  solvent  to  enter  the  solution, 


vi.  HENRY'S   LAW.  77 

the  osmotic  pressure  of  which  is  variable,  and  follows  van't 
Hoff's  law— 

PV=  1-99T, 

where  V  is  the  (variable)  volume  in  which  a  gram-molecule 
is  dissolved.  The  pressure  which  the  substance  exerts  on 
the  piston  is  the  same  as  that  which  would  be  exerted  by  the 
same  number  of  gram-molecules  in  the  gaseous  state,  instead 
of  dissolved,  contained  in  the  same  volume.  If,  therefore, 
by  the  introduction  of  solvent,  the  volume  of  the  solution 
increases  from  VQ  to  Vi  (whilst  the  osmotic  pressure  diminishes 
from  PQ  to  pi)  at  constant  temperature,  the  work  done  by 
the  solution  during  this  process  will  be  the  same  as  that 
done  by  a  mass  of  gas  containing  the  same  number  of  mole- 
cules when  it'increases  in  volume  by  the  same  amount.  At 
constant  temperature  T  this  work  amounts  for  each  gram- 
molecule  of  dissolved  substance  to — 

A  =  1-99T  In  ^  =  1-99T  In  ^ 
^o  pi 

For  substances  which  deviate  from  van't  HofF s  law  the 
value  given  must  be  multiplied  by  i,  just  as  before. 

As  no  known  gas  exactly  follows  the  law  of  Avogadro 
(and  also  those  of  Boyle  and  Gay-Lussac),  we  often  consider 
a  so-called  ideal  gas  which  exactly  obeys  these  laws ;  in  the 
same  way  there  is  no  solution  which  absolutely  obeys  van't 
Hoff  s  law,  and  so  we  often  make  use  of  the  ideal  (dilute) 
solution  to  which  we  assume  the  law  rigidly  applies. 

Henry's  Law. — In  the  following  development  of  the 
laws  of  equilibria  we  start  with  the  fundamental  doctrine 
that,  when  a  substance  is  transferred  from  one  system  to 
another,  and  then  at  the  same  temperature  is  brought  back 
to  its  original  condition,  the  sum  of  the  works  done  is 
zero.  Thus :  if  we  have  a  gas,  e.g.  oxygen,  at  pressure  p, 
in  contact  with  a  liquid,  e.g.  water,  in  a  closed  vessel,  A,  the 
gas  dissolves  to  a  certain  extent;  let  the  osmotic  pressure 
which  it  exerts  when  equilibrium  is  established  be  ?r.  In 
another  closed  vessel,  B,  let  there  be  the  same  gas,  but  at  a 


78     GENERAL   CONDITIONS   OF   EQUILIBRIUM.     CHAP. 

higher  pressure  p\,  also  in  contact  with  the  same  liquid,  and, 
when  equilibrium  has  been  established,  let  the  osmotic 
pressure  be  TTI.  We  now  cause  a  very  small  quantity  of 
the  gas,  a  gram-molecule,  where  a  is  a  small  number,  to  pass 
from  vessel  A  to  vessel  B  at  constant  temperature.  The 
work  done  by  the  change  of  pressure  is  given  by  — 

Ai  =  l-99arinl' 
Pi 

The  a  gram-molecule  of  gas  is  now  forced  into  the  liquid 
in  vessel  B  ;  for  this  no  work  is  necessary,  because  the  gas 
and  solution  are  in  equilibrium,  and  a  is  so  small  that  the 
concentration  in  the  liquid  is  not  appreciably  altered.  On 
the  contrary,  a  (negative)  work  A2,  is  done  by  the  disappear- 
ance of  the  a  gram-molecule  of  gas  — 


The  gas  in  B  is  now  separated  from  the  liquid,  and  by 
means  of  a  semi-permeable  membrane,  which  does  not  allow 
the  gas  to  pass  through,  the  liquid  is  allowed  to  take  up  so 
much  solvent  (vi  c.c.)  as  is  necessary  to  dissolve  the  a  gram- 
molecule,  so  that  the  concentration  is  the  same  as  that 
originally  in  B.  The  corresponding  work  is  — 


(and  it  is  evident  that  the  two  last  processes  can  be  carried 
out  in  several  smaller  portions,  whereby  the  whole  work 
required  to  force  the  gas  into  the  liquid  disappears). 

A  quantity  of  liquid  containing  a  gram-molecule  of  gas 
is  removed  from  vessel  B  (the  contents  of  which  evidently 
return  to  their  original  condition),  and  this  is  allowed  to 
absorb  so  much  solvent  (v  —  v\,  c.c.)  that  its  osmotic  pressure 
sinks  from  TTI  to  TT,  that  which  obtains  in  vessel  A.  The 
work  done  during  this  process  is  — 


vi.  HENRY'S   LAW.  79 

The  new  quantity  of  liquid,  which  still  contains  a  gram- 
molecule  of  dissolved  gas,  is  united  with  the  liquid  in  A— 
the  gas  and  liquid  in  this  vessel  having  previously  been 
separated.  A  volume,  v,  of  liquid  is  now  forced  out  through 
a  semi-permeable  membrane,  whilst  the  a  gram-molecule 
remains  in  the  vessel  A.  The  work  then  done  will  be  — 


Finally,  the  dissolved  a  gram-molecule  of  gas  is  permitted 
to  evolve  from  the  liquid  in  A  into  the  gas  above  at  pressure 
p,  and  the  work  — 


is  done,  the  same  as  when  the  gas  was  forced  into  the  liquid, 
but  with  the  sign  changed.  The  condition  in  A  is  now  the 
same  as  initially. 

Summing  up,  we  have 


f 
L 


in      -f 
Pi 


or —  ±-  =       =  constant, 

Pi         7T1 

i.e.  the  osmotic  pressure  of  the  dissolved  gas  is  proportional 
to  the  pressure  of  the  gas  above  the  solution. 

Since  the  osmotic  pressure  is  proportional  on  the  one  hand 
to  the  concentration,  and  on  the  other  hand  to  the  pressure 
of  the  gas,  it  is  clear  that  the  concentration  of  the  gas  in  the 
solution  must  stand  in  a  constant  ratio  to  the  concentration, 
or  density,  of  the  gas  over  the  solution.  This  law  is  called, 
after  its  discoverer,  Henry's  law. 

The  same  development  would  lead  to  a  different  result  if 
the  substance  in  the  gaseous  state  and  when  dissolved  had 
different  molecular  weights.  If,  for  instance,  the  substance 
when  dissolved  had  a  molecular  weight  double  that  in 
the  gaseous  state,  the  work  A±  would  consist  in  changing 

the  osmotic  pressure  of  ~  gram-molecule  from  osmotic 
pressure  TTI  to  osmotic  pressure  TT,  and  we  should  obtain— 


8o     GENERAL   CONDITIONS  OF   EQUILIBRIUM.     CHAP. 
A1  +  A,=  aT  [21n  £  +  In7"1]  =  0, 

L          pi  7TJ 

[ 


Van't  Hoff  (3)  has  shown  that  when  Henry's  law  —  that 
the  quantity  of  gas  dissolved  per  unit  volume  is  proportional 
to  the  gas-pressure  —  obtains,  the  gas  has  the  same  molecular 
magnitude  in  the  two  conditions  (gaseous  and  dissolved). 
We  might  have  a  solution  of  the  gas  in  another  solvent  (e.g. 
ether)  in  contact  with  the  liquid  (water)  instead  of  the  gas 
itself.  If  in  the  first  process  of  the  foregoing  series  we  make 
use  of  a  semi-permeable  membrane,  which  allows  the  ether 
but  not  the  gas  to  pass  through,  it  can  be  shown  that  — 


0  and  0i  denote  the  osmotic  pressures  of  the  dissolved  gas  in 
the  ether  in  vessels  A  and  B. 

Provided  that  a  substance  —  whether  capable  of  existence 
in  the  gaseous  state  or  not  —  possesses  the  same  molecular 
weight  in  two  solvents,  the  osmotic  pressures,  and  conse- 
quently also  the  concentrations  of  the  substance  in  the  two 
liquids,  must  stand  to  each  other  in  a  constant  ratio. 

Distribution  Law.  —  If  an  aqueous  solution  of  succinic 
acid  be  shaken  with  ether,  part  of  the  dissolved  substance 
passes  into  the  ether.  If  this  be  carried  out  with  aqueous 
solutions  of  different  concentrations,  the  amount  of  succinic 
acid  which  passes  into  solution  in  unit  volume  of  ether  must 
increase  with  rising  concentration  of  the  aqueous  solution. 
Experimentally  it  has  been  found  that  the  following  law  of 
distribution  holds  good  :  when  equilibrium  is  established  the 
concentration  of  the  ethereal  solution  is  proportional  to  that 
of  the  aqueous  solution.  The  following  table  contains  the 
results  obtained  at  15°  by  Berthelot  and  Jungfleisch  (4)] 
ci  and  c2  denote  the  weights  in  grams  of  succinic  acid  in  10  c.c. 
of  water  and  ether  respectively.  At  higher  concentrations 


VI. 


DISTRIBUTION   LAW. 


81 


deviations  occur,  which,  however,  do  not  attain  a  particu- 
larly high  value.     The  influence   of  temperature   on  this 

distribution  ratio  is  such  that  -  increases  with  rising  tem- 

Ca 

perature. 


«1. 

C2. 

£i 

C'2' 

0-024 

0-0046 

5-2 

0-070 

0-013 

5-2 

0-121 

0-022 

5-4 

0-236 

0-041 

5-7 

0-365 

0-061 

6-0 

0-420 

0-067 

6-3 

0486 

0-073 

6-6 

Other  experiments  were  made  on  the  distribution  of 
bromine  and  iodine  between  carbon  disulphide  and  water,  and 
of  benzoic  acid,  oxalic  acid,  malic  acid,  and  tartaric  acid 
between  ether  and  water. 

If  an  excess  of  solid  succinic  acid  be  shaken  with  water 
and  ether,  two  saturated  solutions  are  formed;  and  if  the 
excess  of  solid  be  now  removed,  the  equilibrium  must  never- 
theless persist.  The  distribution  coefficient  of  succinic  acid 
between  water  and  ether  must>  therefore,  be  the  ratio  of  the 
solubilities  of  this  substance  in  the  two  solvents.  It  must, 
however,  be  remembered  that  in  this  case  the  water  is  not 
free  from  dissolved  ether,  and  the  ether  is  not  free  from  dis- 
solved water,  and  consequently  perfect  agreement  cannot  be 
expected  between  the  distribution  result  and  that  obtained 
when  the  solubilities  in  the  pure  solvents  are  used. 

If  a  substance  (or,  more  strictly,  one  kind  of  molecule)  is 
present  in  two  phases  (e.g.  in  aqueous  and  ethereal  solution), 
the  concentration  in  one  phase  must  stand  to  the  concentra- 
tion in  the  other  phase  in  a  constant  ratio,  provided  that  the 
temperature  is  kept  constant  (5).  This  general  statement 
embraces  Henry's  law  as  a  special  case  in  which  one  of  the 
phases  is  gaseous. 

G 


82     GENERAL    CONDITIONS   OF   EQUILIBRIUM.     CHAP. 

Other  special  cases  of  the  law  of  distribution  are  the 
laws  that  a  solid  substance  dissolves  in  a  particular  liquid 
until  a  certain  degree  of  concentration  is  reached  (until  a 
saturated  solution  is  formed),  and  that  liquids  and  solid 
substances  at  a  particular  temperature  give  off  vapour  until  a 
certain  pressure  is  reached. 

Kinetic  Considerations. — The  development  made  above 
is  based  on  the  mechanical  theory  of  heat  (thermodynamics), 
and  is  therefore  strictly  exact.  However,  it  is  usual  also  to 
regard  these  laws  from  a  kinetic  point  of  view,  and  as  this 
has  been  of  great  service  and  is  of  assistance  in  visualising 
the  matter,  a  short  account  may  be  given  here. 

Let  us  suppose  that  we  have  water  at  a  certain  tempera- 
ture in  a  vacuum.  Part  of  the  water  vaporises,  and  so  fills 
the  space  above  with  water  vapour.  This  evaporation  takes 
place  until  the  number  of  molecules  which  pass  into  the 
water  per  second  is  exactly  equal  to  the  number  which  leave 
it.  The  equilibrium  which  obtains  is  mobile.  It  is  clear 
that  this  equilibrium  depends  only  on  the  conditions  in  the 
immediate  neighbourhood  of  the  surface  of  separation  of 
liquid  and  vapour.  If  the  vapour-space  be  increased,  the 
new  volume  must  become  filled  with  vapour  at  the  same 
pressure  as  that  in  the  original  space,  otherwise  there  would 
not  be  an  equilibrium  between  this  latter  and  the  new 
portion.  At  the  surface  of  separation  no  change  whatever 
occurs.  A  liquid,  therefore,  at  a  given  temperature  must 
possess  a  certain  definite  vapour  pressure  which  is  inde- 
pendent of  the  quantity  of  vapour  and  liquid  present. 

In  the  same  way  it  can  be  imagined  that  the  solution  of 
a  solid  substance  in  a  liquid  takes  place  until  in  unit  time 
there  are  as  many  molecules  leaving  the  solid  as  there  are 
molecules  separating  from  the  solution.  The  same  considera- 
tion as  that  used  for  the  evaporation  of  a  liquid  leads  to  the 
conclusion  that  a  solid  substance  in  contact  with  a  liquid 
forms  a  saturated  solution,  the  concentration  of  which  depends 
on  the  temperature,  but  is  entirely  independent  of  the 
quantity  of  solid  and  liquid  present. 


vr.  DEPRESSION   OF   SOLUBILITY.  83 

A  further  consequence  of  this  view  is  that  no  solid 
substance  is  entirely  free  from  gas  pressure  or  entirely  in- 
soluble in  a  liquid,  for  it  must  be  assumed  that  in  a  certain 
time  some,  even  if  few,  molecules  leave  the  solid  and  pass 
either  into  the  gas-space  or  into  the  dissolving  liquid.  This 
conclusion,  although  impossible  to  prove  experimentally  in 
those  cases  where,  by  analytical  methods,  the  presence  of 
dissolved  or  gaseous  substance  cannot  be  recognised,  is  of 
extreme  importance  from  a  theoretical  point  of  view. 

Let  us  consider  more  closely  a  gas  in  contact  with  a 
liquid.  A  number  of  gas  molecules  pass  into  the  liquid  until 
the  equilibrium  between  the  gas  and  the  saturated  solution 
is  reached.  If  now  the  number  of  gram-molecules  in  the 
gas-space  be  doubled,  then  in  unit  time  twice  as  many  mole- 
cules pass  into  the  liquid  as  before,  since  the  movements 
of  the  gas  molecules  are  independent  of  each  other.  In  order 
that  equilibrium  may  exist,  double  as  many  gram-molecules 
must  leave  the  solution  in  unit  time  as  previously.  This 
occurs  when  the  concentration  of  the  solution  in  gas  mole- 
cules has  been  doubled.  It  is  easy,  therefore,  to  see  that  the 
concentration  (partial  pressure)  of  the  gas  must  be  proportional 
to  the  concentration  of  molecules  dissolved  in  the  liquid 
(Henry's  law).  The  general  law  of  distribution  can  be 
derived  in  a  similar  manner. 

Depression  of  Solubility. — Nernst's  method  (6)  of 
determining  the  molecular  weight  by  the  depression  of 
the  solubility  shows  the  analogy  between  a  solution  and  a 
gas.  Ether  dissolves  in  water  at  0°  to  such  an  extent  that  a 
solution  is  obtained  which  freezes  at  —  3'85°  (about  2-normal). 
If  to  this  solution  a  substance  be  added,  like  camphor,  which 
is  soluble  in  ether  and  practically  insoluble  in  water,  the 
vapour  tension  of  the  ether  and  its  solubility  in  water 
will  both  be  diminished,  and  both  in  the  same  proportion. 
When  1  gram-molecule  of  the  substance  to  be  investigated 
is  dissolved  in  N  gram-molecules  of  ether,  the  relative 

lowering  of  the  solubility  of  the  ether  is  — ,  and  the  freezing 


84     GENERAL   CONDITIONS  OF   EQUILIBRIUM.     CHAP. 

O.O~     v>     -JO 

point  of  the  ether-water  solution  rises  by  -  —= ,  which 

can  easily  be  measured  by  a  Beckmann  thermometer. 

To  carry  out  the  determination,  the  tube  of  a  Beckmann 
apparatus  is  filled  with  water  so  that  the  level  of  this  stands 
above  the  bulb  of  the  thermometer,  and  on  to  it  is  poured 
a  weighed  quantity  of  ether.  After  the  water  has  become 
saturated  with  ether,  its  freezing  point  is  determined.  A 
weighed  amount  of  the  substance  is  then  introduced,  and 
after  it  has  dissolved  in  the  ether,  the  freezing  point  is  again 
determined. 

As  already  mentioned,  one  condition  of  the  experiment  is 
that  the  substance  must  not  be  appreciably  soluble  in  water. 
The  principle  of  the  method  is  a  consequence  of  Henry's  law 
applied  to  the  solubility  of  ether  vapour  in  water. 

Homogeneous  Equilibria. — Suppose  we  have  two 
vessels  containing  ammonium  chloride  vapour  at  high  tem- 
perature. The  ammonium  chloride  is  partially  decomposed 
according  to  the  equation — 

NH3  +  HC1  $  NH4C1. 

The  sign  ^  denotes  that  there  is  an  equilibrium — that  in 
any  specified  time  there  is  as  much  ammonium  chloride  de- 
composed as  there  is  formed  from  the  products  of  decomposi- 
tion. Let  the  partial  pressures  of  the  three  components  be 
Ci,  A>  and  03  in  the  first  vessel,  and  C±,  C5,  and  (76  in  the 
second.  Suppose,  further,  that  both  vessels  are  very  large. 
If  now  a  gram-molecule  of  ammonia  and  a  corresponding 
quantity  of  hydrochloric  acid  be  introduced  into  the  first 
vessel  through  a  semi-permeable  wall  under  the  constant 
pressure  Ci  (or  Ci),  the  work  done  is  pv  =  ET  =  l'99r  cal. 
for  each  sort  of  molecule. 

Suppose  that  the  two  substances  then  combine  to  form 
ammonium  chloride,  which  is  simultaneously  removed 
through  a  semi-permeable  wall  in  such  a  way  that  the  pres- 
sure remains  constant.  By  the  passing  out  of  the  gram- 


vi.  HOMOGENEOUS   EQUILIBRIA.  85 

molecule  of  ammonium  chloride  so  formed  work  will  be  done 
which  amounts  to  pv  =  RT  =  l'99rcal. 

Now  allow  the  ammonium  chloride  to  pass  iso thermally 
from  concentration  C3  to  concentration  CQ,  and  the  work  done 
will  be — 

The  ammonium  chloride  is  then  forced  at  this  pressure 
into  the  second  vessel,  where  it  decomposes  into  ammonia 
and  hydrochloric  acid  at  pressures  (74  and  05  respectively,  and 
no  work  has  to  be  done  to  accomplish  this  (exactly  as  in  the 
case  of  the  evaporation  of  water  where  no  work  is  done,  but 
there  is  a  loss  of  heat).  The  new  quantities  of  ammonia  and 
hydrochloric  acid  at  the  pressures  C±  and  05  are  now  removed, 
each  through  a  semi-permeable  wall. 

The  work  done  for  the  gram-molecule  of  ammonium 
chloride  is  pv  =  RT,  and  that  done  by  the  gram-molecule  of 
each  of  the  gases,  ammonia  and  hydrochloric  acid,  ispv  =  RT. 
Finally,  if  the  gram-molecule  of  ammonia  and  that  of  hydro- 
chloric acid  are  allowed  to  expand  isothermally  from  pressure 
(74  to  Oi  or  from  05  to  C%  in  the  different  cases,  the  original 
condition  is  established.  During  this  last  process  the  work 
done  will  be — 

A1  =  RT\n  Q  and  A2  =  RTln  ^. 

GI  G2 

During  the  cycle  certain  amounts  of  work  are  done  on 
the  system,  and  equal  quantities  are  regained  at  other  points 
in  the  process,  but  there  still  remain  -A,  AI,  A%.  Since  the 
cycle  was  carried  out  at  constant  temperature  and  completely 
reversibly  the  sum  of  these  three  quantities  must  be  zero. 
We  therefore  obtain  the  equation — 

-A  +  Ai  +  AZ  =  0  =  - 


or —  —  =     *         ° 

or—  G'i  X  Cz  =  kCa  and  (74  x  C5  =  k( 


86     GENERAL   CONDITIONS   OF    EQUILIBRIUM.     CHAP. 

where  k  is  a  constant,  the  value  of  which  depends  on  the 
temperature. 

If  we  had  an  equation  of  the  form  — 


which  denotes  a  reaction  where  m  molecules  of  a  substance 
P,  n  molecules  of  substance  Q,  and  o  molecules  of  substance 
E,  etc.,  react  to  produce  /  molecules  of  substance  S,  g  mole- 
cules of  substance  Tt  and  li  molecules  of  substance  V,  etc., 
the  result  would  be  — 

m]nCP  +  nlnCq  +  olnCa+   .  .   .    =f  In  Ca  4-  g  In  Cr 

+  h  In  C,+  _-. 
or-  CT  X  C*q    X  C\  =  kC's  x  Cgr  x  C*, 

where  k  is  again  a  constant  and  C  is  the  partial  pressure  of 
each  of  the  substances  indicated  by  the  index. 

Since  at  low  pressures  or  in  very  dilute  solution  the 
partial  pressure  is  almost  proportional  to  the  concentration, 
C  in  this  case  may  be  taken  to  mean  simply  the  concentration. 
The  "  law  of  mass  action  "  expressed  in  the  above  formula  is 
called,  after  its  two  Norwegian  discoverers,  the  Guldberg  and 
Waage  law  (7).  The  law  as  originally  stated  referred  to 
the  concentrations  of  the  reacting  substances,  but  it  was  later 
shown  to  apply  more  strictly  when  C  in  the  above  formula 
indicates  the  partial  pressure. 

The  law  can  be  more  simply  derived  by  considering  the 
action  kinetically.  Let  us  take  the  same  example  as  before, 
that  represented  by  the  equation— 


and  let  us  consider  the  quantities  in  unit  volume  (1  c.c.),  i.e. 
the  concentrations  (73,  61,  and  Ca  of  the  three  substances 
present. 

The  number  of  decomposing  molecules  of  ammonium 
chloride  in  unit  volume  is  proportional  to  the  total  quantity 
of  this  substance  (63)  present  in  the  same  volume,  for  each 


vi.  HOMOGENEOUS    EQUILIBRIA.  87 

molecule  decomposes  independently  of  the  others.  The 
number  of  molecules  decomposing  in  unit  time  is  therefore 
given  by  — 

N  =  kC3 

where  k  is  a  constant  depending  on  the  temperature. 

For  the  formation  of  a  molecule  of  ammonium  chloride 
from  a  molecule  of  ammonia  and  one  of  hydrochloric  acid  it 
is  necessary  for  these  to  meet.  The  number  of  molecules 
formed  must  consequently  be  proportional  to  the  number  of 
such  collisions.  The  possibility  of  a  single  molecule  of 
ammonia  coming  into  collision  with  a  molecule  of  hydro- 
chloric acid  in  unit  volume  is  evidently  proportional  to  the 
number  of  hydrochloric  acid  molecules  present,  i.e.  to  0%.  For 
Ci  molecules  of  ammonia  the  number  of  collisions  with  C% 
molecules  of  hydrochloric  acid  will  be  G\  times  as  great.  The 
number  of  collisions  N\  between  ammonia  and  hydrochloric 
acid  molecules  is  therefore  proportional  to  G\G^  or 


Now,  it  is  required  that  — 

N=Nlt 
therefore  kC$  must  be  equal  to  kiCiCz,  or 

C/3  =  ./LL/iGa. 

To  take  another  example,  if  water  vapour  at  high  tempe- 
rature decomposes  into  hydrogen  and  oxygen  according  to— 

2H20  $  2H2  +  O2, 

then,  in  order  that  a  decomposition  may  take  place,  one  water 
molecule  must  collide  with  another  one  ;  and  on  the  other 
hand,  in  order  that  a  molecule  of  water  may  be  formed,  two 
molecules  of  hydrogen  and  one  molecule  of  oxygen  must 
collide.  If  the  concentrations  of  water,  hydrogen  and 
oxygen,  are  C3,  Ci,  and  <72,  and  K  is  a  constant,  then  in 
the  condition  of  equilibrium  — 


88     GENERAL   CONDITIONS   OF   EQUILIBRIUM.     CHAP. 


The  coefficients  of  the  chemical  equation  become  ex- 
ponents in  the  equation  of  equilibrium,  whilst  the  signs  of 
addition  become  signs  of  multiplication;  in  place  of  the 
molecular  formulae  we  have  the  concentrations  of  the 
substances,  and  the  sign  $  is  changed  into  =K. 

These  equilibria  have  been  studied  both  in  gaseous  and 
liquid  systems.  Lemoine  (8)  found  for  a  mixture  of  iodine 
and  hydrogen  which  combine  partially  to  hydriodic  acid 
according  to  the  equation — 

H2  +  I2  =  2HI, 

the  values  contained  in  the  following  table,  which  apply  to 
the  temperature  440°.  p0  denotes  the  partial  pressure  of 
the  hydrogen  at  the  beginning  of  the  experiment,  p'0  is  the 
corresponding  value  for  the  iodine  gas,  and  x  the  proportion  of 
hydrogen  still  free  after  the  equilibrium  has  been  established. 
It  is  evident  from  the  numbers  quoted  that  the  observed 
values  of  x  agree  satisfactorily  with  those  calculated.  The 
measurements  were  carried  out  by  collecting  the  gas  mixture 
over  water,  which  absorbs  the  acid  formed,  and  the  quantity 
of  hydrogen  was  then  determined  eudiometrically.  The 
reaction  proceeds  so  slowly  at  the  ordinary  temperature  that 
there  is  no  disturbance  of  the  equilibrium  during  the 
measurement. 


Po- 

^0 

Po' 

x  (observed). 

x  (calculated). 

2-2    atmo. 

1 

0-240 

0-280 

2-33    „ 

0-784 

0-350 

0-373 

2-33    „ 

0-527 

0-547 

0-534 

2-31     „ 

0-258 

0-774 

0-754 

1-15    „ 

1 

0-255 

0-280 

0-37 

1-36 

0-124 

0-184 

0-45 

1 

0-266 

0-280 

0-41 

0-623 

0-676  (?) 

0-470 

0-45 

0-58 

0-614  (?) 

0-497 

0-46 

0-56 

0-600  (?) 

0-510 

0-48 

0-53 

0-563 

0-535 

0-48 

0-26 

0-794 

0-756 

025 

1 

0-250 

0-280 

0-10    „ 

1 

0-290 

0-280 

vi.  HOMOGENEOUS   EQUILIBRIA.  89 

Other  similar  equilibria,  such  as  those  represented  by 
the  following  reactions — 

N204  ^  2N02, 
2N02  5>  2NO  +  Oa, 

HC1  +  (CH3)20  ^  (CH3)2OHC1  (methyl  ether  hydrochloride), 

have  been  studied,  and  in  all  cases  a  good  agreement  has 
been  found  between  the  calculated  and  observed  results. 

An  example  of  a  reaction  between  two  liquids  which  is 
governed  by  Guldberg  and  Waage's  law  is  the  formation  (or 
decomposition)  of  ethyl  acetate — 

CH3COOH  +  C2H5OH  •£  CH3COOC2H5  +  H20. 

This  equilibrium  was  first  studied  experimentally  by 
Berthelot  and  Pean  de  St.  Gilles  (9),  and  the  results  were 
afterwards  calculated  by  Guldberg  and  Waage,  and  by  van't 
Hoff(^). 

The  results  are  contained  in  the  following  table;  in 
column  m  is  given  the  number  of  molecules  of  alcohol  which 
reacted  on  one  molecule  of  acid,  and  x  is  the  quantity  of  ester 
formed  when  equilibrium  was  established. 


tn. 

x  (observed). 

^x  (calculated). 

0-05 

0-05 

0-049 

0-18 

0-171 

0-171 

0-33 

0-293 

0-311 

0-50 

0-414 

0-423 

1-00 

0-667 

(0-667) 

2-00 

0-858 

0-845 

8-00 

0-966 

0-945 

The  agreement  between  observed  and  calculated  values  is 
very  good.  Experiments  on  various  equilibria  in  solutions 
have  also  led  to  excellent  agreement  with,  and  a  thorough 
confirmation  of,  the  theory ;  for  details  the  reader  is  referred 
to  a  text-book  on  physical  chemistry. 

In  conclusion,  it  may  be  pointed  out  that  in  a  homogeneous 
system  the  equilibrium  relationships  between  different  kinds 


90     GENERAL   CONDITIONS   OF    EQUILIBRIUM.     CHAP. 

of  molecules  are  controlled  by  Guldberg  and  Waage's  law, 
whilst  the  equilibrium  relationships  of  one  kind  of  molecule 
between  two  phases  of  a  heterogeneous  system  are  determined 
by  the  law  of  distribution.  With  the  help  of  these  two  laws 
every  equilibrium  can  be  calculated.  They  have  been  of  im- 
mense service  in  the  investigation  of  dissociation  phenomena 
at  high  temperature,  and  we  shall  have  to  apply  them  later  in 
our  discussion  of  electrolytic  dissociation. 

Clapeyron's  Formula. — For  the  process  of  evaporation, 
Clapeyron,  in  1834,  making  use  of  Carnot's  theorem,  deduced 
the  following  connection : — 

dp  / 


In  this  formula  /  is  the  heat  of  vaporisation  of  one  gram  of 
the  liquid,  T  is  the  absolute  temperature,  and  V  and  V\  are  the 
volumes  of  one  gram  of  the  vapour  and  liquid  respectively. 

It  is  easy  to  alter  this  formula  so  that  it  applies  to  a 
gram-molecule.  If  we  multiply  numerator  and  denominator 
of  the  expression  by  the  molecular  weight  M  of  the  substance, 
we  obtain  in  the  numerator  M  x  I  =  X,  the  molecular  heat 
of  vaporisation,  and  in  the  denominator  (M V  —  MV\)  = 
v  —  I/-!,  the  difference  between  the  molecular  volumes  of  the 
vapour  and  the  liquid.  Therefore— 

dp  X 

~dT  =  ~(v~ 


We  have  already  (p.  48)  made  use  of  the  formula  in 
this  form.  If  the  temperature  be  sufficiently  removed  from 
the  critical  temperature,  it  is  always  permissible  to  neglect 
the  molecular  volume  vi  of  the  liquid  compared  with  that  v  of 
the  gas,  and  by  introducing  at  the  same  time  pv  =  ET  we 
obtain — 

d$_       _X 

pdT  ~  ET2 

or-  d  ln  p  -    — 

dT        '  ET1' 


vi.  CHANGE    OF   SOLUBILITY.  91 

Change  of  Solubility  with  Temperature.— It  has  been 
shown  that  the  solution  of  a  substance  corresponds  exactly 
with  the  vaporisation  of  a  liquid  into  a  vacuum  if  the  osmotic 
pressure  be  introduced  in  place  of  the  vapour  pressure ;  conse- 
quently for  the  solution  there  must  be  a  connection  analogous 
to  that  expressed  by  the  Clapeyron  formula,  that  is — 

d  In  TT  A 


dT      ~  iRT 

where  TT  is  the  osmotic  pressure  of  the  saturated  solution  and 
i,  as  before,  denotes  the  coefficient  which  occurs  in  the 
formula  w  V  —  iRT  for  the  osmotic  pressure.  If  we  replace 

V,  the  volume,  by  -^  >  the  reciprocal  of  the  concentration,  we 

obtain — 

TT  =  iCRT, 

and  from  this  we  further  obtain — 

d  In  TT  =  rf(ln  C+lu  T)  =  d  In  C  +  ~\ 
one  step  more  leads  to — 

d  In  C       A  -  iRT          AI 


dT  iRT* 

A  denotes  the  heat  which  is  taken  up  when  a  gram- 
molecule  of  liquid  passes  into  gas  at  constant  pressure,  i.e. 
with  increase  of  volume,  and  the  external  work  done  amounts 
to  iRT  =  2iT  (see  p.  76).  On  the  other  hand,  for  the 
solution  we  consider  the  heat,  Ai,  which  is  required  when  the 
process  takes  place  without  doing  external  work,  i.e.  at 
constant  volume.  During  the  solution  the  volume  of  the 
liquid  is  not  appreciably  altered. 

Now, 

Ai  =  A  -  iRT, 

i.e.  the  heat  of  vaporisation  or  of  solution  at  constant  volume 
differs  from  that  at  constant  pressure  by  the  amount  of  the 
external  work  done. 


92     GENERAL   CONDITIONS  OF   EQUILIBRIUM.     CHAP. 

This  connection  between  the  heats  under  the  different 
conditions  was  tested  by  van't  Hoff  (11),  and  was  found 
to  be  experimentally  confirmed,  as  the  numbers  in  the 
following  table  show  : — 


Substance. 

Temperature. 

t           ti 

Solubility. 

S                     Sj 

Heat  of  solution, 
obs.       calc. 

I 

Succinic  acid  
Benzole  acid    

0 

0 
4-5 
12-5 
0 
0 
15-6 
0 
16 
0 
1 
0 
0 
0 
0 
0 
0 
10 

o 

8-5 
75 
81 
10 
12 
54-4 
10 
35 
18 
45 
10 
10 
9-4 
15-4 
10 
9 
50 

2-9 
0-182 
0-16 
5-2 
1-95 
0-13 
1-5 
3-1 
4-23 
7-1 
2-2 
4-6 
3 
3-3 
2-83 
5-2 
6-6 

4-22 
2-193 
244 
8-0 
2-92 
0-103 
2-22 
3-6 
3-0 
10-2 
3-1 
7-4 
4-05 
6-03 
4-65 
7-0 
11-8 

6-7 
6-5 
8-5 
8-5 
5-6 
-2-8 
15-2 

o-i 

-2-8 
2-1 
9-6 
17 
20-2 
10 
25-8 
9-4 
3 

6-5 
6-7 
8-9 
8-2 
5-2 
-2-8 
16-3 
0-7 
-3-3 
1-4 
9-8 
17-3 
21-9 
11 
27-4 
8-8 
3 

•25 

2-6 
2-7 

1-8 
2-36 
4-5 
1-8 
3-6 
2-2 
1-1 

Salicylic  acid  . 

Oxalic  acid  
Boric  acid   . 

Lime  . 

Barium  hydroxide    .     .     . 
Aniline   

Amyl  alcohol  
Phenol 

Potassium  oxalate  (acid)  . 
Potassium  bichromate  .     . 
Alum  

Potassium  chlorate  .     .     . 
Borax     ... 

Barium  nitrate    .... 
Mercuric  chloride    .     .     . 

In  the  first  column  is  given  the  substance  experimented 
upon ;  under  t  and  t\  two  temperatures  at  which  the  solu- 
bilities s  and  si  were  determined  (the  solubility  being 
expressed  in  percentage).  Strictly,  the  solubility  should  be 
measured  in  grams  per  100  c.c.,  but  the  values  which  would  be 
obtained  in  this  way  do  not  differ  much  from  those  contained 
in  the  table,  especially  in  those  cases  where  the  solubility  is 
small.  The  heats  of  solution  are  given  in  large  calories  (1 
Cal.  =  1000  cal.) ;  the  observed  values  are  mostly  those 
found  by  Thomsen,  and  the  calculated  values  are  those 
obtained  by  van't  Hoff  according  to  the  above  law.  Under 
i  is  given  the  value  for  the  various  substances  at  con- 
centration — ^— ^  and  temperature  — ~ — - .  As  is  evident,  the 

agreement  between  the  observed  and  the  calculated  heats  of 
solution  is  eminently  satisfactory. 


vr.     CHANGE    OF   HOMOGENEOUS   EQUILIBRIUM.     93 
When  the  formula  is  integrated  we  obtain— 

i     1       VJ:       L 
Q 


or  —  U\  =  Oqe 

Since  r0Ti  for  a  small  temperature  interval  changes  but 
little,  and  the  variations  of  Xi  and  i  are  not  great,  we  may 
write  with  sufficiently  close  approximation  — 


where  A   represents  •—.  •  ™-™-   and   t\  —   £o  (  =  ^  i  —  ^o)  is 

^sfc      -/O-^l 

reckoned  in  Celsius  degrees.  The  concentration  of  a  saturated 
solution  therefore  increases  with  rise  of  temperature  approxi- 
mately proportionally  to  an  exponential  function,  so  that  the 
solubility  increases  almost  in  the  same  ratio  between  0°  and 
5°  as  between  5°  and  10°,  between  10°  and  15°,  etc.  Attention 
was  first  called  to  this  peculiarity  by  Nordenskiold  (12). 

Change  of  Homogeneous  Equilibrium  with  the 
Temperature.  —  Precisely  the  same  relationships  exist  in  the 
case  of  equilibria  between  a  mixture  of  vapours  and  liquids  as 
between  a  liquid  and  its  vapour.  As  already  pointed  out, 
the  volume  of  the  liquid  does  not  enter  into  the  formula  on 
account  of  ijbs  comparative  smallness.  Let  us  consider  the 
equilibrium  which  exists  in  a  mixture  of  ammonium  chloride 
vapour,  ammonia,  and  hydrochloric  acid,  the  partial  pressures 
of  which  are  p&  p\,  and  p^  If  a  change  of  temperature  takes 
place,  the  change  of  equilibrium  — 

NH4C1$NH3+  HC1 

produced  is  regulated  by  the  above  connection.  It  must, 
however,  be  observed  that  a  gram-molecule  of  ammonium 
chloride  disappears  when  a  gram-molecule  of  ammonia  and 
one  of  hydrochloric  acid  are  formed.  Van't  Hoff  's  application 
(IS)  of  the  Clapeyron  formula  to  this  case  gives  — 

d  In  pi   .   d  In  p%  __  d  In  p3 
dT        ~dT~         AT 


94     GENERAL   CONDITIONS  OF   EQUILIBRIUM.     CHAP. 

where  /x  denotes  the  heat  absorbed  when  a  gram-molecule  of 
ammonium  chloride  is  transformed  into  a  mol  of  ammonia 
and  a  mol  of  hydrochloric  acid.  The  condition  for  the 
applicability  of  this  equation  is  that  the  pressure  remains 
constant  ;  if  the  change  takes  place  at  constant  volume,  then, 
as  in  the  case  of  solutions,  we  may  introduce  the  concentra- 
tions (C)  instead  of  the  pressures,  and  obtain  — 

d(jp.  Ci  +  In  C9  -  In  C3)  _   jj_ 
dT 


dT          RT* 
We  know  that  at  constant  temperature — 
C\C%       v 

~w 

We  therefore  have  for  the  change  of  K  with  change  of 
temperature — 

dlnK          UL 
~dT 

or  integrated — 


where  M  is  a  constant,  or  finally— 


In  general,  for  a  reaction  which  takes  place  according  to 
the  chemical  equation  — 


we  have  the  equilibrium  equation— 

im        ~H        x-^o  -r         if 


vi.     CHANGE  OF  HOMOGENEOUS    EQUILIBRIUM.      95 

where  Kis  a  constant  and  CP,  C<t,  etc.,  denote  the  concentra- 
tions (or,  more  strictly,  the  osmotic  pressures)  of  the  substances 
P,  Q,  etc.  Further,  if  ^  cal.  are  absorbed  when  m  mols  of 
substance  Pt  n  mols  of  substance  ft  etc.,  reac£  to  form /mols 
of  substance  S,  etc.,  then,  provided  that  the  volume  does  not 
change  much  with  the  temperature,  we  obtain  for  the  change 
of  the  constant  K  with  the  temperature  the  same  formula  as 
in  the  above  special  case— 


or- 


log  K  —   9.on9-  •   p(  m  TJ  +  Ml 


when  M  and  i/i  are  two  integration  constants,  which  give  the 
value  of  In  K  and  log  K  at  temperature  TQ.1  Since  JJL  is 
expressed  in  calories,  the  value  of  R  is  1/99. 

When  n  is  positive,  i.e.  when  in   the  reaction   heat  is 

absorbed,  and  TI  'is  greater  than  T0,  (  ^  -  ->_- )  is  evidently 

\2l          Jo7 

negative,  and  In  K  greater  than  M,  indicating  that,  with  rising 
temperature,  the  concentrations  CP,  Cv  etc.,  dimmish,  whilst 
the  concentrations  Cst  CT,  etc.,  increase.  From  this  we  can 
draw  the  following  general  conclusion,  which  is  applicable 
both  to  heterogeneous  and  homogeneous  systems : — 

In  cm  equilibrium  that  system  of  substances,  the  formation 
of  wliick  is  accompanied  ly  an  absorption  of  heat,  increases  with 
rising  temperature. 

Some  examples  illustrating  this  very  important  generali- 
sation may  be  given.  When  a  substance  is  melted,  heat  is 
absorbed,  therefore  the  melted  portion  must  increase  when 
the  temperature  is  raised. 

As  in  this  case  the  system  is  a  condensed  one,  if  the 
pressure  is  kept  constant,  the  transition  takes  place  suddenly 
when  the  melting  point  is  passed.  In  the  same  way  heat  is 
absorbed  when  vaporisation  takes  place  ;  consequently,  if  in 
a  vessel  there  is  an  equilibrium  between  water  and  vapour, 

1  This  signification  of  M  and  MI  is  seen  if  TI  be  set  equal  to  T0. 


96     GENERAL    CONDITIONS   OF    EQUILIBRIUM.     CHAP. 

the  quantity  of  the  vapour  must  increase  at  the  expense  of 
the  water  when  the  temperature  is  raised.  Most  substances 
dissolve  in  water  with  an  absorption  of  heat,  and  in  these 
cases  the  solubility  must  increase  as  the  temperature  rises. 
Lime  and  many  of  the  calcium  salts,  amyl  alcohol,  and  other 
substances,  behave  in  the  opposite  way,  because  heat  is 
evolved  when  they  are  dissolved  in  water.  As  the  decompo- 
sition of  ammonium  chloride  into  ammonia  and  hydrochloric 
acid  is  accompanied  by  an  absorption  of  44,500  cal.,  the 
dissociation  of  this  must  increase  with  the  temperature.  If 
in  the  above  formula  we  set  T  =  0,  we  find  that  In  K  =  oo  , 
i.e.  one  of  the  concentrations,  C8,  CT)  or  CY)  must  be  zero.  At 
the  absolute  zero,  therefore,  the  substances  must  so  react  that 
the  system  which  is  formed  with  absorption  of  heat  passes 
as  completely  as  possible  (until  one  of  the  reacting  substances 
is  fully  used  up)  into  the  opposite  system.  At  the  absolute 
zero,  therefore,  the  assertion  of  the  older  thermochemists, 
that  that  reaction  occurs  which  is  accompanied  by  an  evolu- 
tion of  heat,  is  quite  correct.  For  the  ordinary  temperature, 
which  indeed  does  not  lie  very  high  above  the  absolute  zero, 
most  of  the  reactions  examined  do  take  place  according  to 
that  view,  but  numerous  exceptions  are  known.  The  assump- 
tion may,  therefore,  be  of  use  to  a  certain  extent  in  indicating 
what  direction  a  reaction  will  probably  take  at  normal 
temperature. 

Maxima  and  Minima  in  Equilibria. — It  is  to  be 
observed  that  the  heat  of  transformation  p  often  changes 
with  the  temperature.  The  connection  between  the  heat  of 
vaporisation  of  water  at  constant  pressure,  Qp  and  the  tem- 
perature can  be  represented,  according  to  Kegnault,  by  the 
formula  (for  1  gram) — 

Qp  =  606-5  -  0-695  t  cal. 

If  we  transform  this  formula  so  as  to  make  it  apply  to  a 
gram-molecule,  and  to  the  absolute  temperature,  we  obtain — 

HP  =  (10,917  -  12-51  t)  =  (14,332  -  12-51  T)  cal. 
Let  us  assume  that  the  vapour  is  evolved  in  a  closed 


vi.          MAXIMA   AND    MINIMA   IN    EQUILIBRIA.          97 


space,  then  no  work  is  done.  As  Kegnault's  formula  refers 
to  constant  pressure,  the  heat  of  vaporisation  p,  at  constant 
volume  must  be  smaller  by  2T  cal.  (see  p.  91),  i.e. — 

H.  =  (14,332  -  14-51  T)  cal. 


According  to  this  formula  the  heat  of  vaporisation  should 

As  a 


14332 
be  equal  to  0  at  temperature  T  =  ..  ,.„..  =  715°  C. 


14-51 

matter  of  fact,  the  heat  of  vaporisation  becomes  equal  to  0 
at  a  much  lower  temperature,  namely,  at  the  critical  tempe- 
rature, which  is  about  365°  C. 

Sometimes  the  sign  of  the  value  of  p  becomes  changed  at 
a  particular  temperature.  In  such  cases  the  system  possesses 
either  a  maximum  or  a  minimum.  According  to  the  investiga- 
tions of  Etard  and  Engel  (IJj),  this  behaviour  is  shown  by  the 
solubility  of  the  sulphates,  and  at  high  temperatures  by  salts 
in  general.  Thus,  ferrous  sulphate  has  a  maximum  solubility 
at  63°,  zinc  sulphate  at  82°,  nickel  sulphate  at  122°,  and 
copper  sulphate  at  130°.  At  the  temperature  at  which  this 
occurs  it  is  frequently  found  that  a  change  takes  place  in  the 
solid  whereby  water  of  crystallisation  is  lost,  and  two  different 
salts  are  present,  the  solubility  curves  of  which  cut  each 
other.  Thus,  at  34°  sodium  sulphate  passes  from  the  modi- 
fication Na2S04  +  10H20  (the  ordinary  crystallised  Glauber 
salt)  into  the  anhydrous  salt 
Na2S04.  The  former  dis- 
solves in  water  with  absorp- 
tion of  heat  (18,760  cal. 
according  to  Thomsen),  the 
latter  with  a  slight  evolu- 
tion of  heat  (4600  cal.).  As 
the  temperature  rises,  the 
solubility  of  the  former  salt 
increases,  as  the  diagram 
(Fig.  20)  shows,  and  that  of 

the  latter  salt  diminishes ;  this  gives  rise  to  an  (apparent) 
maximum  solubility  of  Glauber  salt  at  34°.  If  we  may 


FIG.  20. 


98     GENERAL   CONDITIONS   OF   EQUILIBRIUM.     CHAP. 

judge  by  the  curves  given  by  Etard  and  Engel,  which  all 
show  sharp  breaks,  the  maximum  solubilities  of  the  other 
salts  are  to  be  attributed  to  the  same  cause. 

A  true  maximum  in  an  equilibrium  has  been  proved  by 
Troost  and  Hautefeuille  (15)  for  the  dissociation  of  silicon 
chloride,  and  by  Ditte  (16)  for  the  dissociation  of  hydrogen 
selenide.  In  these  cases  it  must  be  assumed  that  the 
quantity  of  heat  which  is  absorbed  by  the  splitting  up  of 
the  compound  is  at  first  positive,  then  at  the  maximum 
dissociation  it  changes  its  sign,  so  that  at  higher  tempera- 
tures the  decomposition  is  accompanied  by  an  evolution  of 
heat. 

More  recently  an  interesting  example  of  a  true  recurring 
point  has  been  found  by  Kniipffer  (17)  in  the  reaction  — 


T1C1  +  KSCN  aq  $  T1SCN  +  KC1  aq 

solid.  solid. 

at  32°. 

The  reaction  expressed  by  the  equation  — 

PbI2  +  K2S04  $  PbS04  +  2KI 

solid.         dissolved.  solid.  dissolved. 

has  been  investigated  by  A.  Klein  (18)  ;  the  electrical  measure- 
ments show  that  below  8°  the  reaction  is  endothermic,  i.e.  is 
accompanied  by  an  absorption  of  heat,  and  above  8°  it  is 
exothermic,  i.e.  takes  place  with  evolution  of  heat. 

The  phenomenon  that  a  chemical  reaction  at  a  sufficiently 
high  temperature  sometimes  take  place  in  the  opposite  direc- 
tion to  that  in  which  it  proceeds  at  the  ordinary  temperature 
is  of  the  greatest  importance  in  chemistry.  Substances  which 
are  not  stable  at  the  ordinary  temperature  may  be  formed  at 
high  temperature,  and  in  the  same  way  substances  may  be 
formed  at  low  temperature  which  at  the  normal  temperature 
decompose  with  absorption  of  heat. 

Influence  of  Pressure.—  Besides  the  temperature  we 
must  also  take  into  consideration  the  pressure  when  dis- 
cussing the  condition  of  a  substance.  As  regards  the  influence 
of  pressure  the  following  statement  is  quite  general  — 


vi.  INFLUENCE   OF   PRESSURE.  99 

Diminution  of  pressure  favours  the  formation  of  the 
system  with  the  greater  volume. 

At  0°,  and  under  a  pressure  of  1  atmo.,  water  and  ice 
are  in  equilibrium.  If  the  pressure  is  increased,  the  ice 
melts,  because  the  specific  volume  of  the  melted  water  is 
smaller  than  that  of  the  ice.  Usually,  however,  a  substance 
when  fused  has  a  greater  volume  than  the  same  substance  at 
the  same  temperature  in  the  solid  state.  Consequently  in 
most  cases  the  melting  point  rises  with  increasing  pressure, 
as  Bunsen  (19)  proved  for  paraffin  and  spermaceti.  As  the 
pressure  is  increased  this  difference  in  volume  seems  to 
disappear,  because  in  the  liquid  state  the  substance  is  more 
compressible  than  when  solid.  It  is  therefore  not  improbable 
that  at  very  high  pressures  most  substances  would  behave 
like  water ;  as  Tammann  (20)  has  pointed  out,  at  a  certain 
pressure  the  fusion  is  not  accompanied  by  a  change  of 
volume. 

The  influence  of  pressure  on  the  solubility  of  salts  has 
been  studied  by  F.  Braun  (21),  and  has  been  found  to  be  in 
agreement  with  the  theory.  Generally  the  influence  of 
pressure  on  the  equilibrium  is  only  very  small,  as  we  are 
not  in  a  position  to  apply  excessively  high  pressures.  It 
is  otherwise,  of  course,  when  we  consider  the  relationships  in 
the  interior  of  the  earth  or  of  the  sun,  where  the  pressure,  on 
account  of  its  enormously  high  value,  plays  an  extremely 
important  part. 


CHAPTER   VII. 
Velocity  of  Reaction. 

Formation  of  the  State  of  Equilibrium. — When  a  chemi- 
cal system  is  not  in  equilibrium  it  approaches  this  state  with 
a  greater  or  smaller  velocity.  Many  reactions  take  place  so 
very  quickly  that  their  course  cannot  be  followed,  whilst 
others  proceed  so  slowly  that  their  progress  is  not  detectable. 
The  influence  of  temperature  in  this  respect  is  very  great.  For 
the  establishment  of  an  equilibrium  in  a  mixture  of  hydrogen 
and  iodine  at  265°  several  months  are  required,  at  350°  about 
as  many  days,  and  at  440°  about  as  many  hours. 

An  explosive  mixture  of  hydrogen  and  oxygen  behaves 
in  precisely  the  same  way.  Above  580°  the  reaction  takes 
place  with  explosive  violence,  whilst  at  155°  it  proceeds  so 
slowly  that  it  is  only  after  months  that  combination  has 
taken  place  to  an  appreciable  extent  [V.  Meyer  (/)].  At 
the  normal  temperature  the  mixture  is  apparently  inactive, 
but  in  all  probability  this  is  not  the  case. 

The  following  reactions,  the  velocities  of  which  have 
been  most  fully  studied,  may  serve  as  typical  for  others  : 
the  inversion  of  cane  sugar  under  the  influence  of  acids, 
the  decomposition  of  ester  into  alcohol  and  acid,  and  the 
saponification  of  esters  with  bases. 

Inversion  of  Cane  Sugar. — The  course  of  the  inversion 
of  cane  sugar  was  first  followed  by  Wilhelmy  (2)  in  1850. 
He  found  that  the  quantity  of  sugar  inverted  in  unit  time  is, 
ceteris  paribus,  proportional  to  the  amount  of  sugar  in  the 
solution.  If  the  concentration  of  the  sugar  is  A  gram- 
molecules  (mols),  and,  after  time  t,  x  mols  are  inverted,  then 


CHAP.  vii.         INVERSION   OF   CANE   SUGAR. 


101 


at  this  point  of  time  there  are  in  the  solution  (A  —  x)  mols 
of  sugar.     The  quantity  dx  which  is  inverted  in  time  dt  is, 
according  to  Wilhelmy,  proportional  to  (A  —  x).    We  therefore 
have,  if  K  is  a  constant  — 
dx 


and  by  integration  we  obtain  — 


The  quantity  of  sugar  present  can  be  accurately  determined 
by  ascertaining  the  angle  through  which  a  definite  length  of 
the  solution  rotates  the  plane  of  polarised  light.  In  the 
next  table  is  given  under  t  the  time  in  minutes  since  the 
beginning  of  the  reaction,  under  a°  the  angle  of  rotation 
produced  by  the  solution  on  polarised  light,  and  the  third 
column  contains  the  constant  — 

-  1  A  *  x° 


which  is  the  specific  velocity  of  the  reaction.  The  original 
dextrorotation  of  the  solution  is  due  to  the  dextrorotatory 
cane  sugar,  and  this  passes  into  a  Isevorotation  when  the 
quantity  of  leevorotatory  invert  sugar  becomes  sufficiently 
great.  When  t  =  =*>  ,  i.e.  after  a  very  long  time,  the  inversion 
is  as  good  as  complete.  The  results  given  were  obtained  at 
25°  with  a  20  per  cent,  cane  sugar  solution,  which  was  also 
0'5-normal  with  respect  to  lactic  acid  — 


t 

o 

K 

0 

34-50 

1435 

31-10 

0-2348 

4315 

25-00 

2359 

7070 

20-16 

2343 

11360 

13-98 

2310 

14170 

10-61 

2301 

16935 

7-57 

2316 

19815 

5-08 

2291 

29925 

-1-65 

2330 

r/^ 

-1077 



loz  VELOCITY   OF   REACTION.  CHAP. 

Saponification  of  an  Ester.  —  Since  in  the  reaction  just 
considered  the  quantity  of  one  of  the  reacting  substances 
remains  constant,  the  concentration  of  only  one  kind  of 
molecule  changes,  corresponding  with  the  given  equation  — 


Van't  Hoff  terms  such  reactions  monomolecular.  Chemical 
reactions  in  which  two  of  the  reacting  substances  disappear 
in  the  course  of  the  action  are  much  more  common.  The 
best  known  example  of  such  a  limoleeular  reaction  is  the 
saponification  of  an  ester.  This  reaction  proceeds  according 
to  the  equation  — 

NaOH  +  CH3COOC2H5  =  CH3COONa  +  C2H5OH. 

If  we  start  with  equivalent  quantities,  A  mols  per  litre,  of 
the  two  substances,  then  after  time  t  the  same  quantity 
of  the  two  substances,  x  mols,  must  have  disappeared,  and 
there  will  remain  (A  —  x)  mols  of  each  in  a  litre.  Now,  the 
quantity  of  sodium  acetate  which  is  formed  in  unit  time  is 
proportional  to  the  concentration  of  the  ethyl  acetate  and 
that  of  the  sodium  hydroxide  ;  therefore  — 


from  which  by  integration  can  be  obtained — 
1  1 

-/X     """""    evQ  JuL     """    52j 

where  ^f,  a  constant,  represents  the  specific  velocity  of  the 
reaction. 

In  order  to  prove  the  validity  of  this  equation,  we  cite  the 
following  results  obtained  by  Madsen  (3)  in  the  investigation 
of  the  strengths  of  sugar,  dextrose,  and  levulose  as  acids. 
The  first  column  contains  the  time  in  minutes,  the  second  the 
concentration~bf  the  base  (2^0  ^-solution  being  taken  as  unit), 
and  the  third  the  constant  for  the  specific  velocity  of  reaction. 


viz.      VELOCITY   IN   HETEROGENEOUS   SYSTEMS.     103 

The  experiments  were  made  at  10'2°  with  solutions  which 
were  0'02485  normal  with  respect  to  ethyl  acetate  and  sodium 
hydroxide. 


t 

A-x 

K 

o-o 

4-60 

3-8 

3-98 

2-23 

7-3 

3-52 

2-28 

12-3 

3-03 

2-28 

16-3 

2-74 

2-28 

20-1 

2-53 

2-23 

24-0 

2-28 

2-28 

27-1 

2-17 

2-23 

Velocity  in  Heterogeneous  Systems. — In  the  preceding 
chapter  it  was  pointed  out  that  the  equilibrium  of  a  system 
of  molecules  is  to  be  regarded  as  "mobile."  The  state  of 
equilibrium  is  therefore  attained  in  a  chemical  system  when 
the  two  reactions  proceeding  in  opposite  directions  have  the 
same  velocity.  If  the  velocity  of  decomposition  of  the  ester 
be  represented  by  the  formula — 


dCL 


dt 


water 


alcohol      acid, 


the  equilibrium  constant  of  the  ester-hydrolysis,  K}  is  equal 
to  the  quotient  of  the  two  velocity  constants  — 


It  has  been  found  by  the  study  of  vaporisation  and  solution 
that  the  relationship  between  velocity  and  equilibrium  is  just 
as  simple  in  heterogeneous  systems. 

Equilibrium  is  attained  between  liquid  and  its  vapour 
when  the  maximum  tension  P  of  the  liquid  is  equal  to  the 
partial  pressure  p  of  its  molecules  in  the  vapour  space,  i.e. 
when  P  =  p.  The  rate  of  evaporation  is  at  every  moment 
proportional  to  the  difference  between  these  two  values,  i.e. 
it  is  equal  to  k(P  —  p). 

Noyes   and  Whitney  (4)  have   found   that   the  rate  of 


104  VELOCITY   OF    REACTION.  CHAP. 

solution  of  a  solid  substance  is  at  any  moment  proportional 
to  the  difference  between  the  concentration  C  when  the 
solution  is  saturated,  and  the  concentration  c  at  that  time 
i.e.  the  rate  is  equal  to  k(C  —  c). 

The  velocity  of  crystallisation  has  recently  been  studied 
by  Tammann  (5).  The  velocity  at  first  increases  with  the 
degree  of  super-cooling,  reaches  a  maximum,  then  by  further 
depression  of  the  temperature  decreases,  and  may  thereafter 
become  very  small.  H.  A.  Wilson  (6)  has  shown  that  the 
velocity  of  crystallisation  v  can  be  represented  by  the 
equation— 


v  =  K 


0o-  0 
V 


where  OQ  —  6  represents  the  super-cooling,  V  the  viscosity  of 
the  liquid,  and  K  a  constant. 

Influence  of  Temperature  on  the  Velocity  of  Reaction. 
— If  we  examine  the  influence  of  temperature  on  the  specific 
velocity  of  a  reaction,  e.g.  the  saponification  of  ethyl  acetate, 
we  find  that  it  can  be  approximately  represented  by  the 
formula  given  on  page  95  for  the  change  of  equilibrium. 
This  is  clearly  seen  from  the  results  given  in  the  following 
tables,  in  which  are  to  be  found :  t,  the  temperature  (Celsius) ; 
p  (observed),  the  observed  velocity  of  reaction ;  and  p 
(calculated),  the  value  calculated  according  to  the  formula 
mentioned : — 

SAPOXIFICATIOX  OF  ETHYL  ACETATE. 


t 

p  (observed). 

p  (calculated). 

o 

3-6 

1-42 

1-48 

7-2                 1-92 

(1-92) 

12-7                 2-87 

2-82 

19-3                4-57 

4-38 

23-G 

6-01 

5-78 

28-4                8-03 

7-81 

34-0 

10-92 

(10-92) 

37-7               13-41 

13-59 

vn. 


INFLUENCE   OF   TEMPERATURE. 


105 


LVVKKSION  OF  CANE  SUGAK. 


t 

p  (observed). 

p  (calculated). 

o 

25 
40 
45 
50 
55 

9-67 
73-4 
139-0 
268-0 
491-0 

(9-67) 
75-7 
144-0 
(268-0) 
491-0 

The  change  of  velocity  constant  with  the  temperature  is 
evidently  very  great.  The  velocity  of  saponification  is 
doubled  for  a  rise  of  10°,  corresponding  with  an  increase 
of  7  per  cent,  per  degree.  With  cane  sugar  the  increase  is 
even  greater,  for  a  rise  of  temperature  of  15°  causes  an 
increase  of  the  velocity  of  inversion  in  the  ratio  1  :  8  =  1  :  23  ; 
the  velocity  is  therefore  doubled  by  an  increase  of  temperature 
through  5°,  which  is  equivalent  to  an  increase  of  15  per  cent, 
per  degree.  As  is  evident  from  the  table,  the  increase  is 
smaller  at  high  temperatures  than  it  is  at  low  temperatures, 
and  this  is  as  would  be  expected  from  the  formula. 

Such  an  exponential  increase  with  the  temperature  as 
that  mentioned  is  scarcely  ever  met  with  for  any  other 
physical  phenomenon  except  evaporation.  A  cubic  centi- 
metre of  saturated  water  vapour  at  0°  contains  double  as 
much  water,  namely  4'9  grams,  as  the  same  volume  at  — 10° 
when  the  amount  is  only  2 '4  grams.  This  consideration  led 
me  to  construct  the  following  hypothesis  (7).  The  cane  sugar 
solution  contains  two  kinds  of  molecules,  one  sort  of  which 
can  be  attacked  (inverted)  by  the  acid,  the  other  sort  can  not. 
The  amount  of  the  former  sort  is  extremely  small  compared 
with  that  of  the  second,  and  both  are  in  equilibrium.  If 
we  denote  the  concentrations  of  the  two  kinds  by  c\  and  c% 
respectively,  we  obtain — 


C-2 


io6  VELOCITY   OF   REACTION.  CHAP. 

where  JJL  is  the  heat  which  is  absorbed  when  ordinary  sugar 
is  transformed  into  the  variety  which  can  be  attacked.  Since 
E,  expressed  in  calories,  is  equal  to  2,  we  calculate  for  cane 
sugar  JJL  =  25,640  cal.  per  grain-molecule.  The  corresponding 
number  for  ethyl  acetate  is  11,160  cal.  per  gram-molecule. 
According  to  this  hypothesis,  the  velocity  of  the  reaction 
should  be  directly  proportional  to  the  concentration  of  the 
molecules  which  can  be  attacked. 

This  view  is  supported  by  experiments  on  the  rate  of 
solution,  p,  of  zinc  in  dilute  (01-normal)  hydrochloric  acid. 
This  velocity  is  hardly  altered  by  change  of  temperature,  as 
is  shown  by  the  results  of  Ericson-Auren  (8)  contained  in  the 
following  table : — 


Temperature. 

p 

0 

9 

0-107 

16-5 

0-122 

23                 0-117 

28 

0-116 

32                 0-105 

40                 0-109 

50                 0-110 

In  this  case  the  velocity  of  reaction  is,  within  the 
experimental  error,  independent  of  the  temperature.  This 
can  be  explained  by  assuming  that  the  ordinary  zinc  mole- 
cules can  be  attacked,  or  are  "  active,"  or  that  the  heat  of 
transformation  of  the  inactive  into  active  molecules  is  zero. 
The  first  assumption  seems  the  more  probable. 

Eothmund's  results  (9)  on  the  influence  of  pressure  on 
the  velocity  of  reaction  are  in  good  agreement  with  the 
hypothesis. 

It  must  be  observed  that  at  higher  concentrations  of  the 
acid  the  temperature  has  a  very  great  influence  on  the  speed 
of  solution  of  zinc,  as  Guldberg  and  Waage  (10)  found. 
This  may  be  due  to  the  formation  of  a  layer  of  concentrated 
zinc  salt  solution  round  the  metal,  which  protects  it  from 
further  action  if  not  removed  by  agitation.  The  agitation  is 


VII. 


VELOCITY   OF   REACTION. 


107 


carried  out  by  the  gas  evolution ;  it  is  the  more  perfect  the 
greater  the  mobility  of  the  solution,  and,  as  is  well  known, 
this  last  factor  increases  with  the  temperature.  A  similar 
reasoning  can  be  applied  to  other  solution  processes. 

Velocity  of  Reaction  and  Osmotic  Pressure. — It  has 
been  shown  that  in  the  inversion  of  cane  sugar  the  quantity 
of  sugar  inverted  is  proportional  to  its  concentration  in 
the  solution.  This  follows  from  the  agreement  between  the 
calculated  values  and  those  found  by  Wilhelmy.  However, 
this  connection  is  only  exact  because  during  the  reaction 
invert  sugar  is  formed.  If  we  start  with  different  concentra- 
tions of  cane  sugar,  we  find  that  fbr  a  40  per  cent,  solution 
the  velocity  constant  is  more  than  double  that  for  a  20  per 
cent,  solution.  The  following  table  contains  the  results 
obtained  by  Ostwald  (11) : — 

INTENSION  OF  CANE  SUGAR  WITH  0'5-NonMAL  HC1. 


c 

p 

P 
u 

E 

p 

E 

40  per  cent. 

11-68 

0-292 

3-41 

3-43 

20    „ 

4-54 

0-227 

1-37 

3-32 

10 

2-07 

0-207 

0-612 

3-38 

4    „ 

0-768 

0-192 

0-228 

3-37 

The  table  contains  under  C  the  number  of  grams  of  sugar 
in  100  c.c.  of  solution,  under  p  the  velocity  of  reaction,  in  the 
third  column  the  ratio  of  these  two,  in  the  fourth  column  the 
depression  of  the  freezing  point  of  a  solution  of  the  given 
concentration,  and  in  the  last  column  the  ratio  between 
velocity  of  reaction  and  the  depression  of  the  freezing  point. 
This  latter  ratio  is  constant  throughout,  whilst  the  quotient 

-  is  entirely  dependent  on  the  concentration. 

G 

This  result  can  be  made  clear  by  a  kinetic  consideration 
of  the  matter.  The  osmotic  pressure  at  constant  temperature 
is  proportional  to  the  number  of  collisions  which  the  sugar 
molecules  make  with  the  sides  of  the  containing  vessel. 


io8  VELOCITY   OF    REACTION.  CHAP. 

(This  is  quite  evident  if  tlie  walls  consist  of  semi-permeable 
membranes  which  do  not  allow  the  sugar  to  pass  through.) 
On  the  other  hand,  there  is  a  proportionality  between  this 
number  and  the  number  of  collisions  of  the  sugar  molecules 
with  the  active  molecules  of  the  inverting  acid.  As  we  shall 
see  later,  it  is  the  hydrogen  ions  of  the  acid  which  must  be 
considered.  Now,  since  the  concentration  of  the  acid  is 
constant  during  the  experiment,  the  number  of  collisions 
between  sugar  molecules  and  acid  molecules  must  be 
proportional  to  the  osmotic  pressure  of  the  sugar.  It  has 
been  assumed  that  the  reaction  only  takes  place  when  an 
acid  molecule  meets  a  molecule  of  sugar  which  can  be 
attacked,  and  therefore  we  should  take  account  only  of 
the  osmotic  pressure  of  the  sugar  molecules  in  this  condition. 
It  is  clear  from  what  has  previously  been  said  (page  86), 
that  if  we  denote  the  osmotic  pressure  of  the  ordinary  sugar 
molecules  by  TTJ,  and  that  of  the  molecules  which  can  be 
attacked  by  ?ra,  then — 

KTT«  =  7r; 
or—  (K  -f  I)TT,(  =  TT;  +  TT,, 

where  K  is  a  constant,  i.e.  the  osmotic  partial  pressure  7ra  of 
the  molecules  which  can  be  attacked  stands  in  a  constant 
ratio  to  the  osmotic  pressure  TT*  -f  ira  of  all  the  sugar  mole- 
cules. From  this  it  follows  that  the  number  of  collisions 
per  second  between  active  molecules  of  acid  and  attackable 
molecules  of  cane  sugar  is  proportional  to  the  osmotic 
pressure  of  the  sugar.  Furthermore,  the  velocity  of  the 
reaction,  i.e.  the  quantity  of  substance  transformed  in  unit 
time,  must  be  proportional  to  the  number  of  such  collisions, 
and  consequently  to  the  osmotic  pressure  of  the  sugar — a 
conclusion  which  is  confirmed  by  experiment. 

It  would  appear,  therefore,  in  calculations  concerned  with 
the  velocity  of  reaction  to  be  more  correct  to  use  osmotic 
pressures  and  not  concentrations,  in  the  same  way  as  has 
been  pointed  out  for  equilibria.  The  above  example  shows 
that  using  the  former  (theoretically  more  exact)  method 


vii.  ACTION    OF   NEUTRAL    SALTS.  109 

correct  results  are  obtained,  whilst  deviations  amounting  to 
as  much  as  40  per  cent,  occur  when  use  is  made  of  the 
concentrations.  It  has  been  found  for  the  majority  of  re- 
actions ,that  the  velocity  increases  more  quickly  than  it  should 
do  on  the  assumption  that  it  is  proportional  to  the  concentra- 
tion. The  osmotic  pressure  shows  the  same  behaviour,  but 
a  thorough  investigation  of  the  connection  between  these  two 
phenomena  has  not  yet  been  made. 

Action    of   Neutral    Salts. — The    specific  velocity  of 

reaction  ^  of  a  10  per  cent,  solution  of  cane  sugar  which 

\j 

contains  10  per  cent,  of  invert  sugar,  is  the  same  as  that  of  a 
20  per  cent,  solution  containing  no  invert  sugar  (p.  101).  But 

for  a  20  per  cent,  cane  sugar  solution  -~  is  ITlf  =  oTpr) 

times  as  great  as  for  a  10  per  cent,  solution  when  no  invert 
sugar  is  present.  The  relative  speed  of  reaction  is  therefore 
increased  by  no  less  than  11  per  cent,  by  the  presence  of  10 
per  cent,  of  invert  sugar.  It  has  been  found  that  the  addition 
of  0*4  gram-molecule  of  sodium  chloride  increases  the  speed 
of  inversion  by  26  per  cent.  Other  salts  exert  a  similar 
action.  Tammann  (12)  found  that  a  solution  which  contained 
cane  sugar  and  copper  sulphate  had  an  osmotic  pressure 
greater  than  the  sum  of  the  osmotic  pressures  of  the  cane 
sugar  without  the  copper  salt  and  of  the  copper  sulphate 
without  the  sugar.  It  is  therefore  probable  that  the  osmotic 
pressure  of  the  sugar  is  increased  by  the  presence  of  foreign 
substances  in  the  solution. 

This  gives  us  a  probable  explanation  of  the  phenomenon 
which  has  been  recognised  for  a  long  time,  namely,  that  the 
specific  velocity  of  reaction  is  increased  by  the  addition  of 
foreign  substances  (the  so-called  action  of  neutral  salts, 
because  the  salts  were  first  investigated  in  this  connection). 


CHAPTER   VIII. 
Electrolytes.    Electrolytic  Dissociation. 

Deviations  shown  by  Electrolytes  from  van't  HofTs 
Law. — In  the  preceding  chapters  a  short  sketch  has  been 
given  of  the  laws  which  obtain  for  substances  in  solution. 
Attention  has  been  called  to  the  fact  that  many  substances 
behave  in  accordance  with  van't  Hoff's  law,  but  that 
salts,  strong  acids  and  bases  in  aqueous  or  alcoholic 
solution  exhibit  deviations.  These  substances  always  have 
an  osmotic  pressure  which  is  too  high,  whether  this  be  found 
from  the  depression  of  vapour  pressure  or  freezing  point,  or 
from  the  raising  of  the  boiling  point.  These  substances,  too, 
are  of  very  great  interest,  both  in  a  chemical  respect  on 
account  of  their  applications  in  analytical  chemistry,  and  in 
a  physical  respect  because  of  their  conducting  the  electric 
current  and  being  at  the  same  time  decomposed. 

Since  electrical  measurements  are  the  sharpest  and  most 
exact  known  in  physical  science,  it  was  to  be  expected  that 
a  complete  electrical  examination  of  these  substances  would 
throw  some  light  on  their  nature  and  peculiarities.  As  a 
matter  of  historical  fact,  the  electrical  examination  led  to  the 
same  point  as  van't  Hoff's  osmotic  investigations,  and  it  was. 
only  after  the  two  studies  were  considered  together  that  the 
problem  of  the  nature  of  solutions  was  satisfactorily  solved. 

Faraday's  Experiments. — We  have  already  referred  to 
Grotthuss'  views,  according  to  which  the  molecules  in  an 
electrolytic  (i.e.  salt)  solution  arrange  themselves  into  a 
sort  of  chain  between  two  metallic  plates  connected  with 


CHAP.  viii.  FARADAY'S    EXPERIMENTS.  1 1 1 

the  poles  of  a  battery  and  immersed  in  the  solution.  It  was 
supposed  that  the  oppositely  charged  constituents  of  the 
nearest  salt  molecules  were  attracted  by  the  electrodes — for 
instance,  in  a  solution  of  potassium  chloride  the  chlorine  was 
attracted  by  the  positive  pole  and  the  potassium  by  the 
negative  pole. 

It  was  assumed  that  the  electrical,  decomposing  force  was 
only  active  near  the  poles,  and  that  it  decreased  greatly  with 
increasing  distance  from  the  poles,  just  as  was  assumed  in  the 
case  of  all  forces  which  were  regarded  as  actions  at  a  distance. 

Faraday,  who  strongly  opposed  the  conception  of  action 
at  a  distance,  showed  in  the  following  simple  way  that  the 
electrical  (electromotive)  force  is 
the  same  at  all  points  of  a  paral- 
lel-sided trough  through  which  a 
current  is  passing.  By  means  of 
the  wires  C  and  D  the  poles  of  the 
battery  B  are  connected  with  two 
poles  immersed  in  a  salt  solution  FIG.  21. 

contained  in  the  trough  T.     While 

the  current  is  passing  through  the  solution  two  strips  of 
platinum,  P  and  PI,  which  are  kept  at  a  fixed  distance  apart, 
are  dipped  into  the  solution.  These  strips  are  connected 
by  the  wires  r  and  s  with  a  galvanometer,  G-.  The  galva- 
nometer shows  a  deflection  indicating  that  a  current  is 
passing  in  the  direction  from  P  to  P\  through  G-,  and 
this  current  may  be  regarded  as  a  branch  of  the  main 
current  passing  through  the  trough  T.  It  is  found  that  the 
galvanometer-needle  shows  the  same  deflection  at  whatever 
point  between  the  poles  the  strips  P  and  PI  are  placed,  so 
long  as  a  line  joining  these  is  parallel  with  the  sides  of  the 
trough.  This  proves  that  the  electromotive  force  between  P 
and  PI,  which  causes  the  current  through  6r,  is  the  same  at 
all  points,  and  independent  of  the  distance  from  the  poles. 
Theoretically  the  experiment  is  simplest  when  the  solution 
used  is  one  of  zinc  sulphate,  and  the  -f  and  —  electrodes 
as  well  as  P  and  PI  consist  of  amalgamated  zinc,  because, 


i  1 2  ELECTROLYTES.  CHAP. 

as  will  be  later  shown,  no  appreciable  polarisation  then 
takes  place.  The  electrical  condition  in  the  trough  can  be 
graphically  represented  as  in  Fig.  22.  At  the  point  4-  the 
electric  potential  has  a  certain  value,  say  A ;  at  the  point  - 
it  has  a  lower  value,  say  J5;  consequently  the  (positive) 

electric  current  flows  in  the 
direction  from  A  to  B,  from 
higher  to  lower  potential.  The 
potential  at  any  point,  P,  be- 
tween +  and  —  is  found  by 
joining  the  end  points  of  A 
and  B,  and  erecting  at  P  a 
perpendicular  which  meets  the 

line  joining  A  and  B  at  R.  PR  then  gives  the  potential  at 
P.  In  the  same  way  P\R\  represents  the  potential  at  point 
PI,  and  the  difference,  d  V,  of  the  potentials  PR  and  P\R\  at 
points  P  and  PI  is  evidently  the  same  throughout,  so  long  as 
the  distance  PPi  is  kept  constant,  because  d  V  =  PPi  tan  a, 
where  a  is  the  inclination  of  the  line  joining  A  and  B  to  the 
abscissae-axis.  The  potential  difference  dV  produces  the 
current  dl  in  the  galvanometer ;  according  to  Ohm's  law — 

IT      dv 
dI-:^ 

where  M  is  the  resistance  in  the  circuit  PGP\.  Since  the 
resistance  M  does  not  vary,  and  d  V  is  the  same  throughout, 
it  is  evident  that  the  deflection  of  the  galvanometer-needle 
must  be  the  same  at  whatever  distance  from  the  poles  P  and 
PI  are  placed. 

Faraday  further  showed  that  chemical  decomposition  may 
also  take  place  without  metallic  poles. 
He  connected  a  point,  A  (Fig.  23),  with 
the  negative  pole  of  an  electrical  ma- 
chine, and  allowed  negative  electricity 
to  stream  from  this  against  a  strip  of 
FIG.  23.  paper,  P,  which  was  moistened  with  a 

solution  of  sodium  sulphate,  made  red 
with  litmus,  and  which  connected  with  the  positive  pole  B 


vin.  THE   IONS.  113 

of  the  machine.     After  some   time  the  paper  became  blue 
immediately  below  A,  proving  that  alkali  had  been  formed. 

A  similar  experiment  described  by  Gubkin  (1)  is  carried 
out  as  follows : — A  solution  of  copper  sulphate  is  placed 
under  A,  and  a  wire  from  B  passes  into  the  solution. 
When  the  negative  electricity  has  passed  across  for  some 
time,  a  thin  film  of  copper  is  formed  on  the  surface  of  the 
solution  just  below  A. 

Faraday  proved,  too,  that  chemical  decomposition  by  an 
electric  current  may  take  place  at  a  considerable  distance 
from  the  poles.  A  layer  of  pure  water  was  placed  over  a 
solution  of  magnesium  sulphate,  and  an  electric  current  was 
passed  from  a  positive  pole  at  the  bottom  of  the  solution  to 
a  negative  pole  near  the  surface  of  the  water ;  it  was  found 
that  a  precipitation  of  magnesium  hydroxide  took  place  at 
the  surface  of  separation  of  the  solution  and  water.  (This 
experiment  was  later  studied  more  completely,  and  explained, 
by  F.  Kohlrausch.) 

The  Ions. — Faraday  assumed  that  the  ions  were  held 
together  in  the  molecule  by  chemical  forces,  and  that, 
further,  the  positive  ion  of  one  molecule  was  attracted  by  the 
negative  ion  of  another  molecule.  This  latter  attraction, 
acting  in  conjunction  with  the  electric  force,  was  sufficient 
to  overcome  the  attraction  within  the  molecule. 

Faraday,  however,  was  astonished  to  find  that  those 
substances,  like  potassium  or  sodium  chloride,  or  salts  in 
general,  which  are  the  bes.t  conductors,  are  those  in  which 
the  ions  were  supposed  to  be  most  firmly  bound  in  the 
molecule.  If  all  the  molecules  were  really  held  together  in 
the  form  of  a  Grotthuss  chain  so  that  a  certain  force  would 
be  necessary  to  break  it,  then  a  certain  electromotive  force 
would  be  required  before  electrolysis  could  take  place. 
Apparently  this  is  really  the  case,  because  polarisation  often 
occurs  at  the  electrodes. 

If,  however,  the  electrodes  consist  of  unpolarisable  metals, 
i.e.  of  the  same  metal  as  the  positive  ion  of  the  salt, 
during  the  passage  of  the  electric  current  the  electrodes  are 

I 


ii4  ELECTROLYTES.  CHAP. 

not  altered,  and  a  current  can  be  obtained  by  using  the 
smallest  conceivable  electromotive  force.  Even  when  work- 
ing with  polarisable  electrodes  it  is  only  in  order  to  transport 
the  electricity  from  the  electrode  to  the  solution,  or  vice  versa, 
that  a  certain  electromotive  force  is  required.  In  this  case 
also  the  smallest  fall  of  potential  is  sufficient  to  cause  a 
current  in  the  liquid.  This  fact  was  proved  by  Buff  (2)  with 
currents  so  small  that  it  was  only  after  months  that  a  cubic 
centimetre  of  explosive  mixture  was  obtained. 

According  to  this,  the  very  smallest  force  is  sufficient  to  * 
split  the  molecules  in  the  Grotthuss  chain.  The  behaviour  of 
gases  indicates  what  the  relationships  would  be  if  the  mole- 
cules of  electrolytes  were  undecomposed.  In  order  to  keep 
a  constant  electric  current  passing  through  a  gas  a  certain 
fall  of  potential  per  centimetre  is  necessary,  and  this  is 
dependent  on  the  pressure  of  the  gas. 

Faraday's  view  is  therefore  incorrect.    The  radicles  of  the  > 
salt  molecule  cannot  be  held  together  by  a  force  of  finite/ 
value.     This  was  first  appreciated  by  Clausius  (1857),  who  ' 
was  led  to  the  assumption  that  in  a  solution  of  an  electrolyte 
a  constant  exchange  of  ions  is  taking  place  between  the  mole- 
cules, or  that,  in  special  exceptional  cases,  free  ions  occur. 
According  to  this   view  the  electrolyte  is  "  electrolytically 
dissociated"  into    its  ions,  although   these   are    present  in 
such  small  quantity  as  not  to  be  recognisable  by  chemical 
tests.     Clausius  arrived  at  these  conclusions  by  the  following 
considerations :   According  to  the  kinetic  theory  heat  is  due     h 
to  the  rapid  motion  of  the  molecules,  and  on  the  average  the 
kinetic   energy  of  a  gram-molecule   of  every  kind  of  gas     p 
molecule  is  the  same.     This  motion  is  very  great ;  at  20°  the 
velocity   of    an   oxygen  molecule   is   425   metre/sec.,   of  a 
hydrogen  molecule  1700  met./sec.,  and   of  a  molecule  of 
water  vapour  566  met./sec. 

It  may  be  incidentally  mentioned  that  a  consequent 
development  of  the  kinetic  theory  leads  to  the  view  that  the 
velocity  of  dissolved  molecules  is  about  as  great  as  that  of 
gaseous  molecules,  because  the  osmotic  pressure  is  about  as 


VIII. 


THE   IONS. 


great  as  the  gas  pressure  at  the  same  temperature,  the  osmotic 
pressure  being  due,  to  the  impacts  of  the  dissolved  molecules 
against  the  semi-permeable  membrane.  For  dissolved  oxygen 
in  aqueous  solution  at  20°  the  velocity  of  the  molecule  is 
therefore  also  425  met/see. 

The  dissolved  molecules  collide  with  the  molecules  of  the 
solvent,  and  ultimately  the  mean  value  of  the  kinetic  energy 
per  gram-molecule  will  be  the  same  for  each.  The  velocity 
of  the  liquid  molecules  of  the  solvent  must  be  the  same  as 
that  in  the  gaseous  state,  therefore  the  velocity  of  water 
molecules  in  both  conditions  will  be  566  met. /sec.,  and  the 
molecules  of  the  solid  should  have  the  same  velocity.  The 
mean  velocity  increases  proportionally  to  the  square  root  of 
the  absolute  temperature. 

Now,  all  molecules  of  one  species  do  not  possess  the  same 
velocity ;  thus,  all  water  molecules  at  20°  do  not  have  the 
velocity  566  met. /sec.,  but  this  number  represents  the  average 
value  (1  in  Fig.  24),  and  most  of  the  velocities  lie  near  this 
(Maxwell).  Velocities  ranging  from  0  to  very  high  values 
occur.  However,  the  further  any  particular  velocity  is  from 
the  mean  value  the  smaller  is  the  number  of  molecules  which 
possess  this  velocity,  as  is  shown  in  the  accompanying 
diagram.  Amongst  the  water  molecules  there  are  therefore 
to  be  found  some  with  a 
velocity,  e.g.  3  times  as  great 
as  the  mean  velocity,  and 
this  corresponds  with  the 
mean  velocity  at  a  tempera- 
ture 9  times  higher  than  the 
temperature  in  question  (273 
+  20°),  i.e.  at  the  tempe- 
rature 2364°.  At  this  high 
temperature  water  is  partially 
dissociated  into  hydrogen 

and  oxygen  molecules,  which  indicates  that  the  water  mole- 
cules cannot  withstand  the  rapid  motion  at  this  temperature 
without  partly  decomposing.  A  small  part  of  the  water  at 


FIG.  24. 


n  6  ELECTROLYTES.  CHAP. 

the  ordinary  temperature  (20°)  must  therefore  be  decomposed 
(dissociated)  into  hydrogen  and  oxygen  molecules.  According 
to  the  method  of  Helmholtz  (3)  it  can  be  calculated  that, 
taking  3  x  1043  water  molecules,  two  are  dissociated  into 
2H2  and  O2. 

In  the  same  way  it  can  be  shown  that  all  possible  com- 
binations of  hydrogen  and  oxygen,  e.g.  0,  H,  OH,  02H,  must 

occur  in  water.     In  a  solution  of  potassium  chloride,  there- 

+  - 

fore,  we  must  have  the  free  ions  K  and  Cl,  but  Clausius 

suggested  that  the  quantity  is  so  small  as  not  to  be  recog— 
nisable  by  chemical  methods.  Nevertheless,  the  quantity 
was  supposed  to  be  sufficient  to  give  an  electric  conductivity 
to  the  solution.  When  Clausius  admitted  that  the  number 
of  free  ions  is  so  small,  this  proof  lost  much  of  its  meaning 
when  we  consider  that  by  the  same  reasoning  we  can  show 
that  even  the  compound  02H  occurs  in  the  water  in  small 
quantity.  For,  although  the  correctness  of  the  development 
cannot  be  doubted,  it  must  yet  be  admitted  that  the  substance 
02H  does  not  really  exist ;  if,  for  instance,  10100  water  molecules 
give  rise  to  only  one  such  molecule,  then  that  has  no  practical 
significance.  Furthermore,  Clausius  was  not  able  to  prove  i  /  */d- 
that  the  extremely  small  quantity  of  ions  present  in  the  salt 
solution  was  sufficient  for  the  transportation  of  the  electricity. 
Charging  Current.  —  If  electricity  be  conducted 
through  a  trough  containing  an  electrolytic  solution,  the 

surface   of  the   liquid   receives   a 

-f          Y    Y  small    charge     during    the     first 

H         .      .        fi  moment.     After  this  has  occurred, 

II  — >  no  further  accumulation   of  elec- 

'  tricity  takes   place   either  in  the 

FIG.  25.  solution  or  at  the  surface.     If  we 

imagine  two  cross  sections,  Y  and 

YI,  of  the  solution  (Fig.  25),  then  as  much  electricity  must 
pass  out  from  the  liquid  between  these  sections  through  YI 
as  enters  it  through  Y.     In  this  way  it  can  be  proved  that      , 
in  any  closed  circuit  the  same  quantity  of  electricity  passes- 
through  every  section  after  the  charging  current  has  ceased. 


vin.  FARADAY'S   LAWS.  117 

Faraday's  Laws. — The  relationship  just  mentioned  was  , 
known  to  Davy.  Faraday  (4),  working  on  this  fact,  in- 
vestigated the  behaviour  of  one  and  the  same  quantity  of 
electricity  when  it  passed  through  several  water-decomposi- 
tion apparatus  which  differed  in  having  their  poles  unequal 
in  size,  divided  into  two,  or  consisting  of  different  metals, 
such  as  platinum,  zinc,  or  copper.  These  decomposition 
apparatus  were  connected  in  series  in  a  circuit,  an  arrange- 
ment which  ensures  that  the  same  quantity  of  electricity 
shall  pass  through  all.  By  such  experiments  Faraday  found 
that,  no  matter  how  the  apparatus  was  arranged,  the  same 
quantity  of  explosive  mixture  (hydrogen  and  oxygen)  was 
obtained  in  each  of  them.  It  was  further  observed  that 
the  same  current  passing  through  the  apparatus  in  one 
case  twice  as  long  as  in  another  gave  twice  as  much  of  the 
explosive  mixture.  In  other  words,  a  given  quantity  of 
electricity  corresponds  with  a  certain  definite  quantity  of 
explosive  mixture.  The  quantity  of  electricity  in  coulombs 
is  generally  measured  by  its  action  on  a  magnetic  needle. 
Kohlrausch  (5)  and  Lord  Eayleigh  (6)  have  determined  that 
for  the  evolution  of  1  gram  of  explosive  mixture  10,720 
coulombs  are  required.  From  this  and  other  determinations 
(with  silver  nitrate,  etc.)  it  can  be  calculated  that  the  charge  ^  y 
for  1  gram-equivalent  is  96,500  coulombs.  Jj**?* 

Faraday  then   sent  the   same   current   through   several 
"  voltameters  "  arranged  in  series,  in  one  of  which  hydrogen 
was  evolved,  in  another   silver   was   deposited,  in  a  third 
copper,  etc.     As  a  result  of  the  experiment,  he  found  that  \\ 
equal  quantities  of  electricity  decomposed  chemically  equiva-  I 
lent  quantities  of  different  substances. 

This  important   result  is  known  as  Faraday 's^second) 
law. 

"Faraday's  first  law,  that  the  quantities  of  electricity  are  ,, 
proportional  to  the  quantity  of  decomposed  substance,  had    \ 
already  been  suggested  by  Berzelius,  but  he  had  not  been  » 
able  to  definitely  prove  it  (compare  pp.  7  and  18). 

The  simplest  conception  which  can  be  derived  from  this 


1  1  8  ELECTROLYTES.  CHAP. 

law  is  that  the  gram-equivalent  of  every  ion  carries  a  charge 
of  96,500  coulombs,  and  consequently  all  equivalents  have 
the  same  charge.  When  the  electricity  passes  through  a 
liquid  it  is  transported  by  the  ions,  the  positive  electricity 
being  carried  by  the  positive  ions,  and  the  negative  by  the 
negative  ions.  The  electricity  is  firmly  bound  to  the  ions, 
and  can  only  be  given  up  at  the  electrodes,  and  th 


j?e_ase  to  exist  as  such.  It  is  easy  to  understand  that  equiva- 
lent quantities  of  different  substances  are  charged  with  the 
same  amount  of  electricity;  for  when  we  mix  solutions  of 
two  electrolytes  —  for  instance,  calcium  chloride  (CaC^)  and 
sodium  nitrate  (Na~NT03),  partial  exchange  takes  place,  and 
there  are  formed  sodium  chloride  (NaCl)  and  calcium  nitrate 
(Ca(N03)2).  Now,  if  one  atom  of  calcium  (  =  2  equivalents) 
were  not  charged  with  the  same  quantity  of  electricity  as 
two  N03  radicles,  or  the  two  sodium  atoms  originally  com- 
bined with  these,  but  had  a  greater  positive  charge,  the 
molecules  of  calcium  nitrate  (Ca(N03)2)  would  be  positively 
charged,  and  the  sodium  chloride  molecules  would  be 
negatively  charged,  since  the  original  solutions  were  electri- 
cally neutral.  By  evaporation  or  by  some  chemical  means, 
one  kind  of  molecule,  e.g.  the  sodium  chloride  molecules, 
can  be  precipitated  from  the  solution,  or  the  two  substances 
can  be  separated  by  diffusion.  After  this  separation  the 
solutions  should  be  electrically  charged.  As  not  the  slightest 
charge  can  be  found  on  the  solutions,  we  must  assume  that 
equivalent  quantities  of  the  various  substances  have  the  same 
charge. 

Composition  of  the  Ions.  —  Berzelius  found  that  in  the 
electrolysis  of  a  solution  of  sodium  sulphate  (Na2S04),  or,  as  he 
wrote  it,  Na^OSOs,  the  base  NaOH  collected  at  the  negative 
pole,  and  the  acid  H2S04  collected  at  the  positive  pole.  He 
therefore  regarded  Na20  and  S03  as  the  ions  which,  with 
water,  formed  2NaOH  and  H2S04.  Others  were  of  the 
opinion  that  the  decomposition  of  Na2S04  takes  place  in  the 
same  way  as  that  of  copper  sulphate,  CuS04,  namely,  into 
the  metal  Na,  which,  with  water,  forms  NaOH  with  evolution 


vin.  COMPOSITION   OF   THE   IONS.  119 

of  hydrogen,  and  the  acid  radicle  S04,  which,  with  water, 
gives  H2S04  and  oxygen.  In  order  to  confirm  this,  Daniel! 
filled  two  voltameters,  A  and  B  (Fig.  26),  one  (A)  with  a 
solution  of  sulphuric  acid,  the  other  (B)  with  a  solution  of 
sodium  sulphate,  and  conducted  a  current  through  both.  In 
both  voltameters  oxygen  and  hydrogen  were  evolved,  and  the 
same  quantity  of  the  corresponding  gases 
in  each,  i.e.  0  =  Oi,  and  H  =  HI. 

It  was  further  found  that  in  the 
voltameter  containing  the  sodium  sul- 
phate solution  there  was  an  equivalent 
quantity  of  sodium  hydroxide  at  the 
negative  pole,  and  a  corresponding  quan-  FlG  26. 

tity  of  sulphuric  acid  at  the  positive. 
If  Berzelius's  view  were  correct — namely,  that  Na20  and  S03 
occurred  as  ions — the  same  quantity  of  electricity  should 
have  loosened  double  as  many  valencies  (those  of  water  and 
of  sodium  sulphate)  in  the  voltameter  B  as  in  voltameter  A 
(only  the  valencies  of  water).  This  is  not  in  agreement  with 
Faraday's  law,  or  the  law  must  be  considerably  modified 
and  receive  a  particular  formulation  for  the  salts  containing 
metals  which  decompose  water.  If  no  water  is  present,  as 
when  fused  salts  are  employed,  the  metals,  and  not  the 
oxides,  are  obtained.  The  later  investigations  of  Hittorf  and 
Kohlrausch  on  the  migration  of  the  ions  and  the  conductivity 
of  electrolytes  have  proved  that  Daniell's  view  is  the  only 
tenable  one. 

Much  discussion  of  the  topic  has  led  to  the  conclusion 
that,  in  electrolytes,  the  hydrogen,  the  metals,  or  the  radicles, 
such  as  ammonium  (NH4),  methylammonium  (CH3NH3), 
phenylammonium  (C6H5NH3),  uranyl  (U02),  etc.,  which  can 
replace  a  metal,  form  the  positive  ions ;  and  the  rest  of  the 
molecule,  hydroxyl  (OH)  in  hydroxides,  S04  in  sulphates,  N03 
in  nitrates,  Cl  in  chlorides,  forms  the  negative  ion. 

It  was  believed  for  a  long  time  that  in  electrolytically 
conducting  substances,  besides  the  electricity  transportation 
performed  by  the  ions  of  the  electrolyte,  "another  sort  of 


120 


ELECTROLYTES. 


CHAP. 


transportation,  the  so-called  metallic  conduction,  went  on 
simultaneously,  and  by  this  there  was  no  decomposition  of 
the  substance.  However,  very  exact  investigations  have 
proved  that  always  so  much  salt  is  decomposed  as  is  required 
by  Faraday's  law.  Occasionally  it  is  found  that  the  quantity 
of  hydrogen  or  oxygen  evolved  is  too  small,  but  this  is  due 
to  the  solubility  of  the  gases  in  the  liquid ;  and  diffusion  of 
the  dissolved  gases  takes  place,  so  that  some  of  the  hydrogen 
passes  to  the  positive  pole,  and  some  oxygen  to  the  negative 
pole,  and  there  (by  contact  action  of  the  platinum)  partial 
recombination  to  water  takes  place. 

Faraday  termed  an  ion  that  product  which  is  formed  at 
a  pole  independently  of  whether  it  is  the  result  of  a  primary 
or  secondary  action.  Amongst  the  ions  he  therefore  included 
not  only  chlorine  and  potassium,  but  also  hydrochloric  acid, 
caustic  potash,  and  oxygen,  but  not  the  compound  hydroxyl 
(OH),  because  this  could  not  be  obtained  in  the  free 
state. 

We  now  understand  by  ions  those  parts  of  an  electrolyt 
which,  electrically  charged,  wander  through  the  liquid  towards 
the  electrodes,  whether  they  suffer  a  secondary  change  at  the! 
electrodes  or  not. 

Application  of  Ohm's  Law  to  Solutions. — Let  us  again 
consider  a  current  passing  through  a  parallel-sided  trough 

(Fig.  27)  with  two  pole- 
plates,  A  being  the  posi- 
tive, and  B  the  negative. 
Suppose,  further,  that  the 
electrodes  are  non-polar- 
isable,  as  would  be  the 
case  if  we  take  amalga- 
mated zinc  plates  in  a 

solution  of  zinc  sulphate.      The   electricity  is   then   tena- 
nt 

ported  by  the  ions  Zn  and  S04,  of  which  the  former,  the 
cation,  goes  to  the  negative  pole  B,  and  the  latter,  the 
anion,  goes  to  the  positive  pole  A. 


r, 


t"  • 

\  \ 

vin.  APPLICATION  OF  OHM'S  LAW  TO  SOLUTIONS.   121 

If  we  now  change  the  number  of  elements  in  the  battery 
E,  the  current  intensity  /,  measured  by  the  galvanometer  G, 
will  be  altered  according  to  Ohm's  law, 


where  E  is  the  potential  difference  between  the  anode  and 
cathode,  and  E  is  the  electrical  resistance  of  the  solution  in 
the  trough.  According  to  the  ordinary  laws  of  electric  forces 

+  + 
the  positively  charged  Zn  ions  pass  from  places  at  higher 

potential  to  places  at  lower  potential,  and  the  negatively 

charged  S04  ions  travel  in  the  opposite  direction. 

According  to  the  doctrine  of  potential,  the  motive  force  for 
a  substance  carrying  unit  charge  is  the  fall  of  potential  per 

XT 

unit  of  length  7  ,  where  /  is  the  distance  between  the  electrodes. 
i 

For  an  ion  with  the  charge  e,  the  motive  force  is  therefore 

JS& 

-^  (compare  p.  6).     Let  us  assume  for  the  moment  that  the 
i 

S04  ions  remain  at  rest,  and  that  only  the  Zn  ions  trans- 
port electricity.  If  E  is  doubled,  the  quantity  of  elec- 
tricity transported  through  the  cross  section  Y  in  unit  of 
time,  will  also  be  doubled.  The  quantity  of  electricity 
passing  through  the  section  Y  of  the  electrolyte  is  bound  to 
the  zinc  ions  which  travel  in  the  direction  from  A  to  B.  If, 
therefore,  using  the  first  current,  all  the  zinc  ions,  which  at 
time  0  are  between  section  Y  and  YI,  after  one  second  —  i.e. 
at  time  1  —  have  wandered  through  the  cross  section  Y,  then, 
using  the  second  current,  double  as  many  zinc  ions  must  have 
passed  across  the  section  Y  after  one  second,  i.e.  all  the  zinc 
ions  which  at  time  0  were  contained  between  the  cross 
sections.  F2  and  Y,  if  the  distance  Y2Y  =  2YiY.  In  other 
words,  in  the  first  case  the  zinc  ions  which  at  time  0  lie  at 
y~2  have  passed  in  one  second  from  Y%  to  Y\t  in  the  second 
case  from  Y%  to  Y.  The  velocity  of  the  zinc  ions  is  therefore 


122  ELECTROLYTES.  CHAP. 

XT 

doubled  when  the  fall  of  potential  per  unit  of  length  y,  'i.e.  the 

motive  force,  is  doubled. 

Now,  not  only  the  zinc  ions,  but  also  the  S04  ions,  migrate 

XT 

under  the  influence  of  the  fall  of  potential  -y,  but  they  go  in 

the  opposite  direction,  namely  from  B  to  A .  Hittorf 's 
experiments,  which  will  be  considered  in  detail  later,  show 
that  the  migration  velocity  of  the  S04  ions  stands  in  a  certain 
definite  ratio  to  the  velocity  of  the  zinc  ions,  and  this  ratio 
is  quite  independent  of  the  current  strength  /.  It  follows 
from  this  that  the  velocity  of  the  sulphuric  acid  ions,  like 
that  of  the  zinc  ions,  is  proportional  to  the  value  of  the 

XT 

motive    force     ..     This    proportionality    between    velocity 

and  motive  force  follows  from  the  validity  of  Ohm's  law  for 
solutions. 

Such  a  law  as  that  the  velocity  with  which  a  particle 
moves  under  the  influence  of  a  certain  force  is  proportional  to 
this  force  is  valid  for  all  liquid  or  gaseous  particles  moving 
between  other  liquid  or  gaseous  particles  so  long  as  collisions 
constantly  take  place.  This  law  can  be  derived  from  the 
principles  of  the  kinetic  theory  of  gases,  as  is  proved  in 
treatises  on  internal  friction. 

We  must  imagine  the  ions  as  particles  of  a  liquid  which 
receive  an  acceleration  under  the  influence  of  some  external 
force,  electrical  or  osmotic,  and  the  velocity  imparted  is 
proportional  to  the  force  acting.  The  ions,  like  liquid 
particles  in  general,  become  more  mobile  as  the  temperature 
rises ;  on  the  other  hand,  gas  particles  at  high  temperatures 
are  more  difficult  to  set  in  motion.  On  account  of  the 
similarity  between  the  resistance  experienced  by  ions  in  a 
solvent  and  the  friction  between  liquid  particles,  the  former 
phenomenon  is  called  galvanic  friction.  This  is,  of  course, 
different  for  different  ions,  and  decreases  with  rising 
temperature. 

Standard  Units  for  Resistance  and   Electromotive 


vin.          STANDARD   UNITS   FOR   RESISTANCE.  123 

Force. — In  Ohm's  law  we  have  two  factors  of  great 
importance,  namely,  the  resistance  and  the  electromotive 
force  or  potential  difference.  Both  of  these  are  measured 
in  units,  which  are  determined  by  the  magnetic  effect  of  the 
electric  current.  As,  however,  these  measurements  are 
difficult  to  carry  out,  conventional  values  for  the  units  have 
been  adopted  in  a  system  in  which  they  are  easy  to  reproduce. 
As  normal  resistance  we  take  the  resistance  offered  by  a 
column  of  mercury,  at  0°  and  760  mm.  barometric  pressure, 
1  metre  long  and  of  1  sq.  mm.  cross  section.  This  choice 
has  been  made  because  it  is  comparatively  easy  to  obtain 
pure  mercury.  This  standard  is  called  a  Siemens'  unit. 
The  ratio  adopted  at  the  Paris  Congress  in  1881  between 
the  ohm  (legal  ohm)  and  the  Siemens'  unit  was  1  :  T06. 
On  account  of  more  exact  measurements,  a  meeting  of 
deputies  from  Germany,  Great  Britain,  and  the  United  States 
in  1891  adopted  the  ratio :  1  ohm  =  1'0630  Siemens' 
units  (S.U.). 

This  new  ohm  (  =  1*0630  S.U.)  is  called  an  international 
ohm,  and  will  be  used  in  the  sequel. 

The  value  of  a  volt  is  so  determined  that  it  is  the 
potential  difference  produced  by  a  current  intensity  of 
1  ampere  at  the  ends  of  a  resistance  of  1  ohm,  because 
according  to  Ohm's  law :  IjgQlt  =  1  ohm  x  1  ampere.  In 
the  course  of  time  the  volt  has  undergone  the  same  changes 
as  the  ohm.  In  recent  times  no  change  has  been  made  in 
the  ampere  (compare  p.  4). 

For  the  comparison  of  potential  differences  use  is  made 
of  the  electromotive  force  of  a  "  constant "  galvanic  element. 
In  order  to  construct  such  a  constant  element,  i.e.  one  whose 
electromotive  force  does  not  change  with  time,  polarisation 
of  the  poles  must  be  rigorously  avoided ;  the  poles  must  be 
non-polarisable,  and  this  is  accomplished  by  making  the 
electrodes  of  the  same  metal  as  the  cation  of  the  salt 
solution  in  contact  with  them.  The  first  element  of  this 
type  was  constructed  by  Daniell;  it  consists  of  a  copper 
pole  in  a  solution  of  copper  sulphate  and,  separated  from 


I24 


ELECTROLYTES. 


CHAP.  VIII. 


FIG.  28. 


this  by  a  porous  cell,  a  solution  of  zinc  sulphate  (or 
dilute  sulphuric  acid,  which  soon  forms  zinc  sulphate) 
containing  a  zinc  pole.  The  electromotive  force  of  this 
combination  varies  between  I'l  and  1'18  volts,  according 
to  the  concentrations  of  the  solutions.  A  more  suitable 
"  normal "  or  "  standard  "  element,  and  that  generally  used, 
is  the  Clark  cell.  This  is  constructed  as  follows :  A  mix- 
ture of  90  per  cent,  mercury  and  10  per  cent,  zinc  (which, 

in  an  electromotive  respect,  acts 
like  pure  zinc)  is  put  into  the 
limb  A  of  a  vessel  AB  of  the 
form  shown  in  Fig.  28.  This 
amalgam,  which  is  easily  fused, 
is  allowed  to  solidify  round  the 
platinum  wire  p.  Pure  mercury 
is  poured  into  the  limb  B  over 
the  platinum  wire  p\.  A  paste, 
made  by  rubbing  together  crys- 
tals of  zinc  sulphate  (ZnS04 

-f  7H20),  solid  mercurous  sulphate,  mercury,  and  a  concen- 
trated solution  of  zinc  sulphate,  is  poured  on  to  the  mercury 
to  the  depth  of  1  cm.,  and  this,  as  well  as  the  zinc  amalgam 
in  At  is  covered  to  a  depth  of  at  least  1  cm.  with  crystals  of  zinc 
sulphate.  The  vessel  is  now  filled  with  a  saturated  solution 
of  zinc  sulphate,  leaving  only  a  small  air  bubble  to  allow  for 
the  expansion  by  heat  of  the  solution;  the  vessel  is  then 
closed  by  a  cork,  P,  through  which  passes  the  thermometer  T. 
The  electromotive  force  of  this  cell  at  15°  has  been  accurately 
determined  to  be  T438  volts.  Between  10°  and  25°  the 
E.M.F.  decreases  by  0'0012  volt  for  a  rise  of  temperature  of 
1°.  As  the  temperature  coefficient  of  this  cell  is  com- 
paratively large,  the  Weston  element  (see  Chap.  XV.)  has 
recently  been  used  to  a  considerable  extent  as  standard,  and 
this  seems  to  be  quite  -justifiable,  since  the  latest  investiga- 
tions prove  that  when  the  composition  is  correctly  chosen 
(12  to  13  per  cent,  cadmium  amalgam)  the  E.M.F.  is  very 
constant. 


CHAPTER   IX. 
Conductivity  of  Electrolytes. 

Horsford's  Method  of  Determining  the  Resistance 
(1). — The  experiment  is  carried  out  in  a  parallel-sided  trough 
containing  a  salt  solution  and  two  non-polarisable  electrodes 
(e.g.  amalgamated  zinc  plates  in  a  solution  of  zinc  sulphate), 
the  sizes  of  which  are  almost  as  great  as  the  cross  section  of 
the  trough.  The  electric  current  from  a  battery  E  (Fig.  29) 
is  led  to  the  anode  A,  and  passes  from  this  through  the  zinc 


FIG.  29. 

sulphate  solution  to  the  cathode  B.  From  B  it  passes  to  a 
movable  contact,  k,  and  returns  to  E  along  the  metal  wire 
Hi.  The  branch  of  the  circuit  between  B  and  k  contains  a 
galvanometer  G-,  and  the  deflection  of  the  needle  of  this  is 
proportional  to  the  current  strength. 

If,  now,  B  is  brought  to  the  position  denoted  by  BI,  the 
resistance  in  the  trough  is  diminished,  and  the  galvanometer 
needle  shows  a  greater  deflection.  If  Jc  is  then  slid  along  lli 
until  the  deflection  of  the  galvanometer  is  the  same  as  before, 
the  total  resistance  in  the  circuit  is  evidently  the  same 
as  originally,  i.e.  the  resistance  of  the  column  of  liquid  BB\t 


iz6          CONDUCTIVITY   OF    ELECTROLYTES.        CHAP. 

which  has  now  been  removed  from  the  circuit,  is  the  same 
as  that  of  the  wire  between  k  and  hi,  which  has  been 
introduced  into  the  circuit.  The  resistance  of  the  wire  ll\  is 
determined  beforehand  by  means'  of  a  Wheatstone  bridge. 

By  measuring  the  resistance  of  columns  of  liquid  of 
different  lengths  it  is  found  that  this  is  proportional  to  the 
length.  If  the  quantity  of  liquid  in  the  trough  be  changed, 
the  cross  section  of  the  liquid  column  is  changed,  and  it 
is  found  that  the  resistance  is  inversely  proportional  to  the 
cross  section. 

These  facts  prove  that  the  laws  of  resistance  are  the  same 
for  electrolytic  solutions  as  for  metals.  The  resistance  of 
salt  solutions,  however,  decreases  as  the  temperature  rises, 
about  2 '4  per  cent,  per  rise  of  temperature  of  one  degree  in 
the  neighbourhood  of  18°,  whilst  that  of  the  metals  increases 
with  rising  temperature.  If  the  concentration  of  the  zinc 
sulphate  is  varied,  the  resistance  changes  so  that  it  becomes 
not  quite  double  when  the  concentration  is  halved. 

Change  of  Conductivity  with  Dilution. — Let  us  assume 
that  in  the  trough  T  (Fig.  30)  the  zinc  sulphate  solution  is 
so  dilute  that  the  number  of  salt  molecules  is  negligible 

compared  with  the  number 
of  water  molecules,  and  let 
this  solution  fill  the  vessel 
to  the  level  mm\.  The  re- 
sistance, or  its  reciprocal 
value  the  conductivity,  of 
this  solution  depends  both 
FlG  30  on  the  number  of  zinc  and 

sulphate  ions  present  and 

on  their  specific  powers  of  transporting  electricity  under  the 
influence  of  a  certain  fall  of  potential. 

This  power  of  the  ions  depends  only  on  the  galvanic 
friction  which  they  experience  against  the  surrounding 
liquid.  Since  this  surrounding  liquid  is  water — the  number 
of  zinc  sulphate  molecules  being,  by  supposition,  small,  and 
consequently  not  able  to  exert  any  power  on  the  galvanic 


ix.    SPECIFIC  AND  MOLECULAR  CONDUCTIVITY.     127 

friction — the  "mobility"  of  the  ions  must  remain  unchanged 
when  the  solution  is  diluted  with  water.  Let  us  now  suppose 
that  water  is  poured  into  the  trough  to  the  level  nn\,  then  if 
the  number  of  zinc  ions  and  sulphate  ions  were  not  altered 
by  the  dilution  the  conductivity  would  be  the  same  as  before, 
since  the  number  and  mobilities  of  the  ions  had  remained 
constant. 

This,  however,  is  not  the  case.  If  we  start,  for  instance, 
with  a  O'Ol  normal  solution  of  zinc  sulphate,  which  contains 
1'61  grams  of  ZnS04  in  a  litre,  then  on  dilution  to  double 
the  volume,  the  resistance  is  reduced  by  IT  7  per  cent.,  or 
the  conductivity  increased  by  about  13'2  per  cent.  (1*132 

=  -     -  ).     If  the   solution  be   diluted   to  four  times  its 

Uooo/ 

original  volume,  so  that  the  level  in  the  trough  is  pp\t  the 
conductivity  is  increased  by  no  less  than  2  6 '3  per  cent. 
To  explain  this  phenomenon  it  must  be  assumed  that  the 
number  of  zinc  and  sulphate  ions  has  been  increased  by  13*2 
and  26*3  per  cent,  respectively  by  the  dilutions.  We  must 
therefore  conclude  that  the  quantity  of  the  ions,  and  con- 
sequently also  the  degree  of  electrolytic  dissociation,  increases 
with  dilution. 

Specific  and  Molecular  Conductivity. — A  large  number 
of  data  has  been  collected  on  the  subject  of  conductivity  of 
solutions,  and  to  express  these  some  important  units  have 
been  adopted,  which  will  now  be  defined. 

The  specific  electrical  resistance  of  a  conductor  is  that 
resistance  offered  by  a  column  of  it  1  metre  long  and 
of  1  sq.  mm.  cross  section.  Usually  the  resistance  is 
expressed  in  Siemens'  units,  and  the  specific  resistance  of 
mercury  at  0°  is  then  equal  to  1.  If  it  be  desired  to  express 
the  specific  resistance  in  ohms,  the  value  in  S.U.  has  to 
be  divided  by  T063.  Eecent  values  of  the  specific  resist- 
ance have  been  expressed  as  the  resistance  of  a  column  1  cm. 
long  and  of  1  sq.  cm.  cross  section,  measured  in  ohms.  The 
specific  resistance  expressed  in  these  units  is  100  x  100  x  1'063 
=  10630  times  smaller  than  in  the  previously  described 


128  CONDUCTIVITY    OF    ELECTROLYTES.         CHAP. 

units.  The  specific  resistance  changes  with  the  concentration, 
temperature,  and  pressure.  The  specific  electrical  conductivity 
is  the  reciprocal  of  the  specific  resistance.  Expressed  in  the 
new  units  it  is  10630  times  greater  than  when  the  older 
units  are  used.  The  specific  conductivity  divided  by  the 
concentration  gives  the  molecular  conductivity.  As  unit  of 
concentration,  use  is  frequently  made  of  the  number  of 
molecules  in  1  c.c.  instead  of  in  1  litre.  The  molecular 
conductivity  expressed  in  this  way  is  1-063  x  107  times 
greater  than  when  expressed  in  the  old  units  (S.U.,  column 
1  metre  long  and  of  cross  section  1  sq.  mm.,  mols  per  litre). 
We  shall  here  make  use  of  the  new  units. 

If  the  degree  of  dissociation  of  the  solution  did  not  change 
with  dilution,  i.e.  if  the  percentage  of  molecules  dissociated 
into  ions  were  independent  of  the  dilution,  the  molecular 
conductivity  (the  specific  conductivity  per  gram-molecule) 
would  also  be  constant.  The  changes  in  the  value  of  the 
molecular  conductivity  give,  therefore — for  not  too  high 
concentrations — a  measure  of  the  increase  in  the  dissociation 
by  dilution.1 

The  specific  electrical  conductivity  is  denoted  by  K.  As 
this,  however,  changes  with  the  dilution  (i.e.  with  the  volume 
v  in  litres  in  which  a  gram-molecule  is  dissolved),  it  is 
customary  to  add  to  K  an  index  denoting  this  volume,  and 
KV  then  expresses  the  specific  conductivity  at  dilution  v. 
For  the  equivalent  conductivity  the  symbol  X  is  used,  and 
this  also  is  provided  with  an  index  v  indicating  the  dilution. 
According  to  the  above  definitions  there  exists  the  following 
connection  between  K,  X,  and  rj  (number  of  equivalents  per  c.c.) : 


\v  also  changes  with  the  dilution,  and  at  infinite  dilution 


1  When  the  concentrations  are  high  (so  that  the  number  of  dissolved 
molecules  cannot  be  neglected)  this  alteration  of  the  molecular  conduc- 
tivity cannot  be  used  as  a  measure  of  the  change  of  degree  of  dissociation. 
For  Jjj-normal  and  more  dilute  solutions,  however,  it  is  generally  valid. 


ix.  THE    WHEATSTONE    BRIDGE.  129 

reaches  the  value  \v,  which  is  the  equivalent  conductivity  at 
infinite  dilution. 

The  Wheatstone   Bridge. — For  the  determination  of 
the  specific  conductivity  of  a  metal  the  apparatus  diagram- 
matically  represented  in  Fig.  31  is  used.     The  metal  wire  M 
to  be  investigated  is  introduced 
into  the  branch  AS  of  the  Wheat-  B 

stone  bridge,  and  between  B  and 
C  there  is  a  rheostat  of  known  re- 
sistance. The  two  other  branches  ^ 
AD  and  DC  consist  of  a  metal 
wire,  generally  platinum,  along 
which  the  sliding  contact  D  can 
be  moved.  A  galvanometer  is 

interposed  between  D  and  B.  When  the  points  A  and  C  are 
connected  with  the  poles  of  some  source  of  electricity,  the 
current  distributes  itself  over  the  various  parts  of  the  bridge 
according  to  Kirchhoff's  law.v  The  galvanometer  shows  no 
deflection  when  the  contact  D  is  at  a  certain  position  on  ACy 
and  the  ratio  between  the  resistance  sought  (in  AB)  and 
that  in  BC  is  then  the  same  as  the  ratio  of  the  resistance  AD 
to  DC.  Since  R,  AD,  and  DC  are  known,  the  resistance  of 
M  can  be  found  from — 

Rx^AD 
~~DC     ' 

This  method  cannot,  however,  be  used  without  modifica- 
tion for  the  determination  of  the  resistance  of  an  electrolytic 
solution,  because  the  current  is  constantly  passing  in  one 
direction,  and  this  causes  polarisation  of  the  electrodes.  This 
disturbing  factor  can  be  avoided  in  two  ways :  either  non- 
polarisable  electrodes  are  used  (Fuchs  and  Bouty),  or  the 
direct  current  is  replaced  by  an  alternating  current  (F. 
Kohlrausch). 

Determination  of  the  Resistance  of  Electrolytes.— 
The  method  employed  by  Fuchs  (#)  and  Bouty  (3)  is  as 
follows:  Two  vessels,  K  and  K\  (Fig.  32),  are  filled  with 
zinc  sulphate  solution,  and  two  non-polarisable  zinc  electrodes 

K 


130  CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 

dip  into  the  cells,  A  into  K  and  B  into  KI.  The  cells  are 
connected  by  a  narrow  tube,  M,  which  contains  the  solution 
whose  resistance,  E\,  is  to  be  determined.  The  ends  of  this 
tube  are  usually  closed  by  a  piece  of  parchment  paper  or 

animal  membrane,  so  that  the 
contents  do  not  mix  with  the 
solutions  in  K  and  K\. 

There  dip  also  into  the  ves- 
sels two  Sond  electrodes,  z  and 
?i,  of  amalgamated  zinc,  which 
are  connected  with  the  quadrant 
electrometer  Q.  The  electrode  B 
is  connected  with  a  known  resistance  (a  rheostat),  which 
is  joined  through  G  to  the  pole  of  a  battery,  E,  the  other 
pole  being  connected  with  the  electrode  A*  The  points 
B  and  0  and  z  and  zi  can  alternately  be  connected  with 
the  electrometer.  In  the  former  case  the  deflection  gives 
the  potential  difference  V  between  B  and  C,  and  in  the 
second  case  that  V\  between  z  and  z\.  If  /  is  the  current 
strength,  then  we  have  the  following  connections  : — 

V=IR,  Fi  =  /#i, 

and  therefore — 

E,  :  E  =  V,  :  V, 

from  which  EI  can  be  calculated, 

In  order  to  determine  the  specific  resistance,  the  tube  is 
first  filled  with  a  liquid  of  known  specific  resistance,  and  from 
the  result  obtained  the  constant  for  the  tube  is  ascertained  ; 
this  method  is  better  than  calculating  from  E  and  the  dimen- 
sions of  the  tube.  It  is  evident  that  the  resistances  of 
different  liquids  in  the  same  tube  bear  the  same  ratio  to  each 
other  as  the  specific  resistances. 

In  place  of  the  quadrant  electrometer  any  other  form  of 
electrometer  may,  of  course,  be  used,  e.g.  a  capillary  electro- 
meter, provided  that  the  conditions  of  the  experiment  are 
suitable. 


ix.  RESISTANCE    OF    ELECTROLYTES.  131 

Kohlrausch's  method  (4)  more  closely  resembles  that 
described  for  the  determination  of  the  resistance  of  metals. 
If  a  current  be  passed  in  the  direction  AB  through  a  column 
of  liquid  lying  between  the  electrodes  A  and  B  (Fig.  31), 
polarisation  takes  place,  and  the  current  is  thereby  weakened. 
If  the  direction  of  the  current  be  now  altered,  i.e.  passes  in 
the  direction  from  B  to  A,  after  it  has  produced  its  greatest 
polarisation  effect,  this  polarisation  intensifies  the  new 
current,  which  becomes  stronger  than  it  would  be  without 
the  conjoint  action  of  the  polarisation.  The  new  current, 
however,  weakens  the  original  polarisation,  which  depends  on 
the  separation  of  a  small  quantity  of  substance  on  the  elec- 
trodes, and  if  it  acts  for  a  sufficient  time,  polarisation  in  the 
opposite  sense  takes  place.  By  making  the  quantity  of 
electricity  which  passes  through  the  liquid  small  in  com- 
parison with  the  surface  of  the  electrodes,  whereby,  according 
to  Faraday's  law,  the  quantity  of  substance  separated  per 
square  centimetre,  and  consequently  the  polarisation,  is 
inconsiderable,  and  at  the  same  time  applying  an  alternating 
current  so  that  the  polarisation  of  the  principal  current  is 
intensified  as  often  as  it  is  weakened,  the  resistance  of 
electrolytes  can  be  measured  according  to  the  same  principle 
as  that  used  in  the  determination  of  the  resistance  of  metals. 
This  is  the  basis  of  the  Kohlrausch  method.  The  source  of 
the  electric  energy  E  (Fig.  31)  consists  of  a  small  induction- 
coil  actuated  by  a  galvanic  element,  and  the  galvanometer 
G,  which  is  not  suitable  for  alternating  currents,  is  replaced 
by  a  telephone.  The  movable  contact  D  is  slid  along  AC 
until  a  tone  minimum  is  established  in  the  telephone,  and 
then  there  exists  the  following  relationship  between  the 
resistances  : — 

AB  :  BC  =  AD  :  DC. 

The  solutions  are  contained  in  "  resistance  "  or  "  conduc- 
tivity vessels,"  the  form  of  which  varies  according  to  the 
magnitude  of  the  resistance  to  be  measured  (Fig.  33,  a,  b,  c,  d). 

The  vessel  is  filled  to  such  an  extent  that  the  electrode  is 


13* 


CONDUCTIVITY   OF   ELECTROLYTES.      CHAP. 


completely  immersed.  The  electrodes  consist  of  platinum 
plates  electrolytically  covered  with  a  film  of  platinum  black, 
so  that  their  surfaces  become  exceedingly  great,1  and  the 


1 JL 


u 


FIG.  33. 


quantity  of  ions   deposited   per   unit  of    surface  is   corre- 
spondingly small,  and  consequently  also  the  polarisation. 

The  capacity  of  the  resistance-cell  is  determined  by 
measuring  the  resistance,  pi,  offered  by  a  solution  of  known 

resistance  I  mi  =  sr  )•     If  the  resistance  of  the  solution  under 

examination  is  p,  the  specific  resistance  and  the  conductivity 
are  found  from  the  relationship — 

p  '.  pi  =  wi  '.  ffi\  =  AI  i  X. 

[The  conductivity  of  electrolytes  may  also  be  measured 
satisfactorily  in  the  following  way,  due  to  Stroud  and 
Henderson  (Phil.  Mag.,  1897,  43, 19).  The  detrimental  effects 
of  polarisation  in  the  electrolytic  cell  are  very  largely  reduced 
by  inserting  a  second  cell  with  a  very  different  length  of 

1  Kohlrausch  found  that  the  surface  of  an  electrode  covered  with 
platinum  black  was  several  thousand  times  greater  than  that  of  the 
polished  electrode.  According  to  Lummer  and  Kurlbaum  (5),  the 
electrode  should  be  platinised  with  a  3  per  cent,  solution  of  platinic  chloride, 
containing  about  -fa  per  cent,  of  lead  acetate. 


ix.  EXPERIMENTAL   RESULTS.  133 

electrolytic  conductor  in  the  corresponding  arm  of  a  Wheat- 
stone  bridge  circuit.  Further,  any  residual  error  arising 
from  differential  polarisation  is  effectively  drowned  by  the 
employment  of  high  potentials  and  high  resistances. 

The  arrangement  of  the  Wheatstone  bridge  circuit  is  as 
follows :  One  arm  of  the  bridge  is  formed  by  the  long- 
column  electrolytic  cell,  C,  in  series  with  which  is  a  resist- 
ance, E,  forming  the  second  arm.  In  parallel  with  these 
is  the  short-column  electrolytic  cell,  c,  and  an  adjustable 
resistance  box,  r ;  these  together  form  the  third  arm  of  the 
bridge,  whose  remaining  arm  consists  of  a  resistance  =  II. 
If  T  be  adjusted  till  there  is  no  deflection  of  the  galva- 
nometer, the  same  current  is  traversing  each  cell,  presumably 
producing,  at  all  events  approximately,  the  same  polarisation, 
and  r  is  equivalent  to  the  resistance  of  a  column  of  the 
electrolyte  equal  to  the  difference  between  the  long  and 
short  columns.  From  the  value  of  r  the  specific  conduc- 
tivity can  be  calculated.  The  voltage  used  is  about  30,  and 
the  adjustable  resistance  about  20,000  ohms.] 

Experimental  Results. — Experiments  carried  out  by 
the  Kohlrausch  method  show  that  pure  water  has  only  a  very 
inappreciable  conductivity.  When  increasing  amounts  of  an 
electrolyte  are  added  to  the  water,  the  conductivity  gradually 
increases,  and  finally  reaches  a  maximum,  provided  that  the 
solubility  of  the  substance  permits  of  reaching  a  sufficiently 
high  concentration ;  as  the  concentration  is  further  increased, 
the  conductivity  falls,  and  for  pure  electrolytes,  e.g.  hydro- 
chloric acid  or  acetic  acid,  it  has  about  the  same  value  as 
for  pure  water.  The  observed  conductivity  consists  of  two 
factors,  namely,  that  of  the  water  used  in  making  the 
solution,  and  that  due  to  the  dissolved  electrolyte.  The 
former  is  generally  caused  by  dissolved  impurities  such  as 
salts,  ammonia,  or  carbon  dioxide,  and  is  only  to  a  very  slight 
extent  due  to  the  real  conductivity  of  the  pure  water ;  in  this 
connection  it  is  of  little  theoretical  interest.  In  practice,  a 
correction  is  introduced  by  subtracting  from  the  conductivity 
of  the  solution  that  of  the  water  used  as  solvent.  The 


134  CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 

conductivities  of  the  electrolytes  are  thus  obtained,  some 
examples  of  which  are  given  in  the  table  on  p.  135. 

The  table  contains  the  specific  conductivity  K  of  sodium 
chloride,  and  the  equivalent  conductivities  X  of  NaCl,  KC1, 
NalTO3,  CH3COOK,  iK2S04,  iMgS04,  HC1,  iH2S04, 
OH3COOH,  and  NH3.  The  numbers  given  refer  to  the 
temperature  18°. 

If  we  consider,  in  the  first  place,  the  values  of  K  for  sodium 
chloride,  it  is  apparent  that  at  high  dilution  these  are  almost 
proportional  to  the  concentration,  i.e.  almost  exactly  inversely 
proportional  to  the  volume  v,  in  which  1  gram-molecule  is 
dissolved.  For  acetic  acid  and  ammonia,  and  for  all  weak 
acids  and  bases,  K  rises  much  more  slowly  with  increasing 
concentration.  At  higher  concentrations  of  all  electrolytes 
the  increase  of  K  is  less  than  proportional  to  the  con- 
centration ;  for  potassium  chloride  the  deviation  is  least. 
In  some  cases  the  maximum  conductivity  is  reached  with- 
in the  limits  given,  e.g.  with  sulphuric  acid,  acetic  acid, 
ammonia,  hydrochloric  acid,  and  magnesium  sulphate.  In 
the  neighbourhood  of  this  maximum  the  conductivity  is 
almost  independent  of  the  concentration,  so  that  it  is  easy 
with  these  electrolytes  to  prepare  a  solution  of  a  particular 
conductivity  for  the  determination  of  the  capacity  of  the 
resistance  cell.  For  this  purpose  sulphuric  acid,  or  magne- 
sium sulphate,  is  usually  employed. 

The  best  conducting  solution  of  sulphuric  acid  contains 
30  per  cent,  by  weight  of  H2S04,  and  has  the  specific  gravity 
1*223.  The  maximum  specific  conductivity  Kmax.18  =  07398, 
and  an  error  of  O'OOo  in  the  specific  gravity  reduces  this  by 
about  0'0004.  Vessels  of  small  capacity  are  standardised  by 
means  of  a  dilute  solution  of  potassium  chloride. 

For  ^-normal  KC1,  Kl8  =  0'011203  ; 
for  yo       „          „      K18  =  0:0023992. 

The  regularities  at  high  dilution  are,  however,  much  more 
striking  when  we  consider  the  molecular  conductivities.  It 
lias  already  been  pointed  out  that  an  increase  in  the  value  of 


IX. 


EXPERIMENTAL   RESULTS. 


135 


O     ifi      OS      CO      O 


t**     O      £*•      i-H     O      O     ^     O 

O      CO      O      *f      C7      (M      i— i      i-H 


r 

<£> 

CO 


»O      CO      O      QO      »O      CM      i-i 
COCOCOC<JCM<N(N<Mt-l-irH 


OOOO 


lOO 
COt- 


O     •*      O 

—    so    oi    cs 

QOiOiO-^ 


i—  iC^OOOO 
O     O      O     ^H      T-H     TfH 


iO'^ 
t^*      O 


tO 
CO 


ooooooooooooooo 


O      O      O      r-i      (M      IO 

fo  o  o  o  o  i— i 
p  p  p  p  p  p 
000000 


i— I      (M      1C 

6      6      6      rH 


36 


CONDUCTIVITY   OF    ELECTROLYTES.        CHAP. 


this  with  dilution  indicates  that,  on  addition  of  water,  more 
ions  capable  of  transporting  electricity  are  formed  at  the 
expense  of  the  undissociated  molecules.  In  this  respect  we 
may  consider  as  types,  ammonia  and  acetic  acid.  With 
increasing  dilution,  X,  assumes  greater  and  greater  values, 
and  it  is  difficult  to  find  that  X,,  approaches  a  certain  limit,  Xw, 
which,  nevertheless,  can  be  ascertained  in  an  indirect  manner. 

The  Clausius  hypothesis  aids  us  in  this  determination. 
When  the  part  of  the  electrolyte  dissociated  into  ions  is  only 
a  small  fraction  of  the  whole  number  of  molecules  present, 
the  quantity  of  ions,  and  therefore  also  X,,  must  increase  on 
dilution  from  10  to  100  by  about  the  same  amount  as  on 
dilution  from  100  to  1000,  etc.,  which  is  actually  the  case  for 
the  types  of  weak  bases  and  acids  mentioned. 

The  other  substances  mentioned — H2S04,  HC1,  MgS04, 
K2S04,  CH3COOK,  NaN03,  NaCl,  and  KC1,  which  may  be 
regarded  as  types  of  good  conductors — behave  otherwise.  At 
high  concentrations  the  increase  in  \v  for  dilution  to  double  the 
volume  is  tolerably  great ;  thus,  e.g.,  for  KC1  the  difference 
X10  -  X5  =  4-07 ;  for  HC1,  X10  -  X5  =  9.  As  the  following 
numbers  show,  this  increase  diminishes  at  higher  dilution :— 


Substance. 

*20-Mo 

MOO-ASO 

^200-  Moo 

**-*» 

^2000  -MOOO 

AUOOO-A™, 

KC1 

3-72 

2-47 

1-98 

1-03 

0-77 

0-30 

HC1 

9 

3 

3 

1 

— 

— 

! 

The  increase  of  X  evidently  approaches  the  value  zero 
with  increasing  dilution,  when  the  concentration  is  always 
changed  in  the  same  ratio,  or  in  other  words,  X  converges 
with  increasing  volume  (v)  to  a  limiting  value  XM.  The 
same  conclusion  is  arrived  at,  but  perhaps  not  quite  so 
clearly,  by  considering  the  conductivities  of  sulphuric  acid 
and  magnesium  sulphate. 

The  only  possible  cause  of  the  fact  that  the  decomposition 
into  ions  reaches  a  certain  limit  is  that  ultimately  all  the 
molecules  are  dissociated ;  or  we  may  say  that  at  very  great 


ix.  DEGREE    OF   DISSOCIATION.  137 

dilution  the  dissociation  is  nearly  complete,  or  the  degree  of 
dissociation,  i.e.  the  proportion  of  molecules  dissociated  into 
ions,  approaches  the  value  1. 

From  this  we  may  conclude  that  the  conductivity  at 
infinite  dilution,  that  is,  when  v  becomes  excessively  large, 
has  a  value  which  is  not  very  different  from  that  for  the 
highest  measured  dilution ;  it  can  be  found  by  graphical 
extrapolation,  and  is  denoted  by  XM.  The  extrapolation  can 
also  be  calculated,  e.g.  for  KC1,  with  the  aid  of  the  following 
differences : — 

Xioo  ~~  XIQ  ==  10*4. 
Xiooo  -  Xioo  =  4-91. 
Xioooo  —  AIOOO  =  1*73. 

These  differences  decrease  almost  in  geometricalr^pro- 
gression. 

The  value  of  X^  for  all  highly  dissociated  electrolytes  can 
be  determined  in  the  same  way. 

According  to  principles  derived  below  from  Kohlrausch's 
law,  the  values  of  the  differences  for  various  electrolytes  are 
approximately  the  same.  In  the  table  on  p.  135  the  value  of 
XM  for  some  salts  is  given. 

Calculation  of  the  Degree  of  Dissociation  in  Electro- 
lytic Solutions. — From  what  has  been  said,  it  is  easy  to 
see  how  the  degree  of  dissociation  of  an  electrolyte  at  any 
particular  dilution  v  is  to  be  calculated.  If  all  the  dissolved 
molecules  took  part  in  the  conduction  of  the  current,  \v  for 
each  single  salt  would  be  independent  of  the  dilution,  and 
in  the  case  of  potassium  chloride  it  would  be  equal  to 
13011. 

Since  all  the  K  ions  transport  the  electricity  at  the  same 
rate,  and  the  same  is  true  for  the  Cl  ions,  then  if  the  value 
of  X  is  different  from  that  of  X^,  the  transportation  of  the 

electricity  must  be  carried  out  by  ~  ions,  i.e.  the  degree  of 

Aoo 

dissociation  a  is  given  by— 

X, 


138  CONDUCTIVITY   OF   ELECTROLYTES.         CHAP. 

In  this  way  the  degree  of  dissociation  can  be  determined 
for  all  salts  of  monovalent  acids  or  bases,  and  for  the 
strongest  acids  (hydrochloric,  hydrobromic,  hydriodic,  nitric, 
chloric  acids,  etc.)  and  bases  (potassium,  sodium,  calcium, 
strontium,  barium  hydroxides,  ammonium  bases,  etc.).  The 
value  of  Aco  (for  a  given  temperature)  is  a  measure  of  the 
mobility  of  the  ion  pair  (K  +  Cl). 

Transport  Number. — It  is  of  interest  to  learn  to  what 
extent  the  conductivity  is  due  to  each  of  the  two  ions  of  a 
"  binary "  electrolyte.  Let  us  assume  that  a  quantity  of 
electricity  corresponding  exactly  with  1  gram-equivalent  (in 
this  case.  1  gram-molecule),  i.e.  96,500  coulombs,  passes 
between  the  electrodes  A  and  B  (Fig.  34)  through  a  solution 

of  potassium  chloride.  This  quan- 

^  +  P  -B  tity  of  electricity  is  transported 
T~~  partly  by  the  K  ions,  which  conduct  - 

I  positive  electricity  in  the  direction 


FIG.  34.  AB,   and   partly   by  the   Cl  ions, 

which  carry  the  negative  electricity 

in  the  opposite  direction  (BA).  If  the  Cl  ions  remained 
stationary,  i.e.  did  not  aid  the  transportation  of  the  elec- 
tricity, a  gram-equivalent  (=  3915  grams)  of  potassium 
would  pass  in  the  direction  AB  through  any  cross  section 
P  of  the  column  of  liquid.  On  the  other  hand,  if  the 
K  ions  remained  stationary  and  the  Cl  ions  alone  trans- 
ported the  electricity,  a  gram-equivalent  (=  3  5 '45  grams) 
of  chlorine  would  migrate  through  the  section  P  in  the 
direction  BA.  As  .a  rule,  however,  both  ions  take  part 
in  the  conduction.  Let  us  assume  that  the  K  ions  transport 
a  fraction,  u,  of  the  electricity,  then  the  Cl  ions  transport 
the  remainder,  (1  -  u).  The  fractions  u  and  (1  -  u)  are 
termed  the  "  transport  numbers  "  or  "  migration  numbers  "  of 
the  potassium  and  chlorine  ions  respectively  in  the  potassium 
chloride  solution.  There  must  then  migrate  across  P  in  the 
direction  AB  u  gram-equivalents  (39!15  X  u  grams)  of 
potassium  and  in  the  direction  BA  (1  -  u)  gram-equivalents 
(=  35'45  —  35'45  x  u  grams)  of  chlorine.  In  order  to 


IX. 


TRANSPORT   NUMBER. 


139 


ascertain  experimentally  the  values  of  u  and  (1  —  u)  it  is 
only  necessary  to  divide  the  liquid  column  into  two  portions 
at  P  after  the  current  has  passed  (e.g.  by  slipping  into 
the  trough  a  well-fitting  glass  plate),  and  then  by  chemical 
analysis  to  find  by  how  much  the  quantity  of  potassium  in 
the  part  BP  has  increased  and  by  how  much  the  amount  of 
chlorine  has  increased  in  the  part  A  P.  As  the  original 
composition  of  the  solution  is  known,  it  is  sufficient  to 
analyse  the  liquid  in  one  part  (AP  or  BP)  after  the  current 
has  passed.  In  these  experiments  appreciable  changes  in 
concentration  take  place  at  the  electrodes,  and,  besides,  there 
is  frequently  an  evolution  of  gas  or  deposition  of  long 
crystals  (dendritic)  which  fall  off  and  so  stir  up  the  liquid. 
The  disturbances  caused  thereby  can  be  avoided  by  various 
devices.  The  apparatus  shown  in  Fig.  35,  devised  by 
Hopfgartner  (6)  from  Hittorf's  model,  gives  good  results 
in  determining  the  changes  of  concentration. 

The  vessel  B  fits  into  the  neck  of  a  thin-walled  flask, 
Af  which  is  provided  with  a  tubu- 
lus,  G.  B  is  connected  with  the  wide 
tube  D  by  means  of  the  u-tube  C. 
By  raising  or  lowering  the  plug  F 
the  vessel  B  may  be  opened  or 
closed.  The  side  tube  K  of  the  u- 
tube  is  closed  by  means  of  a  rubber 
tube  and  clip.  The  anode  is  intro- 
duced through  a  rubber  stopper 
through  6r,  and  mercury  contained 
in  E  is  used  as  cathode. 

Hittorf  (7)  was  the  first  to  in- 
vestigate the  migration  of  the  ions 
and  prove  that  the  anions  and 
cations  have  different  migration 
velocities.  For  the  chlorine  ion  of 
a  very  dilute  solution  of  potassium 

chloride  the  value  of  u  generally  accepted  is  0'503,  and 
consequently  .for  the  potassium  ion  0'497. 


FIG.  35. 


HO  CONDUCTIVITY   OF   ELECTROLYTES.         CHAP. 

Kohlrausch's  Law. — Since  XM  for  potassium  chloride 
evidently  represents  the  sum  of  the  transporting  powers  of 
the  K  and  Cl  ions,  and  since  XKCloo  =  130'11,  the  part  0'503 
X  13011  =  65-44  is  due  to  the  chlorine,  and  O497  X  130'11 
=  64*67  to  the  potassium.  These  numbers  refer  to  the 
temperature  18°,  and  are  termed  the  mobilities  (or  migration 
velocities)  of  the  chlorine  and  potassium  ions  respectively. 
From  the  determinations  of  the  conductivities  X^  of  salts 
and  the  transport  numbers  it  has  been  possible  to  ascertain 
the  mobilities  of  other  ions.  The  mobility  of  an  ion,  e.g.  the 
chlorine  ion,  can  evidently  be  obtained  from  the  investigation 
of  any  chloride,  and  all  the  results  must  be  the  same.  It  is 
better,  perhaps,  to  calculate  the  transport  numbers  from  the 
mean  value  of  the  ionic  mobilities,  and  see  how  the  results 
agree  with  experiment.  This  is  the  method  by  which 
Kohlrausch  proceeded  to  show  the  connection  between 
transport  numbers  and  conductivity. 

Kohlrausch  (8)  stated  the  law  that  the  molecular 
conductivity  of  an  electrolyte  (at  infinite  dilution)  can  be 
calculated  as  the  sum  of  two  numbers,  one  of  which  depends 
only  on  the  cation  and  is  independent  of  the  anion,  whilst  the 
other  depends  on  the  anion  and  is  independent  of  the  cation 
with  which  it  is  combined  in  the  original  salt.  Kohlrausch, 
however,  could  only  prove  this  for  certain  groups  of  similarly 
constituted  electrolytes,  e.g.  for  those  with  two  monovalent 
ions  (so  that  96,500  coulombs  are  transported  per  gram-ion). 
It  appeared  as  if  a  chlorine  ion,  when  present  with  a  potassium 
ion,  possessed  a  different  mobility  from  that  when  it  was  the 
dissociation  product  of  the  barium  salt  the  cation  of  which 
is  divalent,  i.e.  is  charged  with  2  x  96,500  coulombs  per 
gram-ion.  The  difference  in  the  mobilities  of  the  S04  ion 
was  held  to  be  much  greater  when  it  occurred  with  a  mono- 
valent than  when  with  a  divalent  cation.  At  first  it  was  not 
expected  that  the  relationships  would  be  so  complicated; 
the  presumption  that  the  relationships  are  quite  simple 
was  afterwards  confirmed,  and  so  the  general  form  given 
above  was  associated  with  the  law.  The  connection  expressed 


IX. 


TRANSPORT   NUMBERS. 


141 


in  the  law  is  also  approximately  true  for  the  molecular 
conductivity  at  any  given  dilution,  v,  but  only  with  each 
single  group  of  electrolytes ;  attention  was  also  called  to  this 
point  by  Kohlrausch. 

Transport  Numbers  and  Ionic  Mobilities. — As  already 
mentioned,  Hittorf  had  confirmed  his  own  views  on  this 
subject  in  his  famous  experiments  on  the  migration  of  the  ions. 
The  data  found  by  him  refer  for  the  most  part  to  concentra- 
tions at  which  the  transport  numbers  vary  with  the  dilution. 
The  data  contained  in  the  following  table,  which  may  be  re- 
garded as  the  most  exact  known  at  the  present  time,  have  been 
taken  from  the  comprehensive  investigations  of  Jahn  (9) 
and  his  pupils,  and  refer  to  very  dilute  solutions  at  18°.  The 
table  gives  under  uc  (observed)  the  observed  transport  number 
of  the  cation,  and  under  uc  (calculated)  the  value  calculated 
from  Kohlrausch's  results  for  X_  and  the  Hittorf  numbers — 


Salt. 

uc  (observed). 

Observer. 

uc  (calculated). 

NaCl 

0-396 

Bogdan 

0-399 

KC1 

0-497 

0-497 

KBr 

0-496 

5) 

AgNO, 

0-464 

Metelka 

0-478 

0-472 

Mean  value 

of  various 

observers 

CuS04 

0-375 

Metelka 

0-412 

BaCla 

0-447 

0-465 

CdCl, 

0-433 

0-40 

CdI2 

0-442 

?» 

0-40 

The  influence  of  temperature  on  the  transport  number  of 
some  cations  is  shown  by  the  following  results  obtained  by 
Bein  (10) :— 


Salt 

Temperature. 

uc 

Temperature. 

uc 

NaCl 
AgN03 
CuS04 
CdCl, 
CdI2 

0 

20 
10 
15 
20 
20 

0-392 
0-470 
0-362 
0-430 
0-360 

0 

95 
90 
75 
96 
75 

0-449 
0-490 
0-378 
0-430 
0-40 

142 


CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 


It  has  been  found  that  at  higher  temperatures  the  trans- 
port numbers  approach  the  value  0*5,  which  indicates  that 
with  rising  temperature  the  mobilities  of  the  ions  tend  to 
become  the  same.  This  rule  applies  to  all  combinations  of 
a  positive  and  a  negative  ion.  If  we  compare  the  salts  of 
different  positive  ions  with  the  same  negative  ion,  the 
conductivities  of  these  (provided  that  the  degree  of  dis- 
sociation remains  constant)  must  tend  to  a  common  value 
as  the  temperature  rises.  From  this  it  follows  that  the 
worse  the  electrolyte  conducts  the  greater  is  the  percentage 
increase  of  conductivity  with  the  temperature.  This  rule 
ought  to  apply  only  to  the  values  of  \M,  but  it  has  been 
found  to  be  true  for  moderate  dilutions  of  highly  dissociated 
bodies. 

In  the  following  table  are  given  the  mobilities  lm  at 
extreme  dilution  of  the  more  important  ions;  the  positive 
ions  are  given  first,  then  the  negative  ions.  The  temperature 
coefficient  for  the  ions  K,  Cl,  Br,  I,  NH4,  Ag,  and  JS04  is 
about  2-2  per  cent,  of  the  value  at  18°.  For  the  sodium  ion 
and  the  ions  'of  the  organic  acids  the  coefficient  is  about 
2*7  per  cent,  per  degree ;  for  Li,  2' 9  per  cent. ;  for  OH,  TS  per 
cent. ;  and  for  H  only  1-5  per  cent. 

The  increase  for  the  divalent  ions  Ca,  Sr,  Zn,  Mg,  and  Cu 
is  about  2'6  per  cent.,  and  for  Ba,  2'5  per  cent.  From  these 
numbers  the  temperature  coefficients  of  the  conductivities  of 
most  electrolytes — in  dilute  solution — can  be  calculated. 


Cations. 

Zoo 

Anious. 

*00 

Hydrogen,  H 

314 

Hydroxvl,  OH 

172 

Potassium,  K 

64-67 

Chlorine,  Cl 

65-44 

Sodium,  Na 

43-55           Bromine,  Br 

66-4 

Lithium,  Li 

33-44           Iodine,  I 

66-2 

Ammonium,  NH4 

63-6             Nitric  acid,  NOS 

61-78 

Silver,  Ag 

55-0             Chloric  acid,  CIO,              55  5 

Barium,  JBa 

56-6 

lodic  acid,  I03 

33-87 

Strontium,  -JSr                    53"3 

Acetic  acid,  C2H302 

33 

Calcium,  ^Ca 

52-3 

Sulphuric  acid,  S04 

69' 

Magnesium,  JMg 

48-3 

Zinc,  ^Zn 

46-7 

Copper,  |Cu 

48-7 

ix.  ABNORMAL   TRANSPORT    NUMBERS.  143 

Abnormal  Transport  Numbers. — It  is  evident  that 
the  transport  number  must  lie  between  0  and  1,  for  otherwise 
the  positive  ion  would  be  travelling  against  the  current  or  the 
negative  ion  with  the  current,  and  this  is  inconceivable. 
Nevertheless,  Hittorf  found  for  the  transport  number  of 
iodine  in  a  4' 8  per  cent,  solution  of  cadmium  iodide  in 
alcohol  the  value  2*1,  and  in  a  3  per  cent,  solution  the  value 
1*3.  At  a  very  high  dilution  the  value  would  probably  sink 
below  1,  i.e.  would  lose  its  abnormality. 

Hittorf  explained  this  peculiar  phenomenon  as  follows : 
He  assumed  that  cadmium  iodide  forms  complex  molecules 

perhaps  of  the  formula  Cd3I6,  which  form  the  ions  Cdale  and 

+  + 

Cd.     For  the  sake  of  simplicity  let  us  imagine   that   the 

+  + 
cation  Cd  remains  at  rest,  and  that  only  the  anion  Cdgle 

passes  through  the  solution,  in  the  direction  opposite  to  that 
of  the  (positive)  current.  For  every  quantity  of  electricity 

2  x  96,500  coulombs,  a  gram-ion  of  Cd2I6  (986  grams  =  224 
grams  Cd  +  762  grams  I)  must  pass  a  cross  section  of  the 
solution.  Instead  of  2  equivalents  of  iodine,  which  if  iodine 
alone  migrated  would  be  sufficient  to  transport  the  same 
quantity  of  electricity,  an  amount  three  times  as  large  must 
pass  through  the  cross  section.  Consequently,  if  the  transport 
number  of  the  iodine  in  the  former  case  were  1,  it  would  in 
the  second  case  be  3.  Now,  as  the  cation  also  migrates  with 
a  certain  velocity,  the  transport  number  obtained  for  the 
anion  will  be  less  than  3.  However,  it  is  obvious  that  we 
have  only  to  make  the  assumption  of  the  existence  of  a 
particular  molecular  complex  in  order  to  be  able  to 
explain  in  this  way  any  transport  number.  In  the  example 
quoted,  if  the  transport  number  of  the  iodine  is  3,  that 
of  the  cadmium  must  be  —  2,  since  the  sum  must  be  equal 
to  1. 

Cadmium  iodide  in  concentrated  solution  behaves  more 
anomalously  than  in  dilute  solution,  and  it  must  therefore 
be  assumed  that  in  concentrated  solution  there  are  more 


144 


CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 


complex  molecules -than  in, the  dilute  solution,  a  conclusion 
which  indeed  would  be  expected. 

Hittorf  (11)  and  Lenz  (12)  have  proved  that  in  aqueous 
solutions  of  cadmium  iodide  which  are  more  concentrated 
than  normal,  the  transport  number  of  the  iodine  exceeds  1 ; 
for  3-normal  solution  it  is  1*3,  whilst  for  0'03-normal  solution 
it  is  0-61. 

For  analogous  reasons  it  is  found  that  the  transport 
numbers  of  the  majority  of  electrolytes  suffer  a  greater  or 
less  change  with  the  concentration;  this  is  shown  by  the 
results  obtained  by  Goldhaber  (13)  for  cadmium  bromide 
at  18°  contained  in  the  following  table,  in  which  v  indicates 
the  volume  of  the  solution  in  which  a  gram-molecule  of  the 
salt  is  dissolved,  and  nc  is  the  transport  number  for  JCd: — 


V 

UC 

V 

u. 

1-99 

0-218 

16-01 

0-430 

3-98 

0-355 

23-99                 0-433 

7-80 

0-399 

48-02 

0-431 

11-99 

0-423 

79-75 

0-431 

On  further  dilution  uc  remains  constant. 

In  a  O'l -normal  solution  of  copper  sulphate,  the  transport 
number  for  the  anion  S04  is  0*64,  and  in  a  2-nornial  solution 
it  is  0'73.  In  agreement  with  the  explanation  given,  it  is 
found  from  the  depression  of  the  freezing  point  that  formation 
of  molecular  complexes  does  take  place  to  a  very  consider- 
able extent.  A  comparative  investigation  of  the  relationships 
obtained  by  these  methods  would  be  of  great  interest. 

Mobilities  of  Organic  Ions. — The  values  of  the 
mobilities  1M  at  25°  have  been  determined  by  Ostwald  and 
Bredig  for  a  large  number  of  organic  ions,  both  positive  and 
negative.  Ostwald  (14)  found  that  the  mobility  of  the 
negative  ions  decreases  as  the  number  of  atoms  in  the  ion 
increases.  It  is  easy  to  see  why  this  should  be  so,  for  as  the 
number  of  atoms  increases,  so  also  does  the  surface  of  the  ion, 
and  consequently  its  friction  against  the  liquid.  However, 
this  friction  does  not  increase  with  the  mass  of  the  atoms. 


ix.  MIGRATION   OF   IONS   IN    MIXED   SOLUTIONS.   145 

On  the  contrary,  it  is  found  that  in  the  two  groups  of  atoms, 
Li,  Na,  and  K  on  the  one  hand,  and  Ca,  Sr,  and  Ba  on  the 
other,  the  heavier  ions  are  the  more  mobile.  And  again,  the 
ions  Cl,  Br,  and  I,  which  have  very  different  masses,  have 
almost  the  same  mobilities. 

From  the  table  given  below  it  can  be  seen  that  addition 
on  to  an  atomic  group  exerts  more  influence  on  the  smaller 
ions  than  on  the  larger.  Were  this  not  the  case,  then  ions 
consisting  of  a  large  number  of  atoms  would  have  the 
mobility  0,  or  even  an  impossible  negative  value. 


Anion  of 

Formula. 

IK,                             Diff. 

Formic  acid     . 

HC02 

59-6 

Acetic  acid  .     . 
Propionic  acid  . 

CH3C02 
C2H5C02 

46-0 
41-6                 ~  Q 

Butyric  acid     . 

C3H7C02 

37-8                 ** 

Valerianic  acid 

C4H9C02 

35-7                 -K 

Caproic  acid     . 
Succinuric  acid 
Phthalouric  acid 

C5H2N204 
N2H7C904 

34-2 
33-4 
31-2 

Phthalanilic  acid 

NH10C1403 

30-0 

i 

Similar  regularities  were  found  by  Bredig  (7-5)  from 
his  results  with  positive  ions. 

Migration  of  Ions  in  Mixed  Solutions. — Before 
leaving  Hittorf's  work,  an  investigation  which  he  made  on 
the  migration  of  ions  in  mixed  solutions  of  potassium 
chloride  and  potassium  iodide  must  be  mentioned.  When 
the  current  passes  through  this  mixture  only  iodine  appears 
at  the  anode,  and  the  question  arises  whether  the  chlorine 
ions  take  any  part  in  the  conduction  or  not.  According  to 
our  present  views,  of  course,  the  answer  is  self-evident. 
Every  ion  must,  on  account  of  the  charge  which  it  carries, 
be  set  in  motion  when  it  is  in  an  electrical  field  of  varying 
potential.  At  the  time  when  Hittorf  carried  out  his  in- 
vestigation (1853-1859)  the  matter  was  not  so  clear,  for 
the  conducting  molecules  were  then  supposed  to  be  joined 
together,  and  a  large  share  in  the  current  conduction  was 
attributed  to  the  water  (solvent).  Hittorf  found  that  the 

L 


146  CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 

current  is  divided  between  the  two  dissolved  electrolytes  in 
the  ratio  of  their  conductivities.  He  regarded  the  separation 
of  the  chlorine,  as  well  as  the  iodine,  at  the  anode  as  the 
result  of  a  primary  action,  but  it  immediately  reacts  with 
the  potassium  iodide,  producing  potassium  chloride  and  free 
iodine.  Hittorf's  explanation  has  recently  been  confirmed 
by  Schrader  (16)  for  mixtures  of  potassium  chloride  and 
iodide,  and  copper  sulphate  and  sulphuric  acid,  and  further 
by  Hopfgartner  (6). 

Complex  Ions. — In  his  investigation  of  the  so-called 
double  salts,  such  as  potassium  argentocyanide  (KAg(CN)2), 
potassium  ferrocyanide  (K4Fe(CN)6),  sodium  platinichloride 
(Na2PtCl6),  and  sodium  aurichloride  (N"aAuCl4),  Hittorf 
observed  that  the  alkali  metal  always  formed  the  positive  ion, 
whilst  the  negative  ion  consisted  of  the  rest  of  the  molecule 
(termed  a  complex  ion,  on  account  of  its  composition).  This 
observation  was  diametrically  opposed  to  the  chemical  views 
then  held,  according  to  which,  in  consonance  with  the  doctrine 
of  valency,  the  formula  AgCN  +  KCN  was  given  to  potassium 
argentocyanide,  indicating  that  there  is  no  close  connection 
between  the  radicle  ON  of  the  potassium  cyanide  and  the 
AgCK 

Ionic  Migration  and  the  Theory  of  Dissociation.— 
If  we  assume  that  the  ions  are  perfectly  free  and  transport 
the  electricity  quite  independently  of  each  other,  it  is  quite 
natural  to  suppose  that  under  the  influence  of  the  same 
force  they  will  not  pass  through  the  solution  with  the  same 
velocity ;  but  rather  a  different  friction  against  the  liquid  is 
a  priori  to  be  expected.  Even  if  we  suppose  that  the 
molecules  are  not  dissociated  in  the  solution,  but  that  the 
ions  influence  each  other  in  their  migrations,  it  would  be 
natural  to  imagine  that  they  would  travel  with  different  veloci- 
ties. To  us  at  the  present  time,  therefore,  it  seems  incredible 
that  Hittorf's  doctrine  of  the  unequal  migrations  of  the  ions 
was  not  at  once  accepted.  As  a  matter  of  fact,  however,  the 
leaders  in  the  science  opposed  Hittorf's  views,  and  it  was 
only  after  thirty  years  that  these  were  adopted. 


ix.  ABSOLUTE    VELOCITY   OF   THE    IONS.  147 

Calculation  of  AM  for  Slightly  Dissociated  Electro- 
lytes. —  The  equivalent  conductivity  at  infinite  dilution  of 
slightly  dissociated  substances,  such  as  ammonia  or  acetic 
acid,  cannot  be  estimated  by  extrapolation  from  the  results 
at  higher  concentrations.  If  we  know  the  values  1M  for  the 
mobilities  of  the  ions,  however,  we  can  easily  calculate  the 
value  of  AM.  From  what  has  been  said,  it  follows  that 
A^  is  made  up  of  the  sum  of  the  mobilities  of  the  two 
ions  £Moo  and  lAoo  of  the  salt  MA  ;  thus,  at  18°  for  potassium 
chloride,  AM  =  /Koo  +  1&U  (13011  =  64*67  +  65*44);  for 
acetic  acid,  A^  =  347*7  ;  and  for  ammonia,  A^  =  236*2. 

In  order  to  determine  the  value  of  the  conductivity  at 
infinite  dilution  of  a  weak  electrolyte,  the  corresponding 
value  for  one  of  its  salts  is  estimated,  and  from  the  value 
so  obtained  the  number  sought  may  be  calculated  by 
substitution.  Thus,  to  find  the  value  of  A^  for  benzoic 
acid,  A^  is  determined  for  potassium  benzoate,  and  from 
the  result  the  value  of  lKco  is  subtracted,  and  that  of 
lttoa  added. 

Absolute  Velocity  of  the  Ions.  —  As  we  have  seen,  the 
galvanic  conducting  power  of  a  solution  depends  on  the 
number  of  ions  present,  and  on  their  mobilities,  i.e.  on 
their  capability  of  wandering  through  the  solution.  The 
ions  exert  a  kind  of  friction  against  the  liquid,  which  can 
be  calculated  from  the  conductivity  of  the  solution.  This 

"  electrolytic  friction  "  is  measured  by  the  force  required  to 

+ 
impel  a  gram-ion  (1  gram  of  H  or  35*45  grams  of  Cl)  at  a 

speed  of    1   cm.   per   second.     Imagine   a 

column    of   a    normal   solution    of  hydro-  * 

chloric  acid  at  18°,  PPl  in  Fig.  36,  of  1  sq.      ] 

cm.  cross  section.     Suppose  two  planes,  A 


and    B,   laid  through  this  column  perpen-  B 

dicularly,  at  a  distance  of  1  cm.  apart,  and  FIG.  36. 

a   current   flowing    in    the    direction   AB, 
driven  by  a  potential  difference  between  the  two  planes  of  V 
volts.     The  current  strength  is  then  — 

/=  Vx  K 


148  CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 

where  K  is  the  specific  conductivity  of  the  normal  solution. 
If  hydrochloric  acid  were  completely  dissociated  in  normal 


solution,  then  at  18°  /would  be  (3U+n  6ff'4-)  =  ,  or, 

1000 


roughly,  0*380  ampere  per  volt;  of  this  the  first  part  is 
conditioned  by  the  mobility  of  the  hydrogen  ion,  and  the 
second  part  by  that  of  the  chlorine  ion.  That  part  of  the 
current  strength  due  to  the  migration  of  the  hydrogen  ion 
is  /H  =  V  X  0*314  amperes.  Now,  a  gram  -ion  carries  with 
it  96,500  coulombs,  and  between  A  and  B  there  is  1  c.c. 
of  normal  solution,  and  therefore,  assuming  complete  dis- 
sociation, 0*001  gram-ion.  This  quantity  of  hydrogen  ion 
carries  a  charge  of  96'5  coulombs.  Since  the  current 
strength  due  to  the  hydrogen  ions  is  /H  =  0*314xF" 
amperes  (coulombs  per  second),  the  time  — 

96*5  307*3 


must  elapse  before  all  the  hydrogen  ions  between  A  and  B 
have  passed  through  the  plane  B.  If  V  =  1  volt,  the  hydro- 
gen ions  require  about  307  seconds  to  pass  through  1  cm.  ; 
their  velocity  is,  therefore,  0*00325  cm.  per  second. 

Under  the  same  external  conditions,  the  velocity  of  the 
chlorine  ions  is  0*000678  cm.  per  second,  and  that  of  the 
other  ions  is  of  the  same  order  of  magnitude. 

The  assumption  that  the  hydrochloric  acid  is  completely 
dissociated  has  no  influence  on  the  result  of  the  calculation. 
Since  the  velocity  of  the  ions  is  proportional  to  the  mobility 
and  to  the  fall  of  potential  per  unit  length,  and  this  seldom 
reaches  the  value  of  1  volt  per  centimetre,  it  is  usually  found 
that  the  velocity  of  the  ions,  and  of  the  electricity  with  which 
they  are  charged,  is  extremely  small,  scarcely  amounting  to 
0*01  mm.  per  second.  The  following  numbers  give  the 
absolute  velocities,  U  and  Vt  of  the  most  commonly  occurring 
cations  and  anions  at  18°,  under  the  influence  of  a  fall  of 
potential  of  1  volt  per  centimetre  :— 


ABSOLUTE    VELOCITY   OF   THE    IONS. 


149 


Cation. 

rxio-. 

Anion. 

V  X  10°. 

H 

3250 

OH 

1780 

K 

670 

Cl 

678 

Na 

451 

I 

685 

Li 

347 

N03 

640 

NH4 

Ag 

660 
570 

CH3C02 
C2H5C02 

350 
320 

From  these  data  we  can  calculate  the  mechanical  force 
necessary  to  drive  a  gram-ion  through  the  water  with  a 
certain  velocity.  The  volt  is  so  defined  that  the  work 
107  ergs  is  required  to  transport  1  coulomb  against  this 
potential  difference.  Inversely,  if  the  fall  of  potential  is 
1  volt  per  centimetre,  then  107  dyne-cms,  (ergs)  are 
required  to  transport  1  coulomb  through  1  cm.  against  this 
fall,  i.e.  the  force  necessary  for  1  coulomb  is  107  dynes  =  10*18 
kilograms.  The  force  required  for  a  gram-ion  charged  with 
96,500  coulombs  against  this  same  fall  of  potential  is  therefore 
96,500  x  1018  =  983,000  kilograms.  This  force  drives  a 
gram-ion  of  hydrogen  with  the  velocity  325  x  10 ~5  cms.  per 
second.  The  force  required  in  order  that  the  velocity  may  be 

105 
1  cm.  per  second  must  be  ^=  times  greater,  i.e.  it  must  be 

983,000  x  105 

>—- — =  302  x  106  kilograms.     The  following  table 

gives  the  force  in  million  kilograms  required  to  drive  1 
gram-ion  through  water  at  18°  with  a  velocity  of  1  cm.  per 
second : — 


K  .  .  1467 
Na .  .  2180 
Li  .  2833 


NH4 
H   . 


1490  !  Cl  . 
302 


Ag.    .     1725     N0 


1450  |  OH  .  .  552 
1435  !  CH3C02  .  2810 
1536  C2H5C02.  3110 


From  these  numbers  it  can  be  seen  what  enormous 
mechanical  forces  are  required  to  move  the  ions  through 
the  solvent  with  an  appreciable  velocity.  As  the  tempera- 
ture rises,  these  values,  which  are  a  measure  of  the  friction, 
decrease  in  about  the  same  ratio  as  that  in  which  the  mobilities 


150 


CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 


of  the  ions  increase,  i.e.  for  most  ions  about  2*5  per  cent,  per 
degree. 

The  electrolytic  friction  of  the  ions  is  greater  in  other 
solvents  than  in  water.  The  addition  of  a  very  small 
quantity  of  another  non-conductor  to  the  water  appreciably 
increases  the  friction  of  the  ions,  and  consequently  decreases 
the  conductivity  of  the  solution,  just  as  the  internal  friction 
of  the  liquid  is  altered  by  a  similar  addition.  The  action 
of  foreign  substances  on  the  internal  friction  runs  almost 
parallel  with  that  on  the  electrolytic  friction.  Thus  I  have 
found  (17)  that  the  addition  of  one  per  cent,  by  volume 
of  the  non-conductors  mentioned  in  the  following  table  raises 
the  internal  friction,  and  the  electrolytic  friction  of  the 
commonly  occurring  ions  at  25°  by  the  amount  given  in 
the  table.  If  greater  quantities  be  added,  there  is  a  pro- 
portional increase  in  the  electrolytic  friction,  but  also  a 
diminution  of  the  degree  of  dissociation  of  the  electrolyte, 
particularly  if  a  concentrated  solution  of  this  is  used.  On 
this  subject  "Walker  (18)  has  made  an  interesting  investi- 
gation on  the  action  of  alcohols  on  diethylammonium 
chloride.  It  appears  that  the  degree  of  dissociation  is 
most  affected  by  those  substances  which  contain  relatively 
least  hydroxyl. 


Percentage  increase  of  the  internal 
and  ionic  friction  by  addition  of 
1  per  cent,  by  volume  of  the  non- 
conductor. 

Methyl 
alcohol. 

1 

11 

i 

<u 
d 

«3 

• 

1 

Internal  friction  of  the  water 
H  ion  

% 

2-1 
1-6 

31 

I'll 

°/ 

& 

1-91 

A 

1-55 

3 

1-54 

o/ 
/o 

4-6 
2-32 

OH  ion     

1-76 

1-87 

Monovalent  salt  ions   .     .     . 
S04,     C03,     etc.     (divalent 
negative  ions)      .... 
Ba,  Zn,  etc.  (divalent  positive 
ions)      

1-75 
2-06 
1-86 

2-34 
2-65 
2-45 

2-56 
2-95 

2-85 

1-99 
227 
2-21 

1-62 
2-14 
1-73 

2-99 
364 
3-21 

As  the  addition  increases,  the  function  of  the  water  as 
solvent    gradually   diminishes,   and   we   obtain   electrolytic 


ix.  ABSOLUTE    VELOCITY    OF   THE    IONS.  151 

solutions  in  another  solvent  than  water.  Only  few  investi- 
gations have  been  carried  out  with  a  view  to  ascertaining  the 
relationships  in  this  respect.  Kablukoff  (19)  investigated 
solutions  of  hydrochloric  acid  in  various  media,  and  found 
that  benzene  and  other  hydrocarbons  give  the  poorest  con- 
ductors ;  solvents  in  which  the  conduction  is  better  are  ethyl 
ether  and  higher  alcohols;  and  in  ethyl  alcohol,  methyl 
alcohol,  and  water  the  salts  conduct  best.  This  influence 
is,  however,  not  solely  dependent  on  the  differences  of  the 
frictions  against  the  various  liquids,  but  depends  far  more 
on  the  degree  of  dissociation  of  the  electrolyte  in  the 
solvent ;  only  after  these  two  actions  have  been  differentiated 
will  it  be  possible  to  gain  some  exact  knowledge  about  the 
influence  of  additions  on  the  friction  of  the  ions  in 
solution.  The  same  may  be  said  of  the  conductivity  of 
fused  salts. 

Many  attempts  have  been  made  to  directly  measure  the 
velocities  of  the  ions,  particularly  by  Lodge  and  Whetham. 
Lodge  (20),  for  instance,  filled  a  long  glass  tube,  E  (Fig. 
37),  with  sodium  chloride  solution,  which  was  deeply  coloured 
with  some  alkali  and  phenolphthalein. 
In  order  to  avoid  disturbances  in  the 
solution,  agar-agar  was  added.  This  is  a 
gelatinous  substance  which  acts  like  a 
fine  network  in  the  pores  of  which  is  the 
solution,  like  water  in  a  sponge.  The  FlG  37 

ends  of  the  tube  were  immersed  in  sul- 
phuric acid  solution,  contained  in  the  vessels  $  and  Si.  A 
current  from  the  battery  B  was  sent  in  the  direction  from 
S  to  $1  through  E,  so  that  the  hydrogen  ions  of  the  sulphuric 
acid  gradually  passed  along  E,  and  caused  decolorisation 
as  they  went.  The  results  obtained  for  the  velocity  of 
migration  of  the  ions  in  the  tube  E  corresponded  with  those 
predicted  by  theory. 

It  must  be  noted  that  in  these  experiments  it  is  not  the 
true  ionic  mobility  which  is  measured,  but  the  product  of 
ionic  mobility  and  degree  of  dissociation,  because  the  free 


152  CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 

ions  are  being  constantly  changed.  For  example,  if  half  of 
the  molecules  of  an  electrolyte  are  dissociated,  then  during 
the  first  half  of  a  definite  interval  of  time  all  the  ions  are  to 
be  regarded  as  combined,  and  during  the  next  half  they  are 
free.  Consequently,  although  the  fall  of  potential  only  acts 
on  the  free  ions  in  every  infinitely  small  interval  of  time, 
yet  in  a  finite  time  all  the  molecules  will  be  similarly  moved, 
inasmuch  as  during  the  first  half  of  this  time  they  migrate 
as  ions,  and  in  the  second  half  they  remain  at  rest  in  the 
undissociated  state.  The  apparent  velocity  will  in  this  case 
be  only  half  of  the  actual.  In  agreement  with  this,  Whetham 
(21)  found  a  much  lower  velocity  for  the  hydrogen  ions 
from  acetic  acid  than  for  the  same  ions  from  hydrochloric 
acid,  corresponding  with  the  lower  degree  of  dissociation  of 
acetic  acid. 

Eecently  ionic  mobilities  and  degrees  of  dissociation 
in  other  solvents  than  water  have  been  determined  by 
Vollmer  (##),  Carrara  (23),  Euler  (24),  Walden  (25),  and 
others. 

Diffusion.  —  Besides  the  electrical,  other  forces  may  be 
active  in  causing  the  movement  of  the  ions.  Of  these  the 
osmotic  pressure  is  the  most  important.  On  account  of  this 
pressure  a  phenomenon  called  diffusion  (hydrodiffusion)  may 

be  observed.      Consider  a   solu- 
A  —  *-      B  tion  in  a  parallel-sided  trough  of 

1  sq.  cm.  cross  section  (Fig.  38), 
and  imagine  two  planes,  A  and  B, 
perpendicular  to  the  column  of 
liquid,  1  cm.  apart.  Let  the  solu- 


FIG.  38.  tion    at   A    be    (n  -h  J)    normal 

and   that  at   B  (n  —  J)   normal. 

The  osmotic  pressure  at  A  is  then  greater  than  that  at 
B,  and  if  the  molecules  of  dissolved  substance  are  not 
dissociated  the  excess  of  pressure  at  A  is  equal  to  the 
osmotic  pressure  of  a  normal  solution,  i.e.  84'688  x  273 
=  23,120  grams  per  sq.  cm.  at  0°  (compare  pp.  26  and  30). 
This  excess  of  pressure  drives  the  dissolved  molecules  in  the 


ix.  DIFFUSION.  153 

direction  AB.     It  acts  on  all  the  molecules  in  the  cubic 
centimetre  between  A  and  B,  and  as  the  solution  is  (taken 

CM 

as  a  whole)  normal,  it  acts  on  TTTV  gram-molecules.     If  the 


force  necessary  to  drive  a  gram-molecule  of  the  dissolved 
substance  with  a  velocity  of  1  cm.  per  sec.  is  P  kilograms  — 
this  force  is  known  as  the  coefficient  of  friction  of  the  substance 
—  the  velocity  v,  which  is  proportional  to  the  force  acting  on  a 
gram-molecule,  is  given  by  — 

2312    1000  ,. 
v  =  -y>—  •  -    -   (1  4-  at)  cm.  per  second. 

JL  71 

The  factor  (1  +  at),  the  temperature  coefficient,  allows 
the  formula  to  be  applied  for  other  temperatures  than  0°. 
The  quantity  of  dissolved  substance  which  passes  B  in  one 
second  is  found  from  the  number  of  molecules  lying  between 
the  plane  B  and  another  plane  v  cm.  distant.  The  number 
of  milligram-molecules  in  this  volume  (v  c.c.)  is  v  x  n  =  N. 
N  is  therefore  given  by  — 

.  23-12(1  +o<) 


and  is  the  number  of  (milligram-)  molecules  which  are  driven 
through  1  cm.  per  second,  when  the  fall  of  concentration  is  1, 
i.e.  when  the  concentration  changes  by  1  unit  per  centimetre. 
N  is  called  the  diffusion  coefficient. 

This  coefficient  is  1000  times  greater  than  the  osmotic 
pressure  per  sq.  cm.  of  a  normal  solution  at  the  given  tem- 
perature divided  by  the  friction  P  in  kilog.  of  a  gram-molecule 
of  the  substance. 

If  we  have  an  electrolyte  instead  of  a  non-conductor  in 
the  solution,  then,  as  this  is  completely  dissociated  in  dilute 
solution,  the  osmotic  pressure  is  double  that  calculated. 
The  friction  P  is  made  up  of  two  factors,  PI  the  friction 
of  the  positive  ion,  and  P2  that  of  the  negative  ion 
(see  below).  At  18°  we  find  the  value  of  the  numerator 
of  the  expression  for  N  to  be  46,240  (1  +  ^%)  =  49,289. 


154  CONDUCTIVITY   OF   ELECTROLYTES.        CHAP. 

According  to  the  table  on  p.  149,  the  value  of  PI  for  Na 
is  2180  x  106  kilograms,  and  that  of  P2  for  Cl,  1450  X  10° 
kilograms ;  therefore  for  sodium  chloride  (NaCl)  P  =  P\  4-  P 2 
=  3630  x  106  kilograms.  If  we  take  the  day  instead  of 
the  second  as  the  unit  of  time,  the  number  given  has  to  be 
multiplied  by  the  number  of  seconds  in  a  day  (60  x  60  x  24 
=  8-64  x  104).  We  then  obtain  for  sodium  chloride  at  18°- 

N  =  49>289  x  8'64  x  104      -, .-,  ,- 
3,630  x  106 

Nernst  (26),1  who  first  developed  this  theory,  showed 
that  the  calculated  numbers  agree  well  with  those  found  by 
experiment,  as  can  be  gathered  from  the  next  table.  The 
difference  between  the  observed  and  calculated  values  is 
mainly  due  to  the  fact  that  solutions  of  such  concentration 
were  used  that  the  dissociation  was  not  complete;  and  so 
the  osmotic  pressure  was  actually  smaller  than  the  value 
employed  in  the  calculation;  it  will  be  observed  that  the 
calculated  values  are  generally  higher  than  those  found  from 
experiment. 

DIFFUSION  COEFFICIENTS  AT  18°. 
(Unit  of  time,  the  day.) 

Obs.  Calc.  Obs.  Calc. 

HC1 2-30  2-43  i  NaN03.     ....  1-03  1-15 

HN03 2-22  2-32  |  NaC2H302      .     .     .  0-78  0-84 

KOH    .....  1-85  2-07  NaCHO,   ....  0-95  1-02 

NaOH 1-40  1-55  !  NaC6H8SOs   .     .     .  0-74  0-74 

NaCl  1-08  1-17  !  KC1 .  1'29  1-46 


NaBr 1-10        1-13 

Nal.' 1-05        1-12 

KNO,  .  1-22         1-42 


NH4C1 1-30        1-44 

Lid  0-97        0-99 


KBr 1-40  1-47 

KI 1-34  1-47 

LiBr 1-05  I'OO 

Lil 0-94  1-00 

AgN03 1-27  1-29 


It  is  easy  to  see  that  the  temperature  coefficient  of  the 
diffusion  must  be  the  sum  of  the  temperature  coefficients  of 

1  In  his  calculation  Nernst  used  other   figures  than  here  employed, 
and  obtained  for  N  T12  instead  of  1-17. 


IX. 


DIFFUSION. 


155 


the  osmotic  pressure,  which  is  about  0 '0034  at  18°,  and  of  PI 
and  P2,  which  for  the  common  salts  is  about  0'024.  Accord- 
ing to  this  the  diffusion  coefficient  should  increase  by  27 
per  cent,  per  degree  at  18°,  and  this  has  been  experimentally 
confirmed. 

The  friction  coefficient  of  non-conductors  cannot  be 
determined  by  an  electrical  method;  but  its  value  can  be 
estimated  from  the  diffusion  constant.  From  Graham's 
results,  Nernst  has  calculated  the  following  values  :— 


Diffusing  substance. 

Formul  t. 

Number     ^Molecular 
of  atoms.        weight. 

Coefficient  of 
friction. 

Urea   .... 
Chloral  hydrate 

CO(NH2)2 
CC13CH(OH)2 

8              GO 
.  10            165 

2,500x10°  kg. 
3,800 

Mannitol  .     .     . 

C«HM06 

26            182 

5,500 

Cane  sugar  .     . 
Gum  arable  . 

Qi2"-2?Pn 
»(CaH10Ofi) 

45            342 
very  great 

6,700 
16,000. 

Tannic  acid  .     . 

20,000 

Egg  albumen     . 

— 

33,000 

Caramel  .     .     . 

— 

»j 

44,000 

The  friction  evidently  increases  with  the  molecular  weight 
of  the  substance. 

According  to  a  calculation  made  by  Euler  (#7),  the 
friction  of  a  gram-molecule  is  approximately  proportional  to 
the  square  root  of  the  molecular  weight  of  the  substance 
examined.  This  gives  very  good  values  for  substances  ,of 
known  molecular  weight,  provided  that  the  molecular  volume 
does  not  vary  too  much.  If  we  apply  this  method  to  calculate 
the  molecular  weight,  M,  of  the  four  colloids  examined  by 
Graham,  we  find  the  following  values  : — 

Gum  arabic     (n  =  11)  M  =     1,750 
Tannic  acid  2,730 

Egg  albumen  7,420 

Caramel  13,200. 

These  results  are  particularly  interesting  because  we 
have  no  method  free  from  objection  for  determining  the 


156         CONDUCTIVITY  OF  ELECTROLYTES.       CHAP.  ix. 

molecular  weight  of  a  pure  colloid.  It  is  very  certain,  as 
other  investigations  have  also  shown,  that  the  molecular 
weights  of  these  substances  are  very  high. 

It  might  appear  strange  that  a  force  of  302  x  106  kilograms 
is  required  to  move  a  gram  of  hydrogen  ion  in  water  with  a 
velocity  of  1  cm.  per  second.  However,  it  is  known  that 
the  more  finely  divided  a  suspended  substance  is,  the  slower 
does  it  deposit  under  the  influence  of  some  force,  e.g.  gravity 
(or  rather  the  difference  between  the  specific  gravity  of  the 
suspended  solid  and  that  of  the  liquid).  A  good  example  of 
this  is  offered  by  the  fat  globules  in  milk.  The  ions  being 
infinitely  smaller  than  the  particles  of  suspended  matter,  it 
is  therefore  not  so  astonishing  that  these  move  so  slowly 
under  the  influence  of  tolerable  forces. 


CHAPTER   X. 


Degree  of  Dissociation  and  Dissociation  Constant. 

Strong  and  Weak  Electrolytes. — Before  proceeding 
further  it  will  be  advisable  to  classify  the  electrolytes  into 
two  groups — those  highly  dissociated  and  those  dissociated 
only  to  a  slight  extent,  or,  shortly,  strong  and  weak  electrolytes. 
All  salts  belong  to  the  first  class,  with  a  few  exceptions 
which  have  not  yet  been  thoroughly  investigated  (copper 
acetate,  mercury  salts,  potassium  antimonyl  tartrate,  and 
possibly  some  compounds  closely  allied  to  these) ;  and  to  this 
class  belong  also  many  of  the  inorganic  mono-  and  di-valent 
acids  and  bases.  The  organic  acids  and  bases  (but  not  exclu- 
sively these)  are  weak  electrolytes;  as  examples  we  may 
quote  the  already-mentioned  cases  of  acetic  acid  and 
ammonia.  These  latter  substances  at  moderate  dilution  are 
only  dissociated  to  the  extent  of  a  few  per  cents.  There 
are,  of  course,  substances  which  stand  roughly  between  these 
two  groups,  but  their  number  is  comparatively  small. 

Degree  of  Dissociation  of  some  Typical  Electrolytes. 
— In  order  to  give  some  idea  of  the  behaviour  of  various 
electrolytes,  the  following  table  contains  the  degree  of 
dissociation  of  some  commonly  occurring  salts  : — 


1 

V  * 

HC1. 

KCl. 

KCaH302. 

iBa012. 

*K2S04. 

iZnS04. 

0-0001 

0-992 

0-990 

0-992 

0-992 

0-989 

0-001 

0-992 

0-979 

0-973 

0-962 

0-959 

0-890 

0-01 

0-974 

0-941 

0-931 

0-886 

0-873 

0-664 

0-1 

0-924 

0-861 

0-830 

0-759 

0-713 

0-418 

1 

0-792 

0-755 

0-628 

0-579 

0-534 

0-241 

i58 


DEGREE    OF   DISSOCIATION. 


CHAP. 


Of  the  substances  mentioned  hydrochloric  acid  is  the  most 
highly  dissociated. 

The  other  monovalent  strong  acids,  like  nitric,  hydro- 
bromic,  hydriodic,  chloric  acids,  etc.,  have  about  the  same 
degree  of  dissociation ;  the  strong  bases,  such  as  potassium, 
sodium,  lithium,  and  thallium  hydroxides,  and  the  ammonium 
bases,  etc.,  are  also  dissociated  to  about  the  same  extent. 
The  salts  formed  from  monovalent  acids  and  monovalent 
bases  have  a  slightly  lower  degree  of  dissociation,  as  seen 
from  the  numbers  given  for  potassium  chloride  and  potassium 
acetate.  The  degree  of  dissociation  is  much  smaller  for 
salts  formed  from  divalent  acids  with  monovalent  bases  and 
for  those  formed  from  monovalent  acids  and  divalent  bases  ; 
the  degrees  for  these  two  classes  of  salts  are  very  similar 
(compare  potassium  sulphate  and  barium  chloride  in  the 
table).  Salts  produced  from  a  divalent  acid  and  a  divalent 
base  (zinc  sulphate)  have  a  still  lower  degree  of  dissociation. 

We  know  the  mobilities,  lm,  of  almost  all  ions  and  the 
degree  of  dissociation  for  various  salts  (from  the  investiga- 
tions of  Kohlrausch  (7),  Ostwald,  and  Bredig),  and  with  the 
aid  of  these  we  can  calculate  the  conductivity  of  any  salt 
solution.  We  cannot,  however,  make  the  calculation  for 
solutions  of  weak  bases  and  acids.  These  compounds  are 
much  less  dissociated  than  the  salts.  From  the  table  on 
p.  135  we  find  the  following  degrees  of  dissociation,  a,  for 
acetic  acid  and  ammonia : — 


Acetic  acid. 

Ammonia. 

1 
o  ' 

lOOa. 

1  . 

lOOa. 

0-0001 

30-8 

0-0001 

28-0 

0-001 

11-8 

0-001 

11-9 

0-01       .  * 

4-11 

0-01 

4-07 

0-1 

1-32 

0-1 

1-40 

We  shall  return  later  to  these  weak  electrolytes,  which 
appeared  at  first  to  show  the  least  agreement,  but  which 
later  exhibited  more  regularities  than  the  strong  electrolytes. 


x.  OSMOTIC  AND  ELECTRICAL  DETERMINATIONS.   159 

Comparison  between  the  Results  of  the  Osmotic 
and  the  Electric  Determinations  of  the  Degree  of  Dis- 
sociation.— Solutions  of  salts  give  what  appeared  to  be 
anomalous  results  with  respect  to  the  lowering  of  the 
freezing  point,  or  the  vapour  pressure,  and  the  raising  of 
the  boiling  point,  or  the  osmotic  pressure,  inasmuch  as  the 
influence  of  the  salts  was  greater  than  that  of  other  sub- 
stances (see  the  preceding  chapters).  As  mentioned  on  p.  59, 
these  facts  can  be  explained  by  assuming  that  the  salt  is 
partially  dissociated.  From  the  values  obtained  in  any  of 
these  determinations  the  degree  of  dissociation  can  be 
calculated,  and  there  arises  the  question  whether  the  degrees 
found  in  this  way  are  the  same  as  those  obtained  from  the 
electrical  measurements.  In  1887  I  showed  (2)  that  in 
the  case  of  about  a  hundred  solutions  there  was  a  good 
agreement  between  the  degrees  of  dissociation  calculated 
from  Kaoult's  results  for  the  freezing  point  and  from 
Kohlrausch's  measurements  of  the  conductivity. 

The  following  tables  contain  the  degrees  of  dissociation 
found  by  the  two  methods.  The  value  obtained  from  the 
conductivity  is  given  under  ai,  and  under  a%  is  the  result 
calculated  from  the  freezing  point  of  a  1  per  cent,  solution 
of  the  substance.  The  following  consideration  shows  how 
the  latter  calculation  is  made:  If  a  substance  in  solution 
has  the  molecular  weight  M  which  corresponds  with  its* 
chemical  formula,  then  a  solution  which  contains  If  grams 
of  the  substance  in  100  grams  of  solvent  should  have  the 
freezing  point  — 18'6°  (the  molecular  depression  of  the 
freezing  point  of  water),  and  a  solution  containing  1  gram 

1  R*fi° 
in  100  grams  of  solvent  should  freeze  at -^.     Instead  of 

this  the  solution  freezes  at  —  A°,  which  is  lower  than  the 
temperature  already  indicated.  The  depression  of  the  freezing 
point  caused  by  the  dissolved  substance  is  therefore  too  great, 
indicating  that  the  solution  contains  more  molecules  than 
has  been  assumed,  i.e.  a  part  of  the  dissolved  molecules  has 
been  split  up  into  smaller  ones  (the  ions),  so  that  the  number 


i6o 


DEGREE    OF    DISSOCIATION. 


CHAP. 


of  molecules  dissolved  is  greater  than  that  calculated  simply 
from  the  chemical  formula.  Now,  if  a  molecule  can  be  dis- 
sociated into  n  ions  (for  KC1  =  K  +  Cl,  n  =  2  ;  for  K2S04  = 
2K  +  S04,?i=  3;  for  K4(CN)6Fe  =  4K  +  (ClST)6Fe,™  =  5), 
and  if  a2  denotes  the  fraction  of  the  whole  number  of  mole- 
cules which  are  dissociated,  then  in  the  solution  there  must 
be  for  every  gram-molecule  dissolved  1  —  a2  undissociated 
molecules  and  atfi  ions,  which  are  to  be  regarded  as  free 
molecules.  From  every  gram-molecule,  therefore,  we  obtain 
1  —  a2  4-  na%  =  1  -f  (n  —  I)a2  molecules,  and  the  observed 
freezing  point  —  A°  must  be  greater  than  that  calculated 

1  o«c° 

according  to  the  chemical  formula  -    ~~  in  this  ratio  (/). 


That  is  to  say  — 


_f       A   .  18*6  , 

/->  4-r  -y  «  1  +(»,<-  IK 


from  which  a2  can  be  calculated. 


Non-electrolytes. 

Bases. 

Acids. 

Methyl  alcohol 

ai       «2 
0-00     0-06 

al       "2 
Barium  hydroxide    0-84    0-d5 

Hydrochloric  acid     0-90    0-98 

Ethyl  alcohol. 

O'OO     0-06 

Calcium  hydroxide  0-80    0-80 

Nitric  acid      . 

0-92     0-94 

Butyl  alcohol 

O'OO     0-07 

Lithium  hydroxide  0-83    1-02 

Chloric  acid    . 

0-91     0-97 

Glycerol    . 
Mannitol  . 

0-00     0-08 
0-00     0-03 

Sodium  hydroxide    0-88    0-96 
PotassiumhydroxideO-93    0-91 

Sulphuric  acid 
Phosphoric  acid 

0-60     0-53 
0-08     0-44 

Cane  sugar 

o-oo    o-oo 

Ammonia  .     . 

001     003 

Hydrogen  sulphic 

e   0-00     0-04 

Phenol       . 

O'OO     0-16 

Methylamine  . 

0-03     0-00 

Boric  acid  .     . 

O'OO     O'll 

Acetone     . 

0-00     0-03 

Trimethylainine 

0-03    0-09 

Formic  acid    . 

0-03     O'Ot 

Ethyl  ether 

o-oo   o-io 

Ethylamine    . 

o-ot    o-oo 

Butyric  acid   . 

o-oi   o-oi 

Ethyl  acetate 

0-00     0-04 

Propylamme  . 

0-04     O'OO 

Oxalic  acid     . 

0-25     0-13 

Acetamide. 

0-CO     0-04 

Aniline      .     . 

000     0-17 

Malic  acid  .     . 

0-07     0-08 

Salts. 


Salts. 


"1 

«2 

«M 

a-2 

0-86 

0-82 

Barium  chloride    . 

.     0-77 

0-81 

0-81 

0-67 

Lead  nitrate    .     . 

.     0-54 

0-51 

0-82 
0-83 

0-82 
0-86 

Copper  sulphate   . 
Mercuric  chloride 

.    0-35 
.    0-05 

-  0-03 
0-11 

0-69 

0-63 

Cadmium  iodide   . 

0'5(L 

-  0-06 

0-67 

0-56 

Potassium  chloride  . 
Potassium  nitrate 
Sodium  nitrate  .  , 
Potassium  acetate  . 
Potassium  carbonate 
Potassium  sulphate  . 


In   dilute   solution,   too,  unexpected  results  have  been 
obtained.     These,  however,  are  to  be  attributed  for  the  most 


x.    OSMOTIC  AND  ELECTRICAL  DETERMINATIONS.   161 


part  to  errors  of  experiment  with  which  the  methods  are 
infected.  Thus,  Jones  (3)  found  for  a  0*75  per  cent,  solu- 
tion of  cane  sugar  a  molecular  depression  of  the  freezing 
point  which  was  too  great  by  27  per  cent.,  and  all  the 
older  observations  on  dilute  solutions  are  subject  to  similar 
deviations.  Nernst  and  Abegg  (4)  have  shown  that  this 
want  of  agreement  is  partly  attributable  to  the  fact  that 
the  freezing  out  of  the  solid  solvent  does  not  take  place 
instantaneously,  and  in  consequence  the  observed  temperature 
is  to  a  certain  extent  influenced  by  the  temperature  of  the 
surrounding  freezing  mixture.  The  ideal  method  would 
therefore  be  to  work  with  a  freezing  mixture  the  temperature 
of  which  is  only  infinitessimally  lower  than  the  freezing 
point  to  be  determined.  Interesting  observations  in  this 
respect  have  been  made  by  Jones,  Loomis,  Eaoult,  and  others. 
The  salt  which  has  been  most  thoroughly  investigated 
cryoscopically  is  potassium  chloride,  which  possesses  the 
great  advantage  that  the  internal  friction  of  the  solution 
differs  but  slightly  from  that  of  pure  water,  so  that  a  cor- 
rection for  the  influence  of  this  friction  on  the  conductivity, 
within  the  limits  of  concentration  employed,  can  safely  be 
neglected.  Loomis  (-5)  found  the  following  freezing  points 
for  solutions  of  this  salt : — 


Concentration, 

"• 

Freezing  point, 
G. 

G 
m 

(i  +a)l-86. 

Diff.  in  per  cent. 

o-oi 

-0-0360° 

3-60 

3-59 

+  0-3 

0-02 

0-0709 

3-55 

3-56 

-  0-3 

0-03 

0-1055 

352 

3-53 

-0-3 

0-035 

0-1235 

3-53 

3-52 

+  0-3 

0-05 

0-1749 

3-50 

3-50 

o-o 

0-10 

0-3445 

3-445 

3-441 

+  0-1 

0-20 

0-6808 

3-404 

3-386 

+  0-5 

0-40 

1-3411 

3-353 

3-305 

+  1-5 

For  concentrations  up  to  0*2-normal  the  agreement  is 
perfect  (within  the  experimental  error).  The  data  obtained 
by  Loomis  have  been  fully  confirmed  by  Jones,  Abegg,  Barnes, 

M 


162  DEGREE    OF    DISSOCIATION.  CHAP. 

C1 
and  Kaoult.     For  higher  concentrations  —  is  always  greater 

than  the  calculated  value;  the  following  salts,  however, 
which  are  known  to  partially  form  double  molecules  in 
concentrated  solution,  behave  exceptionally  in  this  matter  : 
cadmium  iodide,  magnesium  sulphate,  zinc  sulphate,  copper 
sulphate,  etc.  (compare  p.  143). 

The  more  recent  determinations  by  Hausrath  (0)  show 
that  the  degrees  of  dissociation  at  high  dilution  obtained  from 
the  freezing  point  experiments  agree  well  with  those  found 
from  the  conductivities. 

Dissociation  Equilibrium  of  Weak  Electrolytes.— 
The  laws  mentioned  in  Chapter  VI.  for  ordinary  dissociation 
must  also  obtain  for  the  equilibrium  between  an  electrolyte 
and  its  ions.  As  already  shown,  the  dissociation  of  a 
substance  AB  which  decomposes  into  the  components  A  and 
B  is  regulated  by  the  law  of  mass  action  — 

K  x  (7AB  =  C'A  x  CK 

where  K  is  a  constant. 

If  we  dissolve  an  electrolyte,  for  instance,  acetic  acid, 

it  partially  dissociates  into  the  ions  H  and  CH3C02,  and  the 
above  law  can  be  applied  to  this  decomposition.  This  was 
done  by  Ostwald,  and  almost  simultaneously  by  van't  Hoff 
(7),  whose  results  for  acetic  acid  at  14*  1°  are  given  in  the 
next  table,  ju  denotes  the  molecular  conductivity,  and  a 
(observed)  the  degree  of  dissociation  calculated  from  this. 
Under  a  (calculated)  is  given  the  degree  of  dissociation 
calculated  by  means  of  the  above  formula,  setting  G'A  =  CB, 
since  both  ions  must  occur  in  equal  quantities  ;  v  is  the 
dilution,  i.e.  the  volume  in  litres  in  which  a  gram-molecule 
(60  grams)  of  acetic  acid  is  dissolved. 
Since  — 


'  and  °"  =  CB  =  °' 


X. 


LAW   OF   DILUTION. 


163 


the  formula  K  x  (7AB  =  <7A  x  CB  =  (-)2  can  be  transformed 
into — 


or   A  = 


The  relationship  expressed  in  this  formula  is  known  as 
Ostwald's  law,  or  the  law  of  dilution  (8). 

The  constant  K  is  termed  the  electrolytic  dissociation 
constant  of  acetic  acid. 

ACETIC  ACID  AT  14-1°. 


V. 

Mi" 

lOOa  (observed). 

lOOa  (calculated). 

0-994 

1-27 

0-402 

6-42 

2-02 

1-94 

0-614 

0-60 

15-9 

5-26 

1-66 

1-67 

18-9 

5'63 

1-78 

1-78 

1500 

46-6 

14-7 

15-0 

3010 

64-8 

20-5 

20-2 

7480 

95-1 

30-1 

30-5 

15000                   129 

40-8 

401 

CO 

316 

100 

100 

log  K  =  5-25  -  10(5-25).     K  =  0-0000178. 

As  is  evident  from  the  numbers  given,  the  calculated  and 
observed  degrees  of  dissociation  agree  extremely  well.  In 
no  other  field  in  which  the  law  of  mass  action  has  been 
applied  have  so  good  results  been  obtained. 

This  agreement  between  theory  and  practice,  however,  is 
only  found  for  weak  electrolytes,  of  which  Ostwald  investi- 
gated the  acids  and  Bredig  the  bases  (9). 

It  is  just  possible  that  even  in  this  case  the  law  of  mass 
action  is  not  undisturbed  by  other  factors.  The  deviation 
from  the  law  seems  to  be  greater  the  stronger  the  acid 
is.  Amongst  the  stronger  organic  acids  deviations  occur, 
e.g.  with  formic  acid,  and  to  an  even  greater  extent  with  the 


164 


DEGREE    OF    DISSOCIATION. 


CHAP. 


nitrobenzoic  acids  and  the  chloracetic  acids.  (Phosphoric 
acid,  which  may  be  regarded  as  a  transition  electrolyte  to  the 
strong  acids,  also  shows  great  deviations.)  We  shall  return 
later  to  a  possible  explanation  of  this  unexpected  phenomenon. 
Dissociation  Equilibrium  of  Strong  Electrolytes.— 
Up  till  the  present  it  has  unfortunately  not  been  possible  to 
bring  the  dissociation  of  strong  electrolytes  (salts,  strong 
acids,  and  bases)  into  perfect  agreement  with  the  law  of  mass 
action.  For  this  class  of  substances  Eudolphi  (10)  has 
changed  the  Ostwald  formula  into — 


i.e.  he  has  replaced  the  factor  v  in  the  denominator  by  ^/v. 
As  an  example  we  may  give  the  numbers  for  silver  nitrate. 
In  this  case  the  formula  gives  values  which  are  in  perfect 
agreement  with  the  experimental  results,  and  the  same  is 
true  for  many  other  strong  electrolytes.  The  connection 
expressed  in  the  formula  is  purely  empiric,  and  no  reason 
can  be  given  for  its  validity.  This  anomaly  in  connection 
with  strong  electrolytes  is  the  most  difficult  problem  of  the 
dissociation  theory,  and  several  experienced  investigators 
have  endeavoured  to  solve  it,  but  so  far  without  success. 

SILVER  NITRATE  AT  25°. 


V. 

M«>* 

a  (observed). 

K. 

• 
16                 102-3 

0-828 

1-00 

32 

108-0 

0-875 

1-08 

64                111-0 

0-899 

0-96 

128                 114-3 

0-926 

1-03 

256 

116-9 

0-947 

1-05 

512 

118-7 

0-962 

107 

123-5 

1-00 

JT(mean  value)  =  1*03. 
Another,  and  still   more   exact  formula  connecting  the 


x.      EQUILIBRIUM    OF   STRONG   ELECTROLYTES.     165 

dissociation  of  salts  with  the  dilution  has  been  suggested  by 
van't  Hoff  (11),  namely — 

rr        V 

=  cl' 

whilst  Ostwald's  formula  can  be  expressed  in  the  form — 

r<2 
V         ^f 

^' 

Cj  denotes  the  concentration  of  each  ion  (it  is  the  same 
for  both)  expressed  in  gram-ions  per  litre,  and  C8  is  the 
concentration  of  the  undissociated  part  of  the  electrolyte 
expressed  in  gram-molecules  per  litre. 

Others,  among  them  Storch  (12),  have  expressed  the 
dilution  law  in  the  form — 

sf* 

17          ^f 

=  ^' 

and  have  experimentally  determined  the  value  of  the  exponent 
n,  which  has  been  found  to  vary  for  electrolytes  of  different 
strengths,  but  in  general  is  not  very  different  from  the  value 
1*5  contained  in  van't  Hoff's  form. 

A  possible  explanation  of  this  peculiar  deviation  from 
the  law  of  mass  action  is  that  the  addition  of  the  ions  of  a 
strong  electrolyte  considerably  increases  the  dissociating 
power  of  the  water.  If  this  be  correct,  the  dissociation 
constant  of  the  dissolved  substance  should  be  an  increasing 
function  of  the  quantity  of  salt  ions  dissolved  in  the  water. 
This  action  of  the  ions  recalls  the  much  weaker  and  opposite 
effect  of  some  non-electrolytes  (see  p.  150).  The  assumption 
is  supported  by  some  experiments  in  which  the  dissociation 
equilibrium  of  weak  acids  was  determined  in  presence  of 
salts  (13).  These  experiments  show  that  the  dissociation 
constants  of  the  weak  acids  increase  in  the  same  way  with 
increasing  salt  concentration  as  do  the  constants  for  the 
salts ;  there  is,  however,  a  quantitative  difference,  and  in  the 
case  of  the  salts  their  own  ions  form  the  active  material. 
Whatever  be  the  explanation,  it  may  be  regarded  as  certain 


1 66  DEGREE    OF    DISSOCIATION  CHAP. 

that  the   deviation   from   the  law  of  mass   action  is  only 
apparent. 

Divalent  Acids. — The  above  formulae  apply  to  electro- 
lytes formed  from  two  monovalent  ions.  When  the  con- 
centration is  great,  a  strong  divalent  acid,  such  as  sulphuric 
acid,  appears  to  dissociate  according  to — 

H2S04  =  H  +  HS04. 

As  the  solution  is  diluted,  the  HS04  ions  suffer  further 
dissociation — 

HS04  =  H  +  S04. 

Each  of  these  dissociations  is  regulated  by  a  particular 
equation,  and  the  equilibrium  is  so  masked  thereby  that  it 
cannot  be  determined.  The  same  applies  to  salts  consisting 
of  polyvalent  ions. 

In  the  case  of  most  of  the  di-  and  poly-valent  acids 
(sulphuric  acid  is  almost  the  only  exception)  only  the  first 
phase  of  the  dissociation  takes  place  at  the  dilutions  at 
which  we  commonly  work,  i.e.  only  the  first  hydrogen  ion  is 
split  off.  The  other  possible  dissociation  can  therefore  be 
neglected,  and  with  a  fair  degree  of  exactitude  we  can  apply 
Ostwald's  formula,  although  this  is  only  rigidly  applicable  to 
electrolytes  consisting  of  two  monovalent  ions. 

Influence  of  Substitution  on  the  Dissociation  of 
Acids. — It  has  been  known  for  a  very  long  time  that  an 
acid,  such  as  acetic  acid,  becomes  stronger  by  replacement 
(substitution)  of  one  hydrogen  atom  by  a  chlorine  atom ;  mono- 
chloracetic  acid  (CH2C1COOH)  is  considerably  stronger  than 
acetic  acid  (CH3COOH);  dichloracetic  acid  (CHC12COOH) 
is  stronger  than  monochloracetic  acid ;  and  trichloracetic  acid 
(CC13COOH)  is  the  strongest  of  the  substitution  products.  The 
series  of  strengths  can  be  recognised  from  the  dissociation 
constants,  K,  because  the  greater  this  constant  is  the  greater 
is  the  quantity  of  substance  dissociated  at  a  particular 
dilution,  v,  or  the  degree  of  dissociation  of  the  acid,  and  it 


x.  DISSOCIATION    OF   ACIDS.  167 

is  upon  this  alone  that  the  strength  of  the  acid  depends  (see 
Chap.  XII).  For  the  four  acids  mentioned,  Ostwald  (14) 
has  determined  the  dissociation  constants  to  be — 

CH3COOH     CH2C1COOH     CHC12COOH       CC13COOH 
1-80  X  10~5     155  x  10~5         5140  X  10~5  121000  x  10"3. 

Bromine,  iodine,  cyanogen,  oxygen,  and  the  nitro  group, 
when  introduced  into  the  radicle  of  an  acid  in  place  of 
hydrogen,  increase  the  dissociation  constant,  and  consequently 
the  strength,  of  the  acid;  substitution  by  hydrogen  or  the 
amino  group  weakens  the  acid.  In  the  case  of  the  benzene 
derivatives,  substitution  in  the  ortho  position  exerts  a 
stronger  influence  than  substitution  in  the  meta  or  para 
positions,  which  act  about  equally.  These  regularities  are 
of  great  interest  in  organic  chemistry,  and  have  been  much 
utilised  to  solve  questions  concerning  constitution  and 
grouping  of  the  atoms  in  the  molecule. 


CHAPTER  XL 

Conclusions  from  the   Dissociation  Theory.    Additive 
Properties  of  Solutions. 

General  Remarks. — The  properties  of  a  solution  may  be 
regarded  as  the  sum  of  the  properties  of  the  substances 
present  in  the  solution.  A  solution  of  cane  sugar  contains 
two  substances ;  that  which  is  present  in  excess  is  generally 
termed  the  solvent,  and  the  other  the  dissolved  substance ; 
the  physical,  chemical,  physiological,  and  other  properties  of 
the  solution  can  be  regarded  as  approximately  the  sum  of  the 
corresponding  properties  of  the  two  substances  mixed  (water 
and  sugar). 

Now,  since  salts  are  highly  dissociated  in  aquexms  solution, 
the  properties  of  the  solution  will  be  equal  to  the  sum  of  the 
properties  of  the  solvent  (water),  of  the  ions,  and  of  the 
undissociated  substance.  For  dilute  solutions  the  undis- 
sociated  part  is  comparatively  small,  and  it  appears  in  many 
cases  that  its  properties,  when  they  differ  appreciably  from 
those  of  the  two  ions  (e.g.  with  reference  to  reactivity  and 
occasionally  with  reference  to  colour,  etc.),  are  not  striking. 
For  such  cases  it  is  usual  to  say  that  the  properties  of  the 
salt  solution  are  equal  to  the  sum  of  the  properties  of  the 
two  ions,  and  leave  the  properties  of  the  solvent  out  of 
account.  This  rule  enables  us  to  review  the  properties  of  the 
numerous  salts  in  solutions  (dilute),  because  the  number 
of  ions  obtained  from  these  salts  is  comparatively  small. 
The  experimental  confirmation  of  this  rule  may  be  regarded  as 
a  strong  support  of  the  view  that  the  salts  are  electrolytically 
dissociated. 


CHAP.  xi.     SPECIFIC    GRAVITY   OF    SOLUTIONS. 


169 


Specific  Gravity  of  Electrolytic  Solutions.  —  When  we 
dissolve  a  substance,  e.g.  cane  sugar,  in  water,  the  specific 
gravity  of  the  solution  deviates  more  and  more  from  1  as 
the  concentration  increases.  In  the  case  of  most  electrolytes 
the  specific  gravity  increases.  When  we  examine  the  depend- 
ence of  the  specific  gravity  on  the  normality  n,  we  find  that 
it  can  be  represented  by  a  function  of  the  form  — 


S  = 


an 


Thus,  for  sugar  solutions  at  17  '5°,  we  find,  if  the  density 
of  water  at  17*5°  be  taken  as  unit— 

8=1  +  0-132871  -  0-002^. 

The  first  part  of  the  following  table  shows  how  exactly 
the  specific  gravity  may  be  obtained  from  a  formula  of  this 
type— 


%  Cane  sugar. 

Normality. 

Specific  gravity 
(observed). 

Specific  gravity 
(calculated). 

0 

0 

1 

1 

10 

0-3041 

1-0402 

1-0402 

20 

0-6336 

1-0833 

1-0833 

30 

0-9908 

1-1296 

1-1296 

40 

1-3794 

1-1794 

1-1793 

50 

1-8025 

1-2328 

1-2328 

60 

2-263 

1-2899 

1-2903 

70 

2-765 

1-3510 

1-3520 

10 

0-3041 

1-0402 

1-0399 

20 

0-6336 

1-0833 

1-0832 

30 

0-9908 

1-1296 

1-1301 

The  numbers  in  the  lower  part  of  the  table  have  been 
calculated  from  the  simpler  formula— 

8=1  +  013137&, 

which  gives  the  specific  gravities  up  to  normal  concentration 
(30  per  cent.)  sufficiently  accurately  for  most  purposes. 


i  ;o  THE    DISSOCIATION   THEORY.  CHAP. 

If,  now,  the  specific  gravity  of  solutions  of  a  substance,  A, 
can  be  found  from— 

S  =  1  -f-  an, 

and  that  of  solutions  of  another  substance,  B,  from  — 
S  =  1  +  fin, 

then  for  solutions  containing  both  substances,  ^-normal  with 
respect  to  A,  and  %  normal  with  respect  to  B,  we  have  — 

S  =  1  +  an 


If  we  take  the  case  of  a  highly  dissociated  salt,  e.g.  sodium 
chloride,  we  may  for  the  present  purpose  assume  that  it  is 
completely  dissociated  in  dilute  solution.  The  solution  con- 
tains in  unit  volume  a  certain  number  (n)  of  sodium  ions, 
and  the  same  number  of  chlorine  ions.  Let  us  now  set  the 
coefficient  of  the  chlorine  ions  =  a,  of  the  sodium  ions  =  ]3, 
and,  further,  the  coefficients  for  bromine  ions  =  7,  and  for 
ammonium  ions  =  S,  then  we  obtain  for  O'l  -normal  solutions 
of  the  salts  sodium  chloride  (a),  sodium  bromide  (b), 
ammonium  chloride  (c),  and  ammonium  bromide  (d)  the 
equations  — 

S:i  =  l+  01(«  +  0), 
Sb  =  1  +  01(j3  +  7), 

£  =  1  +  01(a  +  S), 

>s;,  =  i  +  0-1(7  +  3). 

Consequently— 


This  illustrates  a  typical  additive  property.  If  we  have 
numerical  data  of  a  property  for  equally  concentrated  solu- 
tions of  four  salts,  AiKi,  AiK2,  A2Ki,  and  A2K2,  which  are 
formed  from  a  pair  of  positive  ions,  K,  and  a  pair  of 
negative  ions,  A,  then  the"  difference  in  the  value  of  this 
property  for  the  salts  AiKi  and  AiK2  is  the  same  as  the 
difference  between  the  salts  A2Ki  and  A2K2.  We  may  put 
this  in  the  form  — 


xi.  SPECIFIC   GRAVITY   OF   SOLUTIONS.  171 

AJ^  -  A2K!  =  AiK2  -  A2K2. 

If  we  arrange  a  series  of  m  negative  ions,  AI,  A2,  .  .  . 
A,H,  in  a  horizontal  row,  and  a  series  of  n  positive  ions,  BI, 
B2,  .  .  .  Bf0  in  a  vertical  row,  then  by  combination  of 
these  ions  mn  salts  AB  can  be  obtained,  as  the  following 
scheme  shows : — 


Ax 

A2  .  . 

.       Am 

Bl 

AiBi 

A2Bi  .  . 

.  AJfc 

B2 

AiB2 

A2B2  .  . 

.  A,,4B2 

Bw     AiBM     A2BW  .  .  .   AmB« 

In  this  scheme  we  may  write  in  place  of  each  salt  AB  the 
numerical  value  of  one  of  its  properties  in,  for  example, 
normal  solution,  and  this  property  is  to  be  regarded  as 
additive  if  the  following  relationship  exists  between  the 
differences — 

AiBi  -  AiB2  =  A2Bi  -  A2B2  =   .  .  .  AJBi  -  AJBa. 

Expressed  in  words,  this  may  be  stated  thus :  The 
differences  between  two  values  which  are  in  the  same  vertical 
column  and  two  certain  horizontal  rows  must  be  the  same 
(within  the  experimental  error)  for  all  the  vertical  columns 
if  the  property  in  question  is  additive. 

Exactly  the  same  must  hold  good  for  the  differences 
between  the  horizontal  rows  and,  of  course,  for  any  concen- 
tration, provided  this  is  the  same  for  all  the  salt  solutions. 
By  constructing  such  a  table  (the  so-called  additive  scheme) 
and  calculating  the  differences  between  the  rows  and  the 
columns,  it  is  easy  to  decide  whether  the  particular  property 
of  the  dissolved  salt  is  additive  or  not. 

According  to  Valson  (1),  additive  properties  can  also 
be  expressed  by  moduli.  As  an  example,  we  give  below  the 
moduli  for  the  specific  gravities.  Valson  chose  as  his  starting 


172 


THE    DISSOCIATION   THEORY. 


CHAP. 


point  the  specific  gravities  of  ammonium  chloride  solutions, 
which  have  the  following  values  : — 

AMMONIUM  CHLORIDE. 


Concentration, 

Specific  gravity, 
18 

Concentration, 

Specific  gravity, 
18 

n. 

18 

71. 

Is' 

0 

1-0000 

3 

1-0451 

1 

1-0157 

4 

1-0587 

2 

1-0308 

5 

1-0728 

The  following  numbers  multiplied  by  10  4  are  the  moduli 
for  the  various  ions : — 

NH4     K     Na     Li     JBa     JSr     JCa     JMg    pin     £Zn 

0       289    238    78     735     500     280      210      356     410 

JCd     JPb     JCu      Ag       H  Cl     Br        I      N03     iS04 

606     1087     434     1061     16  0     373     733      163      206 
C2H3O2        OH 
-  15  20 

The  specific  gravity  of,  e.g.  a  3n  JCaBr2  solution,  would  be 
calculated  to  be — 

S=  1-0451  +  3(280  +  373) .  10;4  =  1-0431  +  01959  =  1-2397, 

and  by  experiment  1'2395  has  actually  been  found. 

With  the  aid  of  these  moduli  the  specific  gravities  of 
quite  concentrated  solutions  can  be  obtained  fairly  accurately, 
although,  as  the  example  given  proves,  the  salt  is  not  by  any 
means  nearly  completely  dissociated. 

Compressibility,  Capillarity,  and  Internal  Friction 
of  Solutions. — Other  properties  of  solutions  besides  the 
specific  gravity  show  the  same  regularities.  As  an  example, 
we  may  take  the  compressibility,  i.e.  the  volume  change 
suffered  by  1  c.c,  when  the  pressure  is  raised  from  1  atmo.  to 
2  atmos. 

Eontgen  and  Schneider  (2)  found  the  numbers  con- 
tained in  the  following  table  for  0'7-normal  solutions  at  the 


XI. 


REFRACTIVE    INDEX   OF    SOLUTIONS. 


173 


ordinary  temperature,  and  it  will  be  seen  that  the  differences 
for  each  column  are  constant.  Water  and  ammonia,  which 
are  not  very  much  dissociated,  form  exceptions,  and  ought, 
therefore,  not  to  be  included.  The  compressibility  of  water 
is  set  =  1000,  and  the  numbers  refer  to  this  standard. 


H. 

A. 

NH4. 

A. 

Li. 

A. 

K. 

A. 

Na. 

I.  . 

954 

14 

940 

8 

932 

8 

924 

NO3. 

981 

27 

954 

20 

934 

4 

930 

8 

922 

Br  . 

981 

28 

953 

19 

934 

4 

930 

7 

923 

Cl  . 

974 

29 

945 

17 

928 

9 

919 

2 

917 

OH  . 

1000 

(8) 

992 

(97) 

895 

11 

884 

3 

881 

The  capillarity  and  internal  friction  of  solutions  are  also 
additive  properties.  In  proof  of  this  we  subjoin  some  results 
obtained  by  Eeyher  (3)  for  the  internal  friction  of  normal 
salt  solutions  referred  to  that  of  water  at  25°  as  unity. 


CL 

Br. 

C103. 

HOg. 

C104.        H2P04. 

C2H302. 

Na     .     .     .     . 
H      .     .     .     . 

Difference    . 

1-099 
1-070 

1-062 
1-038 

1-089 
1-053 

1-052 
1-022 

1-035 
1-002 

1-476 
1-285 

1-400 
1-127 

0-029 

0-024 

0-036 

0-030 

0-033 

0-191 

0-273 

The  difference  Na  —  H  is  on  the  average  about  0*030, 
except  in  the  case  of  phosphate  and  acetate,  and  this  is  due 
to  the  fact  that  the  corresponding  free  acids  have  only  a  low 
degree  of  dissociation,  and  therefore  do  not  fit  properly  into 
the  scheme. 

Refractive  Index  of  Solutions. — According  to  the 
formula — 

n  =  Nx  +  (a  +  V)x 

we  can  calculate  the  refractive  index  n  of  a  salt  solution  if 
the  normality  (x)  be  known ;  Nx  is  the  refractive  index  of 
another  salt  solution  (taken  as  standard)  of  the  same  con- 
centration, and  ci  and  b  are  the  moduli,  M,  of  the  refractive 
index. 


'74 


THE    DISSOCIATION   THEORY. 


CHAP. 


Bender  (4)  used  a  solution  of  potassium  chloride  for 
comparison,  and  found  the  following  refractive  indices  for  the 
Ha,  D,  H^,  and  Hy  lines  of  the  spectrum  :— 


X. 

Ha.                               D. 

H/3. 

H7. 

Refractive  index  for  KC1. 

1 

1-3409 

1-3428 

1-3472 

1-3505 

2 

1-3498 

1-3518 

1-3565 

1-3600 

3 

1-3583 

1-3603 

1-3651               1-3689 

i 

Moduli  of  the  refractive  index  M  x  10-4  for 


K,  Cl 

0 

0 

0 

0 

Na 

2 

2 

2 

2 

JCd 

38 



40 

41 

Br 

37 

38 

41 

43 

I 

111 

114 

123 

131 

From  this  we  can  calculate,  for  instance,  the  refractive 
index  of  a  2-normal  solution  of  sodium  bromide  for  light  of 
wave-length  Ha  : 


=  1-3498  + 


=  1-3576. 


The  experimental  value  is  1*3578.  It  should,  however, 
be  noted  that  the  agreement  is  not  always  so  good.  Le  Blanc 
(5)  has  shown  that  weak  acids  and  bases  do  not  fit  into 
this  additive  scheme. 

Magnetic  Rotation  of  Solutions.  —  Jahn  (6)  found  the 
following  values  for  the  power  of  salt  solutions  to  rotate  the 
plane  of  polarisation  in  a  magnetic  field.  He  determined 
the  angle  through  which  the  plane  of  polarisation  of  sodium 
light  was  turned  in  passing  through  a  column  of  water  of 
definite  length  in  a  strong  magnetic  field.  This  angle  was 
taken  as  equal  to  100.  Working  under  precisely  the  same 
external  conditions,  he  determined  the  angle  for  normal 
solutions  of  various  electrolytes.  From  this  he  subtracted 


XI. 


MOLECULAR    MAGNETISM. 


the  angle  of  rotation  for  the  water  contained  in  the  solution, 
and  obtained  the  following  values  for  the  ions : — 


01. 

Br. 

I. 

HO,. 

*S04. 

iCOa. 

4-67 

4-61 

.  — 

— 

— 

1-53 

5-36 

9-19    • 

18-46 

1-37 

1-77 

1:76 

5-66 

9-36 

18-95 

1-35 

1-79 

1-78 

4-70 

8-80 

— 

— 

— 

— 

4-86 

9-08 

:  — 

—           —      I     — 

5-05 

9-27 



— 

.  . 

5-89 

9-85 

20-45 

— 

2-58 

4-52 

— 

— 

— 

•1-U 

If  we  take  the  differences  between  two  vertical  rows,  we 
find  that  these  are  nearly  constant,  e.g.  for  Br  —  01 — 


3-83 


K 

370 


JCa 
410 


iSr 
4-22 


JBa 
4-22 


JCd 
3-96. 


The  simplest  relationships  are  found  when  the  particular 
property  is  due  exclusively,  or,  at  any  rate,  for  the  greater 
part,  to  one  of  the  two  ions. 

In  such  cases  all  salts,  which  in  dilute  solution  contain 
the  same  quantity  of  the  particular  ion,  have  the  same  value 
for  the  property  in  question  whatever  be  the  nature  of  the 
other  ion  present.  As  examples  of  this,  we  may  cite  the 
molecular  magnetism  of  the  magnetic  salts  (particularly  iron 
salts),  the  natural  power  of  rotating  plane  polarised  light,  the 
colour  and  the  light  absorption. 

Molecular  Magnetism. — Experiments  on  magnetic  salt 
solutions  were  made  by  G.  Wiedemann  (7).  The  liquid 
to  be  investigated  was  placed  in  a  small  flask,  which  was 
suspended  at  one  end  of  the  horizontal  rod  of  a  Coulomb 
torsion  balance,  and  this  was  equipoised  by  means  of  a  weight. 
A  strong  electromagnet  was  placed  near  the  flask,  and  when 
the  current  was  started,  the  flask  was  attracted  on  account  of 
the  induced  magnetism  in  the  solution.  This  attraction  was 
measured  for  several  solutions,  and  was  found  to  vary.  By 


176  THE    DISSOCIATION   THEORY.  CHAP. 

measuring  the  attraction  suffered  by  the  flask  empty,  and 
when  filled  with  water,  then  from  the  value  obtained  with 
the  solution,  the  part  due  to  the  dissolved  salt  can  easily  be 
calculated.  The  attraction  is  ^proportional  to  the  quantity 
of  dissolved  salt.  If  the  flask  contains  1  gram-molecule 
of  dissolved  salt,  the  attraction  is  a  direct  measure  of  the 
molecular  magnetism.  In  the  '  same  way  the  atomic 
magnetism  of  a  gram-atom  of  iron  can  be  determined. 
Wiedemann  found  that  all  the  ferrous  salts  possess  the  same 
molecular  magnetism  ;  thus  he  obtained  for  the  sulphate,  the 
nitrate,  and  the  chloride,  the  relative  numbers,  3900,  3861, 
and  3858  ;  whilst  for  the  ferric  salts  he  obtained  as  mean 
value,  4800.  The  nitrate,  sulphate,  and  chloride  of  nickel 
gave  1433,  1426,  and  1400;  manganous  sulphate,  nitrate, 
acetate,  and  chloride  gave  4695,  4693,  4586,  and  4700 ;  and 
cupric  nitrate,  acetate,  and  chloride,  480,  489,  and  477. 

If  we  set  the  atomic  magnetism  of  iron  in  ferric  salts  = 
100,  we  obtain  the  following  values  for  the  magnetism  of  a 
gram-atom  of  the  metal  in  the  salts :  in  manganous  salts, 
100*4 ;  in  ferrous  salts,  83*1 ;  in  cobaltous  salts,  67*2 ;  in 
nickelous  salts,  30*5 ;  in  didymium  salts,  22' 6 ;  in  cupric 
salts,  10* 8  ;  in  eerie  salts,  10'3  ;  and  in  chromic  salts,  41*9. 

It  is  noteworthy  that  the  temperature  coefficient  for  the 
temporary  magnetism  is  almost  the  same  for  all  salt  solutions  ; 
it  is  given  by— 

mt  =  m0(l  -  0-00325  t) 

where  t  is  the  temperature  (centigrade),  and  mt  and  m0  the 
temporary  magnetisms  at  £°  and  0°. 

Kecent  and  more  exact  determinations  by  du  Bois  and 
Liebknecht  (8)  have  proved  that  the  atomic  magnetism  is 
not  strictly  additive,  but,  on  the  other  hand,  the  additivity 
mentioned  is  so  general  that  it  can  be  applied  not  only  to 
solutions,  but  also  to  crystallised  salts,  in  which  the  dis- 
sociation is  very  small  if  it  takes  place  at  all. 

Natural  Rotatory  Power  in  Solution. — Some  few 
organic  compounds  are  capable  of  rotating  the  plane  of 
polarisation  of  light  passed  through  them.  If,  therefore,  we 


XI. 


LIGHT   ABSORPTION   OF   SOLUTIONS. 


177 


combine  say  an  anion  possessed  of  this  power  with  an 
inactive  cation,  which  in  combination  with  most  ions  gives 
inactive  salts,  equivalent  quantities  of  all  the  salts  of  this 
anion  must,  in  dilute  solutiqn,  have  equal  rotatory  powers. 
This  has  been  confirmed  in  one  or  two  instances ;  the  salts  of 
quinic  acid  in  ^-normal  solution  give  the  following  molecular 
rotations  : — 


Potassium 48-8° 

Sodium 48-9 

Ammonium  47*9 


Barium 46-6° 

Strontium 48'7 

Magnesium      ....     47*8. 


The  differences  are  quite  inconsiderable.  For  the  sake 
of  comparison,  it  may  be  added  that  the  molecular  rotation  of 
a  f -normal  solution  of  quinic  acid,  which  is  very  little  dis- 
sociated, is  43 -4°. 

The  molecular  rotation  of  tartaric  acid  (little  dissociated) 
is  15°  at  20°,  that  of  the  salts  is  from  26'30°  to  27'62°. 
Oudemans  (9)  and  Landolt  (10}  have  examined  these  salts 
of  optically  active  acids  and  bases. 

Light    Absorption    of    Solutions. — Another    optical 
property   of   dilute    solutions 
which  is  of  great  importance  is 
their  power  of  absorbing  light. 
Ostwald,  who  carried  out  ex- 
periments   in   this    direction, 
applied  a  photographic  method 
(11).      He   produced   on    the 
same  photographic  plate  spec- 
tral images  of  different  solu- 
tions,   which    contained    the 
same  "coloured  "  ion  in  equiva- 
lent   quantities   with  various     cu 
cations.     In  most  cases  these     H 
absorption  spectra  are  identi-     A1 
cal ;  Fig.  39  shows  the  absorp- 
tion spectra  of   0'002-normal  FIG.  39. 
solutions    of    permanganates, 
Mn04  with  10  different  cations.     Only  in  a  few  cases  were 

N 


Li 


Cd 


NH4 


Zn 


Mg 


1  78  THE    DISSOCIATION   THEORY.  CHAP. 

deviations  from  this  observed,  and  these  could  be  attributed 
to  disturbing  factors.  Since  the  colour,  i.e.  the  absorption, 
of  a  compound  suffers  a  very  considerable  change  by  a 
comparatively  small  chemical  change,  such  as  the  replace- 
ment of  bromine  by  chlorine,  the  constancy  observed  with 
the  salt  solutions  can  hardly  be  otherwise  explained  than 
by  assuming  that  the  salt  molecules  have  decomposed  into 
ions.  Further,  since  a  spectrum  consists  of  several  parts, 
and  the  agreement  in  all  parts  is  perfect,  Ostwald's  investi- 
gation, which  covered  4  positive  and  13  negative,  "  coloured  " 
ions,  may  be  mentioned  as  strong  evidence  in  favour  of  the 
dissociation  theory. 

This  is  the  reason  why  all  salts  containing  the  same  ion 
have  the  same  colour  in  dilute  solution.  All  nickelous  salts 
in  dilute  solution  are  green,  all  cupric  salts  blue,  all  manga- 
nous  salts  pink,  all  ferrous  salts  green,  and  all  ferric  salts 
colourless.  The  last-mentioned  solution  has  a  yellow  colour 
due  to  the  presence  of  colloidal  ferric  hydrate.  The  ferrous 
and  ferric  salts  are  differently  coloured,  because  they  contain 


different  ions,  namely,  Fe  and  Fe  ;  in  the  same  way  the 
ferrocyanide  and  the  ferricyanide  ions  have  different  colours. 
A  large  number  of  examples  are  known,  particularly  amongst 
organic  compounds. 

The  application  of  indicators  in  the  titration  of  acids  and 
bases  is  based  on  this  colour  of  the  ions.  Phenolphthalein, 
which  behaves  as  a  weak  acid,  is  colourless  in  solution, 
whilst  its  salts  (in  solution)  possess  a  brilliant  pink  colour. 
The  acid  is  hardly  dissociated,  and  therefore  does  not  show 
the  colour  of  the  anion,  for  this  does  not  exist  in  acid  solu- 
tion. In  the  same  way,  litmus  is  a  weak  acid  with  a  red 
colour,  whilst  the  anion  produced  from  the  dissociation  of  its 
salts  is  blue. 

Chemical  Properties  of  the  Ions.  —  In  mentioning 
indicators  we  have  touched  upon  one  of  the  most  important 
additive  properties  of  salt  solutions  ;  one  which  is  the  basis 
of  analytical  chemistry.  Let  us  consider  a  solution  containing 


XL         CHEMICAL    PROPERTIES   OF   THE    IONS.         179 

chlorine.  On  the  addition  of  a  reagent,  usually  silver  nitrate, 
it  is  found  that  the  solution  gives  a  reaction  characteristic  for 
chlorine,  inasmuch  as  a  curdy  precipitate  of  silver  chloride  is 
formed.  It  can  easily  be  proved  that  this  reaction  will  not 
detect  every  chlorine  atom,  but  only  those  existing  as  ions, 
for  a  number  of  substances  containing  chlorine,  such  as 
potassium  chlorate,  monochloracetic  acid,  and  other  organic 
and  inorganic  compounds  in  which  the  presence  of  chlorine 
can  otherwise  be  proved,  do  not  give  this  characteristic 
reaction.  These  substances  do  not  dissociate  to  give  chlorine 
ions.  When  a  substance,  such  as  mercuric  chloride,  gives 
only  a  small  amount  of  chlorine  ion,  then  on  addition  of 
silver  nitrate  this  is  removed  from  the  solution  as  silver 
chloride.  By  the  removal  of  the  chlorine  ion  the  dissociation 
equilibrium  is  disturbed,  and  in  order  to  re-establish  it  more 
chlorine  ion  must  be  formed  at  the  expense  of  undissociated 
mercuric  chloride  molecules.  Consequently,  one  part  of  the 
chlorine  after  another  is  precipitated,  until  the  whole  of  it 
is  completely  removed  from  the  solution.  If,  however,  the 
number  of  chlorine  ions  at  the  beginning  is  extremely  small, 
it  may  happen  that  on  the  addition  of  silver  nitrate  the 
solubility  product  of  silver  chloride  is  not  reached,  and  con- 
sequently there  will  be  no  precipitation  of  this  substance. 
The  reagent  silver  nitrate  can  nevertheless  be  used  to  detect 
the  presence  of  a  certain  extremely  small  quantity  of  chlorine 
ion  in  solution.  This  and  other  chemical  means  are  often 
very  delicate,  and  are  therefore  of  great  use  in  determining 
the  occurrence  of  ions  in  solutions  in  which  the  electric  con- 
ductivity gives  no  certain  result  on  account  of  the  presence 
of  other  ions. 

The  same  sort  of  behaviour  is  exhibited  by  most  of 
the  chemical  reagents  generally  used  in  ordinary  "wet" 
analysis. 

An  example,  to  which  I  (12)  called  attention  in  1884, 
is  the  behaviour  of  the  ferrocyanides,  which,  although  they 
contain  iron,  do  not  give  the  reactions  characteristic  of  iron, 
or  rather  of  the  iron  ions.  Cases  like  this  were  previously 


i8o  THE   DISSOCIATION   THEORY.  CHAP. 

classed  amongst  those  in  which  the  "retention  of  the  type" 
takes  place  against  the  ordinary  chemical  rules.  By  the 
action  of  other  salts,  where  exchange  of  ions  takes  place,  a 
ferrocyanide  always  gives  a  ferrocyanide,  and  not  a  cyanide 
and  a  ferrous  salt.  In  order  to  bring  about  such  a  rearrange- 
ment, more  energetic  chemical  means  must  be  employed ;  in 
this  case,  for  instance,  potassium  ferrocyanide  may  be  heated 
(fused),  and  it  is  decomposed  into  potassium  cyanide,  nitrogen, 
and  iron  carbide,  and  this  last  compound,  on  treatment  with 
hydrochloric  acid,  gives  ferrous  chloride. 

As  a  rule  the  ions  are  much  more  reactive  than  other 
chemical  substances.  The  exchange  of  ions  in  precipitation 
and  similar  reactions  takes  place,  as  far  as  we  can  judge, 
instantaneously,  whilst  other  reactions  often  take  place  very 
slowly  and  only  at  high  temperature  with  a  measurable 
velocity.  We  might  even  go  so  far  as  to  say  that  only  ions 
can  react  chemically.  However,  it  would  be  difficult  to 
definitely  prove  this ;  but  we  may  assume  that  in  the  case 
of  reactions  which  take  place  very  slowly  ions  are  present, 
although  not  in  measurable  quantity  so  far  as  our  present 
methods  are  able  to  detect  them. 

Gore  (13)  has  shown  that  absolutely  anhydrous  hydro- 
chloric acid,  which  does  not  conduct  an  electric  current,  does 
not  react  with  the  oxides  or  carbonates  of  magnesium  and 
the  alkaline  earth  metals,  whilst  in  aqueous  solution  these 
substances  are  violently  attacked.  Concentrated  sulphuric 
acid  does  not  act  upon  iron  until  water  is  added. 

Physiological  Action  of  the  Ions. — The  physiological 
actions  of  different  salt  solutions  as  curative  agents  or  poisons 
are  of  great  practical  interest.  It  has  been  known  for  a  long 
time  that  morphine  given  in  the  form  of  sulphate,  chloride, 
acetate,  etc.,  always  has  the  same  effect  when  used  in 
equivalent  quantities.  The  negative  ion  present  with 
the  morphine  has  no  physiological  influence.  Similar 
observations  have  been  made  with  other  substances,  such  as 
quinine,  etc. 

Mention  may  here  be  made  of  some  observations  with 


xi.        PHYSIOLOGICAL   ACTION   OF   THE    IONS.         181 

poisons.  It  was  found  that  potassium  chlorate  is  poisonous, 
and  this  led  to  an  investigation  of  the  action  of  other 
potassium  salts.  Solutions  of  a  definite  strength  were 
introduced  into  living  organisms,  and  the  degree  of 
poisonousness  was  determined  by  the  length  of  time  required 
to  kill  the  organism.  The  result  of  this  investigation  was  to 
show  that  all  potassium  salts,  with  the  exception,  of  course, 
of  those  containing  a  poisonous  negative  ion,  like  potassium 
cyanide,  have  nearly  the  same  poisonous  effect  in  solutions 
of  equal  concentration. 

Eecently  Kahlenberg  (14)  and  Loeb  (15),  as  well  as  Paul 
and  Kronig  (16),  have  investigated  the  action  of  salts  on 
bacteria  and  spores.  All  the  results  obtained  agree  very 
perfectly  with  what  would  be  expected  from  the  dissociation 
theory.  Paul  and  Kronig  exposed  spores  for  a  certain  length 
of  time  to  the  action  of  salt  solutions  at  18°,  and  determined 
the  vitality  of  the  spores  by  the  number  of  bacteria  colonies 
formed  when  placed  under  conditions  favourable  to  their 
growth.  The  degree  of  dissociation  of  the  following  mercuric 
salts  in  equivalent  solution  decreases  in  the  order  given : 
chloride,  bromide,  thiocyanate,  iodide,  cyanide,  and  it  was 
found  that  their  powers  of  killing  spores  of  the  anthrax 
bacillus  were  in  the  same  order,  so  that  the  cyanide  has  the 
least  action.  The  influence  of  complex  salts  is  still  smaller, 
e.g.  potassium  mercuricyanide,  K2(CN)4Hg,  which  gives 
hardly  any  mercuric  ions.  Similar  relationships  were  found 
for  gold  and  silver  salts.  By  the  addition  of  neutral  salts, 
such  as  sodium  chloride  and  potassium  chloride,  both  the 
degree  of  dissociation  and  the  poisonousness  are  diminished. 
In  some  other  cases,  for  instance  with  acids,  not  only  does 
the  hydrogen  ion  exert  a  poisonous  influence,  but  also  the 
negative  ion  with  which  it  is  present,  so  that  the  action  of 
hydrofluoric  acid  is  greater  than  that  of  hydrochloric  acid, 
although  the  latter  is  dissociated  to  the  greater  extent. 
Nevertheless,  the  weak  acids,  formic  and  acetic  acids,  have 
the  smallest  effect  of  any  acids  so  far  examined,  whilst  phenol 
shows  peculiar  relationships. 


i8z 


THE    DISSOCIATION   THEORY. 


CHAP. 


Catalytic  Action  of  Hydrogen  and  Hydroxyl  Ions. — 

As  mentioned  in  Chapter  VII.,  cane  sugar  in  aqueous  solution 
is  converted  in  presence  of  acids  into  invert  sugar. 

Now,  since  the  characteristic  of  all  acids  is  the  presence 
of  hydrogen  ions,  it  might  be  supposed  that  the  hydrogen  ion 
was  the  cause  of  this  change.  Further,  since  the  degree  of 
dissociation  of  an  acid  is  proportional  to  its  molecular  con- 
ductivity and  inversely  proportional  to  its  conductivity  at 
infinite  dilution,  it  might  be  expected,  since  this  latter  value 
is  nearly  the  same  for  all  acids,  that  the  velocity  of  inversion 
of  cane  sugar  would  be  proportional  to  the  conductivity  of 
the  acid  added  if  equivalent  quantities  of  different  acids  were 
employed.  In  1884  I  (12)  showed  on  theoretical  grounds 
that  this  velocity  must  be  proportional  to  the  conductivity 
of  the  catalysing  acid,  and  shortly  afterwards  Ostwald  (17), 
who  was  then  investigating  reaction  velocities,  experimentally 
confirmed  this  conclusion.  Ostwald  obtained  the  numbers 
given  in  the  next  table  for  the  conductivity  (I)  and  the  velocity 
of  inversion  (p)  of  different  acids  at  the  same  concentration ; 
the  conductivity  of  hydrochloric  acid  (in  normal  solution)  is 
set  =  100,  and  the  velocity  of  inversion  caused  by  this  same 
acid  (in  0'5-normal  solution)  is  also  set  =  100. 


Acid. 

i. 

P' 

a. 

Hydrochloric  acid  
Nitric  acid    
Chloric  acid 

100 
100 
100 

100 
100 
104 

100 
92 
94 

Sulphuric  acid   . 

59-5 

54 

55 

Benzenesulphonic  acid     .     .     . 
Trichloracetic  acid      .... 
Dichloracetic  acid  
Monochloracetic  acid  .... 
Acetic  acid    

33-0 
6-41 
0-67 

104 

75 
27-1 
4-84 
0-4 

99     . 
68 
23 
4-3 
0-34 

Formic  acid  . 

2-3 

1-5 

1-3 

The  values  given  under  <r  are  for  the  velocity  of  saponi- 
fication  of  esters  in  presence  of  0'67-normal  solutions  of 
the  acids  mentioned. 


xi.      HYDROGEN  AND  HYDROXYL  IONS.     183 

From  the  numbers  it  can  be  seen  that  there  is  a  good 
parallelism  between  the  conductivities  and  the  effects  on  the 
inversion.  However,  a  more  exact  and  thorough  investiga- 
tion seemed  advisable.  I  carried  out  an  investigation  (18) 
on  this  velocity  of  inversion,  and  it  was  afterwards  extended 
by  Palmaer  (19).  The  result  of  these  experiments  was  to 
show  that  at  high  dilution  of  the  acids  and  constant  sugar 
concentration  the  velocity  of  inversion  is  proportional  to  the 
concentration  of  the  hydrogen  ion  present.  At  higher  con- 
centrations deviations  are  observed  of  the  same  nature  as 
those  caused  by  the  addition  of  neutral  salts,  the  so-called 
action  of  salts  (see  p.  109).  By  addition  of  a  large  quantity 
of  acid,  the  osmotic  pressure  of  the  cane  sugar  is  increased  so 
that  the  velocity  of  reaction  p,  instead  of  being  proportional 
to  the  quantity  m  of  hydrogen  ion  present,  is  regulated  by 
the  formula  — 


p  =  am  -f 


The  coefficient  a  is  the  same  for  all  acids,  i.e.  it  is  inde- 
pendent of  the  nature  of  the  anion  ;  6,  on  the  other  hand,  is 
dependent  on  the  anion,  for  this  ion  also  acts  so  as  to  increase 
the  osmotic  pressure  of  the  sugar,  and  all  anions  do  not  act 
to  the  same  extent  in  this  direction.  The  fact  that  a  is  the 
same  for  all  acids  evidently  indicates  that  (at  low  concentra- 
tion) all  hydrogen  ions  exert  the  same  influence  independently 
of  the  acid  from  which  they  are  formed.  It  is  therefore 
possible  to  calculate  the  velocity  with  which  any  acid  can 
invert  sugar  if  we  know  the  velocity  in  the  case  of  another 
acid,  say  hydrochloric  acid,  and  the  "salt  action"  of  the 
various  ions  (which  can  be  determined  by  other  methods). 
The  following  table  gives  the  reaction  velocities  for  several 
concentrations  of  the  acids.  Under  p  (observed)  are  given 
the  numbers  found  by  Ostwald. 


1 84 


THE    DISSOCIATION   THEORY. 


CHAP. 


Concentration. 

p  (observed). 

p  (calculated). 

HC1     . 
HBr    ..... 

0-5 
0-1 
0-01 
0-5 

20-5 
3-34 
0-317 
22-3 

20-1 
3-41 
0-318 
22-2 

H2S04 

0-1 
0-01 
0-25 

3-41 
0-318 
10-7 

3-50 
0-324 
11-1 

HCOOH  ...... 

0-05 
0-005 
05 

2-08 
0-265 
0-332 

2-09 
0-256 
0-345 

CHgCOOH    
C2H5COOH       .... 

C3H7COOH  . 

0-1 
0-01 
0-5 
0-1 
0-5 
0-1 
0-01 
0-5 

0-135 
0-0372 
0-1005 
0-0430 
0-0771 
0-0341 
0-0097 
0-0791 

0-134 
0-0360 
0-1005 
0-0409 
0-0750 
0-0325 
0-0095 
0-0749 

C2H4(COOH),    .... 

0-1 

o-oi 

0-25 
0-05 
0-005 

0-0362 
0-0100 
0-1210 
0-0536 
0-0202 

0-0355 
0-0095 
0-1280 
0-0531 
0-0190 

Similar  relationships  are  shown  in  the  case  of  other 
reactions,  the  velocities  of  which  are  accelerated  by  acids,  but 
they  have  not  been  so  fully  investigated. 

In  the  saponification  by  bases  it  has  been  found  that  all 
strong  bases  exert  about  the  same  action.  The  velocity  of 
reaction  at  9 '4°  is — 


2-31 


2-30 
2-29 


Sr(OH)2 


Ba(OH)2  .  . 


2-20 
2-14 


NaOH    .     .     . 
KOH     .     .     . 

Ca(OH)2      .     . 

The  numbers  are  for  ^-normal  solutions,  in  which  the 
strong  bases  may  be  regarded  as  completely  dissociated; 
in  equivalent  quantity  they  should  exert  the  same  action, 
which,  according  to  the  above  numbers  of  Eeicher  (20), 
they  actually  do.  The  corresponding  value  for  the  weakly 
dissociated  ammonia  is  O'Oll. 

Objections  to  the  Assumption  of  Electrolytic  Dis- 
sociation.— However  it  may  be  with  some  details  not  yet 


xi.  ELECTROLYTIC   DISSOCIATION.  185 

explained,  it  is  quite  certain  that  the  degree  of  dissociation 
found  from  the  osmotic  method  generally  agrees  closely  with 
that  found  by  the  electrical  method.  Such  an  agreement  was 
essential,  in  order  that  the  idea  of  electrolytic  dissociation 
might  be  valid. 

The  most  important  objection  which  has  been  raised  by 
chemists  is  that  salts  in  solution  show  a  higher  osmotic 
pressure  than  corresponds  with  their  chemical  formulae,  and 
this  seems  to  correspond  with  the  phenomenon  that  a  gas — as, 
for  instance,  ammonium  chloride — shows  a  higher  gas  pressure 
than  would  be  expected  from  the  composition  of  the  mole- 
cule NH4C1.  In  this  latter  case  it  was  admitted  that  the 
deviation  from  the  gas  laws  was  only  apparent  and  due  to 
the  decomposition  of  the  molecule  into  simpler  constituents 
(NH3  and  HC1).  However  at  that  time  it  could  be 
shown  that  the  products  of  dissociation  might  be  separated 
by  diffusion,  and  the  question  arose  why  it  is  not  possible 
to  effect  a  similar  separation  by  diffusion  of  the  products  of 
dissociation  of  sodium  chloride  (sodium  and  chlorine). 

The  explanation  of  our  inability  to  effect  this  separation 
lies  in  the  extraordinarily  high  charge  of  96,500  coulombs 
per  equivalent  which  the  products  of  electrolytic  dissociation, 
i.e.  the  ions,  receive,  whilst  the  products  from  an  ordinary 
dissociation  remain  unelectrified.  If  we  had  a  layer  of  pure 
water  over  a  solution  of  sodium  chloride,  then  if  this  charge 
had  no  influence,  the  chlorine,  which  is  appreciably  more 
mobile  than  the  sodium  (in  the  ratio  68  :  45),  would  be  found 
to  be  in  excess  in  the  upper  layer.  Let  us  assume  that 
10  ~1'2  gram-equivalents  more  of  chlorine  than  of  sodium  have 
diffused  into  the  pure-water  layer,  then  this  would  have  a 

negative  charge  of  — '-^-    coulombs,    or   290   electrostatic 

units,  a  quantity  of  electricity  which,  if  brought  on  to  a 
sphere  of  10  cms.  radius,  would  be  able  to  give  a  spark 
0'2  cm.  long.  Now,  it  can  easily  be  shown  that  the  electric 
(electromotive)  forces  which  would  be  exercised  by  even  so 
small  a  quantity  (10  "12  gram-equivalent)  would  far  exceed 


186  THE    DISSOCIATION   THEORY.  CHAP. 

all  osmotic  forces,  whereby  the  sodium,  would  receive  an 
acceleration,  but  the  chlorine  a  retardation.  As  the  unit  of 
electromotive  force  is  equal  to  300  volts  when  expressed  in 
electrostatic  units,  the  290  electrostatic  units  mentioned 

would  possess  a  potential  of =  8700  volts.     This 

charge,  when  communicated  to  a  solution  in  the  form  of  a 
cube,  the  length  of  whose  side  is  10  cms.,  would  be  at  a 
tension  of  the  same  order  of  magnitude,  or,  in  round  numbers, 
104  volts. 

Let  us  consider  a  column  of  1  sq.  cm.  cross  section  and 
1  cm.  high,  one  end  of  which,  A  (Fig.  40),  has  a  potential  of 
104  volts,  whilst  at  the  other  end,  B,  the 
potential  is  0.     Let  the  liquid  between  A 
and  B  contain  dissolved  sodium  chloride, 
so  arranged  that   at  A    the   concentration 
is  0,  at  B  1-normal,  i.e.  in  toto  0'5-normal. 
i     And,  further,  we  assume  that  the  sodium 
chloride    is   completely   dissociated.      The 
chlorine  ions  are  acted  on  (compare  p.  121) 

FIG.  40.  V  V  . 

by  an  electric  force  —e,  where  --   is   the 

'  i> 

fall  of  potential  per  centimetre,  in  this  case  equal  to  104 
volts,  and  e  denotes  the  number  of  coulombs  with  which 
the  chlorine  ions  are  charged,  here  equal  to  ^01(T096,500=48<2, 

since  the   cubic   centimetre  of  the  solution   contains  — - 
gram-ions.     The  force  acting  is  therefore  (see  p.  6) — 
48-2  x  104  volt-coulombs  per  cm.  =  48'2  x  1011  dynes. 

The  osmotic  force  acting  on  the  same  chlorine  ions  is 
given  by  the  difference  between  the  osmotic  pressure  of  the 
normal  solution  at  B,  and  that  of  concentration  0  at  A. 
According  to  p.  26,  this  is  for  the  temperature  18° 
=  291°  abs.- 

84,688  x  291  X  £*&  =  2*42  x  107  dynes. 

The  force  is  therefore  2  x  105  times  smaller  than  the 


xi.  ELECTROLYTIC   DISSOCIATION.  187 

former,  and  an  excess  of  O5  x  10~5  x  10~12  gram-ions  of 
chlorine  over  the  number  of  sodium  ions  should  be  sufficient 
to  prevent  a  further  separation  of  the  chlorine  ions  by 
diffusion.  Such  small  quantities  (5  x  10  ~18  gram-equivalent) 
cannot  be  detected  by  chemical  means. 

Since  a  millivolt  can  be  detected  by  an  electrometer,  the 
10~7th  part  of  the  charge  mentioned  can  be  determined. 
The  smallest  weighable  quantity  is  usually  O'l  milligram,  so 
that  if  the  equivalent  weight  is  100,  10~3  milligram-equiva- 
lent, or  10~6  gram-equivalent  can  be  measured.  The  electro- 
metric  analysis  is  therefore  in  this  case  1013  times  more 
delicate  than  the  chemical  method. 

In  the  diffusion  the  more  mobile  chlorine  moves  slightly 
quicker  than  the  sodium,  and  the  liquid  becomes  negatively 
charged  at  A  where  pure  water  is,  and  positively  charged 
at  B,  so  that  an  electric  current  can  be  obtained  when 
unpolarisable  electrodes  are  placed  at  the  ends  and  joined  by 
a  wire.  We  return  later  to  these  so-called  concentration 
currents.  The  separation  of  the  ions  can,  at  any  rate,  be 
effected  by  taking  from  them  their  electric  charges,  as  is 
done  in  electro-analysis, 

Since  electric  forces  come  into  play  when  electrolytic 
dissociation  takes  place  and  do  not  in  the  case  of  ordinary 
dissociation,  the  number  of  phenomena  which  accompany  the 
former  is  greater  than  that  associated  with  the  latter.  On 
account  of  the  delicacy  of  the  electrical  methods  of  measure- 
ment, no  other  dissociation  has  been  so  thoroughly  studied, 
and  from  so  many  points  of  view,  as  that  of  electrolytes 
into  ions. 


CHAPTER   XII. 
Equilibrium  between  Several  Electrolytes. 

Isohydric  Solutions. — In  Chapter  X.  we  have  discussed  the 
equilibrium  between  the  ions  and  the  undissociated  part  of 
an  electrolyte ;  but,  of  course,  when  several  electrolytes  are 
simultaneously  present  in  the  solution  the  relationships 
become  somewhat  more  complicated. 

Let  us  consider  aqueous  solutions  of  two  acids  which 
obey  Ostwald's  dilution  law  (see  p.  162).  Let  there  be  a 
gram-ions  of  one  acid,  A,  in  volume  F~A,  and  )3  gram-ions  of 

the  other  acid,  B,  in  volume  FB.     Then  if  —  =  •*—,  no  change 

PA       PB 

in  the  dissociation  will  occur  when  the  two  solutions  are 
mixed.  For  if  7TA  is  the  dissociation  constant  of  the  first 
acid,  then  for  the  solution  we  have  the  following  equation : — 


where  n  is  the  number  of  gram-molecules  of  the  acid  (which 
is  supposed  to  be  monovalent).  After  mixing,  the  quantity 
a  of  the  an  ion  from  acid  A  will  be  changed  to  01,  and  the 
quantity  )3  of  the  anion  of  acid  B  becomes  |3i.  The  quantity 
of  positive  (H)  ion  from  A  becomes  ai  +,  )3i,  and  the  volume 
is  changed  from  FA  to  F"A  +  FB.  Consequently,  after  mixing, 
we  have — 


rB) 


CHAP.  xii.  PRECIPITATION.  189 

If  Pi  —  ^  ^  faQ   £WO  equations  are  similar,  only  a   is 

'B          'A 

replaced  by  ai.  Therefore  a  is  equal  to  01,  and  in  the  same 
way  it  can  be  shown  that  /3  is  equal  to  )3i.  This  relationship, 
developed  for  weak  acids,  can  also  be  applied  to  strong 
electrolytes.  Solutions  which  on  mixing  do  not  change 
their  dissociations  (and  consequently  their  other  properties) 
are  extremely  important,  and  are  called  isokydric  solutions. 
The  conductivity  of  a  mixed  solution  can  thus  be  easily 
arrived  at  ;  we  have  only  to  think  of  the  solvent  water  so 
distributed  between  the  dissolved  substances  that  the  solu- 
tions formed  are  isohydric,  i.e.  contain  the  same  number 
of  gram-ions  per  litre.  If  the  substances  contain  a  common 
ion,  no  change  in  dissociation  takes  place  on  mixing,  and 
the  conductivity  can  be  calculated  as  the  sum  of  the  con- 
ductivities of  the  several  ions. 

If  two  salts,  as,  for  instance,  potassium  chloride  and 
sodium  nitrate,  have  not  a  common  ion,  there  are  formed 
in  the  mixed  solution  the  other  two  possible  salts,  in 
this  case  potassium  nitrate  and  sodium  chloride.  It  can 
easily  be  proved  that  for  the  four  salts  KC1,  KN03,  Nad, 
and  NaN03,  present  in  the  quantities  M\,  M2,  M3,  and  M±, 
and  whose  degrees  of  dissociation  are  ai,  a2,  as,  and  a4,  there 
exists  the  following  relationship  :  — 


aii  X  a         =  azz  X 

Precipitation.  —  The  connection  just  mentioned  is  valid 
for  homogeneous  systems,  but  it  must  be  slightly  modified 
when  one  of  the  reacting  substances  is  difficultly  soluble. 
Silver  acetate  in  water  is  a  case  in  point.  The  saturated 
solution  of  this  substance  at  18'6°  is  0'0593-normal,  and  the 
difficult  solubility  is  due  to  the  fact  that  water  can  dissolve 
only  little  of  the  undissociated  part  of  this  salt.  The 
dissolved  quantity  of  the  salt  may  as  a  close  approxima- 
tion be  assumed  to  be  constant  ;  let  it  be  represented  by 
(7(AgCH3COO).  If  a  foreign  substance  be  added  to  the 
solution,  which  substance  on  dissolving  gives  (silver  ions  or) 


190     EQUILIBRIUM    BETWEEN    ELECTROLYTES.    CHAP. 

acetate  ions,  we  have,  according  to  the  law  of  mass  action, 
before  the  addition — 

6'0(Ag)  x  6'0(CH3COO)  =  K  x  C'(AgCH3COO), 
and  after  the  addition— 

Ci(Ag)  x  ft(CH8COO)  =  K*  tf(AgCH8COO). 

C'(AgCH3COO)  is  the  same  in  both  cases.  On  the  other 
hand,  Ci(CH3COO)  is  greater  than  <70(CH3COO)  on  account 
of  the  addition  of  CH3COO  ions  from  sodium  acetate 
or  other  compound.  Consequently  (72(Ag)  must  be  just  as 
much  smaller.  The  amount  of  dissolved  silver  is  there- 
fore smaller  in  the  second  case  than  in  the  first.  This 
agrees  with  the  long-known  fact  that  the  solubility  of  many 
difficultly  soluble  salts  is  decreased  by  the  addition  of  neutral 
salts  with  a  common  ion.  Apparent  exceptions  to  this  rule, 
e.g.  increase  of  solubility  of  silver  cyanide  by  the  addition  of 
potassium  cyanide,  are  due  to  the  formation  of  double  salts 
(such  as  KAg(CN~)2).  In  order  to  effectively  precipitate 
difficultly  soluble  salts,  e.g.  barium  sulphate,  it  is  usually 
recommended  in  analytical  descriptions  to  add  excess  of  the 
precipitant,  in  this  case  barium  chloride  or  sulphuric  acid. 

Van't  Hoff  (1)  first  suggested  that  the  product  of  the 
ionic  concentrations  of  a  difficultly  soluble  electrolyte  is 
constant. 

As  already  mentioned  (p.  164),  salts  deviate  from  the 
law  of  mass  action  so  that  their  dissociation  constants,  Ky 
must  be  replaced  in  this  relationship  by  a  function  of  the 
quantity  of  the  ions  present,  therefore  the  equations  given 
cannot  claim  an  absolute  exactitude. 

Another  circumstance  aids  the  deviation  of  the  equations 
from  exactness.  The  solubility  of  these  difficultly  soluble 
substances  (in  water)  is  frequently  considerably  influenced 
by  the  presence  of  even  quite  small  quantities  of  foreign 
substances,  such  as  alcohols,  cane  sugar,  glycerol,  etc. 
Euler  (3)  and  Eothmund  (-?)  have  shown  from  their  own 
and  previous  experiments  that  ions  possess  in  a  marked 


xii.  DISTRIBUTION  OF  BASE  BETWEEN  TWO  ACIDS.  191 

degree  the  power  of  influencing  the  solubility  of  other  sub- 
stances present  in  the  solution.  It  might  well  happen  that 
the  undissociated  part  of  the  silver  acetate  in  the  example 
cited  did  not  remain  constant  after  increasing  quantities  of 
sodium  acetate  had  been  added.  As  a  matter  of  fact,  experi- 
ments indicate  that  the  solubility  of  undissociated  silver 
acetate  is  appreciably  depressed  by  the  addition  of  sodium 
acetate. 

These  two  disturbing  factors  act  in  opposite  directions. 
They  thus  partially  compensate  each  other  (in  cases  so  far 
investigated  almost  exactly),  so  that  the  view  of  the  constancy 
of  the  ionic  products  is  far  more  applicable  than  might  have 
been  supposed. 

Distribution  of  a  Base  between  Two  Acids  (Avidity). 
—  The  condition  of  equilibrium 


is  of  very  great  importance  for  determining  the  relative 
strengths  of  acids  and  bases.  If,  for  instance,  acetic  acid  is 
added  to  a  solution  of  sodium  formate,  some  formic  acid  and 
some  sodium  acetate  will  be  formed.  By  applying  the  above 
equation  we  obtain  as  result  that  the  ratio  between  the 
quantity  of  formate  and  that  of  acetate  is  equal  to  the  ratio 
of  the  square  roots  of  the  dissociation  constants  of  the  corre- 
sponding acids.  The  ratio  between  the  degrees  of  dissociation 
of  the  two  acids  at  equal  concentrations  is  also  the  same. 
The  distribution  of  a  'base  between  two  acids  can  easily  be 
•calculated  by  means  of  this  rule.  Thorn  sen  and  Ostwald 
have  experimentally  ascertained  the  value  of  this  distribution 
for  several  cases.  Thomsen  (4)  observed  the  heat  change 
which  accompanied  the  addition  of  an  acid  to  the  solution  of 
a  salt  of  the  other  acid,  whilst  Ostwald  (6)  determined 
the  change  of  volume  or  of  the  refractive  power  under  the 
same  conditions.  The  fact  that  a  change  does  take  place 
indicates  that  a  reaction  has  occurred,  and  from  the  magnitude 
•of  the  change  the  extent  of  the  reaction  can  be  calculated. 
The  following  table  contains  some  distribution  ratios.  The 


192     EQUILIBRIUM    BETWEEN   ELECTROLYTES.    CHAP. 

value  O76  for  the  ratio  between  nitric  acid  and  dichloracetic 
acid  signifies  that  on  mixing  three  equal  volumes  of  normal 
solutions  of  these,  two  acids  and  sodium  hydroxide,  76  per 
cent,  of  the  alkali  is  converted  into  nitrate  and  24  per  cent, 
into  dichloracetate.  The  calculated  values  are  given  as  well 
as  those  found  by  experiment.  According  to  Thomsen's 
phraseology,  nitric  acid  has  an  avidity  J|  =  3*17  times  greater 
than  that  of  dichloracetic  acid.  Except  in  the  case  of  the 
ratio  between  formic  acid  and  gly collie  acid,  the  experimental 
values  agree  well  with  those  calculated,  and  this  exception 
is  no  doubt  due  to  an  error  of  observation. 

The  numbers  given  were  obtained  by  Ostwald,  and  apply 
to  the  ordinary  temperature. 


Observed. 

Calculated. 

Nitric  acid  •  Dichloracetic  acid  .... 

0-76 

0-69 

Hydrochloric  acid  :     „           „     
Trichloracetic  acid  :    ,,           ,, 

0-74 
0*71 

0-69 
0-69 

Dichloracetic  acid  :  Lactic  acid  . 

0-91 

0-95 

Trichloracetic  acid  :  Monochloracetic  acid     . 
„              „    :  Formic  acid    .... 
Formic  acid    Lactic  acid  . 

0-92 
0-97 
0-54 

0-91 
0-97 
0-56 

Acetic  acid  .                        .  ~. 

0-76 

0-75 

,         ,         Butyric  acid     
Isobut\7ric  acid 

0-80 
0-79 

0-79 
O79 

Propionic  acid  .... 

0-81 

0-80 

Glycollic  acid  

0-44 

0-53 

Acetic  acid  :  Butyric  acid       .               ... 

0-53 

0-54 

•  Tsobutyric  acid 

0-53 

O54 

Strength  of  Acids  and  Bases. — For  a  long  time  it 
has  been  customary  to  determine  the  strength  of  acids  by 
measuring  their  avidities,  which,  as  shown  above,  are  pro- 
portional to  their  degrees  of  dissociation.  Now,  since  the 
strength  of  acids  varies  a  good  deal,  it  was  assumed,  in  agree- 
ment with  the  conception  formulated  by  Bergman,  that  the 
stronger  acids  replaced  the  weaker  from  their  salts.  Berthelot 
(6)  has  given  us  a  large  amount  of  data  as  to  which  of 
two  acids  is  the  stronger,  or,  according  to  his  view,  which 


xii.  THE    DISSOCIATION   OF    WATER.  193 

completely  displaces  the  other  from  its  salts.  He  found  that 
the  acid  which  conducts  best  is  the  stronger.  This  suggested 
to  me  (in  1884)  that  the  strength  of  an  acid  is  proportional 
to  its  conductivity  (7),  or,  more  correctly,  to  its  degree  of 
dissociation  (according  to  our  more  recent  theories).  A 
corresponding  connection  is  shown  by  bases. 

The  Dissociation  of  Water. — In  my  theoretical  dis- 
cussions (7)  of  1884  I  regarded  water  as  either  a  weak 
acid  or  a  weak  base.  If  we  dissolve  alkali  salts  of  weak 
acids,  such  as  carbonic  acid  or  hydrocyanic  acid,  in  water, 
the  solutions  have  an  alkaline  reaction  indicating  the  presence 
of  free  alkali.  Water,  HOH,  therefore  replaces  part  of  the 
weak  acid  HCN  from  the  KCN  and  forms  the  compound 
KOH,  just  as  any  recognised  weak  acid  would  do.  This 
view  has  been  confirmed  by  later  investigations.  Shields  (#} 
found  2 '4  per  cent,  of  free  alkali  in  a  ^-normal  solution  of 
potassium  cyanide,  and  7*1  per  cent,  in  a  sodium  carbonate 
solution  of  the  same  concentration,  whilst  iri.  a  OT-normal 
solution  of  sodium  acetate  he  found  0*008  per  cent,  of 
alkali.  These  determinations  were  made  by  ascertaining 
the  powers  of  the  solutions  to  effect  the  decomposition  of 
ethyl  acetate. 

Shields  determined  the  extent  of  decomposition  of  an 
acetate  solution  into  acid  and  base,  the  so-called  hydrolysis, 
and  from  this  we  can  calculate  the  strength  of  water  (as  an 
acid)  compared  with  that  of  acetic  acid.  Since  the  degree  of 
dissociation  of  acetic  acid  is  known,  it  is  possible  to  calculate 
the  degree  of  dissociation  of  water.  I  (9)  have  calculated  this 
to  be  2-03  x  10~9  at  25°,  so  that  in  a  litre  of  water  there 
is  T113  x  10~7  dissociated  gram-molecule. 

In  aqueous  solution  methyl  acetate  is  slowly  decomposed 
into  methyl  alcohol  and  acetic  acid.  In  this  case  it  is  the 
hydroxyl  ion  of  the  water  which  is  the  active  agent.  By 
comparing  the  action  of  water  with  that  of  a  solution  of 
sodium  hydroxide,  Wijs  (10)  determined  the  number  of 
dissociated  gram-molecules  in  a  litre  of  water  to  be  1*2  x  10~7 
at  25°,  which  agrees  well  with  the  value  given  above. 

o 


i94     EQUILIBRIUM    BETWEEN   ELECTROLYTES.    CHAP. 

From  the  electromotive  force  of  the  element  H2(Pt)  | 
Base  |  Acid  |  H2  (Pt),  Ostwald  (11)  determined  the  degree 
of  dissociation  of  water,  and  found  7  X  10~7  to  7'4  X  10~7. 

From  the  hydrolysis  of  aniline  hydrochloride,  Bredig 
(12)  found  the  degree  of  dissociation  6  x  10~7.  These  two 
last  values  do  not  agree  so  well  with  those  found  by  Wijs  and 
myself. 

By  repeated  distillation  of  water  in  a  vacuum,  Kohlrausch 
and  Heydweiller  (13)  obtained  water  much  purer  than  any 
which  had  previously  been  prepared,  and  found  that  it  con- 
ducted about  20  times  worse  than  the  best  sample  of  water 
distilled  in  the  air.  The  conductivity  at  18°  was  386  X  10~10 
(expressed  in  the  new  units). 

Since  A*  for  OH  =172  and  for  H  it  is  314,  the  number 
of  dissociated  gram-molecules  per  litre  at  18°  is  0'8  x  10~7. 
At  25°  the  value  is  1*05  X  10~7.  The  degree  of  dissociation, 
which  is  5 5' 5  times  smaller,  has  therefore  the  value 
1-4  x  10~9  at  18°,  and  1'9  x  10~9  at  25°. 

The  agreement  between  the  values  found  by  these  different 
methods  for  the  dissociation  of  water  is  extremely  good,  and 
Kohlrausch  regards  this  as  the  best  proof  of  the  correct- 
ness of  the  dissociation  theory.  Kohlrausch  and  Heydweiller 
give  the  following  numbers  for  the  number  of  gram-ions  of 
hydrogen  (A)  in  a  litre  of  water  at  the  various  temperatures  : — 

Temp.     0°       10°      18°       26°      34°      42°       50° 
0'35     0-56     0-80     1-09     T47     1-93     2-48. 


Heat  of  Dissociation  of  Water. — The  influence  of 
temperature  on  the  dissociation  of  water  can  be  calculated  as 
follows.  According  to  the  result  arrived  at  on  p.  94,  the 
equation — 

dlnK      'jg 

dT      ~  RT* 

can  be  applied  to  the  dissociation  of  water,  where  K  is  the 
dissociation  constant,  T  the  absolute  temperature,  and  /m  the 
heat  of  dissociation.  The  value  of  R  is  T99  cal.  (see  p.  13) 


XIL          HEAT   OF   DISSOCIATION    OF   WATER.  195 

For  water,  which  contains  5 5' 5  gram-molecules  in  a  litre,  we 
have — 

K  x  55-5(1  -  o)  =  (55-5a)2, 

or,  since  the  degree  of  dissociation,  o,  is  small  in  comparison 
with  1— 

d  In  a  =  Jd  In  K 

Therefore,  if  we  know  /*,  i.e.  the  heat  which  is  absorbed 
when  a  gram-molecule  of  water  dissociates  into  hydrogen 
and  hydroxyl  ions,  we  can  calculate  the  change  of  a  with 
temperature.  In  order  to  find  ft  we  make  the  following 
consideration.  Suppose  we  have  1  gram-molecule  of  hydro- 
chloric acid  and  1  gram-molecule  of  sodium  hydroxide  each 
in  such  dilution  that  we  may  assume  without  appreciable 
error  that  they  are  completely  dissociated.  Leaving  the 

water  out  of  account,  these  solutions  contain  1  gram-equiva- 

+  — 

lent  of  each  of  the  ions  H  (1  gram)  and  Cl  (35*45  grams), 

+ 
and  of  the  ions  Na  (23  grams)  and  OH  (17  grams)  respectively. 

When  these  two   solutions  are  mixed,  sodium  chloride  in 

+         - 
the  dissociated  condition,  i.e.  NSL  +  Cl,  and  water  are  formed 

according  to  the  equation — 

H  +  01  +  Na  +  OH  +  aq  =  NSL  +  Cl  +  H20-f-  aq 

where  aq  denotes  the  water  present  in  the  system  in  large 
quantity.  The  only  change,  therefore,  which  has  actually 

taken  place  is  the  union  of  a  gram-ion  of  H  with  a  gram-ion 

of  OH  to  form  a  gram-molecule  of  water.  The  heat 
developed  was  determined  by  Thomsen  to  be  14,247  cal.  at 
1014°  and  13,627  cal.  at  24'6°.  Evidently  this  is  the  same 
quantity  of  heat  (fj)  which  would  be  absorbed  when  a  gram- 
molecule  of  water  dissociates  into  H  and  OH.  Kohlrausch 
was  then  able  to  calculate  the  change  of  K  and  a  with 
temperature  after  I  had  pointed  out  the  meaning  of  the  heat 
of  neutralisation.  The  agreement  between  the  calculated 


196     EQUILIBRIUM    BETWEEN   ELECTROLYTES.    CHAP. 

and  observed  conductivities  of  water  as  found  by  Kohlrausch 
and  Heydweiller  is  very  perfect,  as  the  numbers  in  the  follow- 
ing table  show.  The  equivalent  conductivity  (X^)  is  taken 
as  equal  to  340  -f  St. 

SPECIFIC  CONDUCTIVITY  (K)  OF  WATER. 


Temperature. 

10(!K  (observed).                  I0<vc  (calculated). 

-2° 

0-0107 

0-0103 

+  4° 

0-0162 

0-0158 

10° 

0-0238 

0-0236 

18° 

0-0386 

0-0386 

26° 

0-0606 

0-0601 

34° 

0-0890                       0-0901 

42° 

0-1294                        0-1305 

50° 

0-1807 

0-1839 

Heat  of  Neutralisation.— From  the  description  given 
above,  it  follows  that  the  heat  of  neutralisation  must  be  the 

same  for  all  dilute  strong  acids  and  bases,  independent  of  the 

+ 
nature  of  the  acid  and  base,  since  in  all  cases  only  the  H  and 

OH  combine  to  form  H20.  This  fact,  which  had  been  known 
for  a  very  long  time,  seemed  peculiar  until  the  dissociation 
theory  (1884) 1  gave  the  key  to  the  explanation. 

The  development  can,  however,  only  be  applied  to  strong 
acids  and  bases,  because  at  the  dilutions  at  which  we  com- 
monly work  the  weak  acids  and  bases  are  only  dissociated 
to  a  slight  extent.  For  these  also,  however,  the  heat  of 
neutralisation  can  be  determined  from  electrical  measurements. 

If  we  investigate  a  solution  of  succinic  acid,  for  example, 
we  find  that  in  0'28-normal  solution  (the  concentration  used 
by  Thomsen)  the  acid  is  only  dissociated  to  the  extent  of  1/5 
per  cent,  at  21/5°.  In  order,  therefore,  to  compare  this  acid 
with  the  strong  acids,  we  must  first  supply  so  much  heat  as  is 
necessary  for  the  dissociation  of  the  remaining  98'5  per  cent. 

1  It  may  not  be  out  of  place  here  to  rectify  the  common  belief  that 
the  dissociation  theory  was  suggested  in  1887.  As  a  matter  of  fact,  it  was, 
in  a  less  perfect  form,  propounded  by  Arrhenius  in  his  Inaugural  Dissertation 
in  1884.— TK. 


XII. 


HEAT   OF   NEUTRALISATION. 


197 


Then  the  process  would  become  exactly  like  the  former.  The 
heat  of  dissociation,  /m,  of  the  succinic  acid  can  be  calculated 
from  the  change  of  the  dissociation  constant  with  the 
temperature,  by  means  of  the  same  equation  as  we  have 
applied  to  water.  If  jn  thus  found  be  multiplied  by  0'985, 
and  the  product  subtracted  from  the  heat  of  neutralisation 
of  strong  acids,  we  must  obtain  the  correct  value  for  the 
neutralisation  of  succinic  acid.  I  (14)  have  calculated  the 
heat  of  neutralisation  of  several  acids  in  this  way,  and  have 
obtained  values  which  agree  with  those  determined  calori- 
metrically  by  Thomsen. 

HEAT  OF  NEUTRALISATION  AT  21*5°. 


Acid. 

Observed. 

Calculated. 

Hydrochloric  acid    .... 
Plydrobromic  acid    .... 
Nitric  acid  

13,447 
13,525 
13550 

13,740 
13,750 
13,680 

Acetic  acid     
Propionic  acid     
Butyric  acid    .     . 

13,263 
13,598 
13957 

13,400 
13,480 
13800 

Succinic  acid  .     . 

12430 

12400 

Dichloracetic  acid    .... 
Phosphoric  acid  
Hypophosphorous  acid      .     . 
Hydrofluoric  acid     .... 

14,930 
14,959 
15,409 
16,320 

14,830 
14,830 
15,160 
16,270 

The  heat  of  neutralisation  of  most  acids  is  evidently 
greater  than  the  heat  of  dissociation  of  water,  which  I  have 
calculated  to  be  13,212  cal.  at  21'5°.  The  cause  of  this  is 
that  the  heat  of  dissociation  of  most  acids  is  negative,  i.e. 

jm    is  negative,  or,  in  other  words,  the  dissociation  constant, 

and  consequently  also  the  degree  of  dissociation,  decreases 
with  rising  temperature.  This  may  appear  strange  since 
in  the  ordinary  dissociations  the  degree  increases  with 
rising  temperature.  But  cases  of  ordinary  dissociation  are 
known,  e.g.  the  decomposition  of  hydrogen  selenide  and 
hydrogen  telluride  into  the  elements,  in  which,  at  any  rate  at 


198     EQUILIBRIUM    BETWEEN   ELECTROLYTES.    CHAP. 

certain  temperatures,  the  dissociation  decreases  as  the  tem- 
perature rises.  The  decomposition  of  ozone  into  oxygen — 

203  =  30,, 

which  takes  place  with  evolution  of  heat,  is  another  example. 
The  fact  that  the  degree  of  dissociation  of  electrolytes  as  a 
rule  decreases  with  rising  temperature  is  perhaps  connected 
with  the  fact  that  the  dielectric  constant  of  water  decreases 
as  the  temperature  rises  (by  about  0'6  per  cent,  per  degree 
at  0°,  according  to  Abegg).  According  to  the  theory 
of  J.  J.  Thomson  (15)  and  Nernst  (16),  the  degree  of 
dissociation  should  increase  with  the  dielectric  constant. 
It  roust  be  noted,  however,  that  the  heat  of  neutralisation 
of  many  acids  is  smaller  than  the  heat  of  dissociation  of 
water,  and  therefore  their  degree  of  dissociation  must  increase 
with  rising  temperature,  as  is  the  case  with  succinic  acid, 
and  to  a  greater  extent  with  hydrocyanic  acid  (heat  of 
neutralisation  3000  cal.). 

Electrolytes  with  a  Negative  Temperature  Co- 
efficient for  the  Conductivity. — As  the  degree  of  dissocia- 
tion of  several  acids,  as  well  as  that  of  some  salts,  decreases 
with  rising  temperature,  it  may  happen  that  the  product 
a\x  which  is  equal  to  A4),  i.e.  that  the  equivalent  conductivity, 
and  with  it  the  specific,  diminishes  as  the  temperature  rises ; 
in  other  words,  that  the  temperature  coefficient  becomes 
negative,  although  as  a  rule  XM  (for  acids)  increases  by 
about  1*7  per  cent,  per  degree.  It  is  to  be  expected  that 
this  will  most  probably  be  the  case  with  acids  which  have 
a  high  heat  of  neutralisation.  The  theory  also  predicts  that 
this  will  happen  more  readily  at  high  than  at  low  tempera- 
tures. Experiment  shows  that  the  temperature  coefficient 
for  hypophosphorous  acid  above  54°  and  for  phosphoric  acid 
above  74°  (both  in  normal  solution)  is  negative.  These 
results  were  quite  unexpected,  for  it  was  formerly  supposed 
that  the  conductivity  of  all  electrolytes  must  increase  as 
the  temperature  was  raised. 

Neutralisation  Volume. — On  mixing  a  solution  of  an 


XII. 


NEUTRALISATION   VOLUME. 


199 


acid  with  one  of  a  base,  a  change  of  volume  ensues  which 
amounts  to  19  c.c.,  when  each  solution  (dilute)  contains  a 
gram-equivalent.  This  is  the  neutralisation  volume.  This 
regularity,  like  that  of  the  heat  of  neutralisation,  only  holds 
good  for  strong  acids  and  bases.  For  weak  electrolytes  a 
correction  must  be  introduced,  the  dissociation  volume,  i.e. 
the  change  of  volume  which  takes  place  when  a  gram- 
molecule  of  acid  splits  up  into  its  ions.  This  volume  can 
be  theoretically  derived  from  the  formula  developed  by 
'  Planck  (17)— 


. 
dp 

where  the  constant  R  has  the  value  81'8  (atmospheres  per 
square  centimetre,  see  p.  26),  p  denotes  the  pressure  in  atmo- 
spheres, K  the  dissociation  constant  of  the  acid,  and  A9  the 
dissociation  volume  in  c.c.  at  the  absolute  temperature  T. 

Fanjung  (18)  investigated  the  influence  of  pressure  on 
the  dissociation  constant  of  weak  acids,  and  calculated  the 
values  of  A,  from  his  results.  He  found  that  A,  is  always 
negative,  which  proves  that  the  ions  occupy  a  smaller  volume 
than  the  undissociated  molecules,  and  from  this  it  follows 
that  the  dissociation  increases  with  rising  pressure  (see 
p.  99).  These  results  were  compared  with  those  calculated 
from  Ostwald's  experiments  on  the  increase  of  volume  on 
neutralisation,  and,  as  the  following  table  shows,  a  very 
perfect  agreement  was  found  :  — 

NEUTRALISATION  VOLUMES. 


Acid. 

Calculated  by 
Fanjung. 

Observed  by 
Ostwald. 

Formic  acid  

c.c. 

8-7 

c.c. 

7-7 

Acetic  acid.  . 

10-6 

10-5 

Propionic  acid  .... 
Butyric  acid  

12-4 
13-4 

12-2 
13-1 

Isobutyric  acid  .... 
Lactic  acid  

13-3 
12-1 

13-8 
11-8 

Succinic  acid    .... 

11-2 

11-8 

Malic  acid     

10-3 

11-4 

200  EQUILIBRIUM  BETWEEN  ELECTROLYTES.  CHAP.  XH. 

It  is  remarkable  that  the  ions  in  the  solution  occupy 
a  smaller  volume  than  the  compound  molecules.  In  this 
branch  of  our  subject,  however,  many  peculiarities  are  to 
be  found,  as,  for  instance,  the  fact  that  certain  substances 
(sodium  hydroxide,  etc.)  cause  such  a  contraction  of  the 
water  that  the  solution  has  a  smaller  volume  than  the 
solvent  used. 

It  can  easily  be  seen  that  all  strong  acids  and  bases  must 
have  almost  the  same  neutralisation  volume ;  that  this  is 
actually  the  case  may  be  gathered  from  the  following 
numbers : — 


Acid. 

AB  on  neuti 
KOH 

alising  -with 
NaOH 

HN03 
HC1 
HBr 
HE 

20-05 
19-52 
19-63 

19-80 

19-77 
19-24 
19-34 
19-54 

For  ammonia  the  volume  change  on  neutralising  with  a 
strong  acid  amounts  to  26  c.c. 

The  opinion  of  Nernst  and  Drude  (19)  is  that  the  ions 
influence  the  volume  of  the  water  on  account  of  the 
strong  electric  field  which  they  give  rise  to.  All  liquids, 
whose  dielectric  constant  is  increased  by  pressure — and  this 
is  probably  always  the  case  (20) — suffer  a  contraction  in 
a  strong  electric  field.  This  phenomenon  is  known  as 
dectrostriction.  The  ions  in  water,  alcohol,  or  other  solvent 
cause  such  an  electrostriction. 


CHAPTER  XIII. 
Calculation  of  Electromotive  Forces. 

Introduction. — We  have  treated  in  the  preceding  chapters, 
with  the  aid  of  the  theory  of  electrolytic  dissociation,  of  the 
several  physical  and  chemical  properties  of  homogeneous 
electrolytic  solutions ;  and  we  have  developed  the  laws  which 
regulate  the  equilibrium  which  obtains  between  two  phases 
of  a  heterogeneous  system.  We  now  pass  on  to  the  con- 
sideration of  the  free  energy  which  can  be  obtained  when  an 
electrolyte  passes  from  one  solution  to  another,  or  from  one 
phase  to  another,  and  shall  study  particularly  those  cases  in 
which  the  transport  of  material  is  associated  with  a  transport 
of  electricity.  In  such  cases  the  whole  of  the  mechanical 
energy  may  be  transformed  into  electric  energy,  and  the 
latter  can  be  very  easily  estimated  by  measuring  the 
electromotive  force  produced  simultaneously  with  the  mass 
transport. 

This  mass  transport  (or  transport  of  material)  may  consist 
partly  in  removing  ions  from  one  solution  to  another,  and 
partly  in  the  separation  of  the  ions  at  the  electrodes.  The 
ions  are  always  accompanied  by  their  electric  charges,  but 
when  they  separate  at  the  electrode  they  are  quickly  trans- 
formed into  uncharged  molecules,  and  give  up  their  electricity 
to  the  electrode.  In  practice,  this  latter  process  is  by  far  the 
more  important,  although  the  theory  has  been  most  completely 
developed  for  the  former. 

The  greatest  progress  in  the  theory  of  this  subject  has  been 
made  by  Helmholtz  and  Nernst.  By  applying  the  second  law 
of  thermodynamics,  Helmholtz  showed  the  connection  between 


202  ELECTROMOTIVE    FORCE.  CHAP. 

the  heat  absorbed  in  a  galvanic  element,  its  electromotive 
force,  and  the  change  of  this  with  temperature.  He  succeeded 
also  in  calculating,  on  thermodynamic  principles,  the  electro- 
motive force  of  certain  concentration  cells. 

Nernst  treated  the  subject  more  from  a  kinetic  point  of 
view,  and,  by  means  of  the  theory  of  osmotic  pressure,  cal- 
culated the  electric  forces  associated  with  the  transport  of  the 
ions.  Here,  too,  the  kinetic  view  gives  us  a  better  picture 
of  the  process,  but  the  thermodynamic  method  gives  more 
trustworthy  results.  Nernst  showed  how,  by  the  kinetic 
method,  we  can  calculate  the  single  electromotive  force  at  the 
surface  of  contact  of  two  liquids,  whilst  by  the  other  method 
only  the  total  effect  can  be  obtained. 

Galvanic  Elements. — These  may  consist  of  a  com- 
bination of  conductors  of  the  first  and  second  class,  metals 
and  electrolytes,  or,  as  in  the  liquid  cells,  only  of  electro- 
lytes. It  is  true  that  in  the  liquid  cells  there  are  always 
places  of  contact  between  metals  and  electrolytes,  but 
these  are  so  arranged  that  they  exactly  balance  each  other. 
Liquid  elements  are  of  great  interest,  because  Nernst  first 
gave  the  mechanical  description  of  the  production  of  an 
electromotive  force  for  them.  They  are  not,  however,  practi- 
cally used  as  sources  of  electricity. 

Of  the  so-called  hydro-elements,  the  best  known  is  the 
Volta  pile — 

Zn  |  H2S04  |  Cu, 

in  which  zinc  passes  into  solution  and  hydrogen  separates 
at  the  copper  pole.  This  is  a  type  of  the  irreversible  elements. 
The  hydrogen  is  evolved  and  the  original  condition  is  not  re- 
established when  a  current  is  passed  through  the  element  in 
the  opposite  direction ;  in  this  case  copper  is  dissolved  and 
hydrogen  is  evolved  at  the  zinc  pole  when  the  current  is 
passed  from  copper  to  zinc  through  the  solution. 

In  the  theoretical  respect,  the  so-called  reversible  elements 
behave  much  more  simply ;  in  these  the  electrodes  are  non- 
polarisable,  i.e.  surrounded  by  an  electrolyte,  the  positive  ion 


xin.  GALVANIC   ELEMENTS.  203 

of  which  is  the  same  as  the  metal  of  the  electrode.     The 
commonest  of  these  elements  is  the  Daniell  cell — 

Zn  |  ZnS04  |  CuS04  |  Cu, 

in  which  zinc  is  dissolved  with  formation  of  zinc  sulphate, 
and  copper  is  deposited  from  the  copper  sulphate.  When  a 
current  is  passed  in  the  opposite  direction,  i.e.  from  the  copper 
to  the  zinc  through  the  solutions,  the  deposited  copper  is 
dissolved  and  zinc  is  separated,  so  that  the  original  condition 
can  be  re-established.  Combinations  of  the  type  of  the  Clark 
cell  (see  p.  124)  are  also  reversible.  The  commonly  used 
.  Bunsen  and  Leclanche  cells  belong  to  the  group  of  irreversible 
elements. 

In  order  to  express  electric  energy  in  the  ordinary  units, 
we  recall  what  has  already  been  said  (pp.  6  and  11). 
Electrical  work  is  expended  when  a  given  quantity  of  positive 
electricity,  q  coulombs,  is  brought  from  a  place  of  lower 
potential,  F0  volts,  to  a  place  of  higher  potential,  V\  volts. 
The  work  done  then  amounts  to — 

ri—  • 

q(  FI  -  FO)  volt-coulombs. 

The  same  work  has  to  be  done  to  bring  the  quantity  q  of 
negative  electricity  from  the  higher  potential  V\  to  the  lower 
potential  F0,  and  the  calculation  for  the  simultaneous  trans- 
port of  the  two  electricities  (positive  and  negative)  can  be 
made  in  an  analogous  manner. 

Now,  according  to  definition,  the  value  of  a  volt-coulomb 
is — 

1  volt-coulomb  =  107  ergs  =  01018  kilogram-metres 
=  0-239  cal. 

To  separate  a  gram-equivalent  of  a  metal  96,500  coulombs 
are  required  ;  the  work  done  for  such  a  quantity  of  electricity 
is  therefore — 

23,070(F0  -   FOcal. 
Transformation  of  Chemical  into  Electrical  Energy  in 


204  ELECTROMOTIVE    FORCE.  CHAP. 

a  Daniell  Cell.  Thomson's  Rule.— We  may  now  go  more 
fully  into  the  processes  which  take  place  in  a  Daniell  element. 
If  this  developes  96,500  coulombs,  then  at  the  same  time  a 
gram-equivalent  (327  grams)  of  zinc  is  dissolved,  and  a 
gram-equivalent  (31*8  grams)  of  copper  is  deposited.  A 
certain  amount  of  heat  is  evolved  during  this  change,  and  can 
be  determined  calorimetrically ;  it  amounts  to  25,065  cal. 
If  the  electric  work  done  by  the  element  were  exactly  equal 
to  the  quantity  of  heat  evolved,  or,  in  other  words,  if  the  heat 
evolved  in  the  Daniell  cell  were  completely  changed  into 
electric  work,  it  could  move  the  96,500  coulombs  against 
an  electromotive  force  VQ  —  V\,  which  is  given  by  the. 
relationship — 

23,070(Fi  -  Fi)  =  25,065. 

The  value  of  F0  -  FI  would  then  be  1*086  volts,  i.e.  the 
element  would  be  able  to  bring  the  unit  charge  of  96,500 
coulombs  from  potential  0  to  potential  1*086  volts.  If  we 
connect  the  zinc  pole  of  the  cell  with  the  earth,  and  the 
copper  pole  with  a  condenser  at  potential  P,  the  elec- 
tricity can  pass  to  this  condenser,  i.e.  the  condenser  can 
be  charged,  so  long  as  P  is  smaller  than  the  electromotive 
force  of  the  element.  The  greatest  work  which  an  element 
can  do  in  this  way  is  to  charge  a  condenser  to  the  same 
potential  as  the  electromotive  force  of  the  element. 

If  our  assumption  be  correct,  that  the  Daniell  element 
changes  the  whole  of  the  chemical  energy  used  up  into 
electrical  energy,  then  its  electromotive  force  must  be  1*086 
volts.  Experiment  shows  that  the  electromotive  force  almost 
reaches  this  value  (1  dll.  =  about  1*10  volts,  see  p.  124), 
and  on  this  account  it  was  for  a  long  time  believed  that  the 
electromotive  force  of  an  element  could  be  calculated  from 
the  heat  value  (per  gram-equivalent)  of  the  chemical  process 
taking  place  by  simply  dividing  this  (expressed  in  gram- 
calories)  by  the  number  23,070.  According  to  this,  if  E  is 
the  electromotive  force  and  H  the  quantity  of  heat  developed 
by  the  chemical  reaction  per  gram-equivalent,  then — 


XIII. 


THOMSON'S   RULE. 
H 


205 


~  23,070 

This  idea  was  first  suggested  by  Helmholtz  (1),  and 
was  afterwards  taken  up  by  Lord  Kelvin  (W.  Thomson) 
(2),  and  is  known  as  the  Thomson  rule. 

Several  attempts,  notably  by  Raoult  and  J.  Thomsen, 
have  been  made  to  confirm  the  Thomson  rule,  and  it  has 
been  found  that  in  the  cases  investigated  the  experimental 
values  agree  well  with  the  theory.  Thus,  Thomsen  (3) 
obtained  the  following  values  for  the  electromotive  forces  of 
several  elements,  1  dll.  being  taken  as  unit :— 


Element. 

Heat 
evolution. 

Electromotive  force. 
Calculated.   '    Observed. 

Zn 

H2S04  +  100  aq  1  CuS04  1  Cu           25065 

1-00 

1-00 

Zn 

H2S04  |  CdS04  |  Cd      ...             8295             0-33 

0-33 

Zn 

HC1  1  A<rf!l  1  Acr        -                           9704-0              1-08 

1-06 

Zn 

H2S04 

HN03  1C... 

48040 

1-92 

1-86 

Zn 

H2S04 

HN03  +  7H20  |  C 

41405 

1-65 

1-69 

Cu 
Cu 

H2S04 
H2S04 

K2Cr207  +  H2S04  |  C 
HN03  1C... 

49895 
22995 

1-99 
0-92 

1-85 

0-88 

Cu 

H2S04 

HNO,  +  7H90  1  C 

16340 

0-65 

0-73 

Fe 

FeCl2  |  Fe2Cl6  |  C      .     .     . 

22215             0-89 

0-90 

When  concentrated  nitric  acid  was  used,  Thomsen 
assumed  that  nitrogen  peroxide  (NgO^  was  formed,  and 
remained  dissolved  in  the  liquid ;  when  more  dilute  nitric 
acid  (HN03  +  7H20)  was  used,  he  assumed  that  nitric 
oxide  (NgOa)  was  produced.  Consequently  there  was  a 
different  heat  evolved  when  these  were  employed.  In  the 
chromic  acid  cell  it  was  assumed  that  chromic '  oxide  was 
formed,  and  in  the  ferric  chloride  cell  that  ferrous  chloride 
was  produced. 

Criticism  of  Thomson's  Rule. — When  the  Thomson 
rule  was  more  fully  examined  difficulties  arose.  The  cause 
of  the  deviations  was  sought  for  in  so-called  secondary 
processes  by  which  heat  is  evolved,  but  which  were  supposed 
to  have  no  influence  on  the  electromotive  force. 


206  ELECTROMOTIVE   FORCE.  CHAP. 

At  that  time  it  was  believed,  as  Yolta  had  assumed,  that 
the  seat  of  the  electromotive  force  was  at  the  place  of  contact 
of  the  two  metals,  in  the  Daniell  cell  at  the  place  of  con- 
tact of  the  copper  and  the  zinc ;  the  electromotive  force 
between  these  two  metals  was  supposed  to  be  about  1  volt. 
Edlund  (4)  determined  how  much  heat  is  evolved  when  a 
definite  quantity  of  electricity  is  passed  through  a  junction  of 
copper  and  zinc  (the  Peltier  effect).  According  to  the  above 
principle  we  should  be  able  to  calculate  this  quantity  of  heat. 
The  observed  result  was,  however,  very  much  smaller  than 
expected,  the  potential  difference  for  Cu  |  Zn  being  only 
0'006  volt  instead  of  1  volt.  This  result  induced  Edlund  to 
investigate  the  correctness  of  the  Thomson  rule. 

In  his  discussion  he  made  use  of  some  results  which  had 
been  obtained  by  Eaoult.  Eaoult  observed  that  in  the 
electrolysis  of  water  in  a  voltameter,  besides  the  evolution 
of  gases,  there  is  a  local  heating  which  is  not  due  to  the 
friction  of  the  ions  against  the  liquid,  and  is  therefore 
different  from  the  Joule  effect.  In  these  experiments  Eaoult 
also  measured  the  electromotive  force. 

Edlund  gave  the  following  explanation.  In  the  volta- 
meter a  back  electromotive  force,  e,  is  produced.  If  96,500 
coulombs  are  moved  against  this  force,  then  for  each  volt 
there  will  be  an  evolution  of  heat  amounting  to  23,070  cal. 
(23,900  cal.  for  1  dll.,  according  to  the  numbers  then 
accepted).  In  one  case,  for  instance,  the  back  electromotive 
force  was  2'04  dll.,  and  there  should  therefore  be  an  evolu- 
tion of  48,756  cal.  If  we  subtract  from  this  the  quantity  of 
heat,  34,462  cal.,  required  for  the  decomposition  of  the  water, 
we  obtain  for  the  local  heating  14,294  cal.,  whilst  Eaoult 
found  14,898  cal.  Several  similar  experimental  results  of 
Eaoult  were  calculated  with  the  same  success  (1869).  Edlund 
later  showed  that  in  the  electrolysis  of  silver  salts  a  local 
cooling  may  take  place.  Xow,  if  Thomson's  rule  were 
correct,  such  local  heat  effects  should  not  occur,  but  the 
heat  necessary  for  the  decomposition  should  be  exactly 
sufficient  to  produce  the  electromotive  force  of  the  element. 


xin.  HELMHOLTZ'S   CALCULATION.  207 

Braun  (5)  made  a  number  of  observations  with  ele- 
ments which  do  not  follow  the  Thomson  rule,  which 
continued  to  be  supported  by  Fr.  Exner.  W.  Gibbs  (6) 
proved  that  with  electrodes  which  can  be  used  at  their  melt- 
ing points  (bismuth,  lead,  tin)  there  is  no  change  of  the 
electromotive  force  at  this  point,  as  there  should  be  according 
to  the  Thomson  rule. 

Helmholtz's  Calculation.— In  1882  Helmholtz  (7)  gave 
the   following   simple   deduction   from    the    second   law  of 
thermodynamics.     In   the   diagram 
(Fig.  41)   V  represents  the  electro- 


T+c/T 


motive  force  of  an  element,  and  the 
quantity  of  electricity,  q,  which 
passes  through  the  element  is 
chosen  as  abscissa.  The  work  is 
measured  by  the  product  q-V.  In 
the  first  place,  let  the  quantity  of 
electricity  q  pass  through  the  ele- 
ment, which  is  supposed  to  be  a  F  41 
perfectly  reversible  one,  at  the 

absolute  temperature  T  4-  dT,  and  so  do  the  greatest  possible 
(maximum)  work.  If  the  electromotive  force  of  the  element 
is  P  at  the  temperature  T,  then  at  T 4-  dTii,  is — 


dP. 

ct-  JL 

The  work  done  by  the  element  at  T  4-  dT  is  therefore  — 


The  temperature  of  the  element  is  now  allowed  to  fall  to 
T,  and  by  doing  mechanical  work  (say,  by  a  dynamo)  the 
quantity  q  is  forced  through  the  element  in  the  opposite 
•direction.  The  electromotive  force  of  the  element  is  now 
reduced  to  P}  therefore  the  work  expended  by  the  dynamo 


208  ELECTROMOTIVE    FORCE.  CHAP. 

The  completely  reversible  element  has  now  returned  to 
its  initial  condition,  leaving  the  temperature  out  of  account, 
for  the  same  quantity  of  electricity  has  passed  through  it  in 
both  directions.  Practically  no  work  has  to  be  done  to  raise 
its  temperature  by  dT. 

Let  the  quantity  of  electricity  q  be  96,500  coulombs,  and 
the  heat  evolved  in  the  chemical  process  be  W,  then  at  the 
temperature  T  +  dT  the  quantity  of  heat  {(P  +  dP)23,070 

-  W}  cal.  is  taken  from  the  element  (and  therefore  from  the' 
surrounding   medium  which  keeps  the  temperature  of  the 
element  constant).     At  the  temperature  T  the  quantity  of 
heat  (P  x  23,070  —  W)  cal.  is  introduced  into  the  element, 
whilst   the  quantity  23,070 .  dP  is  transformed  into  work. 
Now,  if  a  quantity  of  heat,  Q  cal.,  passes  from  the  temperature 
T  +  dT  to  Ty  and  if  the  work  done  thereby  is  dA  cal.,  then, 
according  to  the  second  law  of  thermodynamics — 

dA  =  dT 
~Q  ~     T 

In  the  case  taken,  dA  =  23,070dP,  and  Q  =  P  X  23,070 

-  W.     Therefore— 

dT 


23,070P  -  W       T 
•  If  —  =  0,  i.e.  if  the  electromotive  force  of  the  element 

does  not  change  with  the  temperature — 

W 


P  = 


23,070 


and  in  this  case  Thomson's  rule  is  correct.  As  a  matter  of 
fact,  the  electromotive  force  of  a  series  of  elements  is  almost 
independent  of  the  temperature,  for  instance,  the  Daniell 
element,  and  for  these  Thomson's  rule  is  applicable. 

Elements  are  known  which,  when  functionating,  absorb 
heat — their     electromotive     force     increases     with     rising 


XIII. 


FREE   AND    BOUND    ENERGY. 


209 


temperature — and  others  are  known  which  give  up  heat 
to  the  surrounding  medium,  and  their  electromotive  force 
decreases  as  the  temperature  rises. 

Helmholtz's  deduction  has  been  fully  confirmed  by 
experiment,  most  thoroughly  by  Jahn  (8),  who  measured 
the  heat  evolution  by  means  of  an  ice  calorimeter.  The 
following  table  gives  the  results  of  his  experiments.  In  the 
column  headed  Cede,  are  given  the  values  of  23,070  X  P  —  W, 
calculated  by  Helmholtz's  method  from  the  observed  tempera- 
ture coefficients,  and  in  the  column  headed  Ols.  the  calori- 
metrically  observed  values  are  given.  The  experiments  were 
made  at  0°  (273°  absolute). 


Element. 

23070P-W. 

P. 

23070P.        W. 

Obs. 

Gale. 

Cu 
Cu 

CuS04 

+  100H20  |  ZnS04  +  100H20  |  ZQ       . 
1302)2  +  100H20  |  Pb(C2H302)2 

1-096 

25263  !     25035 

208 

214 

+  1001: 

20  |  pb 

0*476 

10980   '       8261 

2718 

2422 

Ag  |  AgCl 

ZnCl2  +  100H20  |  Zn     .     .     .     .     . 

1-031 

23753        26085 

-2330 

-2574 

Ag  |  AerOl 

ZnCl2  +  50H20  1  Zn  

1-017 

9.-U48 

24541 

-1093 

-1322 

tf 

AgCl 
AgBr 

ZnCl2  +  25H20  |  Zn  

0-974      22454 
0'841      19386 

23573 
19963 

-1169 
—  582 

-1270 
—  667 

ZnBr2  +  25H20  I  Zu 

Ag 

AgNO 

„  1  PhfWO«Y^     Ph  . 

0*932      25435 

914.QO 

39  7  K 

3945 

AC 

AgNOo  1  OiifTCOo^    Ou  

0-458       15090         10560           4460 

4460 

4 

Hg20 

|  KOH  |  KOl  |  HgCl  !  Hg  (Bugarszky) 

0-328 

7566       -3820        11386 

11276 

From  the  numbers  quoted,  it  can  be  seen  that  the  value  of 
2  3, 07 OP  is  sometimes  greater  and  sometimes  smaller  than  W, 
the  difference  amounting  to  even  as  much  as  50  per  cent. 
Indeed,  in  Bugarszky's  element  these  two  values  have 
different  signs.  It  is  noteworthy  that  such  a  small  addition 
of  water  to  the  zinc  chloride  in  the  element  Ag  —  Zn  is  able 
to  produce  such  a  great  change  in  its  behaviour. 

Free  and  Bound  Energy.— As  already  mentioned,  the 
view  was  previously  entertained  that  the  whole  heat  energy 
of  an  element  might  be  transformed  into  electric  energy. 
Helmholtz,  however,  showed  by  the  above  reasoning  that 
this  is  not  always  the  case,  and  he  therefore  introduced  the 
idea  of  free  energy  as  that  part  of  the  total  energy  which  can 
be  completely  transformed  into  mechanical  work.  The  energy 
23,070  .  P  in  the  above  case,  is  evidently  of  this  kind,  for 

p 


210  ELECTROMOTIVE    FORCE.  CHAP. 

electric  energy  can  (theoretically)  be  totally  converted  into 
mechanical  work.  (Practically,  of  course,  the  energy  trans- 
formation cannot  be  carried  out  without  loss  of  work,  because 
no  machine  works  ideally;  the  best  electric  motors  give  a 
yield  of  about  95  per  cent,  in  mechanical  work.)  The  free 
energy  of  an  element  amounts  therefore  to  23,070 .  P  for  every 
gram-equivalent  decomposed,  when  P  is  the  electromotive 
force  of  the  element  in  volts.  If  W  is  the  corresponding- 
total  energy,  measured  by  the  heat  change,  the  difference, 
W  -  23,070  .  P,  is  the  bound  energy. 

The  free  energy  of  a  system  plays  a  very  important  part ; 
it  gives,  so  to  say,  the  maximum  work  which  the  system  is 
capable  of  doing  when  a  certain  change  takes  place.  The 
complete  using  up  of  the  free  energy  is  only  conceivable  in 
the  case  of  reversible  processes  ;  and  in  this  connection  it 
must  be  noticed  that  in  reality  any  process  can  only  be 
carried  out  more  or  less  approximately  in  a  reversible 
manner ;  part  of  the  free  energy  is  always  lost  in  over- 
coming unavoidable  friction  resistances.  The  free  energy 
of  a  system  always  decreases  when  a  spontaneous  process 
takes  place  in  it.  It  corresponds  with  the  amount  of  work 
stored  in  the  system.  Thermochemists  formerly  believed 
(erroneously)  that  this  store  of  work  was  represented  by  the 
total  heat,  in  which  case  Thomson's  rule  would  be  quite 
valid. 

The  rule  has  a  certain  practical  importance,  for  it  may 
be  applied  in  estimating  the  electromotive  force  of  a  new 
galvanic  combination,  the  corresponding  heat  change  of  the 
reaction  being  generally  known  from  direct  measurements. 

G.  Meyer's  Concentration  Element.— The  work  which 
can  be  obtained  by  the  decomposition  of  a  gram-equivalent 
in  an.  element  is  given  by  23,070. P.  Occasionally  this 
work  A  can  be  measured  in  another  way.  Then  from  the 
equation — 

A  =  23,070  .  P 
the  electromotive  force  of  the  element  can  be  calculated. 


xin.     G.    MEYER'S   CONCENTRATION    ELEMENT.      211 

A   case   of  this   nature  was   studied  by  G.  Meyer  (9). 
The  arrangement  of  the  element  used  by  him  was — 


Concentrated  amal- 
gam of  a  metal,  M. 


Aqueous  solution  of 
a  salt  of  metal,  M. 


Dilute  amalgam 
of  a  metal,  M. 


He  examined  the  metals — zinc,  cadmium,  lead,  tin,  copper, 
and  sodium.  Now,  if  one  mol  of  one  of  these  metals  passes 
from  the  concentrated  amalgam  of  concentration  G\  to  the 
dilute  amalgam  of  concentration  C%,  the  work  done  will  be 
(see  Chap.  VI.  p.  77)— 

A  =  HTln~. 

C/2 

If  the  work  is  measured  in  gram- calories,  11  =  I1 99. 
An  element  of  this  kind,  which  depends  for  its  action  on 
differences  of  concentration,  is  called  a  concentration  element. 

If,  now,  the  circuit  of  a  combination  of  two  amalgams  be 
closed  by  a  metal  wire,  a  current  passes  through  the  solution 
in  the  direction  indicated  by  the  arrow,  so  that  metal  is 
dissolved  from  the  concentrated  amalgam,  and  just  as  much 
is  deposited  at  the  dilute  amalgam.  The  total  result  of  the 
process  is  that,  simultaneously  with  the  transportation  of 
96,500  coulombs,  one  gram-equivalent  of  metal  passes  from 
one  amalgam  to  the  other,  and  the  concentration  of  the 
solution  between  the  two  remains  unaltered. 

If    a  gram-molecule   contains   n    equivalents,   the   same 

work  will  be  done  by  the  motion  of      gram-molecule.     The 

n 

work  obtainable  is,  therefore,  in  general— 

A  =  23,070P  =  -  ETlu  %. 
n  ft 

By  measuring  the  electromotive  force  P,  Meyer  verified 
this  result.  From  this  he  determined  the  value  of  n,  and 
found  numbers  which  agree  well  with  those  arrived  at  by 


212  ELECTROMOTIVE    FORCE.  CHAP. 

Tammann,  Hey  cock  and  Neville  (10),  and  others.  The 
metals  examined  were  found  to  be  monatomic. 

Helmholtz's  Concentration  Element. — In  his  theo- 
retical deductions  (1877)  Helmholtz  (11)  considered  a 
combination  consisting  of  two  copper  sulphate  solutions  of 
different  concentrations,  which  were  in  contact,  and  into  each 
of  which  was  immersed  a  copper  electrode.  For  the  sake  of 
simplicity,  let  us  imagine  that  the  difference  of  concentrations 
of  the  two  solutions  is  infinitesimally  small,  so  that  the 
concentration  of  one  may  be  represented  by  0,  and  that  of 
the  other  by  C+  dC.  Let  the  Hittorf  transport  number 
for  copper  be  m,  then  that  for  S04  will  be  (1  —  m) ;  and, 
further,  let  the  potential  difference  between  the  two  electrodes 
be  d  V.  If  we  pass  through  the  combination — 

dilute  — >  concentrated 

Cu  Cu  |  CuS04  |  CuS04  CuS04  |  Cu, 

2  x  96,500  coulombs  (because  a  mol  of  CuS04  corresponds 
with  two  gram-equivalents)  in  the  direction  indicated  by  the 
arrow,  the  concentration  will  then  be  represented  by  the 
following  scheme : — 


or.   (1  -  m)  Cu 
Cu     CuS04  \, 


(1  -  m)  S04 


mCu 
mS04 


CuS04  I  Cu  Cu. 


In  the  direction  of  the  current  (from  left  to  right)  m 
gram-ions  of  copper  have  passed  through  the  surface  •  of 
separation  of  the  two  solutions,  and  (1  —  m)  gram-ions  of 
S04  have  passed  through  in  the  opposite  direction.  A  gram- 
ion  of  copper  has  dissolved  from  the  left  electrode,  and  this 
same  quantity  has  been  deposited  on  the  right  electrode. 
This  latter  change  is  connected  with  no  expenditure  of  work, 
for  it  consists  simply  in  moving  63'6  grams  of  copper  in  a 
horizontal  plane  (if  the  copper  electrodes  were  not  at  the 
same  height,  the  work,  which  appears  in  the  so-called  gravita- 
tion elements,  might  be  neglected,  provided  the  difference  in 
the  heights  is  not  great). 

The    principal    ctiange     consists     in     moving    (1  —  m) 


xin.  HELMHOLTZ'S  CONCENTRATION   ELEMENT.  213 

gram-molecule  of  copper  sulphate  from  the  concentrated 
solution  to  the  more  dilute  one.  The  electrical  work 
amounts  to — 

dA  =  2  x  23,070 rf real., 

or,  in  general,  when  the  electrolyte  used  contains  n  gram- 
equivalents  per  gram-molecule — 

dA  =  nX  23,070  d  Fcal. 

This  work  may  be  used  to  re-establish  the  old  conditions 
of  concentration,  which  is  done  by  separating  so  much  of 
the  dilute  solution  as  contains  (1  —  m)  mol  of  copper  sulphate, 
and  evaporating  water  partly  from  this  and  partly  from  the 
concentrated  solution  at  constant  temperature  until  the  old 
concentration  is  reached.  This  quantity  of  water  vapour  is 
now  compressed  until  it  reaches  the  same  concentration  as 
the  vapour  over  the  dilute  solution,  and  it  is  then  forced  into 
this  solution.  The  only  work  done  in  this  process  is  used  in 
the  compression  of  the  water  vapour  at  low  pressure  over  the 
concentrated  solution  to  the  high  pressure  over  the  dilute 
solution.  This  was  the  method  used  by  Helmholtz  in  his 
deduction. 

The  same  result  can  be  attained  more  simply  by  making 
use  of  semi-permeable  membranes,  which  allow  water,  but  not 
salt,  to  pass  through.  Let  the  concentration  of  the  solution 
to  the  left,  which  contains  1  mol  of  copper  sulphate,  be  c,  its 

osmotic  pressure  TT,  and  its  volume  v  =  -,  and  let  this  be 

c 

separated  from  the  solution  to  the  right  by  a  semi-permeable 
membrane,  MI  ;  further,  let  the  characteristics  for  this  second 
solution  be  c  +  dc,  TT  -f  dir,  and  v  —  dv.  Another  semi-perme- 
able membrane,  Jf2,  is  used  to  separate  from  the  remainder 
such  a  quantity  of  the  dilute  solution  as  contains  (1  -  m) 
gram-molecule  dissolved  copper  sulphate.  The  arrangement 
can  then  be  expressed  by  the  following  scheme  : — 

dil.  sol.  M2          dil.  sol.  Mx  cone.  sol. 

|  c,  TT,  v  |  (1  -  m)CuS04  |  c  +  dc,  TT  +  d-rr,  v  -dv  \  . 


214  ELECTROMOTIVE    FORCE.  CHAP. 

In  the  first  place,  we  force  through  M2  towards  the  left 
(1  —  m)dv  c.c.  of  water.  This  process  takes  place  against  an 
osmotic  excess  pressure  which  rises  from  0  to  dir,  because  at 
the  beginning  the  concentration  in  the  middle  partition  is  the 
same  as  that  to  the  left,  and  at  the  end  it  is  the  same  as  that 
to  the  right.  The  corresponding  work  is  — 

dA\  =  ^dir  .dv  .(I  —  m), 

or,  since  the  osmotic  pressure  TT  of  a  copper  sulphate  solution 
is  regulated  by  vant  HofFs  equation  (see  p.  76)  — 

TTV  =  iET  or  TT  =  RTd, 
therefore— 

dAl  =  l  ~-mdv  .  d(RTci). 

2i 

Now  let  MI  be  removed,  and  so  much  water  forced  from  right 
to  left  as  was  contained  between  M2  and  Mb  namely  (1  —  m) 
(v  —  dv)  c.c.  This  requires  the  work— 

dAs  =  (1  -m)(v  -  dv)d(RTd). 

Since  dv  can  be  neglected,  on  account  of  its  srnallness 
compared  with  v,  the  whole  work  done  is  expressed  by  — 


dA1  +  dAz  =  (1  -  m)ET         =  (1  -  m)RT  \di  +  i     \ 

c  \  c  * 


since  v  =-. 
c 


Xow,  dA  must  be  equal  to  dA\  -f  dA%.    Consequently  — 


nr  \  u 

dV  =  -  (1  —  m)  -^  volts. 

n.  23,070  c 

We  may  imagine  a  whole  series  of  solutions  of  only 
slightly  differing  concentrations  placed  side  by  side,  so  that 
between  the  two  end  ones  there  is  a  finite  difference  of  con- 
centration. The  total  electromotive  force,  V,  between  these 


xin.  HELMHOLTZ'S   CONCENTRATION  ELEMENT.  215 

end  solutions  must  be  equal  to  the  sum  of  all  the  d  V  values 
for  the  various  contiguous  solutions,  and  therefore — 


1 1  C| 

I  J(l  -  m)di  +  [(l-m)unncj  volts. 


.2?,  070  1 

co  c0 

If  we  had  used  a  concentration  element  of  the  following 
composition— 

dil.  sol.        cone.  sol. 

Ag  AgCl  AgCl  |  KC1  |  KC1  KC1  |  AgCl  Ag  Ag 

where  the  unpolarisable  electrodes  are  of  the  second  order, 
and  if  n .  96,500  coulombs  were  conducted  through  the  combi- 
nation in  the  direction  indicated,  we  should  have  found  the 
following  result : — 

\      \      A    m  I  -K-rn  m^- 
AgAgAgCl|Iv01mC1 

The  principal  action  in  this  case  would  be  that  m  gram- 
molecules  of  the  salt  would  be  transported  from  the  concen- 
trated to  the  dilute  solution.  In  a  similar  way  we  should 
calculate  the  electromotive  force  by  means  of  the  ex- 
pression— 


V  = —-  \  I  mdi  +  I  mid  In  c  I  volts. 

n. 23,070  (J  J 

<-o  <>o 

In  the  example  given  n  =  I  (for  KC1).  In  concentration 
elements  with  unpolarisable  electrodes  of  the  second  order, 
the  electromotive  force  strives  to  drive  the  current  through 
the  liquid  from  the  concentrated  to  the  dilute  solution ;  with 
unpolarisable  electrodes  of  the  first  order  the  current  is 
driven  in  the  opposite  direction.  (It  is  assumed  that  m  is  a 
proper  fraction,  which  is  generally  the  case :  see  pp.  137  and 
143.) 

Elements  of  the  latter  kind  have  recently  been  exactly 
studied  by  Jahn  (12).  The  liquids  used  were  dilute 


2l6 


ELECTROMOTIVE    FORCE. 


CHAP. 


solutions  of  potassium  chloride,  sodium  chloride,  and  hydro- 
chloric acid.  According  to  the  results  obtained  by  Loomis 
and  Hausrath,  we  may  set  i  =  1  +  a  (approximately),  where 
a  is  the  degree  of  dissociation  calculated  from  the  conduc- 
tivity. In  the  following  table  Jahn's  experimental  values 
(E,  observed)  are  given  along  with  those  calculated  (E, 
calculated).  The  concentrations  (in  gram-molecules  per 
litre)  of  the  solutions  used  are  given  in  the  columns  headed 
x\  and  x%. 


Electrolyte. 

X]. 

x.2. 

E  (observed). 

E  (calulated). 

Difference. 

KC1 

0-03349 

0-00167 

0-07028 

0-07173 

-  2-0% 

55 

0-01669 

5? 

0-05424 

0-05539 

-2-1 

57 

0-01114 

«y 

0-04497 

0-04579 

-  1-8 

55 

0-00833 

i? 

0-03844 

0-03885 

-  1-1 

55 

0-00670 

|j 

0-03330 

0-03364 

-  i-o 

}5 

0-00557 

j5 

0-02895 

0-02920 

-0-9 

HC1 

0-03342 

0-001665 

0-11955 

0-12122 

-  1-4 

55 

0-01665 

7 

0-09235 

0-09334 

-  1-1 

55 

0-01113 

0-07664 

0-07710 

-0-6 

55 

0-00831 

0-06487 

0-06534 

-0-7 

55 

0-00669 

j 

0-05614 

0-05652 

-0-7 

51 

0-00556 

0-04884 

0-04906 

-0-4 

NaCl 

003344 

0-001674 

0-05614 

0-05679 

-.1-1 

5J 

0-01673 

y 

0-04360 

0-04395 

-0-8 

55 

0-01117 

7 

0-03608 

0-03636 

-0-8 

5? 

0-00836 

0-03073 

0-03089 

-0-5 

5» 

0-00669 

> 

0-02652 

0-02663 

-0-4 

The  agreement  between  the  observed  and  calculated 
values  is  very  satisfactory.  The  observed  values  are  always 
somewhat  smaller  (on  the  average  about  1  per  cent.),  which 
points  to  a  constant  experimental  error. 

The  formulte  given  above  for  V  are  perfectly  exact,  but 
they  are  more  or  less  inconvenient,  since  they  cannot  be 
directly  integrated.  They  can,  however,  be  integrated  if  we 
assume  that  they  are  constant,  and  that  the  law  of  mass 
action — 

— - —  =  const. 
c  -9 


xin.  HELMHOLTZ'S  CONCENTRATION   ELEMENT.  217 

is  valid,  where  r  is  the  number  of  ions  contained  in  a  mole- 

cule of  the  salt,  and  -  denotes  the  degree  of  dissociation.   We 

c 

then  obtain  — 


d(ci)  =  d(c  +  (r  -  l)g)  =  dc  +  (r  -  l)dg 

C  C  G 

By   differentiating    the   equation   for    mass    action    w 
obtain  — 


r(c  —  #)d</  =gdc  - 

^  =  dc  +  (r  - 

g 

d(ci)  __  rdy 


c          g 
from  which  it  follows  that  — 


where  Fi  is  applicable  for  concentration  elements  with 
unpolarisable  electrodes  of  the  first  order,  and  V%  for  those 
with  unpolarisable  electrodes  of  the  second  order  (log  denotes 
the  ordinary  logarithm).  Without  appreciable  error  we  may 

set   2^025  =  10'4.     These   formulae,  which  are  convenient 

23,070 

for  calculating,  agree  with  those  of  Nernst.  The  product  of 
concentration  and  degree  of  dissociation,  g,  is  a  measure 
of  the  concentration  of  the  ions.  For  electrolytes  consisting 
of  two  monovalent  ions  r  =  2  and  n  =  1.  Most  of  the 
determinations  which  have  been  carried  out  were  made  with 
such  electrolytes. 


218  ELECTROMOTIVE    FORCE.  CHAP. 

Nernst's  Calculation  of  the  Electromotive  Force  at 
the  Surface  of  Separation  of  Two  Solutions  of  the  Same 
Salt    (13).—  WQ     begin    with     salts    which 
consist  of  two  monovalent  ions.     Suppose  two 
solutions  in  contact,  in  which  each  of  the  two 
kinds  of  ions  have  the  osmotic  pressures  p\ 
and  p-2  respectively  (Fig.  42).     Let  us  calculate 
the  work  necessary  to  move  the  quantity  of 
electricity  96,500  coulombs  through  the  surface  of  separation 
#;  this  work  corresponds  with  the  electromotive  force  at 
this  surface.     If  the  migration  velocity  of  the  cation  C  is  u, 

and  that  of  the  anion  A  is  v.  then  —  --  equivalents  of  C 

v  4-  u 

pass  through  the   contact   plane   to   the  right,  and  - 

ilb   *"i      i/ 

equivalents  to  the  left.     The  work  clone,  expressed  in  heat 
units,  is  for  the  cation— 


u 


and  for  the  anion— 


The  total  work  must  be  equal  to  23,070?r,  where  TT  is 
the  required  potential  difference  (expressed  in  volts)  at  G. 
Therefore  — 

23,0707r  =  W,  +  W,  = 


u  +  v      pz 

or  »  =  86T  .  10-"  !LT-  .«  in  &  =  1-99  .  10T  log  &. 

° 


u 


These  electromotive  forces  come  into  play  in  liquid 
elements  in  which  the  electrodes  are  so  arranged  that  there 
are  no  resulting  electromotive  forces  between  the  metals  and 
the  liquids.  . 

Thus,  for  instance,  in  the  element  — 


XIII. 


ELECTROMOTIVE    FORCE. 


219 


Hg  |  HgCl  |  01  KC1  |  0-01  KOI  |  0-01  HC1  |  01  HC1  | 
01  KOI  |  HgCl  |  Hg 

the  two  electromotive  forces  at  the  ends  exactly  balance  each 
other,  since  they  are  equal,  but  act  in  opposite  directions. 

Furthermore,  the  electromotive  force  between  01  HC1  | 
01  KOI  must  be  equal  to  that  between  O'Ol  KOI  |  0-01  HC1, 
but  with  the  opposite  sign,  since  the  electromotive  force 
depends  on  the  ratio  of  the  concentrations  of  two  solutions, 
and  not  on  the  absolute  values.  The  remaining  electromotive 
forces  are  therefore — 

0-1  KOI  |  0-01  KC1,  and  O'Ol  HC1  |  01  HC1, 

which  can  be  calculated  according  to  the  above  formulae. 
Nernst  (13)  has  made  a  large  number  of  observations  with 
such  elements,  and  we  give  below  some  of  his  results.  The 
experiments  were  carried  out  at  18°,  and  in  this  case  we 
obtain — 


In  10, 


from  which  we  find  — 


=  5-T8.i<H^-*- 

( u  -f  v 


+ 


Electrolytes. 

U-t,       «*-> 

1 

1  i     JT  (observed). 

TT  (calculated). 

U  +  P       MX  +  « 

KC1,  NaCl    .... 

+  0-237 

0-0111 

0-0137 

KC1,  LiCl     
KC1,  NH4C1 

0-366 
0-019 

0-0183 
0-0004 

0-0211 
0-0011 

NH4C1,  NaCl 

0-218 

0-0098 

0-0126 

KC1,  HC1      .     .     . 

-  0-688 

-  0-0357 

-  0-0397 

KOI,  HN03 

0-719 

—  0*0378 

—  0*0414 

KC1,  H03SC9Hn   .... 

-  0-902 

-  0-0469 

-  0-0520 

The  calculated  values  are  all  about  12  per  cent,  higher 
than  those  observed.  A  deviation  of  about  5  per  cent, 
can  be  explained  by  incomplete  dissociation,  but  the  cause 


220  ELECTROMOTIVE   FORCE.  CHAP. 

of  the  remainder  of  the  deviation  has  not  yet  been  found. 
For  some  silver  salts  the  disagreement  was  still  greater; 
the  observed  values  were  0*0214  and  0*0146  volt,  whilst 
calculation  gives  0*0109  and  0*008  respectively. 

If  the  above  combination  consists  of  %-valent  ions,  then 
for  each  mol  n.  9  6,500  coulombs  must  be  passed  through  the 
element,  and  we  obtain  for  the  electric  work  — 


In 


u  +  v 


Consequently  n  passes  into  the  denominator   of  the   final 
formula,  and  we  have  — 


Nernst's  Calculation  of  the  Electromotive  Forces  of 
Concentration  Elements  (14)  —  Let  us  again  consider  the 
Helmholtz  combination  — 

Cu  |  dilute  CuS04  |  concentrated  CuS04  |  Cu. 
p*  Pi 

When  a  current  passes  through  this  element  in  the 
direction  indicated  by  the  arrow,  the  following  changes 
occur  :  — 

(1)  A  gram-ion  (63*6  grams)  of  copper  is  dissolved  from 
the   copper   electrode  in   contact   with    the    dilute    copper 
sulphate  solution,  and  is  transformed  from  the  metallic  to 
the  ionic  condition  ; 

(2)  At  the  surface  of  separation  of  the  two  solutions  the 
same  process  takes  place  as  described  in  the  previous  case  ; 
and 

(3)  A  gram-  ion  (63'6  grams)  of  copper  is  deposited  from 
the  concentrated  solution  on  the  copper  electrode  in  contact 
with  it,  the  copper  passing  from  the  ionic  to  the  metallic 
condition. 

The  final  result  of  processes  (1)  and  (3)  is  that  a  gram-ion 
of  copper  passes  from  the  concentrated  to  the  dilute  solution. 


XIIL  ELECTROMOTIVE    FORCE.  221 

If  the  work  which  can  be  gained  from  this  be  measured  in 
gram-calories,  the  corresponding  electromotive  force  can  be 
calculated  from  the  equation  — 

23,070.  n.w  =  1-99.  T.lnP~, 

P* 

T997MO  *       pi 

or  TT  =  -  log  —  . 

n  *  p2 

To  this  we  must  add  the  process  (2),  which  is  analogous  to 
that  already  described  (p.  218),  but  which  takes  place  in  the 
opposite  direction.  In  the  former  case  the  cation  moves  from 
the  solution  of  osmotic  pressure,  pi  (osmotic  pressure  with 
reference  to  the  cation),  to  that  of  osmotic  pressure,  p%  ;  here 
the  motion  takes  place  in  the  opposite  direction,  and  gives 
rise  to  the  electromotive  force  — 

.  10~4    v  ~u  . 


-  -  .   -         —  .  —. 

n  v  -f  u       &  p% 

By  adding  together  TT  and  7^,  we  obtain  the  total  electro- 
motive force  P  — 

1-992MO-*       2v  Pl 

P  =  TTl  +  7T2  =  ~  .  -         -  .  lOg  —  . 

n  u  +  v       to  p% 

The  direction  of  the  current  is  always  from  the  dilute  to 
the  concentrated  solution,  since  it  is  in  this  way  that  the 
concentration  difference  can  disappear. 

Instead  of  an  element  of  this  type  with  unpolarisable 
•electrodes  of  the  first  order?  we  may  consider  a  type  with  un- 
polarisable electrodes  of  the  second  order,  say  the  combination  — 

Hg  |  HgCl  |  0-01  HCl~foi  HC1  |  HgCl  |  Hg. 
When  a  quantity  of  electricity  n  .  96,500  coulombs  (in  this 

1  By  unpolarisable  electrodes  of  the  first  order,  we  mean  electrodes  in 
an  unsaturated  solution  of  a  salt  containing  a  cation,  the  same  as  the  metal 
of  the  electrode  ;  by  an  unpolarisable  electrode  of  the  second  order,  is 
meant  a  metal  in  a  solution  of  one  of  its  salts,  which  by  being  in  contact 
with  excess  of  solid  salt,  is  always  kept  saturated. 


222  ELECTROMOTIVE    FORCE.  CHAP. 

case  n  =  1,  since  the  electrolyte  HC1  consists  of  monovalent 
ions)  is  passed  through  the  element  in  the  direction  of  the 
arrow,  i.e.  from  the  dilute  to  the  concentrated  solution,  the 
following  changes  take  place  :— 

(1)  A  gram-equivalent  of  mercury   combines   with   an 
equivalent    of     chlorine     from     the     calomel,    and    forms 
HgCl; 

(2)  The  gram-equivalent  of  mercury  thus  set  free  from 
the  calomel  combines  with  an  equivalent  of  chlorine  from 
the  0'01-normal  HC1  solution.    This  latter  solution,  therefore, 
loses  a  gram-ion  of  chlorine ; 

(3)  At  the  contact  surface  of  concentrated  and  dilute 
solution    the    same    process   takes   place   as  in  the   above 
example ; 

(4)  A  gram-equivalent  of  hydrogen  from  the  OT-normal 
HC1  solution  combines  with  an  equivalent  of  chlorine  from 
the  adjacent  calomel  solution,  and  forms  a  gram-molecule  of 
hydrochloric  acid.     The  concentration  of  the  latter  solution 
is  thereby  increased ;  and 

(5)  The  gram-equivalent  of  mercury,  which  becomes  free 
on  account  of  process  (4),  is  deposited  at  the  mercury  electrode. 

The  result  of  these  processes  may  be  summed  up  as 
follows : — 

By  processes  (1)  and  (5)  the  left  side  loses  and  the  right 
side  (in  the  diagram)  gains  a  gram-ion  of  mercury.  The  old 
equilibrium  can  be  re-established  by  allowing  this  quantity 
of  mercury  to  flow  back  from  right  to  left,  and  no  work  is 
required  for  this.  This  part  of  the  whole  process  cannot, 
therefore,  cause  any  electromotive  force.  By  processes  (2)  and 
(4)  a  gram-ion  of  chlorine  is  brought  from  the  dilute  to  the 
concentrated  solution.  This  process  is  therefore  the  same, 
but  in  the  opposite  direction,  as  when  unpolarisable  electrodes 
of  the  first  order  are  used,  and  consequently  the  same  electro- 
motive force  occurs,  but  with  the  other  sign.  By  process 
(3)  we  obtain  the  same  electromotive  force  at  the  surface  of 
contact  as  in  the  former  example.  The  total  electromotive 
force  is  therefore  given  by — 


xin.  EXPERIMENTAL  CONFIRMATION  OF  THEORY.  223 

1-99.  7MO-4      2u      ,     pi 
PlBSir.+  wt---     —    -._j_.log-. 

The  negative  sign  indicates  that  the  electromotive  force 
strives  to  drive  the  electricity  in  the  opposite  direction  to 
that  assumed  in  the  development  of  the  formula,  i.e.  the 
electricity  goes  through  the  element  from  the  concentrated 
to  the  dilute  solution. 

Experimental  Confirmation  of  the  Theory.—  In  his 
investigations  Helmholtz  only  considered  concentration 
elements  with  unpolarisable  electrodes  of  the  first  order. 
His  results  were  experimentally  confirmed  by  Moser  (15) 
and  Miesler.  Similar  experiments  were  later  carried  out 
by  Nernst  (16).  Nernst  found  for  the  element  — 

Ag  |  01  AgN03  |  0-01  AgN03  |  Ag 

the  electromotive  force  O055  volt  at  18°,  whilst  the  theory 
leads  to  — 


=  1-99  x  291  X  1-058  x  10~4  =  0-0613  volt, 

when  T  =  291,  u  =  55'0,  and  v  =  61/8  (see  p.  142). 

The  agreement  is  satisfactory.  Now,  since  the  dissocia- 
tion is  in  reality  not  complete,  as  is  assumed,  we  may 
introduce  a  correction  for  this  disturbing  factor,  and  then 
obtain  the  value  0*0574  volt, 

Nernst  has  measured  a  large  number  of  electromotive 
forces  with  elements  which  are  reversible  with  respect  to 
the  anion,  that  is  to  say,  with  unpolarisable  electrodes  of 
the  second  order.  His  results  are  given  in  the  following 
table,  where  GI  and  ca  denote  the  normalities  of  the 
concentrated  and  dilute  solutions,  and  e  obs.  and  £  calc.2 
the  electromotive  forces,  the  latter  calculated  by  means  of 
Nernst's  formula  :  — 


224 


ELECTROMOTIVE    FORCE. 


CHAP. 


Electrolyte. 

cx. 

C2. 

c  obs. 

ccalc.j. 

e  calc.2. 

HC1      ..... 

HC1      
HBr     
KC1            .... 

0-105 

o-io 

0-126 
0-125 

0-018 
0-01 
0-0132 
0-0125 

0-0710 
0-0926 
0-0932 
0-0532 

0-0717 
0-0939 
0-0917 
0-0542 

c)-<>73<; 

0-0962 
0-0940 
0*0565 

NaCl    

0-125 

0-0125 

0-0402 

0-0408 

0-0429 

LiCl     
NH4C1  
NaBr         .... 

0-10 
0-10 
0125 

0-01 

o-oi 

0-0125 

0-0354 
0-0546 
0-0417 

0-0336 
0-0531 
0-0404 

0-0355 
0-0554 
0-0425 

NaOH  

0-235 

0-030 

0-0178 

0-0183 

0-0188 

In  the  calculation  of  t  calc.i,  Kerns  t  took  account  of  the 
incomplete  dissociation,  and  set  the  ratio  of  the  osmotic 
pressures  of  the  two  solutions  equal  to  the  ratio  of  their 
conductivities,  and  not  to  that  of  their  concentrations.  The 
values  calculated  in  this  way  agree  very  well  with  those 
observed  directly. 

The  activity  of  a  concentration  element  can  be  easily 
shown  ;  this  is  best  done  by  the  experiment  made  by  Bucholz 
in  1804.      A  glass  cylinder  is  half  filled  with 
a  strong  solution  of  stannous  chloride  (layer 
&  in  Fig.  43),  and  this  is  covered  by  a  layer 
of  pure  water  (a).     A  tin  rod  is  immersed  in 
the  liquid.     A   current   is  produced   which 
passes  from  the  lower  end  of  the  rod  upwards ; 
this  causes  solution  of  the  tin  at  the  upper 
FIG.  43.          end,  and  dendritic  crystals  of  tin  are  formed 

at  &. 

Another  kind  of  concentration  cell  has  been  suggested  by 
von  Turin  (17).  This  has  the  combination — 


Mercury  |  Mercuric  salt  in  solution 


Amalgam. 


In  order  that  the  mercury  may  not  expel  the  dissolved 
metal  in  the  amalgam,  it  is  necessary  that  this  be  "  nobler  " 
than  mercury:  for  example,  gold.  In  this  arrangement 
mercury  will  be  transported  through  the  solution  from  leftj 


to  right. 


This  corresponds   exactly  with  a  distillation 


xin.  SOLUTION    PRESSURE    OF    METALS.  225 

mercury  to  the  amalgam,  the  vapour  pressure  of  which  must 
necessarily  be  lower  than  that  of  the  pure  substance.  The 
electromotive  force  is  evidently  proportional  to  the  depression 
of  the  vapour  pressure,  and  this  again  is  proportional  to 

syj 

-pr,  where  n  is  the  number  of  dissolved  molecules,  and  N  the 

number  of  solvent  (mercury)  molecules.  By  measuring  the 
electromotive  force  of  such  an  element,  the  molecular  weight 
of  the  dissolved  metal  can  be  determined  (compare  Meyer's 
concentration  element,  p.  210). 

Solution  Pressure  of  Metals. — In  concentration  ele- 
ments we  have  three  electromotive  forces,  which  act  at  the 
three  contact  surfaces.  For  one  of  these,  namely,  that 
between  the  concentrated  and  dilute  solution,  Nernst  has 
deduced  (see  p.  218)  the  expression — 

1-99x10-  .r.^.!      P., 

n  u  +  v  pz 

where  pi  and  p%  denote  the  osmotic  pressures  of  the  two 
solutions,  u  and  v  the  migration  velocities,  and  n  is  the 
valence  of  the  ions.  For  the  other  two  electromotive  forces 
we  have  obtained  (see  p.  221) — 

7T   =   7TO  +   7T2  =    1/99  .  10~4   T  .  log  ^. 

Pz 

It  would  be  of  interest  to  ascertain  the  value  of  each  of 
these  electromotive  forces,  e.g.  between  Cu  and  dilute  CuSOi, 
and  between  Cu  and  concentrated  CuS04,  and  not  only,  as  the 
above  formula  gives  us,  their  sum. 

In  order  to  obtain  some  analogy  with  the  other  formulae, 
the  form — 

TTO  +  7ra  =  1-99  . 10-4  T.  log  -  -  1-99  . 10-4  T .  log  — 

has  been  given  to  the  above  one. 

p 
The   factors   containing   the   expression   log  —  give  the 

Q 


226  ELECTROMOTIVE   FORCE.  CHAP. 

electromotive  forces  between  copper  and  dilute  copper  sul- 
phate, and  between  copper  and  concentrated  copper  sulphate. 

In  order  to  explain  a  formula  of  this  sort,  Nernst  intro- 
duced the  following  conception,  which  was  afterwards  further 
developed  by  Ostwald  (18). 

Suppose  we  have  a  substance,  e.g.  sugar,  in  contact  with 
a  liquid,  e.g.  water,  the  solid  dissolves  until  a  saturated 
solution  is  formed.  This  process  corresponds  exactly  with 
the  vaporisation  of  a  liquid,  which  goes  on  until  the  vapour 
space  is  saturated  and  the  vapour  possesses  a  certain  pressure 
— its  maximum  pressure  at  the  particular  temperature. 

On  account  of  this  analogy  the  osmotic  (partial)  pressure 
exerted  by  the  saturated  solution  of  sugar  is  termed  the 
solution  pressure,  or  solution  tension,  of  the  sugar  at  the 
particular  temperature  (according  to  van't  HofFs  law). 

Now,  if  we  consider  the  metals — for  instance,  zinc  in 
sulphuric  acid — we  see  that  they  do  not  pass  into  solution 
unchanged,  but  that  they  strive  to  dissolve  as  ions.  It  seems 
natural  to  suppose  that  the  metal  passes  into  solution  until 
the  concentration  of  the  ions,  and  with  it  the  osmotic 
pressure,  has  reached  a  certain  value,  which  pressure  is 
termed  the  electrolytic  solution  pressure. 

We  shall  denote  this  pressure  by  P.  Let  us  suppose  that 
a  gram-ion  (65  grams)  of  zinc  passes  into  solution  in  the  form 
of  ions,  and  in  the  solution  the  zinc  ions  have  the  osmotic 
pressure  p ;  this  process  can  be  conducted  reversibly  by  dis- 
solving the  zinc  at  constant  pressure  P,  whereby  no  work  is 
done  (just  as  when  water  evaporates  into  a  vacuum),  and 
then  by  expanding  the  zinc  ions  from  pressure  P  to  pressure 
p,  whereby  the  work  done  is — 

&  =  -RTi*  £. 

IP  p 

The  total  work  done  is  therefore — 

-. 

P 


XIIL  PLANCK'S    FORMULA.  227 

The  electric  work  which  can  be  obtained  from  this  is 
n  .  96,500  .  TTO,  where  TTQ  is  the  electromotive  force  at  the 
surface  of  contact ;  therefore  when  p  =  p%  (see  p.  218) — 


-H/ -L  1          Jt  OU    .     ./     .    10       ^        -          _£ 

*0  =  ;r9poo  'lnF=     -ir  -•1V2' 

This  applies  to  the  pole  at  which  the  zinc  dissolves ;  at 
the  other  pole  (where  p  =  pi)  an  electromotive  force  in  the 
opposite  direction  is  set  up,  and  this,  consequently,  has  the 
opposite  sign.  We  have,  therefore— 

86.T.10-6    ,     P 

7T2  = -  .  In  — .  • 

n  pi 

The  sum  of  TTQ  and  ir^  is — 

86  .  T  .  10~6    .    p!      1-99  .  T.  10~4    ,      »x 

7TQ  +  7T2  =   -  —  .  In  —   =    -  -    .  lOg  *-  , 

n  p%  n  p2 

which  is  the  same  expression  as  we  found  above. 

Planck's  Formula. — Nernst  only  developed  the  expres- 
sion for  the  electromotive  force  at  the  contact  surface  between 
two  solutions  of  the  same  electrolyte  at  different  concen- 
trations. Planck  (19),  taking  a  more  general  view  of  the 
problem,  has  deduced  a  formula  for  the  electromotive  force  at 
the  contact  surface  between  any  two  electrolytic  solutions. 
If— 

U  =  up  +  uipi  +  u^pz  +  .  .  . 
and —  V  =  vq    +  v\q\  -f  v%qz  4-  •  •  • 


where  u,  u\y  u%,  etc.,  are  the  transport  numbers  of  the  positive 
ions  ;  v,  vi,  v%,  etc.,  those  of  the  negative  ions ;  p,  pi,  p%,  etc., 
and  q,  q\,  q2)  etc.,  the  osmotic  pressures  of  these  ions ;  and  if 
c  is  the  total  concentration  of  all  the  positive  ions,  and  there- 
fore of  all  the  negative  ions,  provided  that  all  the  ions  are 
monovalent,  then  we  have  to  find  expressions  for  Ui  and  U%, 


228  ELECTROMOTIVE    FORCE.  CHAP. 

V\  and   F"2,  c\  and  c2,  which  are  applicable  to  each  of  the 
solutions  which  are  in  contact. 

Planck  found  that  the   electromotive  force   at   such   a 
surface  of  contact  can  be  expressed  by  — 

TT  =  1-99.  10~4.r.  log  5, 
where  %  is  given  by  the  equation  — 

In  *  -  In  £     - 


When   two   solutions   of  the   same   electrolyte   are   ex- 
amined — 


and  by  introducing  these  values  into  Planck's  formula,  we 
obtain  that  of  Nernst  (see  p.  218)— 

TT=  1-99.  lO-4.^7^^  log51. 
u  +  v     °  c2 

A  further  simplification  occurs  when  ^  =  c2,  *.«.  when  the 
total  concentration  is  the  same  on  both  sides  of  the  contact 
surface.  In  this  case  we  have  — 

ri  Ei  +  F2 

"  Fx  +  ^2 

and—  TT  =  1-99  .  10~4  .  T  .  log  £*  "j"  !12  - 

r  i  -f-    C/2 

For  a  solution  of  one  electrolyte,  U\  =  up,  and  V\  =  vp  ; 
and  for  that  of  another  electrolyte,  Z72  =  MI#>,  and  F2  =  v^?. 
Several  combinations  of  this  type  were  examined  by  Nernst, 
and  his  results,  as  well  as  those  calculated  by  Planck's 
formula,  are  contained  in  the  following  table  :  — 


XIII. 


PLANCK'S   FORMULA. 


Solutions. 

TT  (observed). 

it  (calculated). 

HC1,  KC1     . 

0-0285 

0-0282 

HC1,  NaCl    .     .     . 

0-0350 

0-0334 

HC1,  LiCl     .     .     . 

0-0400 

0-0358 

KC1,  NaCl    .     .     . 

0-0040 

0-0052 

KCl,LiCl     .     .     . 

0-0069 

0-0077 

NaCl,  LiCl    .     .     . 

0-0027 

0-0024 

The  agreement  between  observed  and  calculated  values  is 
very  satisfactory. 

Similar  experiments  carried  out  later  by  Negbaur  (20) 
also  showed  a  very  perfect  agreement  with  the  theory. 


CHAPTEK   XIV. 
Potential  Difference  between  Two  Bodies. 

Electrical  Double-layer. — When  a  zinc  plate  is  immersed 
in  a  solution  of  zinc  sulphate,  it  tends  to  send  more  ions  into 
the  solution,  provided  that  the  osmotic  pressure  p  of  the  zinc 
ions  is  smaller  than  the  electrolytic  solution  pressure  P  of 
the  metal. 

The  solution  becomes  positively  charged  by  these  positive 
zinc  ions,  and  the  zinc  plate,  which  was  formerly  neutral, 
takes  on  a  negative  charge.  At  the  surface  of  separation  a 
highly  charged  double-layer  is  formed,  corresponding  with 
a  Franklin  condenser  one  side  of  which  consists  of  the 
negatively  charged  zinc  and  the  other  of  the  positively 
charged  ions  in  the  zinc  sulphate  solution. 

On  the  other  hand,  if  we  have  a  metal  whose  electrolytic 
solution  pressure,  P,  is  smaller  than  the  osmotic  pressure  p 
of  the  corresponding  cations  in  the  salt  solution,  say  copper 
in  copper  sulphate  solution,  some  of  the  positive  ions  are 
deposited  on  the  metal,  which  thereby  becomes  positively 
charged,  whilst  the  solution  becomes  negatively  charged. 
The  two  parts  of  the  Franklin  condenser  are  then  the  positive 
metal  and  the  solution  which,  on  account  of  the  excess  of 
negative  ions,  is  negatively  charged.  This  sort  of  charged 
contact  surface  has  been  termed  by  Helmholtz  an  electrical 
douUe-layer. 

In  the  first  case,  the  smaller  the  osmotic  pressure  of  the 
zinc  ions  in  the  solution,  the  more  ions  must  go  into  solution 
when  this  is  in  contact  with  the  metal,  and  the  stronger  will 


CHAP.  xiv.  POTENTIAL   DIFFERENCE.  231 

be  the  negative  charge  on  the  zinc.  When  the  charge  has 
reached  a  certain  value,  solution  of  the  zinc  ceases  ;  this  takes 
place  when  the  potential  difference  due  to  the  charges  attains 
the  value — 

86  x  10-6    .     P 

TTO  =  -  -  .  In  — > 

n  p 

for  then  it  exactly  counterbalances  the  effect  of  the  solution 
pressure  of  the  metal. 

Potential  Difference  between  a  Metal  and  a  Liquid. 
—When  there  is  a  potential  difference  V  between  two  con- 
denser plates  of  area  S  which  are  at  distance  d  apart,  and 
when    the    insulator  is   the    light   ether,   the   quantity   of 
electricity  on  the  condenser  is  given  by — 

VS 
q       lird 

If  we  know  q,  V,  and  S  for  one  plate,  which  is  polarised 
in  an  electrolyte,  then  d  can  be  calculated,  d  being  the 
distance  between  the  polarised  plate  and  the  nearest  layer 
of  ions.  Thus,  Helmholtz  (1)  found  in  the  case  of  polarised 
platinum  04  x  10 "7  to  0'8  x  10~7  cm.,  which  corresponds 
almost  with  molecular  dimensions. 

If  we  use   a   liquid   metal,  for  instance   mercury,   the 
surface  tension  comes  into  play — that  is  to  say,  the  surface 
of    separation    between    mercury    and    an 
electrolyte    in    contact   with    it    tends    to        -  Electrolyte 
decrease.     If  the  contact  surface  is  charged,  +  Hg 

the   electricity  tends    to    bring   about   the  FlG  ^ 

opposite  effect.  The  electricity  strives  to 
spread  itself  over  as  large  a  surface  as  possible,  and  since 
it  is  bound  at  the  surface  it  tends  to  increase  this.  Con- 
sequently, if  we  have  an  electrical  double-layer  at  the  contact 
between  mercury  and  an  electrolyte,  the  surface  tension — i.e. 
the  force  with  which  the  surface  tends  to  diminish  itself— 
is  determined  by  the  natural  surface  tension  of  the  metal 
diminished  by  the  force  with  which  the  electric  charge 


232 


POTENTIAL   DIFFERENCE. 


CHAP. 


FIG.  45. 


tends  to  increase  the  surface.     The  latter  increases  with  the 
magnitude  of  the  charge. 

Capillary  Electrometer. — In  order  to  observe  the  change 
of  surface  tension,  the  mercury  is  put  into  a  tube  which  is 
drawn  out  to  a  capillary,  slightly  conical 
point,  R  (Fig.  45),  so  that  the  pressure  of 
the  mercury  column  acts  on  the  con- 
tents of  the  capillary.  The  lower 
meniscus  of  the  mercury  is  in  contact 
with  a  saturated  solution  of  mercurous 
sulphate  in  sulphuric  acid  contained  in 
the  vessel  K,  in  the  bottom  of  which 
is  placed  a  layer  of  mercury.  If  the 
charge  at  the  contact  surface  be  altered  by  introducing  a 
potential  difference  (electromotive  force)  at  P}  there  is  a 
simultaneous  change  of  surface  tension.  If  this  tension  is 
decreased,  the  mercury  meniscus  in  R  falls ;  if  it  increases, 
the  mercury  rises  in  R,  and  the  movement  can  be  observed 
with  a  microscope,  M.  An  instrument  of  this  kind,  called 

a  capillary  electrometer,  was  first 
constructed  by  Lippmann  (#).  It 
can  be  used  to  determine  when 
the  potential  difference  reaches 
the  value  0,  and  is  therefore  useful 
for  comparing  potential  differences. 
It  is  most  commonly  employed  as 
a  null  instrument  in  the  form 
shown  in  Fig.  46. 

At  the  beginning  of  the  experi- 
ment let  the  potential  difference  be  zero,  i.e.  P  —  0.  If  now 
P  be  so  altered  that  the  mercury  in  the  tube  becomes  nega- 
tively charge^,  the  mercury  rises  in  the  tube,  i.e.  the  surface 
tension  increases.  The  cause  of  this  is  that  the  original 
charge  of  the  mercury  is  diminished,  which  proves  that  this 
was  positive.  Mercury,  therefore,  in  contact  with  sulphuric 
acid  becomes  positively  charged,  and  the  acid  negatively. 
If  the  contact  surface  be  now  charged  with  increasing 


FIG.  46. 


xiv.  DROPPING   ELECTRODES.  233 

electromotive  forces  which  conduct  negative  electricity  to 
the  mercury,  the  surface  tension  of  the  metal  rises  until  the 
charge  of  the  double-layer  becomes  equal  to  0.  When  this 
limit  is  exceeded,  the  mercury  becomes  negatively  charged, 
whilst  the  sulphuric  acid  receives  a  positive  charge.  This 
occurs  when  P  has  a  value  of  about  1  volt.  Mercury  in  the 
ordinary  condition  exhibits,  when  in  contact  with  sulphuric 
acid,  a  potential  difference  towards  it  of  about  1  volt,  the 
mercury  being  positively  and  the  acid  negatively  charged. 

A.  Konig  (3)  arrived  at  practically  the  same  result  by 
examining  the  curvature  of  mercury  drops  in  sulphuric  acid ; 
this  method  also  permits  of  the  determination  of  the  surface 
tension.  It  is,  however,  not  easy  to  ascertain  the  maximum 
surface  tension  in  this  way. 

Dropping  Electrodes. — From  these  results,  Helmholtz 
came  to  a  conclusion  which  led  to  the  construction  of  the 
so-called  dropping  electrodes.  Let  us  suppose  that  we  hav 
a  quantity  of  mercury  which  can  be  allowed  to  flow  out 
through  a  fine  tube  into  an  electrolyte.  If  the  mercury  is 
positively  charged,  the  surface  of  contact  will  be  vastly 
increased  by  the  flowing  out,  and  the  charge  must  become 
smaller.  The  charge,  however,  will  only  diminish  provided 
that  no  new  mercury  ions  pass  from  the  solution  into  the 
mercury,  and  thus  recharge  the  mercury  electrode;  the 
solution  in  contact  with  mercury  always  contains  some 
mercury  salt.  With  an  arrangement  of  this  kind  Helmholtz 
(4)  found  that  the  dropping  mercury  possesses  the  same 
potential  as  a  drop  of  mercury  which  is  polarised  to  the 
maximum  surface  tension.  Ostwald  repeated  these  -experi- 
ments, but  Paschen  (5)  was  the  first  to  successfully  construct 
dropping  electrodes,  which  he  did  by  arranging  the  tube 
so  that  the  stream  of  mercury  is  broken  up  into  drops  just 
at  the  surface  of  the  electrolyte  under  examination.  The 
opening  of  the  tube  should  be  from  0'02  to  O05  mm.  in 
diameter. 

According  to  Nernst  (6'),  the  action  of  dropping  elec- 
trodes can  be  explained  as  follows.  Mercury  is  a  "  noble  " 


234 


POTENTIAL   DIFFERENCE. 


CHAP. 


FIG.  47. 


metal  (see  below),  i.e.  it  possesses  a  low  solution  pressure. 

Now,  if  a  liquid,  W(Fig.  47),  in  which  there  hangs  a  mercury 
drop,  A,  from  a  capillary  electrometer, 
K,  contains  mercury  ions,  even  in 
minute  quantity,  then,  provided  that  its 

osmotic  pressure  is  greater  than  10 
atmos.,  this  pressure  is  higher  than  the 
solution  pressure  of  the  mercury.  A 
sufficient  number  of  mercury  ions  pass 
into  solution  to  establish  this  condition 
by  oxidation  and  solution  of  the  small 
amount  of  the  mercury  which  has  fallen 
from  the  dropping  electrode  and  rests 

at  the  bottom  of  the  liquid   W.     This 

+  + 
determines  that  mercurous  ions,  Hg2,  must  separate  from  the 

liquid  W  and  deposit  on  the  falling  drop,  which  thereby 
becomes  positively  charged;  this  positive  electricity  is 
carried  to  the  layer  of  mercury  at  the  bottom,  and  the  solution 
becomes  negatively  charged.  By  this  process  the  liquid  near 
the  place  where  the  drops  are  formed  loses  mercurous  ions, 
and  consequently  mercury  salt,  whilst  that  at  the  bottom  of 
the  vessel  becomes  more  concentrated,  as  Palmaer  (7)  has 
directly  proved. 

This  process  should  theoretically  continue  until  the  con- 
centration of  the  mercury  ions  in  the  liquid  at  A  has 
decreased  to  a  certain  value  corresponding  with  the  solution 
pressure  of  the  mercury ;  this  condition  can  be  nearly  attained 
by  allowing  the  drops  to  form  quickly,  but  it  cannot  be 
perfectly  reached  on  account  of  diffusion  of  mercurous  ions 
from  the  lower  to  the  upper  part  of  the  vessel.  Suppose  this 
condition  has  been  established,  then  evidently  no  more  ions 
would  pass  from  the  solution  to  the  drop,  no  double  layer 
would  be  produced,  and  the  mercury  would  have  the  same 
potential  as  the  liquid. 

An  analogous  process  takes  place  when  any  other  metal 
of  low  solution  pressure — copper,  silver,  etc. — is  brought  into 


xiv.  THE   VOLTA   EFFECT.  235 

contact  with  an  aqueous  solution.  A  small  quantity  of 
oxide  is  formed;  this  dissolves,  and  ions  are  then  able  to 
deposit  on  the  metal,  which  thus  becomes  positively  charged, 
whilst  the  solution  receives  a  negative  charge.  The  opposite 
effect  is  produced  when  a  metal  of  high  solution  pressure  is 
immersed  in  a  solvent.  The  ions  then  pass  from  the  metal, 
leaving  this  negatively  charged  and  communicating  a  positive 
charge  to  the  liquid. 

The  Volta  Effect. — The  above  method  of  viewing  the 
process  explains  the  Volta  effect  for  combinations  of  metals 
and  liquids.  If  we  are  concerned  with  two  liquids,  the 
charges  are  due  to  the  dissimilar  mobilities  of  the  ions  (see 
p.  218).  However,  the  Volta  effect  is  also  produced  between 
metals  and  insulators,  as,  e.g.,  varnish.  In  this  case  the 
varnish  may  be  conceived  as  a  medium  (a  solvent)  in  which 
traces  of  metal  oxides  or  salts  dissolve.  When  air  is  the 
insulator,  it  is  simplest  to  imagine  that  the  metal  reacts 
with  the  oxygen  ions  (of  the  air),  and  is  thus  oxidised, 
whereby  the  metal  becomes  negatively  electrified  and  the 
air  positively. 

Now,  if  we  have,  as  in  Volta's  original  experiment,  two 
metals,  A  and  B,  in  the  air,  these  are  oxidised  to  different 
extents  according  to  their  "chemical  affinities"  for  oxygen. 
As  a  consequence  of  this  the  potential  difference  between 
the  metal  A  and  the  air  will  be  different  from  that  between 
the  metal  B  and  the  air.  In  other  words,  there  is  a  certain 
potential  difference  between  the  two  metals,  so  long  as 
they  are  not  in  metallic  contact,  and  the  potential  difference 
is  such  that  the  more  easily  oxidisable  metal  is  negatively 
electrified. 

If  the  two  metals  be  joined  by  a  wire,  the  difference  of 
potential  disappears  by  positive  electricity  passing  to  the 
more  easily  oxidisable  metal,  and  negative  electricity  passing 
to  the  more  "noble"  metal.  If  the  metals  be  in  the  form 
of  plates,  and  if  they  be  brought  close  together,  so  that 
the  distance  between  them  is  small,  a  condenser  is  produced, 
as  in  Volta's  experiment,  and  therefore  the  electricities 


236  POTENTIAL   DIFFERENCE.  CHAP. 

"  bind "  each  other,  so  that  fresh  and  comparatively  large 
quantities  of  electricity  collect  on  the  plates  in  order  to 
maintain  the  electrical  equilibrium. 

Now  let  the  connecting  wire  be  removed,  and  the  plates 
separated  from  each  other.  The  previously  "  bound  "  elec- 
tricities become  free,  and  the  more  easily  oxidisable  metal  is 
found  to  be  positively  electrified,  and  the  "nobler"  metal 
negatively.  This  explains  why  the  metals  can  be  arranged 
in  an  "  electromotive  series  "  (with  reference  to  one  and  the 
same  gas),  and  why  the  most  easily  oxidisable  metals  occur 
at  the  beginning  of  the  series,  and  the  least  oxidisable  at 
the  end. 

If  we  use  other  gases  which  act  on  the  metals  we  obtain 
a  different  series  (e.g.  with  chlorine,  hydrogen  sulphide,  etc.), 
as  J.  Brown  (8)  has  proved. 

The  actual  potential  difference  between  two  metals  is 
ascertained  by  conducting  a  known  quantity  of  electricity 
through  the  junction  and  determining  the  heat  developed 
(the  so-called  Peltier  effect).  Since  1  volt-coulomb  =  0'239 
cal.,  the  potential  difference  can  easily  be  calculated  in  volts  ; 
these  differences  of  potential  seldom  reach  so  much  as  a  few 
hundredths  of  a  volt. 

Pellat's  Method. — A  fourth  method  of  determining  when 
the  potential  difference  between  mercury  and  a  liquid  in 
contact  with  it  becomes  zero  was  devised  by  Pellat  (9),  who 
observed,  in  a  capillary  electrometer,  the  polarised  mercury 
surface,  which  could  be  increased  in  R  (Fig.  44)  by  suction. 
The  potential  difference  P  could  be  altered  as  desired. 

If  there  is  a  difference  of  potential  between  the  mercury 
and  the  solution,  and  the  surface  of  contact  be  suddenly 
increased,  a  current  flows  through  a  galvanometer,  G,  placed 
at  P,  to  the  newly  formed  parts  of  the  surface,  so  as  to  charge 
these  to  the  same  potential  as  the  original  parts.  If, 
however,  the  contact  surface  is  uncharged,  no  current  is 
produced.  This  occurs  when  P  is  equal  to  the  potential 
difference,  Hg  |  Hg2S04  in  H2S04.  Pellat,  by  altering  P  until 
this  point  was  reached,  obtained  the  value  P  =  —  0'97  volt. 


xiv.  EXPERIMENTAL    DETERMINATIONS.  237 

Results  of  Experimental  Determinations.  By  means 
of  these  various  methods  the  difference  of  potential  between 
mercury  and  electrolyte  can  be  determined.  The  starting- 
point  chosen  by  Ostwald  (10)  was— 

Hg  |  HgCl  in  w-HCl  =  -0'560  volt, 
or—  Hg  |  Hg2S04  in  rc-H2S04  =  -0-99  volt. 

If  one  potential  difference  is  known,  then  all  the  others 
can  be  measured  by  a  suitable  combination  of  galvanic 
elements.  Thus,  if  it  be  required  to  ascertain  the  tension 
between  zinc  and  normal  zinc  sulphate  solution,  we  should 
form  the  element — 

Hg  |  Hg2S04  in  HaS04(7i)  |  ZnS04(»  |  Zn. 

The  electromotive  force  of  this  element  has  been  found 
to  be  1*514  volts.  If  we  subtract  from  this  0-99  volt 
for  Hg  |  w-H2S04,  we  obtain  as  remainder  O524  volt  for 
Zn  |  ZnS04.  (For  a  correction,  see  p.  240.) 

The  potential  differences  given  below  between  metals 
and  normal  solutions  of  their  salts  have  been  determined  in 
this  way. 

From  the  values  so  obtained  the  electrolytic  solution 
pressure  P  for  metals  in  normal  solutions  of  their  salts 
can  be  calculated  by  means  of  the  formula — 

RT ,    P 

71"  =  — JCT  m  —  • 
n&        p 

The  values  for  ?r  and  P  contained  in  the  following  tables 
have  been  obtained  by  Ostwald :  — 

POTENTIAL  DIFFERENCE,  ?r,  BETWEEN  METALS  AND  THEIR  SALTS  IN 
NORMAL  SOLUTION. 


Volt*. 

Magnesium +1*22 

Zinc +0-51 

Aluminium +O22 

Cadmium +0-19 

Iron +0-06 

Nickel   .                            .  -0-02 


Volts. 

Lead -0-10 

Hydrogen -0-25 

Copper  , -0-60 

Mercury     ......  -0-99 

Silver  -1-01 


238  POTENTIAL   DIFFERENCE.  CHAP. 

SOLUTION  PRESSURE,  P,  OF  THE  METALS  ix  ATMOSPHERES. 


Lead   . 10~2 

Hydrogen 10~4 

Copper     .     ...     .     .     .  10-12 

Mercury 10~15 

Silver .  10~15 


The  elements  used  in  these  determinations  were  (the  sum 
of  Metal  |  Zn  and  Zn  |  ZnS04  is  taken  as  equal  to  0*518 
volt  :  see  p.  240)— 


Magnesium 
Zinc 

1018 

Aluminium 
Cadmium  .     . 
Iron  . 

....     1013 
103 

Nickel   . 

Zn 

ZnS04 

MgS04  |  Mg 

Volls. 

=  -0-725 

.'.  Mg 

I  MgS04  = 

Volts. 

1-243 

Zn 

ZnS04 

CdS04    j  Cd 

=      0-360 

.'.  Cd 

j  CdS04   = 

0-158 

Zn 

ZnS04 

FeS04 

Fe 

=      0-440 

.'.  Fe 

FeS04   = 

0-078 

Zn 

ZnS04 

PbAc2 

Pb 

=      0-607 

/.  Pb 

PbAc2   ^ 

-0-089 

Zn 

ZnS04 

CuS04 

Cu 

=    1-100 

.-.  Cu 

CuS04   = 

-0-582 

Zn 

ZnS04 

Ag2S04 

Ag 

=      1-539 

/.Ag 

Ag2S04  = 

-  1-024 

Zn 

ZnS04 

H2S04 

H2(Pd) 

=      0-760 

/.H2 

H2S04    = 

-0-240 

Heat  of  lonisation.  —  As  Ostwald  has  shown,  we  can 
calculate  W,  in  this  case  the  heat  of  ionisation,  from  the 
formula  already  given  — 


if  we  know  P,  the  potential  difference  between  metal  and 
solution.     The  value  of  -^  can   easily  be  determined   by 

arranging  in  opposition  to  each  other  two  surfaces,    Metal 
|  Salt  solution     kept  at  different  temperatures.      Thus  we 

find  for    Copper     Copper  acetate,    -T™  =  0  '000774  volt;  for 

Copper  |  Copper  sulphate,      0  '000  75  7  volt,  or  as  the  mean 
value  0*000766  volt  per  degree.     Therefore,  if  T  =  290°— 

23,070  x  0-000766  x  290  =  23070  x  0'60  -  W, 
from  which  — 


W  =  13,842  -  5124  =  8718  cal. 


XIV. 


HEAT   OF   IONISATION. 


239 


The  above  formula  is  valid  for  the  condition  that  q  = 
96,500  coulombs,  i.e.  for  an  equivalent,  so  that  the  heat  of 
ionisation  obtained  refers  to  a  gram-equivalent  of  copper 
(=  31/8  grams).  For  a  gram-ion  (63'6  grams),  the  heat  is, 
of  course,  twice  as  great;  i.e.  for  the  transformation  of  63'6 
grams  of  copper  from  the  metallic  to  the  ionic  condition, 
2  x  8718  (=  17,436)  cal.  are  required. 

As  a  rule,  heat  is  evolved  when  ions  are  formed ;  that  is 
to  say,  the  heat  of  ionisation  is  negative.  If  we  know  the 
heat  of  ionisation  of  one  metal,  that  of  any  other  metal  can 
be  calculated  from  the  thermochemical  data.  For  instance, 
when  copper  is  displaced  from  copper  sulphate  by  zinc, 
25,055  cal.  are  evolved  per  equivalent.  This  process  consists 
partly  in  the  transformation  of  an  equivalent  of  zinc  from 
the  metallic  to  the  ionic  condition,  and  partly  in  the  trans- 
formation of  an  equivalent  of  copper  from  the  ionic  to  the 
metallic  condition.  The  heat  evolution  for  the  latter  has 
been  shown  to  be  8718  cal.  For  the  former,  therefore,  there 
remain  16,337  cal.  Now,  since  the  heat  changes  which  occur 
when  one  metal  displaces  another  from  its  salts  are  known 
from  thermochemical  measurements,  it  is  easy  to  calculate 
in  the  above  manner  the  heats  of  ionisation,  as  has  been  done 
by  Ostwald  (10),  whose  values  for  equivalent  quantities 
are  contained  in  the  following  table.  The  heat  of  ionisation 
of  hydrogen  is  almost  zero ;  it  amounts  to  550  cal.  The  heat 
of  ionisation  of  a  metal  is,  therefore,  equal  to  the  negative 
heat  of  solution  of  the  metal  in  an  acid  less  550  cal. 


HEATS  OF  IOXISATIOX  IN  CALORIES  (SMALL). 


Potassium -61,000 

Sodium -  56,300 

Lithium -62,000 

Strontium -57,800 

Calcium -53,500 

Magnesium  .........  -  53,400 

Aluminium -39,200 

Manganese  .......  24,000 

Iron,  divalent  ....  - 10,000 

Iron,  2-3  valent   .     .     .  +12,100 


Cobalt -   7,300 

Nickel -   6,800 

Zinc -16,300 

Cadmium     .....     -   8,100 
Copper,  divalent  .     .     .     +  8,800 

Mercury +20,500 

Silver +26,200 

Thallium     ......   1,000 

Lead  .....    \    ,     +      500 

Tin     .......•-   1,000 


240  POTENTIAL   DIFFERENCE.  CHAP. 

Seat  of  the  Electromotive  Force  in  a  Daniell  Ele- 
ment. —  From  what  has  been  said  it  is  easy  to  form  a 
conception  of  the  mode  of  action  of  a  Daniell  element, 
Cu  |  CuS04  |  ZnS04  [  Zn.  In  this  there  occur  four  potential 
differences,  namely— 

Zn  |  Cu, 

Cu  |  CuS04, 
CuS04  I  ZnS04, 
ZnS04  Zn. 

Of  the  first  of  these  electromotive  forces  we  may  assume 
that  its  value  can  be  measured  by  the  Peltier  effect,  accord- 
ing to  Edlund  (11),  and  it  is  therefore  a  few  thousandths 
of  a  volt  (0-006  volt).  The  potential  difference  between  the 
liquids  is,  according  to  Planck  (see  p.  228),  of  the  same 
order  of  magnitude.  In  the  case  cited,  when  the  concentra- 
tions are  the  same,  it  is  almost  zero,  because  copper  and  zinc 
sulphates  have  nearly  the  same  transport  numbers.  When 
the  concentrations  are  different,  the  difference  of  potential 
may  rise  to  a  few  millivolts.  When  the  two  solutions  are 
of  about  the  same  concentration,  therefore,  the  electromotive 
forces  referred  to  cannot  contribute  much  to  the  total  electro- 
motive force,  which  reaches  the  value  of  1T14  volts.  There 
remain  the  other  two  potential  differences  between  metals 
and  solutions.  The  values  of  TT  in  the  table  on  p.  237  have 
been  corrected  for  these  two  small  electromotive  forces. 

If  the  solution  pressure  of  copper  is  PI,  the  osmotic 
pressure  of  the  copper  ions  in  the  copper  sulphate  solution 
pi,  and  if  the  corresponding  values  for  zinc  are  P2  and  p-2> 
the  total  electromotive  force  is  given  by  —  - 

1-99  X  10-V/i      Pi       ,      Pa\ 
E  =  -  —1  (  log—  -  -  log-- 

s     i          *     */ 


In  this  case  E  has  a  high  negative  value,  since  P&  the 


xiv.  DANIELL   ELEMENT.  241 

solution  pressure  of  zinc,  is  very  much  greater  than  PI,  that 
of  copper.  The  value  of  log  —  can,  as  a  rule,  be  neglected. 

It  shows,  however,  that  the  electromotive  force  of  the  element 
will  be  the  greater  according  as  the  value  of  p%  is  great  and 
that  of  pi  small.  In  spite  of  the  difficulties  attending  the 
experiments  on  account  of  the  smallness  of  the  potential 
differences,  this  has  been  directly  proved.  If  a  Daniell 
element  contains  solutions  of  zinc  sulphate  and  copper 
sulphate  of  such  concentrations  that  pi  and  p%  are  equal, 
whilst  in  another  case  the  solutions  are  of  such  concentration 
that  pi  =  1000^2,  the  difference  in  the  electromotive  forces 
is  only — 

1  -QQ   v/    1  H-4 

-  .  291  x  log  1000  =  0-087  volt. 
2 

It  can,  therefore,  be  seen  that  quite  large  differences  of 
concentration  exert  only  a  comparatively  small  influence. 
When  the  zinc  sulphate  in  a  Daniell  element  is  replaced  by 
sulphuric  acid,  the  potential  difference  must  evidently  become 
higher;  this  is  due  to  the  fact  that  in  this  case  p%  is 
exceedingly  small,  particularly  at  the  beginning. 

From  the  formula  given  we  may  conclude  that  the 
potential  difference  in  such  an  element  depends  mainly  (almost 
exclusively)  on  the  ratio  of  the  solution  pressures.  Some 
exceptions  will  be  later  considered  in  detail. 

This  rule,  gained  by  experience,  has  been  confirmed  by 
the  following  numbers  found  by  Streintz  (12).  Nevertheless, 
varying  numbers  have  been  obtained  for  the  same  metals,  the 
differences  amounting  in  some  cases  to  as  much  as  0'2  volt, 
and  further  investigation  on  this  subject  is  required  to  clear- 
up  the  cause  of  these  peculiarities. 

The  following  table  gives  the  magnitudes  of  the  electro- 
motive forces  of  some  elements  of  the  type  of  the  Daniell 
cell,  that  is,  with  unpolarisable  electrodes  of  the  first  order. 
The  salts  used  in  these  elements,  in  normal  solution,  are 
indicated  by  their  negative  ions.  The  numbers  in  brackets 

^  E 


POTENTIAL    DIFFERENCE. 


CHAP. 


are  those  obtained  48  hours  after  the  element  had  been  put 
together,  the  others  were  obtained  immediately  after  the 
element  had  been  constructed. 


ZnCu. 

MgCu. 

CdCu. 

ZnCd. 

S04 
NO,  .     .     . 

Cl      .     .     . 

100-0 
100-0(100-0) 
90-0 

i 

167-5 
159-1(179-7) 
180-4(177-8) 

67-6 
81-8(68-1) 
79-6(75-9} 

32-6 
17-5(32-0) 
20-2^25-0) 

Very  Small  Ionic  Concentrations. — Occasionally  the 
values  of  pt  and  p-2  are  extremely  small,  namely,  when  the 
salt  is  very  difficultly  soluble,  and  when  double  salts  are 
formed.  As  an  example  of  the  former  case,  we  may  take 
the  silver  halides.  Quite  different  values  are  obtained 
when  these  are  used  from  those  found  when  a  salt  solu- 
tion of  finite  concentration  is  employed.  Wright  and 
Thompson  found  the  following  values  for  the  electromotive 
forces  of  elements  constructed  on  the  plan  :  silver  |  silver 
salt  |  zinc  sulphate  |  zinc,  when  different  silver  salts  were 
used : — 


Volts. 

Sulphate 1-54 

Nitrate 1-53 

Acetate  1-49 


Volts. 

Chloride 1-10 

Bromide O91 

Iodide  0-71 


In  this  case  the  silver  corresponds  with  the  copper  in  a 
Daniell  element.  Consequently  the  electromotive  force  of 
the  element  is  the  greater  the  higher  the  concentration  of 
silver  ions  in  the  neighbourhood  of  the  silver.  For  the  three 
comparatively  easily  soluble  silver  salts,  sulphate,  nitrate, 
and  acetate,  the  electromotive  force  is  almost  the  same,  but 
for  the  difficultly  soluble  chloride,  bromide,  and  iodide  it  is 
decidedly  lower. 

In  other  experiments  the  solution  contained,  besides  the 
silver  halide,  other  chlorides,  bromides,  or  iodides,  w^hich 
depress  the  solubility  of  the  silver  salt.  As  a  consequence 
of  this,  it  was  found  that  the  electromotive  forces  were 
appreciably  smaller,  the  smallest  being  obtained  with  the 


xiv.       VERY   SMALL   IONIC   CONCENTRATIONS.        243 

iodide.     The  same  remarks  apply  to  the  chlorides,  bromides, 
and  iodides  of  lead  and  mercury. 

Double  salts  behave  in  quite  the  same  way.  In  the 
element  Cu  |  KCN  |  ZnS04  |  Zn  the  current  does  not  go 
in  the  usual  direction  from  zinc,  through  the  solution,  to 
copper,  but  in  the  opposite  direction.  The  reason  for  this 
is  that  the  osmotic  pressure  of  copper  ions  in  potassium 
cyanide  solution  is  exceedingly  small.  When  copper  dis- 
solves in  this  solution,  the  double  salt  K2(CN)4Cu  is  formed 

with  the  ions  2K  and  Cu(CN)4,  and  only  a  trifling  quantity 

+  + 
of  Cu(CN)2  is  produced,  which  dissociates  into  Cu  and  2(CN). 

The  osmotic  pressure  p\  of  the  copper  ions  thus  becomes 
so  small  that  the  expression  log  ±2.  counterbalances  the 

P2 

expression  log  —  • 
ft. 

Measurements  of  the  electromotive  force  may  be  used  to 
determine  the  solubility  of  difficultly  soluble  salts  or  the 
degree  of  dissociation  of  double  salts.  The  alkalis,  their* 
sulphides,  thiocyanates,  ferrocyanides,  and  similar  salts, 
behave,  in  aqueous  solution,  like  potassium  cyanide.  If 
the  electromotive  force  of  the  element,  silver  |  potassium 
cyanide  |  potassium  nitrate  |  silver  nitrate  |  silver,  is  1*14 
volts  at  17°  (T  =  290°),  it  follows  that— 

1-14  =  0-0002 


Now,  if  the  silver  nitrate  solution  is  0'1-normal,  log 
pi  =  —  1,  therefore^  =  10  "207,  i.e.  108  grams  of  silver  are 
contained  in  10207  litres  of  potassium  argentocyanide  in  the 
form  of  silver  ions. 

Since,  in  a  Daniell  element,  the  solution  pressure  of  the 
zinc  is  very  much  greater  than  that  of  the  copper,  the  zinc 
replaces  the  copper  dissolved  as  ions,  and  we  may  rightly 
regard  the  Daniell  element  as  a  machine  which  is  driven 
by  osmotic  pressure  (really,  solution  pressure). 


CHAPTER  XV. 

Oxidation  and  Reduction  Elements. 
Secondary  Elements. 

Becquerel's  Experiments  —  Becquerel  (1)  has  shown  that 
when  two  platinum  or  gold  electrodes  are  surrounded,  one 
with  an  oxidising  and  the  other  with  a  reducing  agent,  a 
current  passes  in  the  liquid  from  the  reducing  to  the 
•oxidising  agent.  Ostwald  and  his  pupils  have  made  a 
study  of  these  so-called  oxidation  and  reduction  elements. 
Bancroft  (2)  found  an  electromotive  force  for  the  ele- 
ment — 


Pt  in  SnCl2  |  NaCl  |     aCl  +  Br2  at  Pt 

of  1171  volts. 

In  place  of  stannous  chloride,  any  reducing  agent,  such 
as  sulphurous  acid  or  ferrous  sulphate,  may  be  used;  and 
instead  of  bromine,  any  oxidising  agent,  like  gold  or  mercuric 
chloride,  potassium  permanganate,  etc.  ;  in  this  way  quite 
considerable  electromotive  forces  can  be  obtained.  Bancroft 
arranged  the  oxidising  and  reducing  agents  examined  in 
this  way  in  a  series  which  describes  well  their  chemical 
position. 

In  these  elements  we  have  evidently  a  direct  trans- 
formation of  chemical  into  electrical  energy.  Ostwald 
terms  this  "  chemical  action  at  a  distance."  The  oxidation 
and  reducing  agents  which,  when  mixed,  react  chemically 
on  each  other,  are  here  separated,  and  can  only  react  when 
an  electric  current  passes  through  the  liquid  and  brings 


CHAP.  xv.         BECQUEREL'S   EXPERIMENTS.  245 

hydrogen  ions  to  the  oxidising  agent,  and  negative  ions  to 
the  reducing  agent. 

In  a  similar  way,  the  chemical  energy  which  is  obtained 
when  solutions  of  sodium  chloride  and  silver  nitrate  are 
brought  into  contact  (silver  chloride  being  precipitated,  and 
sodium  nitrate  remaining  in  solution)  may  be  transformed. 
This  can  be  done  in  the  element  — 


Ag  |  NaCl  |  NaN03  |  AglST03  |  Ag. 

This  may  be  viewed  as  a  concentration  element.  The 
osmotic  pressure  of  the  silver  ions  in  the  sodium  chloride 
solution  is  very  small,  therefore  silver  ions  pass  into  solu- 
tion there,  and  silver  is  separated  from  the  silver  nitrate 
solution.  A  layer  of  silver  chloride  is  formed  evidently  at 
the  expense  of  the  silver  nitrate  and  sodium  chloride  solu- 
tions, with  simultaneous  production  of  sodium  nitrate,  as 
shown  by  the  scheme  — 

(1)  AgAg  |  CINa  |  K03Ka  |  N03Ag  |  Ag, 

(2)  Ag  |  AgCl  |  NaN03  +  NaN03  |  AgAg. 

It  is  a  characteristic  of  all  galvanic  elements  that  at  the 
poles  two  (or  more)  substances  are  present  which,  when 
brought  into  contact,  react  with  one  another  chemically, 
but  which  are  so  separated  in  the  element  by  one  (or  more) 
electrolyte  from  each  other  that  no  chemical  action  takes 
place  between  them  except  that  due  to  unavoidable  diffusion. 
By  means  of  the  current,  ions  are  transported  from  the 
separating  electrolytes,  and  so  the  chemical  action  becomes 
possible.  In  a  Daniell  element,  for  instance,  the  reacting 
substances  are  zinc  and  copper  sulphate,  which  are  at 
the  poles,  but  are  separated  from  each  other  by  sulphuric 
acid,  zinc  sulphate,  or  some  other  sulphate—  magnesium 
sulphate  in  Meidinger's  modification  (3)  of  the  element.  By 
putting  the  poles  in  metallic  connection,  a  current  is  spon- 
taneously produced,  which  transports  the  ions  according  to 
the  scheme  — 


Cu  |  CuSO^xSO*  |  ZnZn, 


246     OXIDATION  AND  REDUCTION  ELEMENTS.     CHAP. 

so  that  we  obtain — 

CuCu  |  S04X  |  S04Zn  |  Zn, 

where  X  is  divalent,  hydrogen  (H2)  or  zinc  in  the  Daniell 
element,  magnesium  in  Meidinger's  element.  On  account 
of  the  passage  of  the  current,  the  chemical  reaction— 

CuS04  +  Zn  =  Cu  +  ZnS04 

between  zinc  and  copper  sulphate  takes  place  in  the  element 
through  the  medium  of  the  ions,  although  the  two  reacting 
substances  are  spatially  separated  from  each  other.  On 
account  of  the  charges  on  the  ions,  electricity  is  transported 
during  the  reaction,  and  so  the  ion  may  be  regarded  as 
a  sort  of  machine  for  transforming  chemical  into  electrical 
energy. 

We  can  imagine  Bancroft's  measurements  carried  out  as 
follows.  Several  platinum  wires,  each  surrounded  by  its 
oxidising  or  reducing  agent  (A,  B,  C,  D,  etc.),  are  immersed 
in  a  conducting  liquid.  The  potential  difference  between 
A  and  D  will  then  be  equal  to  the  sum  of  the  differences 
between  A  and  B,  B  and  C,  and  C  and  D.  All  the 
substances  examined  may  be  arranged  in  a  series,  starting 
with  the  strongest  reducing  agent,  stannous  chloride  in 
potassium  hydroxide  solution,  and  ending  with  the  most 
energetic  oxidising  agent,  potassium  permanganate  in  sul- 
phuric acid.  The  numbers  in  this  series  (see  the  following 
table)  give  the  potential  differences  between  the  compound 
indicated  and  the  last  in  the  series,  potassium  permanganate 
in  sulphuric  acid.  It  may  be  noticed  that  quite  considerable 
potential  differences  exist  between  stannous  chloride  in 
potassium  hydroxide  and  stannous  chloride  in  hydrochloric 
acid,  between  chlorine  in  potassium  hydroxide  and  chlorine 
in  potassium  chloride,  etc.  In  the  first  case,  stannic  chloride 
is  formed,  which  decomposes  into  4HC1  and  Sn(OH)4,  and 
the  hydrochloric  acid  is  neutralised  by  the  potassium 
hydroxide  present.  Consequently,  in  presence  of  potassium 
hydroxide  more  chemical  energy  is  capable  of  being 


XV. 


NEUTRALISATION    ELEMENT. 


247 


transformed  into  electrical  energy  than  in  presence  of 
hydrochloric  acid.  According  to  this  view, 

SnCl2  in  KOH  |  SnCl2  in  HC1 

is  a  kind  of  concentration  element  with  respect  to  hydrogen 
ions,  which  are  present  to  a  large  extent  in  the  hydrochloric 
acid  solution,  but  only  occur  in  small  quantity  in  the  alkali 
solution. 

Chlorine  in  potassium  hydroxide  behaves  in  the  same 
way  towards  chlorine  in  potassium  chloride.  In  the  former 
solution  it  is  reduced  by  the  hydrogen  ions  to  hydrochloric 
acid. 


SnCl2inKOH     .     .     .     . 

NaSH  ....... 

Hydroxylamine  in  KOH  . 
Chromous  acetate  in  KOH 
Pyrogallic  acid  in  KOH  . 
Hydroquinone  in  KOH  . 
Zinc  hydro-sulphite  .  .  . 
Potassium  ferro-oxalate  . 
Chromous  acetate  .  .  . 
Potassium  ferrocyanide  . 
Iodine  in  KOH  .... 

SnCl2inHCl 

Potassium  arsenite  .     . 


Volts. 

2-06 
1-86 
1-83 
1-79 
1-68 
1-53 
1-49 
1-48 
1-40 
1-29 
1-28 
1-27 
1-26 
1-25 
1-20 
1-19 
1-18* 
1-17 
1-13 
1-12 

NaHS03    
H2S03  

Volts. 

1-10 
1-04 
0-97 
0-91 
0-88 
0-78 
0-70 
0-63 
0-58 
0-52 
0-51 
0-50 
0-45 
0-37 
0-35 
0-34 
0-27 
0-14 

o-io 
o-oo 

Ferrous  sulphate  in  H2S04    ' 
Potassium  ferrioxalate      .     . 

Potassium  ferricyanide     .     . 
Potassium  bichromate      .     . 
Potassium  nitrite  in  H2S04  . 
Chlorine  in  KOH     .... 

Nitric  acid 

KC104inH2S04     .     .     .      . 
Br2  in  KOH  

H2Cr207    

KC108  in  H2S04      .     .     .     . 
Br2  in  KBr 

.  KI03  in  H2S04                 .    . 

Mn02  in  HC1 

C12  in  KC1 

KMn04inH,S04    .     .     .     . 

Cu2Cl2 

Na2S203 

Na2S03 

Na2HP03 

FeS04 

Hydroxylamine  in  HC1 


Neutralisation  Element. — In  the  following  element 
electrical  energy  is  produced  on  account  of  the  neutralisation 
process  which  takes  place  : — 

PdH  |  OHK  |  N03K  |  X03H  |  HPd. 
It  gives— 

Pd  |  H20  |  KN03  |  KN03  |  HHPd, 
and  therefore  the  process  consists  of  the  transformation  of 


248     OXIDATION  AND  REDUCTION  ELEMENTS.     CHAP. 

KOH  +  HN03  into  KN03  +  H20.  On  the  basis  of  older 
experiments  with  platinum  instead  of  palladium,  Ostwald 
(4)  assumes  that  the  electromotive  force  is  about  0*74  volt. 
This  electromotive  force  (E)  is  governed  by  the  formula  — 

^=0-0002  ^log—  =  0-0002  Tlog  ~ 

1\  ^i 

where  pa  and  Ca  are  the  osmotic  pressure  and  the  concen- 
tration of  hydrogen  ions  in  the  acid,  p^  and  Cb  the  corresponding 
values  for  the  hydrogen  ions  in  the  solution  of  potassium 
hydroxide.  Since  Ca  is  known,  the  value  of  Cb  can  be  calcu- 
lated. If  the  concentration  of  the  hydroxyl  (OH)  ions  in  the 
alkali,  which  is  known,  be  denoted  by  CV  the  equation  of 
equilibrium  (see  p.  87)  is  — 


where  CS^Q  is  the  concentration  of  the  water  in  the  solution, 
and  it  may  be  regarded  as  constant  (55'5  gram-molecules  per 
litre).  From  this,  K,  the  dissociation  constant  of  water,  may 
be  calculated. 

For  water,  in  which  the  number  of  hydrogen  ions  is  equal 
to  the  number  of  hydroxyl  ions  (Co),  we  have  the  equation, 


However,  in  the  element  cited,  electromotive  forces  appear 
at  the  surfaces  of  separation  of  KOH  and  KN03,  and  at  that 
between  KN03  and  HN03,  and,  according  to  Planck's 
formula,  the  combined  value  for  these  is  0'065  volt,  which 
must  be  subtracted  from  the  total  electromotive  force  in 
order  to  give  that  due  to  the  neutralisation.  From  the  data 
obtained  in  this  way  we  arrive  at  the  result  that  the  number 
of  gram-ions  of  hydrogen  in  a  litre  of  water  is  0'8  x  10'7,  a 
value  which  agrees  excellently  with  that  found  by  Kohlrausch, 
0-8  x  10  ~7  at  18°  (see  p.  194). 

Irreversible  Elements.  —  If  we  construct  an  element 
according  to  the  scheme  Zn  |  H2S04  |  Pt,  we  find  that  it  gives 
rise  to  a  current  which,  however,  soon  ceases  because  H2  is 


xv.  IRREVERSIBLE   ELEMENTS.  249 

deposited  at  the  platinum  electrode,  and  we  then  really  have 
the  element — 

Zn  |  ZnS04  |  H2S04  |  H2  on  Pt. 

The  current  is  weakened  because  the  hydrogen  bubbles 
dimmish  the  conductivity,  but  this  we  may  neglect.  It  is 
further  weakened  on  account  of  the  deposited  hydrogen, 
which  possesses  a  higher  solution  pressure  than  the  platinum. 
This  solution  pressure  is,  moreover,  proportional  to  the 
pressure  of  the  evolved  hydrogen ;  it  may  easily  be  imagined 
that  if  this  pressure  is  sufficiently  great,  the  solution 
pressure  of  the  zinc  would  not  exceed  that  of  the  hydrogen, 
and  the  current  would  stop.  This  would  take  place  only 
at  an  enormously  high  pressure,  and  it  cannot  be  realised. 
The  quantity  of  hydrogen  in  the  neighbourhood  of  the 
electrode  can  be  diminished  by  addition  of  an  oxidising 
agent,  such  as  chromic  acid  (Poggendorff's  element,  E  =  2'0 
volts),  nitric  acid  (Grove's,  Bunsen's  element,  E  =  1*9  volts), 
manganese  dioxide  (Leclanche's  element,  E  =  1*48  volts),  etc. 
The  greater  the  intensity  with  which  the  oxidising  agent 

reduces  the  pressure  of  the  hydrogen  at  the  platinum,  the 

p 
greater  does  log  —  become,  where  P  is  the  solution  pressure 

of  the  zinc,  and  p  that  of  the  hydrogen  gas,  and  the  higher  is 
the  electromotive  force  of  the  element.  These  elements  may, 
therefore,  be  regarded  as  a  kind  of  oxidation  elements.  If 
the  current  strength  becomes  too  great  it  may  happen  that 
the  oxidising  agent  does  not  diffuse  sufficiently  quickly  to  the 
platinum  in  Grove's  element,  or  to  the  carbon  in  Bunsen's 
element,  to  allow  of  complete  depolarisation.  This  is  par- 
ticularly the  case  when  manganese  dioxide  is  used  as 
depolariser,  for  in  this  case  the  separated  hydrogen  must 
diffuse  to  the  oxide  in  order  to  be  oxidised.  Consequently, 
too  much  current  must  not  be  drawn  from  these  elements 
if  it  be  required  that  the  electromotive  force  is  not  to  sink 
too  greatly.  A  small  diminution  of  the  electromotive  force 
always  takes  place,  because  the  oxidising  agent  gradually 


250     OXIDATION  AND  REDUCTION  ELEMENTS.     CHAP. 

becomes  used  up.  Nevertheless,  these  elements  are  largely 
used  in  practice,  for  with  them  a  fair  yield  of  current  can  be 
obtained  at  an  almost  constant  electromotive  force  com- 
paratively cheaply.  Before  the  introduction  of  accumulators 
the  commonest  element  in  use  was  the  Bunsen  :  Zn  |  HaS04 
|  HN03  |  C.  The  great  disadvantage  possessed  by  this  ele- 
ment is  that  it  gives  off  unpleasant  nitrous  fumes. 

Leclanche's  element  differs  from  these  others,  inasmuch  as 
the  electrolyte  is  not  sulphuric  acid,  but  a  concentrated  solution 
of  ammonium  chloride.  In  common  with  acids,  this  substance 
possesses  the  power  of  dissolving  metal  oxides  (ZnO)  which 
are  formed  during  the  passage  of  the  current ;  water  and 
ammonia  are  formed,  and  this  latter  combines  partially  with 
the  metal  chloride  simultaneously  produced.  Ammonium 
chloride  is  also  used  in  other  elements,  such  as  Pollak's 
regenerative  element,  which  consists  of  porous  (air-absorbing) 
carbon  coated  on  the  under  side  with  galvanically  deposited 
copper,  ammonium  chloride  solution,  and  zinc.  The  copper 
is  first  oxidised  by  the  absorbed  oxygen,  and  then  dis- 
solved by  the  ammonium  chloride  with  formation  of  cupric 
chloride.  Zinc  then  dissolves  with  production  of  zinc  chloride, 
and  an  equivalent  quantity  of  copper  is  deposited  at  the 
positive  pole  (the  carbon),  thus  giving  rise  to  the  current. 
When  the  element  is  at  rest  the  copper  is  again  oxidised. 

Alkalis  can  also  dissolve  certain  metallic  oxides,  and 
therefore  may  replace  acids  in  a  Volta  pile.  This  is  made 
use  of  in  the  element  of  Lalande  and  Chaperon  (copper 
element)  (5),  which  consists  of  a  metal  (iron  or  copper) 
coated  with  copper  oxide,  40  per  cent,  potassium  hydroxide 
solution,  and  zinc.  In  order  to  prevent  absorption  of  carbon 
dioxide  by  the  alkali  this  must  be  covered  tightly,  or  protected 
from  the  access  of  air  by  a  film  of  petroleum.  The  chemical 
process  which  takes  place  is  that  zinc  is  oxidised  by  the 
copper  oxide,  and  the  zinc  oxide  dissolves  in  the  alkali,  with 
formation  of  potassium  zincate.  Copper  is  deposited  at  the 
negative  pole,  and  by  roasting  this  in  the  air  it  can  again  be 
oxidised. 


xv.  NORMAL    ELEMENTS.  251 

As  already  mentioned,  these  irreversible  elements  never 
possess  an  absolutely  constant  electromotive  force ;  for  the 
measurement  of  electromotive  forces  we  must,  therefore,  use 
reversible,  so-called  normal,  elements. 

Normal  Elements. — The  first  element  which  was 
designed  to  fulfil  this  purpose  was  the  Daniell  cell.  It  was, 
however,  soon  found  that  the  electromotive  force  varied  with 
the  concentration  of  the  solutions,  and  so  standard  solutions 
were  adopted.  The  normal  Daniell  element  consists  of 
pure  copper,  copper  sulphate  solution  of  sp.  gr.  T195  at  18°, 
solution  of  pure  sulphuric  acid  of  sp.  gr.  T075  at  18°,  and 
amalgamated  pure  zinc.  Kesults  obtained  with  this  element 
give— 

1  normal  Daniell  =  1176  [1  -f  0'0002(£  -  18)]  volts. 

One  disadvantage  of  this  element  is  that  the  copper 
sulphate  gradually  diffuses  to  the  zinc  where  copper  is 
deposited,  and  so  the  element  is  spoiled.  It  must,  therefore, 
be  freshly  set  together  immediately  before  use. 

The  only  negative  metal  (according  to  Volta's  designation) 
which  by  deposition  on  amalgamated  zinc  (the  positive  metal) 
does  not  change  the  electromotive  force  of  this  is  mercury  ; 
it  unites  with  the  amalgam  at  the  surface  of  the  zinc,  and  by 
dissolving  a  corresponding  quantity  of  fresh  zinc  leaves  the 
positive  metal  unaltered. 

For  this  reason  all  the  other  normal  elements  contain 
mercury  as  negative  metal.  In  order  to  diminish  the 
diffusion  as  much  as  possible,  the  mercury  is  covered  with 
an  excess  of  a  difficultly  soluble  mercurous  salt,  so  that  the 
mercury  forms  an  unpolarisable  electrode  of  the  second 
order.  An  example  of  this  kind  of  normal  element  is  the 
Helmholtz  calomel  element  (6),  in  which  the  positive 
mercury  pole  is  covered  with  a  paste  of  mercurous  chloride 
and  10  per  cent,  zinc  chloride  solution.  The  electromotive 
force  of  this  element  is — 

1  normal  Helmholtz  =  1'074  [1  +  0'0001(£  -  20)]  volts. 


252     OXIDATION  AND  REDUCTION  ELEMENTS.      CHAP. 

This  element  suffers  from  the  disadvantage  that  the  con- 
centration of  the  zinc  chloride  may  change  by  evaporation, 
and  from  the  fact  that  when  current  is  drawn  from  it  the 
concentration  of  the  salt  may  alter  on  account  of  zinc 
dissolving. 

To  avoid  these  disturbing  factors,  a  zinc  salt  easy  to 
prepare  pure  and  in  the  crystalline  form  is  used  for  making 
up  the  solution,  and  a  layer  of  this  salt  is  placed  over  the 
zinc. 

The  most  suitable  salt  which  has  so  far  been  used  is  the 
sulphate,  which  is  employed  in  the  normal  Clark  cell  (7), 
already  referred  to  (p.  124).  The  electromotive  force  of 
this  is — 

1  normal  Clark  =  1433[1  -  0'0084(J  -  15)]  volts. 

In  the  Weston  element  (8)  the  zinc  is  replaced  by 
the  closely  related  metal,  cadmium.  This  cell  consists  of 
mercury,  mercuric  sulphate  paste,  saturated  cadmium  sul- 
phate solution,  and  cadmium  amalgam  covered  with  cadmium 
sulphate  crystals.  The  cadmium  amalgam  is  made  up  of  six 
parts  of  mercury  and  one  part  of  cadmium.  The  electro- 
motive force  of  the  element  is — 

1  normal  Weston  =  r019[l  +  0'00004(£  -  20)]  volts. 

This  element  has  the  great  advantage  of  possessing  a  very 
small  temperature  coefficient,  so  that  it  is  unnecessary  to 
exactly  determine  the  temperature  when  it  is  used  (it  is 
sufficient  to  state  that  the  experiment  was  carried  out  at  the 
ordinary  room  temperature).  For  the  composition  of  the 
cell,  see  p.  124. 

The  elements  mentioned,  containing  difficultly  soluble 
mercury  salts,  cannot  withstand  veiy  appreciable  current 
strengths,  for  such  cause  the  deposition  of  the  small  quantity 
of  mercury  ion,  and  it  requires  a  considerable  time  before 
a  sufficient  amount  of  salt  dissolves  to  re-establish  the  neces- 
sary mercury  ion  concentration.  Of  the  normal  elements  the 
calomel  cell  can  stand  the  greatest  current  strength,  and  this 


xv.  SECONDARY   ELEMENTS.  253 

is  due  to  the  fact  that  mercurous  chloride  is  appreciably  more 
soluble  at  the  ordinary  temperature  than  mercurous  sulphate. 

Secondary  Elements. — Secondary  elements  produced  by 
the  polarisation  of  two  electrodes  may  be  regarded  as  a 
special  type  of  oxidation  and  reduction  elements.  If  we 
connect  two  plates  of  platinum  (or  other  metal  not  attacked), 
which  are  immersed  in  an  electrolytic  solution,  with  the  poles 
of  a  galvanic  battery,  a  separation  takes  place  at  each  plate. 
If  the  electrolyte  is  a  base,  an  oxygen  acid,  or  the  alkali  salt 
of  an  oxygen  acid,  hydrogen  is  separated  at  the  cathode  and 
oxygen  at  the  anode.  If,  after  disconnecting  the  battery,  the 
two  plates  be  joined  by  a  wire,  we  obtain  a  current  in  the 
opposite  direction  to  that  of  the  polarising  current  (see  p.  1). 
We  may  therefore  regard  the  two  pole  plates  as  electrodes 
of  different  metals,  and  the  whole  as  a  galvanic  element. 
Such  gas  elements  were  suggested  by  Eitter  at  the  beginning 
of  the  nineteenth  century,  and  have  been  much  studied  since 
then. 

Polarisation  Current. — The  strength  of  the  polarising 
current  falls  quickly  when  a  small  electromotive  force  (under 
1  volt)  is  used  for  the  polarisation.  It  never,  however,  com- 
pletely disappears,  because  the  polarised  plates  become 
gradually  depolarised  by  diffusion,  so  that  new  quantities  of 
gas  must  be  separated  in  order  to  maintain  the  polarisation 
near  the  polarising  electromotive  force.  By  breaking  the 
circuit  and  examining  the  electromotive  force  of  polarisation 
at  different  times,  it  has  been  found  that  the  speed  with 
which  the  polarisation  spontaneously  disappears  by  diffusion 
of  the  separated  gases,  partly  in  the  liquid  and  partly  in  the 
electrodes  (particularly  if  these  be  platinum  or  palladium),  is 
not  only  dependent  on  the  nature  of  the  electrodes,  but  also 
on  that  of  the  liquid.  The  smallest  current  strength  required 
to  replace  the  gas  which  is  lost  by  diffusion  is  called  the 
polarisation  current. 

Smale's  Experiments. — When  higher  electromotive 
forces  (T062  volts)  are  used,  Smale  (9)  found  some 
.comparatively  simple  relationships.  He  electrolysed  sulphuric 


254     OXIDATION  AND  REDUCTION  ELEMENTS.     CHAP. 

acid  between  palladium  electrodes,  which,  as  is  well  known, 
have  the  power  of  absorbing  the  separated  gases,  particularly 
hydrogen,  and  noticed  a  slight  evolution  of  gas.  The  gas 
element  thus  produced  was  found  to  be  reversible,  for  by 
discharging  it  fairly  quickly,  it  showed  the  same  electro- 
motive force  as  the  polarising  element  had  to  overcome 
during  charging. 

Since  the  combustion  of  a  gram-equivalent  of  hydrogen  is 
accompanied  by  the  evolution  of  the  quantity  of  heat  (  W) 
34,200  cal.,  Thomson's  rule  requires  for  this  element  an 
electromotive  force  of  §f§${{  =  1*480  volts,  which  is  higher 
by  0*418  than  that  found  by  Smale.  The  change  of  electro- 
motive force  of  this  element  with  temperature  was  found  to 
be  at  20°— 

—  =  -0-00142  volt  per  degree, 
dT 

from  which,  by  the  Helmholtz  relationship  (see  p.  208),  we 
find— 


23,Q70P~-  W      p  __ 


W 


23,070  23,070          dT 

=  293(-  0*001  42)  =  -0-416  volt; 

whilst  by  experiment  the  difference  was  — 

=  1-062  -1-480  =  -0-418  volt, 


which  shows  a  very  good  agreement  with  the  value  calcu- 
lated. From  this  it  can  be  gathered  that  the  element  is 
reversible. 

Bose  (10),  too,  found  that  the  hydrogen-oxygen  cell 
works  reversibly,  although  he  found  a  somewhat  higher 
electromotive  force  (about  111  volts)  than  Smale  did. 

Helmholtz's  Investigation  on  the  Influence  of 
Pressure.  —  When  platinum  electrodes  are  used  it  is  found 
that  higher  electromotive  forces  are  required  to  produce  an 


xv.  INFLUENCE   OF    PRESSURE.  255 

evident  evolution  of  gas.  Since  the  gas  must  have  a  pressure 
at  least  equal  to  the  external  pressure  in  order  to  be  able  to 
leave  the  electrode  in  the  form  of  bubbles,  it  is  clear  that  the 
electromotive  force,  as  in  Meyer's  concentration  element, 
will  be  the  greater  the  higher  the  external  pressure  is. 
Helmholtz  (11)  investigated  the  relationship  by  varying 
the  pressure  from  P0  =  10  mm.  of  water  to  PI  =  742  mm.  of 

mercury.     The  ratio  of  these  pressures  is  1  :  1000,  therefore 

-p 
log  -1  =  3.     The  concentration  of  the  gas  in  the  liquid  must 

•M) 

be  in  the  same  ratio,  according  to  Henry's  law,  and  the 
difference  in  the  electromotive  force  for  the  hydrogen 
electrode  will  be  (see  the  formula  on  p.  211)  — 

9T7 

dE  =     .  In  1000  =  0-0879. 


A  molecule  of  hydrogen  (H2)  contains  two  equivalents  (H), 
therefore  in  the  formula  n  =  2. 

For  the  oxygen  the  corresponding  difference  dE\  is  only 
half  as  great  (for  n  =  4),  and  we  therefore  obtain  — 

dE  +  dEl  =  0-0879  +  0'0440  =  0'1319  volt, 

whilst  Helmholtz  actually  found  that  the  electromotive  force 
of  polarisation  rose  from  1/635  volt  to  1/805  volt  ;  dE  +  dE\ 
was,  therefore,  0'17  volt,  which  is  in  tolerable  agreement 
with  the  requirement  of  the  theory. 

If  the  electromotive  force  of  polarisation  is  known  for  a 
certain  pressure,  we  may  evidently  calculate  how  great  the 
partial  pressure  of  the  hydrogen  and  of  the  oxygen  must 
be  in  order  that  the  polarisation  may  become  zero.  Now, 
since  the  concentration  of  hydrogen  and  oxygen  in  water  is 
regulated  by  Henry's  law  at  a  given  external  pressure,  and 
the  absorption  coefficients  of  the  two  gases  are  known,  we 
may  easily  calculate  what  quantities  of  the  gases  are  con- 
tained in  unit  volume  of  the  liquid  when  the  electromotive 
force  is  zero,  assuming  that  the  hydrogen  and  oxygen 
are  present  in  equivalent  quantities.  If  we  are  below  this 
limit,  the  back  electromotive  force  is  negative,  i.e.  by  the 


256     OXIDATION  AND  REDUCTION  ELEMENTS.     CHAP. 

decomposition  of  the  water  work  is  done.  In  other  words, 
the  water  spontaneously  decomposes  until  this  concentration 
is  reached;  the  liquid  therefore  contains  0*7  X  10"27  gram- 
molecules  of  hydrogen,  and  half  as  much  oxygen  per  litre 
at  20°.  In  this  calculation  Smale's  result,  .#  =  1-062,  and 
Bunsen's  absorption  coefficients  of  the  two  gases  in  water  have 
been  used. 

If  the  concentration  of  the  oxygen,  by  being  in  equilibrium 
with  the  oxygen  of  the  air,  is  kept  constant  (2'5  x  10~4 
gram-molecules  per  litre  at  20°,  according  to  Bunsen),  the 
quantity  of  hydrogen  is  also  determined  (OT  x  10  ~50  gram- 
molecule  per  litre),  for  the  product  of  the  concentrations 
must,  at  any  given  temperature,  be  constant  (see  p.  85). 

Strength  of  the  Polarisation  Current. — Suppose  we 
work  with  an  electromotive  force,  E,  which  is  not  sufficient  to 
produce  an  evident  separation  of  gas.  Further,  suppose  that 
the  quantity  of  dissolved  oxygen  in  the  water  near  the  anode 
is  kept  constant  by  being  in  equilibrium  with  the  oxygen  of 
the  air.  The  electromotive  force  E  then  increases  propor- 
tionally to  the  logarithm  of  the  concentration  of  the  hydrogen 
(/)  near  the  cathode,  so  that — 

E=  A  +  T  x  10-4log/, 

where  A  is  a  constant. 

A  polarisation  current  is  produced  by  the  diffusion  of  the 
dissolved  hydrogen  from  the  cathode  into  the  water,  which, 
according  to  our  assumption,  contains  less  hydrogen.  The 
quantity  of  hydrogen  which  diffuses  in  a  second  must,  ceteris 
paribus,  be  proportional  to  the  excess  pressure  of  the  hydrogen 
at  the  cathode  over  that  in  the  liquid  (see  p.  153).  This 
latter  is  so  small  that  it  may  be  entirely  neglected.  The 
quantity  of  hydrogen  which  diffuses  is  replaced  by  that 
separated  by  the  polarisation  current  in  one  second,  and  this 
is  proportional  to  the  current  strength  i  of  the  polarisation 
current.  We  therefore  obtain — 

i  =  const./,  and  E  =  AI  +  T  x  10~4  log  i, 
where  AI  is  a  new  constant. 


xv.  LE    BLANC'S    INVESTIGATIONS.  257 

According  to  theory,  therefore,  the  strength  of  the  polari- 
sation current  must  increase  proportionally  with  an  ex- 
ponential function  of  the  electromotive  force — 

i  =  const.  ecE 
where  c  denotes  a  constant. 

In  reality  the  intensity  of  the  polarisation  current  in- 
creases enormously  quickly  with  the  polarising  electromotive 
force  until  visible  gas  evolution  occurs,  when,  of  course,  / 
cannot  further  rise.  It  has,  nevertheless,  been  found  that 
even  after  this  point  has  been  reached,  E  increases  with  the 
strength  i  of  the  polarising  current.  This  phenomenon  may 
be  due  to  a  sort  of  supersaturation  of  hydrogen  taking  place 
in  the  water.  (The  same  applies,  of  course,  to  the  oxygen.) 
Jahn  (12)  assumes  that  this  supersaturation  is  proportional 
to  the  current  density,  and  obtains  for  visible  electrolysis 
a  formula  analogous  to  the  above  one,  only  with  different 
constants  (c  is  greater  than  in  the  former  case).  As  a  matter 
of  fact,  it  is  observed  that  immediately  after  the  beginning  of 
the  gas  evolution  there  is  a  much  greater  increase  of  the 
current  density  for  the  same  increase  of  the  polarising 
electromotive  force  (E)  than  before. 

Le  Blanc's  Investigations. — By  means  of  a  galva- 
nometer or  capillary  electrometer  the  value  of  E  can  be 
determined  at  the  decomposition  point. 

Le  Blanc  (13)  found,  as  required  by  theory,  that  the 
electromotive  force  of  polarisation  is  independent  of  the 
nature  of  the  electrolyte,  provided  that  the  substance  separated 
at  the  platinum  electrodes  is  the  same,  a  condition  which  is 
fulfilled  when  the  ordinary  oxygen  acids  or  bases  are  used. 
The  values  obtained  by  him  for  E  were— 

Volts,    i  •        Volts. 


Sulphuric  acid 1*67 

Nitric  acid 1'69 

Phosphoric  acid 1'70 

Monochloracetic  acid  .     .     .  1-72 

Dichloracetic  acid    ....  1*66 

Malonic  acid 1-69 

Perchloric  acid 1'65 

Tartaric  acid      .  JL-62   \ 


Sodium  hydroxide  .     .     .     .  T69 

Potassium  hydroxide   .     .     .  1'67 

Ammonia 1'74 

Methylamine 1*75 

Diethylamine 1-68 

Tetramethylammonium     hy- 
droxide      .  1-74 


258    OXIDATION  AND  REDUCTION  ELEMENTS.    CHAP. 

On  the  other  hand,  if  the  products  of  the  electrolysis  are 
not  the  same,  as  is  the  case  with  hydrochloric  acid  (H2  and 
C12),  hydrobromic  acid  (H2  and  Br2),  hydriodic  acid  (H2 
and  I2),  different  tensions  are  obtained :  in  these  three  cases, 
1-31,  0'94,  and  0'52  volt  respectively  for  normal  solutions. 
In  the  case  of  some  organic  acids,  such  as  oxalic  acid, 
trichloracetic  acid,  etc.,  deviating  results  were  obtained, 
because  in  these  instances  the  secondary  processes  which  take 
place  at  the  electrodes  play  an  important  part. 

For  these  acids,  which  all  show  a  lower  value  for  E  than 
1-67  volt,  corresponding  with  the  separation  of  hydrogen  and 
oxygen  at  the  platinum  electrodes,  the  influence  of  the 
secondary  processes  diminishes  with  rising  dilution,  and  at 
the  same  time  the  reduction  of  the  separated  oxygen  does  not 
take  place  so  readily.  The  polarisation  for  a  normal  solution 
of  oxalic  acid  is  0'95  volt,  whilst  for  a  0'067-normal  solu- 
tion it  rises  to  T04  volts.  A  similar  behaviour  is  exhibited 
by  hydrochloric  acid  solutions,  in  which  more  and  more 
oxygen  instead  of  chlorine  is  separated  as  the  dilution 
increases.  Thus  a  normal  solution  of  hydrochloric  acid  shows 
the  tension  of  polarisation  E  =  1-31  volts,  and  for  a  ^-normal 
solution,  E  =  T69  volts,  i.e.  as  great  as  for  oxygen  acids. 
The  oxygen  acids  show  no  appreciable  change  of  electro- 
motive force  with  dilution,  so  that  E  =  1/67  volts  both  for  a 
normal  and  for  a  ^-normal  solution  of  sulphuric  acid. 

The  alkali  salts  of  the  oxygen  acids  behave  somewhat 
differently.  With  these  the  decomposition  products  are  not 
only  02  and  H2,  but  base  and  acid  as  well,  i.e.  OH  and  H 
ions.  Consequently  more  work  is  required  for  the  electro- 
lysis of  these  than  for  acids,  but  about  the  same  for  all  salts. 
Using  platinum  electrodes,  Le  Blanc  found  the  following 
polarisation  electromotive  force  E : — 

Volts.    I  Volts. 

Sodium  nitrate 2' 15  |  Sodium  sulphate      .     .     .     .  2-21 

Potassium  nitrate    ....  2'17  i  Potassium  sulphate      .     .     .  2-20 

Lithium  nitrate 2'11  j  Sodium  acetate 2-10 

Strontium  nitrate    ....  2*28  I  Ammonium  nitrate.  2'08 


Calcium  nitrate       .     .     .     .     2*11 
Barium  nitrate    .  2-25 


Ammonium  sulphate  .     .     .     2*11 


XV. 


MAXIMUM    POLARISATION. 


259 


These  decomposition  tensions  exceed  those  of  the  acids  by 
0*47  volt  on  the  average.  The  difference  between  the  decom- 
position tensions  of  the  chlorides,  bromides,  and  iodides  and 
the  corresponding  acids  is  somewhat  greater,  as  can  be  seen 
from  the  following  values  found  by  Le  Blanc  : — 


Sodium  chloride 
Potassium  chloride  . 
Lithium  chloride     . 
Calcium  chloride 
Strontium  chloride  . 


Volts. 

1-98 
1-96 
1-86 
1-89 
2-01 


Volts. 

Barium  chloride  .  .  .  .  1*95 
Sodium  bromide  ....  1'58 
Potassium  bromide ....  1*61 
Sodium  iodide  .  .  .  .  .  1-12 
Potassium  iodide  1'14 


The  difference  amounts  to  about  0'87  volt  for  the 
chlorides,  O67  volt  for  the  bromides,  and  0'61  volt  for  the 
iodides  when  these  are  compared  with  normal  solutions  of 
the  acids.  If  for  comparison  we  take  a  2I2'Ilormal  solution 
of  hydrochloric  acid,  the  difference  for  the  chlorides  would 
only  be  O49  volt.  It  is  difficult  to  give  the  preference  to  one 
or  other  concentration  of  the  acid  on  any  rational  basis.  If 
the  difference  of  the  decomposition  products  between  the 
halogen  acids  and  their  salts  were  the  same  as  between  the 
oxygen  acids  and  their  salts,  then  the  difference  in  the  electro- 
motive force  would  necessarily  be  the  same  in  both  cases. 

Maximum  Polarisation. — It  was  formerly  supposed 
that,  with  increasing  current  strength,  the  value  of  E  rose 
asymptotically  to  a  maximum.  From  Jahn's  results  this 
conclusion  is  rendered  doubtful ;  he  found  that  E  increases 
almost  proportionally  with  log  i.  The  increase,  however, 
takes  place  so  slowly  that  we  may  assume  for  the  currents 
which  are  used  practically  that  there  is  a  maximum  electro- 
motive force  of  polarisation;  without  appreciable  error  we 
may  take  the  value  of  this  to  be  2 '5  volts  for  acids  and 
bases,  and  3'3  volts  for  the  salts  of  oxygen  acids. 

Polarisation  by  Deposition  of  Solid  Substances.— 
When  a  solution  of  copper  sulphate  is  electrolysed  between 
platinum  plates,  copper  is  deposited  at  the  cathode,  and  S04 
at  the  anode,  and  this  latter,  by  reaction  with  the  water,  gives 
H2S04  and  02.  ,  If  the  electrolysis  be  carried  to  a  certain 


260    OXIDATION  AND  REDUCTION  ELEMENTS.    CHAP. 


point,  the  platinum  cathode  becomes  covered  with  a  film 
of  copper,  and  in  an  electromotive  respect  behaves  like  a 
copper  plate.  However,  the  deposited  film  must  assume  a 
certain  (although  very  small)  thickness  before  it  acts  quite 
like  pure  copper.  Oberbeck  (14)  found  that  when  the 
deposited  film  on  the  platinum  electrodes  is  2*7  millionths 
of  a  millimetre  thick  in  the  case  of  zinc,  and  T9  millionths 
of  a  millimetre  in  the  case  of  cadmium,  the  same  electromotive 
force  is  obtained  as  when  the  pure  metals  (zinc  or  cadmium) 
are  used.  This  phenomenon  is  also  termed  polarisation,  and 
we  therefore  say  that  the  electromotive  force  of  polarisation 
in  the  decomposition  of  copper  sulphate  is  for  the  cathode  the 
same  as  the  electromotive  force  Cu  |  CuS04. 

Grove's  Investigations. — Grove  (15)  immersed  in  a 
dilute  solution  of  sulphuric  acid  two  platinum  plates  covered 
with  films  of  different  gases.  Between  the  platinised  platinum 
plates  charged  with  different  gases  and  a  platinum  electrode 
saturated  with  hydrogen,  he  obtained  the  following  tensions 
in  volts  (the  unit  adopted  by  Grove  =  2  volts) : — 


Volt. 

Chlorine 0*63 

Bromine 0*50 

Oxygen 0-48 

Iodine 0'48 

Nitrous  oxide  O43 


Volt. 

Cyanogen O42 

Carbon  dioxide 0-42 

Nitric  oxide O41 

Air 0-41 

Pure  platinum    .....     O40 


In  the  form  used  by  Grove  these  elements  are  by  no 
means  reversible,  otherwise  he  would  have  found  the  same 
potential  difference  as  Smale  (9)  did  for  the  combination 
oxygen  |  hydrogen  at  a  palladium  electrode,  whilst  he  only 
obtained  something  less  than  half  this  value. 

Cathodic  and  Anodic  Polarisation. — In  studying 
polarisation  phenomena,  the  action  of  the  cathode  can  be 
distinguished  from  that  of  the  anode  by  comparing  the 
potential  of  each  electrode  with  that  of  a  so-called  normal 
electrode,  generally  mercury  under  calomel  and  a  OT-normal 
solution  of  potassium  chloride,  the  polarisation  vessel  being 
connected  with  the  normal  electrode  by  means  of  a 


xv.  ACCUMULATORS.  261 

fine  syphon  or  wet  thread  containing  0'1-normal  KC1. 
Any  unpolarisable  electrode  may  be  used  as  a  normal 
electrode.  Since  the  polarisation  diminishes  rapidly  after  the 
circuit  is  broken,  it  should  be  measured  as  soon  as  possible 
(within  O'Ol  second)  after  the  current  is  stopped :  the  measure- 
ment can  best  be  made  with  an  electromagnetic  tuning-fork. 
Accumulators. — The  accumulators  constructed  by  Plante 
(16)  in  1859  are  a  particular  kind  of  secondary  elements.  The 
simplest  form  consists  of  two  lead  pole  plates  immersed  in 
a  15  to  30  per  cent,  solution  of  sulphuric  acid.  When  a 
current  is  conducted  through  this  element,  hydrogen  is 
separated  at  one  side,  and  oxygen  at  the  other,  which 
gradually  oxidises  the  positive  plate  to  lead  peroxide. 
When  this  process  has  taken  place  for  some  time,  the 
current  is  reversed,  so  that  the  lead  peroxide  is  reduced 
to  lead  oxide,  which,  with  the  sulphuric  acid,  forms  lead 
sulphate,  and  this,  by  further  reduction,  leads  to  a  spongy 
mass  of  lead.  At  the  same  time  the  surface  of  the  other 
plate  becomes  covered  with  a  film  of  lead  peroxide.  By 
repeatedly  reversing  the  direction  of  the  current,  the  lead 
peroxide  permeates  deeper  and  deeper  into  the  positive 
plate,  which  becomes  more  porous.  This  successive  charge 
and  discharge  necessary  to  "form"  the  accumulator  plates 
requires  a  very  long  time,  and  formerly  about  a  year  was 
spent  on  this  process.  Chemical  and  mechanical  means  were 
afterwards  introduced  for  treating  the  lead  plates,  so  that  the 
change  into  spongy  lead  was  so  far  accelerated  that  the  process 
may  now  be  carried  out  in  about  fourteen  days,  or  even  less. 
In  order  to  still  further  aid  the  "forming"  of  the  plates, 
Faure  (17)  introduced  the  process  of  mechanically  fixing 
litharge,  or  red  lead,  upon  the  lead  plates.  This  succeeds 
well,  for  both  litharge  and  red  lead  form  a  sort  of  cement 
with  sulphuric  acid,  which  (on  account  of  the  formation  of 
lead  sulphate)  assumes  a  solid  consistency,  and,  according  to 
the  process  of  Sellon  and  Volckmar  (18),  a  mixture  of  this 
sort  is  brought  into  properly  disposed  cuts  on  the  lead  plates. 
Finely  divided  lead,  moistened  with  water  and  sulphuric  acid, 


z6z    OXIDATION  AND  REDUCTION  ELEMENTS.    CHAP. 

behaves  similarly,  and  may  be  used  to  fill  the  rills  of  the  lead 
plates.  The  cuts  are  now  made  so  deep  that  the  lead  plate 
has  the  appearance  of  a  sort  of  framework  (or  grid),  with  the 
spaces  filled  with  the  mixture  described.  These  plates  are 
"  formed  "  against  an  ordinary  plate.  An  objection  to  such 
plates  is  that  the  substance  of  the  electrode  does  not  hold 
together  well,  and  cannot  withstand  high  current  strengths. 
The  passage  of  the  current  is  accompanied  by  chemical 
processes,  which  take  place  with  change  of  volume ;  if  these 
occur  quickly,  pieces  of  the  filling  material  break  off  from 
the  plates,  and  fall  to  the  bottom  of  the  containing  vessel. 
[In  the  Tudor  process  the  positive  grid  is  constructed  by 
pickling  it  in  a  bath  of  sulphuric  acid  containing  nitric  acid, 
and  then  obtaining  the  stratum  of  lead  peroxide  by  electro- 
lysis, using  an  ordinary  plate  as  cathode.  The  negative  plate 
is  an  open  grid,  pasted  with  litharge,  but  not  reduced  before 
leaving  the  factory.] 

The  liquid  in  the  accumulator  must  be  free  from  certain 
impurities,  such  as  chlorine,  nitrates,  and  foreign  metals,  for 
if  these  are  present  the  lead  plates  are  violently  attacked ; 
[the  presence  of  arsenic  is  particularly  detrimental].  If 
foreign  metals  are  present,  local  currents  are  set  up,  provided 
that  the  metal  deposited  on  the  lead  plate  during  the  charging 
is  more  negative  (as,  e.g.,  copper)  than  lead.  It  is  particularly 
important  that  the  water  used  in  filling  up  the  vessel  to 
replace  that  lost  by  evaporation  should  be  entirely  free  from 
chlorides  and  nitrates. 

In  charging  an  accumulator,  a  certain  current  density, 
which  depends  on  the  kind  of  plates,  should  not  be  exceeded. 
Formerly,  O6  ampere  per  square  decimetre  was  recommended. 
According  to  more  recent  experience,  the  current  density  may 
safely  be  raised  to  1  amp./sq.  dm.,  and,  with  the  best  plates 
(prepared  by  the  PI  ante  method),  it  may  even  be  as  high  as 
2*6  amp./sq.  dm.  In  discharging,  too,  the  current  density  must 
be  maintained  within  the  same  limits.  At  the  beginning  of  the 
charging,  the  back  electromotive  force  (the  pole  tension)  has 
a  value  of  about  2*07  volts,  which  rises  slowly  to  2'20  volts, 


xv.  ACCUMULATORS.  263 

and  then  quickly  to  about  2 '5  volts.  When  the  charging  is 
nearly  complete,  persulphuric  acid  is  formed  at  the  peroxide 
plate,  and  this  partially  decomposes  into  sulphuric  acid  and 
oxygen.  The  oxygen  evolves  (the  accumulator  "  boils  "),  and 
when  this  occurs  it  shows  that  the  accumulator  is  fully 
charged ;  at  the  same  time  hydrogen  is  evolved  at  the  other 
plate ;  according  to  Darrieus  (19\  the  former  plate  is  then 
permeated  by  persulphuric  acid,  and  the  latter  has  absorbed 
hydrogen.  During  the  discharge  the  comparatively  small 
quantities  of  these  substances  are  used  up,  and  this  causes 
the  electromotive  force  to  sink  to  about  2  volts.  Thereafter 
the  principal  reaction  is — 

Pb  (spongy)  -f  Pb02  +  2H2S04  +  aq  =  2PbSO,  +  2H20  +  aq, 

which  evolves,  according  to  the  measurement  of  J.  Thomsen, 
43,500  cal.  for  every  gram-equivalent  of  spongy  lead  which  is 
transformed.  During  the  course  of  this  reaction,  the  electro- 
motive force  falls  slowly  to  1/9  volts,  and  then  more  quickly 
to  T8  volts,  provided  that  the  discharge  does  not  take  place 
too  fast.  If  the  discharge  is  carried  out  very  rapidly,  the 
electromotive  force,  after  a  certain  time,  falls  to  a  lower 
value  than  that  mentioned,  and  this  is  probably  due  to  a 
kind  of  polarisation,  inasmuch  as  the  chemical  action  cannot, 
so  to  say,  keep  up  with  the  electrical  process.  When  the 
voltage  has  been  reduced  to  1/8,  no  more  current  should 
be  drawn  from  the  cell,  as  this  is  apt  to  spoil  it.  If  the 
discharge,  however,  be  carried  further,  the  electromotive  force 
very  rapidly  decreases.  This  shows  that  by  slowly  dis- 
charging an  accumulator  more  electricity  (calculated  in 
ampere-hours,  at  3600  coulombs)  can  be  obtained  than 
when  it  is  quickly  discharged;  for  in  the  latter  case  the 
voltage  more  quickly  reaches  the  value  1/8,  i.e.  after  a  shorter 
number  of  ampere-hours. 

The  number  of  ampere-hours  (at  the  rate  of  3  to  5 
amperes  per  sq.  dm.  of  the  positive  plate)  which  an 
accumulator  can  yield  determines  its  capacity.  This  is, 
therefore,  greater  for  weak  currents  than  for  strong  ones ;  it 


264    OXIDATION  AND  REDUCTION  ELEMENTS.    CHAP. 

amounts,  for  instance,  to  140  ampere-hours  when  the  discharge 
takes  10  hours,  and  only  to  100  ampere-hours  when  the  cell 
is  discharged  in  3  hours.  A  discharged  element  should  not 
be  kept  in  this  condition  for  any  length  of  time,  because  the 
lead  sulphate  formed  easily  sets  to  a  hard  mass,  which  can 
only  with  difficulty  be  transformed  during  charging. 

It  is  of  interest  to  learn  what  is  the  economic  value  or 
the  so-called  efficiency  of  an  accumulator.  This  can  be 
judged,  on  the  one  hand,  by  the  number  of  ampere-hours 
which  the  element  can  give  compared  with  the  number 
required  for  charging  it.  On  the  other  hand,  the  efficiency 
may  be  determined  by  the  quantity  of  energy,  generally 
estimated  in  watt-hours  at  3600  coulombs,  which  the 
element  can  yield  compared  with  that  absorbed  by  it  during 
charging.  According  to  the  former  method,  the  efficiency 
amounts  to  from  82  to  94  per  cent.,  whilst  by  the  latter 
method  it  is  from  75  to  83  per  cent,  [and  is  frequently  as 
low  as  60  per  cent.],  depending  on  the  current  density.  If  an 
accumulator  be  left  for  some  time  unused,  it  spontaneously 
loses  part  of  its  charge,  i.e.  its  efficiency  diminishes. 

By  means  of  Thomson's  rule  we  calculate  that  the  electro- 
motive force  of  an  accumulator  is  ff  §?{)-  =  1*886  volts.  On 
the  basis  of  Helmholtz's  theorem  the  temperature  coefficient 
of  the  electromotive  force  must  be  taken  into  account ;  this 
amounts,  however,  to  only  2  to  4  millionths  per  degree,  and 
so  the  correction  dees  not  exceed  0*001  volt.  Now,  the 
electromotive  force  of  an  accumulator  during  the  principal 
reaction  is,  on  the  average,  T9  volts,  i.e.  slightly  higher  than 
the  calculated  value,  and  even  more  so  at  the  beginning  of 
the  principal  reaction  when  the  electromotive  force  may  be 
as  high  as  2  volts.  The  reason  for  this  difference  is  that 
the  sulphuric  acid  of  the  element  is  more  concentrated  than 
was  assumed  by  Thomsen  in  his  calculation.  Streintz 
(20)  found  that  the  electromotive  force  of  an  accumulator 
at  the  beginning  of  the  principal  process  is  given  by  the 
formula — 

E  =  1-850  +  0-917  (S  -  1), 


xv.  ACCUMULATORS.  265 

where  S  is  the  specific  gravity  of  the  sulphuric  acid  used. 
In  practice,  sulphuric  acid  of  20  to  24  per  cent,  with  specific 
gravity  varying  from  1*144  to  1*173  is  employed.  [In  the 
Tudor  cell  acid  of  specific  gravity  1*20  is  used.] 

It   is  easy  to  see  why  the   electromotive   force   of  an 
accumulator  increases  with  the  concentration  of  the  sulphuric 
acid.     Suppose  we  have  two  ac- 
cumulators, A  and  B,  filled  with 
25    per    cent,   and   15   per   cent, 
sulphuric    acid  respectively,   and 
suppose  that  they  are  so  connected 
that  their  electromotive  forces  are 
opposed  to  each  other,  as  shown  FlG  48 

in  Fig.  48.  Just  as  the  concentra- 
tion of  a  layer  of  25  per  cent,  sulphuric  acid  tends  by 
diffusion  to  come  into  equilibrium  with  a  layer  of  15  per 
cent,  acid  with  which  it  is  in  contact,  so  in  the  system 
depicted  a  current  arises  which  tends  to  establish  the  same 
equilibrium,  i.e.  the  common  concentration  of  20  per  cent. 
Now,  since  on  the  discharge  of  an  accumulator  water  is 
formed  and  sulphuric  acid  disappears,  whilst  the  opposite 
reaction  takes  place  during  charging,  the  accumulator  A  must 
discharge  in  order  to  establish  the  equilibrium,  and  at  the 
same  time  this  charges  B.  It  can  easily  be  found  thermo- 
dynamically  how  much  work  can  be  gained  by  transferring 
18  grams  of  water  from  B  to  A,  and  98  grams  of  sulphuric 
acid  from  A  to  B  (see  p.  75).  Dolezalek  (21)  has  ascer- 
tained in  this  way  the  electromotive  force  of  the  above 
combination,  and  from  this  calculated  how  the  electromotive 
force  of  an  accumulator  changes  with  varying  concentration 
of  the  sulphuric  acid.  The  calculation  is  in  good  agreement 
with  the  result  found  by  Streintz. 

On  account  of  the  many  advantages  possessed  by  accu- 
mulators, they  have  almost  entirely  replaced  in  practice  all 
the  older  galvanic  elements,  with  the  exception  of  those  of 
Leclanche  [and  of  Daniell],  which  are  more  suitable  for  cases 
when  only  a  weak  current  is  required,  and  that  for  only  a 


266    OXIDATION  AND  REDUCTION  ELEMENTS.    CHAP. 

short  time,  as  with  bells,  telephones,  in  telegraphy,  etc.  Iii 
scientific  work,  too,  accumulators  have  been  of  great  service, 
both  for  producing  comparatively  large  currents  and  for 
obtaining  high  potentials.  For  the  latter  purpose  a  large 
number  of  small  elements  is  used ;  these  elements  are  con- 
structed with  small  preparation  tubes  containing  sulphuric 
acid  and  strips  of  lead.  In  charging,  a  large  number  of 
elements  is  arranged  in  parallel,  whilst  on  discharging  all 
the  cells  are  connected  in  series.  Batteries  of  this  sort, 
which,  on  account  of  the  smallness  of  the  electrodes,  have 
only  a  small  capacity,  are  frequently  used  for  the  study 
of  electrical  phenomena  in  gases,  insulators,  and  poor 
conductors. 

Certain  disadvantages  also  attend  the  use  of  accumulators. 
The  lead  of  which  the  electrodes  consist  must  be  used  in 
fairly  large  pieces  if  any  degree  of  rigidity  is  to  be  obtained, 
and  this,  of  course,  means  a  considerable  weight.  Further- 
more, lead  is  very  easily  attacked  chemically.  In  order  to 
avoid  these  objections,  attempts  have  been  made  to  use  lead 
containing  small  amounts  of  foreign  metals ;  4  per  cent, 
of  antimony  (so-called  Julien  metal)  and  other  metals  have 
been  tried. 

Every  reversible  element  is  in  a  certain  sense  an  accumu- 
lator. For  instance,  if  a  current  is  impressed  through  a 
Daniell  cell  in  the  direction  opposite  to  that  of  its  own 
electromotive  force,  zinc  is  deposited  from  the  zinc  sulphate, 
and  copper  dissolves  to  copper  sulphate.  When  left  to 
itself,  the  process  takes  place  in  the  opposite  direction.  In 
this  case,  however,  the  reversibility  is  more  of  a  theoretical 
than  of  a  practical  nature,  because,  on  account  of  diffusion 
of  the  two  electrolytes,  copper  is  deposited  on  the  zinc.  This 
gives  rise  to  a  vigorous  "  local  action,"  whereby  the  zinc  is 
rapidly  destroyed,  and  there  is  an  evolution  of  hydrogen  in  the 
short-circuited  element  consisting  of  zinc,  deposited  copper, 
and  sulphuric  acid  (or  sulphate  solution).  A  similar  dis- 
turbance vitiates  the  usefulness  of  the  copper  element  (which 
it  was  hoped  would  prove  a  valuable  accumulator),  because 


XV. 


ACCUMULATORS. 


267 


some  of  the  copper  oxide  dissolves  in  the  alkali  and  diffuses 
to  the  zinc.  In  this  respect  mercury  takes  up  an  exceptional 
position  (see  p.  251).  Attempts  have,  therefore,  been  made 
to  use  mercury  as  the  positive  pole  plate  of  accumulators, 
but  no  practical  success  has  been  attained  by  this.  Since  in 
lead  accumulators  no  fear  of  disturbances  due  to  diffusion 
need  be  entertained,  the  distance  between  the  plates  may  be 
made  very  small,  and  in  this  way  the  internal  resistance 
reduced  to  a  minimum.  According  to  Streintz  (20),  lead 
peroxide  conducts  like  a  metal,  and  this  also  tends  to  reduce 
the  internal  resistance  of  lead  accumulators. 

In  this  latter  respect  aluminium  stands  in  sharp  contrast 
to  lead.  At  the  ordinary  temperature  an  anode  of  this 
metal  becomes  covered  with 
a  film  of  oxide,  which  offers 
such  a  large  resistance  that 
the  passage  of  the  current 
is  almost  entirely  stopped. 
Based  on  this  property, 
Graetz  (22)  has  constructed 
a  commutator  of  some  theo- 
retic interest.  In  a  trough 
filled  with  a  salt  solution,  in  which  are  a  platinum  and  an 
aluminium  electrode,  the  current  can  only  pass  in  the  direc- 
tion from  the  platinum  through  the  solution  to  the  aluminium, 
on  account  of  the  property  mentioned.  If  we  introduce  into 
the  circuit  of  an  alternating  current  two  such  troughs 
arranged  as  in  Fig.  49,  the  current  goes  through  each  branch 
almost  entirely  in  the  direction  indicated  by  the  arrows. 


FIG.  49. 


CHAPTER  XVI. 
Electro-analysis. 

Determination  of  the  Quantity  of  Salt  in  a  Solution 
by  measuring  the  Conductivity. — If  we  know  the  con- 
ductivity of  solutions  of  a  particular  salt  at  various  concen- 
trations, then  inversely  by  determining  the  conductivity  we 
can  find  the  concentration. 

If  we  have  a  solution  containing  two  given  salts,  then  by 
making  two  determinations  we  find  the  quantity  of  each 
present ;  one  of  the  determinations  may  be  the  conductivity, 
the  second  some  other  property,  such  as  the  total  weight  of 
dry  substance.  Erdmann  (1)  determines  in  this  way  the 
quantity  of  potassium  chloride  in  presence  of  potassium 
iodide  or  rubidium  chloride,  etc. 

In  many  cases  the  proportions  of  the  constituents  present 
are  nearly  constant;  this  is  the  case,  for  instance,  with 
different  samples  of  sea  water  containing  varying  total 
amounts  of  dissolved  substance.  In  such  cases  the  determi- 
nation of  the  resistance  is  sufficient  to  indicate  the  quantities 
present,  and  this  method  of  analysis  has  actually  been 
employed. 

Occasionally  non-electrolytes  are  present  in  the  solution 
to  be  analysed  (for  instance,  in  the  estimation  of  the  ash  of 
cane  sugar  or  molasses),  and  these  diminish  the  conductivity. 
When  this  happens  a  correction  must  be  introduced,  and  the 
magnitude  of  this  can  be  ascertained  either  from  the  data 
given  on  p.  150,  or  it  has  to  be  found  by  a  special  experiment. 

For  some  salts,  e.g.  silver  chloride,  the  conductivity  is 


CHAP.  xvi.      ELECTROMETER   AS   AN   INDICATOR.     269 

not  known  from  direct  experiment,  but  in  these  cases  the 
molecular  conductivity  at  infinite  dilution  can  be  ascertained, 
as  also  the  degree  of  dissociation  which  is  set  equal  to  that 
of  some  closely  allied  salt  (here,  silver  nitrate)  at  the  same 
dilution.  The  concentration  of  a  given  solution  of  silver 
chloride  can  be  estimated  from  the  conductivity,  and  if  a 
saturated  solution  be  used  we  obtain  the  solubility.  The 
solubilities  of  several  difficultly  soluble  salts,  such  as  silver 
chloride,  silver  bromide,  silver  iodide,  barium  sulphate, 
calcium  sulphate,  strontium  sulphate,  and  various  silicates 
have  been  determined  in  this  way  by  Kohlrausch  and  Eose 
(2)  much  more  exactly  than  could  be  done  by  ordinary 
analysis. 

At  high  dilution  all  salts  when  applied  in  equivalent 
quantity  conduct  almost  equally  well.  Consequently  when 
it  is  desired  to  find  approximately  how  many  gram-equivalents 
of  salt  are  present  in  a  water  (e.g.  a  well  water),  this  can  be 
done  simply  by  determining  the  resistance. 

Application  of  the  Electrometer  as  an  Indicator.— 
Behrend  (3)  introduced  this  instrument  for  the  titration 
of  mercury.  Suppose  we  have  two  solutions  of  mercurous 
nitrate  over  mercury  in  two  beakers,  and  that  the  concentra- 
tion of  one  of  the  solutions  is  known  (e.g.  OT-normal), 
whilst  that  of  the  other  is  to  be  found.  The  two  solutions 
are  connected  by  a  syphon  tube  containing  nitric  acid,  and 
two  platinum  wires  dip  into  the  mercury  in  the  vessels — the 
wires  are  fused  through  glass  tubes,  so  that  only  the  ends 
remain  free.  The  platinum  wires  are  connected  with  the 
poles  of  an  electrometer;  and  the  electromotive  force  of 
the  concentration  element  thus  constructed  is  measured  with 
the  electrometer.  To  the  solution  whose  concentration  is  to 
be  determined  a  standard  solution  of  a  chloride,  e.g.  potassium 
chloride,  is  added,  and  the  mercury  is  precipitated  as  calomel. 
This  causes  the  electromotive  force  to  change  slowly  until 
almost  all  the  mercury  has  been  thrown  out  of  solution. 
The  logarithm  of  the  concentration,  the  value  of  which 
determines  the  electromotive  force,  then  changes  very 


270  ELECTRO-ANALYSIS.  CHAP. 

quickly  and  most  suddenly,  just  when  the  last  quantity  of 
mercury  is  precipitated.  The  electrometer  then  indicates 
a  spring  of  about  O'l  volt,  and  may  thus  be  used  as  an 
indicator.  This  kind  of  analysis,  which  can  be  applied  in 
other  similar  cases,  has  not  been  used  in  practice  to  any 
extent. 

Analysis  by  Metal  Deposition. — The  electrolytic  de- 
position of  metal,  on  account  of  the  ease  with  which  it  can 
be  carried  out,  is  the  most  frequent  electrical  method  of 
analysis.  For  the  separation  of  a  metal  a  certain  electro- 
motive force  (see  p.  257)  and  a  definite  quantity  of  electricity 
are  required.  The  former  can  be  ascertained  from  the 
polarisation,  the  latter  by  means  of  Faraday's  law,  according 
to  which  1  gram-equivalent  of  any  substance  is  precipitated 
by  a  current  strength  of  1  ampere  in  96,500  seconds,  i.e.  26 
hours  48  minutes.  If  we  used  an  electromotive  force  for  the 
separation  exactly  equal  to  the  back  electromotive  force  of 
polarisation,  it  would  require  an  infinitely  long  time  to  carry 
out  the  deposition.  In  practice,  therefore,  it  is  customary  to 
use  an  appreciably  higher  electromotive  force  (higher  by  1  to 
2  volts).  The  potential  difference  between  the  cathode  and 
anode  determines  what  electromotive  force  must  be  used, 
and  between  these  an  electrometer  is  interposed  in  a  branch 
circuit.  In  order  to  obtain  a  good,  coherent  deposit,  the 
current  density  (given  below  in  amperes  per  square  deci- 
metre) must  be  judiciously  chosen.  In  order  to  be  able  to 
control  this  an  ammeter  is  introduced  before  the  decomposi- 
tion cell.  To  regulate  the  current  density,  a  metal  wire 
rheostat  is  used,  and  arranged  so  that  different  lengths  of  wire 
can  be  interposed  at  will.  The  electromotive  force  is  best 
obtained  from  a  battery  of  accumulators  (only  few  elements 
are  required,  for  the  electromotive  force  never  exceeds  5  volts). 
The  instruments  "do  not  need  to  be  very  exact,  for  an  approxi- 
mate measurement  of  the  electromotive  force  and  the  current 
density  suffices. 

When  the  times  required  for  the  deposition  are  calculated 
by  Faraday's  law,  it  is  always  found  that  they  are  too  small. 


xvi.  ANALYSIS    BY    METAL   DEPOSITION.  271 

In  many  cases  it  is  necessary  to  prolong  the  electrolysis  for 
five  times  as  long  as  the  time  indicated  by  Faraday's  law. 
The  reason  for  this  is  that  a  large  part  of  the  current  is 
used  up  for  other  processes  than  the  metal  deposition.  To 
determine  when  the  deposition  is  complete,  it  is,  therefore, 
advisable  to  withdraw  small  portions  of  the  solution  from 
the  cell,  and  by  means  of  some  delicate  reaction  ascertain 
wrhen  all  the  metal  has  been  precipitated  from  the  solution. 
The  quantity  of  solution  taken  out  must,  of  course,  be 
exceedingly  small,  so  that  the  solution  may  not  be  robbed 
of  an  appreciable  amount  of  the  metal. 

The  solution  to  be  electrolysed  should  not  be  more  than 
about  100  c.c.,  and  should  be  placed  in  a  perfectly  clean 
platinum  basin  of  10  cm.  diameter,  which  serves  as  cathode. 
If  the  basin  is  not  clean,  a  good  deposit  cannot  be  obtained. 
In  order  to  cause  the  deposit  to  cling  well  to  the  basin,  this 
is  often  provided  with  a  matt  surface.  The  basin  is  placed 
on  a  metal  ring,  which  is  carried  by  an  upright  stand,  the 
two  being  united  by  means  of  an  insulator,  and  the  ring  is 
connected  with  the  negative  pole  of  the  battery.  The  form  of 
the  anode  may  be  a  perforated  plate,  a  wire  spiral,  a  cylinder 
of  foil  or  a  foil  cone  of  platinum.  This  anode  is  held  by  the 
same  stand  which  carries  the  cathode  ring,  by  means  of  a 
metal  arm  connected  with  the  positive  pole  of  the  battery. 
If  the  electrolysis  be  carried  out  in  a  glass  vessel,  the  cathode 
should  have  the  form  of  a  cylinder  or  cone.  The  anode  must 
not  possess  any  surface  to  which  large  bubbles  of  gas  may 
cling,  because  when  these  are  ultimately  evolved  they  might 
easily  carry  away  some  of  the  liquid  to  be  electrolysed.  For 
safety  a  glass  funnel  should  always  be  inverted  over  the  basin 
to  catch  any  drops  which  may  be  spirted  out  of  the  liquid. 

Most  of  the  processes  for  electrolytic  analysis  proceed 
better  at  a  somewhat  elevated  temperature  (50  -  60°)  than 
at  the  ordinary  temperature.  For  this  purpose  a  small 
burner  is  placed  below  the  basin,  so  that  a  current  of  hot 
air  ascends  and  warms  the  solution.  It  is  convenient  to 
have  the  burner  fixed  to  the  stand  carrying  the  cell.  The 


272  ELECTRO-ANALYSIS.  CHAP. 

efficacious  action  of  the  heat  may  be  in  part  due  to  the 
convection  current,  to  which  it  gives  rise  in  the  liquid. 

When  the  electrolysis  is  complete  the  cathode  basin  is 
washed  out.  The  deposit  should  be  washed  three  times  with 
about  50  c.c.  of  cold  water,  then  three  times  with  about  the 
same  quantity  of  alcohol,  after  which  it  is  placed  for  about 
five  minutes  in  an  air  bath  at  80°,  dried  in  a  desiccator, 
and  finally  weighed  when  cold.  It  frequently  happens  that 
the  liquid  in  the  basin  (acid  liquids  particularly)  exerts  a 
dissolving  action  on  the  deposited  metal  so  soon  as  the 
current  is  stopped.  In  these  cases  the  liquid  must  be 
removed  from  the  basin  by  means  of  a  syphon  while  the 
current  is  still  passing.  Occasionally  some  substance  is 
added  to  the  liquid  in  the  basin  in  order  to  diminish  the  rate 
of  solution,  e.g.  sodium  acetate  to  a  sulphuric  acid  solution 
from  which  copper  has  been  deposited.  The  sulphuric  acid 
is  replaced  by  the  acetic  acid,  and  in  this  wise  the  solution 
process  is  as  good  as  prevented.  Sometimes  the  adjuncts  for 
washing  out  are  mounted  on  the  stand  along  with  the 
electrodes. 

After  the  deposit  has  been  weighed  it  is  removed  by 
some  chemical  solvent,  which,  as  a  rule,  offers  no  difficulty. 
In  certain  cases  the  deposit  adheres  closely  to  the  platinum 
surface,  e.g.  with  zinc  or  tin,  and  the  platinum  becomes  more 
or  less  porous  when  the  deposit  is  dissolved  off.  To  prevent 
this  the  basin  may  first  be  coated  with  a  thin  film  of  copper 
or  silver.  Precipitated  gold  is  best  removed  by  chromic 
anhydride  dissolved  in  a  saturated  solution  of  sodium 
chloride. 

Should  the  level  of  the  liquid  sink  during  the  electro- 
lysis, part  of  the  deposited  metal  will  be  exposed,  and 
probably  suffer  oxidation.  This  may  easily  be  avoided  by 
replacing  any  water  lost  by  evaporation. 

It  is  characteristic  of  the  depositions  used  for  analytical 
purposes  that  they  almost  all  result  from  secondary  pro- 
cesses (see  p.  282).  So  much  substance  should  be  taken 
for  the  analysis  that  a  deposit  of  O'l  to  0'4  gram  of  metal 


xvi.  ANALYSIS   BY   METAL   DEPOSITION.  273 

will  be  obtained.  In  order  to  assist  the  secondary  electro- 
lysis various  electrolytes  may  be  added.  In  the  simplest 
case,  the  corresponding  acid  is  added  to  the  solution  of 
the  electrolyte.  Here  a  considerable  part  of  the  metal  is 
deposited  primarily.  This  method  is  employed  in  the 
following  analysis :  for  the  deposition  of  cadmium  (slightly 
acid  (H2S04)  solution,  t  =  70  -  80°,  current  density  per 
square  decimetre,  D  =  0'6  —  1  amp.),  copper  (solution  con- 
taining 8  —  10  per  cent,  of  nitric  or  sulphuric  acid,  D  =  1 
—  1*5  amp.  in  warm  or  cold  solution ;  in  sulphuric  acid 
solution  the  addition  of  0'5  gram  of  hydroxylamine  sulphate, 
or  1  gram  of  urea,  assists  the  formation  of  a  good,  coherent 
deposit ;  chlorides  must  be  entirely  absent),  mercury  (5  per 
cent,  nitric  acid,  D  =  0*5  amp.),  bismuth  (deposited  as 
amalgam  when  the  solution  contains  a  corresponding 
quantity  of  mercury  salt ;  if  the  electromotive  force  is  less 
than  1'3  volts  only  mercury  is  separated),  platinum  (with 
3  per  cent,  of  sulphuric  acid  gives  a  coherent  deposit  at 
t  =  65°  and  D  =  0*05,  but  platinum  black  (or  sponge) 
at  the  ordinary  temperature  when  Z>  =  O'l  —  0*2,  E  = 
1'2  volts),  and  palladium  (conditions  the  same  as  for 
platinum) . 

In  other  cases  double  salts  are  used.  The  double  salts 
of  nickel  and  cobalt  with  ammonium  sulphate  give  good 
deposits  in  ammoniacal  solution  (30  —  40  c.c.  of  ammonia 
solution,  t  =  50°,  D  =  0*5  —  1*5)  according  to  Fresenius  and 
Bergmann. 

The  majority  of  the  heavy  metals  give  with  ammonium 
oxalate  double  salts  which  are  suitable  for  deposition.  The 
methods  in  these  cases  have  been  mostly  worked  out  by 
Classen  (4).  In  depositing  iron,  the  absennp.  pf  m'traj-,^  is 
essential.  The*splutions  should  be  kept  slightly  acid  with 
oxalic  acid  when  zinc,  cadmium,  copper,  and  tin  are  being 
separated.  An  equivalent  quantity  of  ammonium  oxalate  is 
about  the  amount  to  be  added  to  the  salt  solution. 

The  following  metals  are  deposited  in  this  manner : — 
Iron  (t  =  20  -  40°,  D  =  1  - 1-5,  E  =  3'6  -  4'3  volts),  cobalt 

T 


274  ELECTRO-ANALYSIS.  CHAP. 

(t  =  60  -  70°,  D  =  1,  E  =  31  -  3-8  volts),  nickel  (t  =  <)0 

-  70°,  D  =  1,  ^  =  2-9  -  31  volts),  zinc  (*  =  50  -  60°,  D  =  1, 
j?  =  3-5  -  4-8  volts),  cadmium  (t  =  70°,  D  =  0'5  -  1,  E  =  3 

-  31  volts),  copper  (t  =  80°,  D  =  1,  E  =  2'5  -  31  volts), 
mercury  (ordinary  temperature,  Z>  =  01  —  1,  E  =  2'5  —  3 '5 
volts),  and  tin  (ordinary  temperature,  Z>  =  0'2  -  0'6,  .#  =27 
—  3*8  volts).     From  such  solutions  aluminium  and  uranium 
are  deposited  as  hydrates ;  chromium  is  oxidised  to  chromic 
acid,  and  beryllium  is  converted  into  acid  carbonate. 

The  double  cyanides,  so  much  used  in  the  technical  deposi- 
tion of  metals,  are  also  of  considerable  importance  in  electro- 
analysis.  Potassium  cyanide  is  added  to  the  solution  until  the 
precipitate  at  first  formed  is  re-dissolved,  after  which  a  slight 
excess  of  it  is  added.  The  following  metals  can  be  deposited 
in  this  way  :  Zinc  (t  =  50°,  D  =  0'5  -  1),  cadmium  (t  =  20°, 
D  =  0-5),  copper  (t  =  20  -  60°,  D  =  0'2  -  0-5,  E  =  2-5  volts), 
silver  (t  =  20  -  60°,  D  =  0'2  -  0-5,  E  =  37  -  48  volts), 
mercury  (t  =  20  -  60°,  D  =  0-5  -  1,  E  =  37  -  4'5  volts ; 
washing  with  alcohol  must  be  avoided),  and  gold  (t  =  50 

-  60°,  D  =  0-3  -  0-8,  E  =2-7-4  volts). 

The  sulpho-salts  of  antimony  and  tin  also  give  good 
deposits  on  electrolysis  (for  antimony  t  =  70  -  80°,  D  =  1 

-  1-5,  E  =  1  -  1-8  volts ;  for  tin  t  =  50  -  60°,  D  =  1  -  2, 
E  =  4  —  5  volts).      The   sodium  salt  is   recommended   for 
antimony,  the  ammonium  salt  for  tin. 

Occasionally  the  double  tartrates  are  used,  for  instance, 
with  zinc  (addition  of  sodium  potassium  tartrate  and  sodium 
hydroxide,  t  =  40  -  50°,  D  =  0'4  -  07),  and  with  tin  (6 
grams  of  tartaric  acid,  6  grams  of  ammonium  acetate,  and 
1  gram  of  hydroxylamine  chloride  or  sulphate  are  added  for 
each  gram  of  stannous  chloride,  t  =  60  —  70°,  D  =  0'7 

-  1-0). 

Zinc  can  also  be  deposited  well  from  the  double  lactates, 
and  copper  from  the  sodium  phosphate  double  salt. 

Peroxide  Precipitates. — Lead  and  manganese  cannot 
be  deposited  conveniently  at  the  cathode.  The  former  is 
separated  quantitively,  but  it  oxidises  extremely  readily 


xvi.     REDUCTION  OF  NITRIC  ACID  TO  AMMONIA.     275 

during  washing  and  drying.  On  the  other  hand,  the  peroxides 
of  both  metals  can  be  produced  at  the  anode  in  a  stable, 
coherent  form.  To  obtain  the  best  results  a  matt  platinum 
basin  should  be  used.  When  a  lead  salt  is  electrolysed,  at 
least  10  per  cent,  of  nitric  acid  must  be  added,  which 
completely  prevents  deposition  of  lead  at  the  cathode  (t  =  50 
_  60°,  D  =  1-5,  E  =  2-5  volts).  The  precipitate  must  be 
washed  before  the  current  is  stopped,  and  in  order  to  get  rid 
of  hydrate  water  it  must  be  dried  at  180  -  190°.  The 
presence  of  chlorides  or  metals  precipitable  by  hydrogen 
sulphide  should  be  avoided. 

In  depositing  manganese  as  peroxide,  about  10  grams 
of  ammonium  acetate  and  2  grams  of  chrome  alum  are  added 
to  0*7  gram  of  manganous  sulphate,  and  the  electrolysis  is 
carried  out  at  80°  with  a  current  density  of  about  0'6  —  0'9 
amp./sq.  dm.  (E  =  3  —  5  volts).  The  chrome  alum  removes 
the  oxygen  separated  at  the  anode,  which  would  otherwise 
prevent  the  deposition  of  a  coherent  precipitate.  After  wash- 
ing, the  precipitate,  which  consists  of  a  hydrated  peroxide,  is 
converted  into  mangano-manganic  oxide,  Mn304,  by  heating 
the  platinum  basin  with  the  point  of  a  blow-pipe  flame.  It 
is  advisable  also  to  rewash  this  residue  in  order  to  free  it 
from  chromic  acid.  When  other  metals  are  present  which 
would  be  precipitated  on  account  of  the  existence  of  the 
chromium  in  the  solution,  the  chrome  alum  is  replaced  by 
5  -  10  c.c.  of  alcohol  (t  =  70°,  D  =  015,  E  =  T2  volts). 
Good  results  can  only  be  obtained  in  the  absence  of  chlorides. 

Reduction  of  Nitric  Acid  to  Ammonia.— Another 
secondary  process  which  has  been  used  in  analysis  is  the 
cathodic  reduction  of  nitric  acid  to  ammonia.  According  to 
Ulsch  (£),  the  best  method  of  carrying  out  the  reduction  is  to 
add  to  the  nitrate  solution  a  known  excess  of  sulphuric  acid, 
and  to  use  a  copper  wire  spiral  as  cathode,  and  a  platinum  wire 
held  in  the  centre  of  this  as  anode.  The  current  density  at 
the  cathode,  which  at  the  beginning  may  be  about  1*5  amp./ 
sq.  dm.,  gradually  sinks  as  the  amount  of  acid  becomes 
smaller.  In  the  earlier  parts  of  the  process  the  hydrogen 


276  ELECTRO-ANALYSIS.  CHAP. 

is  wholly  used  up  in  reducing  the  nitric  acid,  but  after  a  time 
it  begins  to  be  evolved  at  the  cathode.  When  evolution  of 
hydrogen  has  taken  place  for  a  short  time  (ten  minutes  if  a 
2  per  cent,  nitric  acid  solution  be  used),  the  reduction  may 
be  assumed  to  be  complete. 

Copper  Refining. — The  different  behaviours  of  solutions 
of  various  metals  on  electrolysis  have  led  to  methods  for 
separating  the  metals  from  each  other.  Some  metals,  like 
aluminium  and  uranium,  are  not  deposited  by  the  current, 
some  of  low  solution  pressure  are  deposited  by  an  electro- 
motive force  between  the  pole  plates  which  is  insufficient  to 
separate  those  of  high  solution  pressure.  As  an  example  of 
this  type  of  separation  we  may  take  the  technically  important 
deposition  in  the  refining  of  copper  which  has  recently  been 
fully  studied  by  Neumann  (6). 

In  the  refining  of  this  metal  thin  plates  of  copper  are 
used  as  cathode,  and  the  anode  is  a  piece  of  crude  cast 
copper.  These  are  suspended  in  a  wide  vessel  containing 
copper  sulphate  solution  and  sulphuric  acid.  When  the 
current  is  passed,  copper  deposits  in  a  coherent  form  on  the 
cathode,  and  the  crude  copper  is  dissolved  from  the  anode. 
The  electromotive  force  may  be  from  0*25  to  0*7  volt,  and  as 
a  rule  the  tension  between  the  electrodes  is  0'35  volt ;  the 
current  density  is  generally  between  0*2  and  0*9  ampere  per 
square  decimetre.  The  optimum  temperature  for  the  process 
is  about  40°.  The  impurities  in  the  crude  copper,  metals  of 
higher  solution  pressure  (iron,  zinc,  nickel,  and  cobalt), 
gradually  dissolve,  so  that  the  solution  in  the  bath  becomes 
richer  in  the  sulphates  of  these  metals,  and  poorer  in  copper 
sulphate.  The  other  impurities,  such  as  gold,  silver,  bismuth, 
antimony,  and  lead,  remain  undissolved,  or  form  insoluble 
compounds  (principally  basic  salts),  and  falling  from  the 
anode,  collect  in  the  so-called  anode  slime.  Arsenic,  arid 
also  antimony  and  bismuth  partially,  pass  into  solution,  and 
must  occasionally  be  removed  from  the  bath  by  the  addition 
of  copper  oxide.  (Tin  also  may  pass  into  solution,  but  is 
without  influence  on  the  nature  of  the  copper  deposit.) 


xvi.  COPPER   REFINING.  277 

It  might  be  supposed  that  it  would  be  advantageous  to 
separate  all  the  copper  at  the  cathode.  According  to 
Neumann,  however,  this  is  attended  with  poor  results,  for 
the  deposit  is  then  very  spongy.  In  these  investigations, 
Neumann  used  as  anode  a  metal  containing  50  per  cent, 
copper  and  50  per  cent,  nickel  in  one  case,  and  in  another 
65  per  cent,  copper  and  35  per  cent.  zinc.  In  the  former 
case  the  electrolyte  contained  46  grams  of  copper  and 
150  grams  of  sulphuric  acid,  in  the  latter  case  23 
grams  of  copper  and  40  grams  of  sulphuric  acid.  The 
temperatures  were  30°  and  50°  respectively,  and  the  electro- 
motive force  0*5  volt.  From  these  data  we  may  conclude 
that  only  about  2  per  cent,  of  the  current  passed  through  the 
copper  sulphate,  and  therefore  the  greater  part  of  the  copper 
must  have  been  deposited  as  the  result  of  a  secondary  process. 
The  current  density,  which  at  the  beginning  was  2*0  or  1*3, 
gradually  diminished  to  I'O  or  0'6  ainp./sq.  dm.  respectively. 
Until  the  quantity  of  nickel  or  zinc  in  the  bath  became 
double  that  of  the  copper,  the.  deposit  was  extremely  good. 
If  the  proportion  of  copper  is  further  decreased,  the  deposit 
becomes  bud-like  or  warty,  and  later  very  spongy  on 
account  of  the  simultaneous  separation  of  hydrogen ;  at  the 
same  time  the  yield  obtained  from  the  current  is  greatly 
diminished.  When  this  happens,  a  fresh  quantity  of 
electrolyte  should  be  taken,  and  the  copper  in  the  old 
solution  separated  from  the  impurities  by  means  of  hydrogen 
sulphide.  On  account  of  secondary  actions  more  metal  is 
dissolved  than  is  precipitated.  Consequently  the  concentra- 
tion of  the  sulphuric  acid  diminishes  (provided  that  the 
volume  of  the  liquid  does  not  decrease  by  evaporation  of 
water).  In  the  technical  refining  of  copper  insoluble 
sulphates  are  formed,  and  these  sink  to  the  bottom  of  the 
cell.  The  mode  of  action  of  the  acid  can  be  seen  from  the 
results  obtained  by  Forster  (7).  It  may  first  be  mentioned 
that  the  acid  greatly  increases  the  conductivity  of  the 
electrolyte  in  the  bath,  and  therefore  prevents  a  good  deal 
of  loss  of  energy  in  the  form  of  Joule  heat.  In  the  solution, 


278  ELECTRO-ANALYSIS.  CHAP. 

however,  the  principal  part  is  played  by  the  cuprous  ions. 
When  the  current  density  is  very  small  (less  than  0*01) 
cuprous  sulphate  is  formed  at  the  anode  (at  the  ordinary 
temperature).  As  the  current  density  increases,  greater 
quantities  of  cupric  sulphate  are  produced.  The  relative 
proportion  of  cuprous  to  cupric  sulphate  formed  increases 
with  rising  temperature,  so  that  at  100°  and  with  current 
densities  up  to  0*3  amp./sq.  dm.  cuprous  salt  is  almost 
exclusively  formed.  This  cuprous  salt  is  highly  detrimental 
to  the  electrolysis ;  for  it  decomposes  partially  according  to 
the  equation — 

Cu2S04  +  H20  ^  Cu20  +  H2S04 
(or  2C+u  +  H20  ^  Cu20  +  2H). 

The  more  acid  (i.e.  hydrogen  ion)  is  present,  the  higher 
may  the  cuprous  ion  concentration  be  without  this  decom- 
position occurring. 

On  the  other  hand,  the  cuprous  ions  are  in  equilibrium 
with  the  cupric  ions — 

2Cu  =  Cu  +  Cu 

(cuprous  ion  =  copper  +  cupric  ion). 

At  a  certain  acid  (hydrogen  ion)  concentration,  which 
increases  with  rising  temperature,  no  cuprous  oxide  is 
precipitated.  When  it  does  deposit  partially  at  the  cathode 
and  forms  badly  conducting  spots, .  it  gives  rise  to  the 
warty  appearance  of  the  deposited  copper.  The  copper 
is  therefore  less  coherent,  and  the  separation  of  the  cuprous 
oxide  should  consequently  be  prevented  by  addition  of 
sulphuric  acid.  The  formation  of  cuprous  oxide  may  also 
be  hindered  by  the  addition  of  certain  organic  substances 
(e.g.  alcohol).  Probably  the  organic  substance  simply  acts 
in  a  reducing  capacity.  Oettel  (8),  who  studied  the 
accuracy  of  the  copper  voltameter,  found  that  an  addition  of 
5  per  cent,  of  alcohol  is  sufficient  to  prevent  the  disturbing 
effect  of  cuprous  oxide  at  the  cathode  when  the  current 
density  is  small.  In  practice  sulphuric  acid  is  used,  for  the 


xvr.  PRECIPITATION   OF   METAL.  279 

organic  substance  would  be  too  costly.  The  concentration 
of  the  sulphuric  acid  and  the  current  density  must  not  be 
too  high,  for  otherwise  so  much  hydrogen  is  separated  at  the 
cathode  that  it  is  not  completely  removed  by  the  secondary 
processes,  and  the  deposited  copper  becomes  spongy  and 
pulverulent.  Small  changes  can  be  brought  about  in  the 
deposited  metal  by  altering  the  current  density,  and  these 
have  a  great  influence  on  the  hardness  and  electrical 
conductivity  of  the  copper;  use  is  made  of  this  fact  in 
practice. 

The  smaller  the  number  of  cupric  ions  the  lower  is  the 
concentration  of  cuprous  ions ;  according  to  the  above 
equation  the  concentration  of  the  latter  is  proportional  to 
the  square  root  of  that  of  the  cupric  ions.  The  concentra- 
tion of  the  cupric  ions  is  greatly  reduced  by  the  addition  of 
the  acid,  and  to  a  still  greater  extent  by  the  addition  of  salts 
which  are  able  to  form  copper  double  salts.  It  may 
easily  be  conceived  that  similar  relationships  hold  good  for 
other  metals.  In  the  deposition  of  silver,  organic  substances 
are  frequently  added  to  the  bath  "  to  increase  the  polish  of 
the  metal." 

Precipitation  of  Metal  from  a  Solution  containing 
Two  Metal  Salts. — If  a  solution  contains  two  metals  of 
different  solution  pressures,  say  silver  and  copper  as  nitrates, 
two  cases  may  occur  on  electrolysis.  The  electromotive  force 
used  is  either  so  great  (over  T14  volts)  that  it  exceeds  the 
solution  pressures  of  both  silver  and  copper,  or  it  is  sufficient 
(between  O7  and  1*14  volts)  just  to  overcome  the  solution 
pressure  of  one  of  the  metals.  This  leads  to  a  method, 
suggested  and  applied  by  Freudenberg  (9),  for  the  separa- 
tion of  one  metal  from  another  analytically.  The  method  is 
not  good  when  the  solution  pressures  of  the  two  metals  lie 
close  together.  In  technical  work,  too,  great  use  has  been 
made  of  this  principle,  for  instance  in  the  separation  of  gold 
from  the  platinum  metals  '(the  gold  being  much  more  readily 
deposited  from  hydrochloric  acid  solution),  or  of  silver  from 
copper  and  other  metals  (from  nitric  acid  solution).  The 


280  ELECTRO-ANALYSIS.  CHAP. 

refining  of  copper  also  belongs  to  this  category  of  pro- 
cesses. 

If  the  electromotive  force  is  sufficient  to  precipitate  both 
metals,  both  are  generally  deposited  simultaneously.  Very 
often,  however,  after  the  primary  deposition  a  secondary 
reaction  takes  place  between  the  metal  of  higher  solution 
pressure  and  the  salt  of  the  other  metal.  Thus,  e.g.,  if  a 
solution  containing  copper  and  zinc  sulphates  be  electrolysed, 
both  metals  are  deposited,  but  a  secondary  reaction  then 
takes  place,  in  which  zinc  dissolves  and  an  equivalent  amount 
of  copper  is  separated.  This  sort  of  action  occurs  particularly 
when  the  deposition  is  carried  out  very  slowly,  i.e.  when  the 
current  density  is  small.  If  the  solution  contains  much 
zinc  and  little  copper,  it  may  easily  happen  that  all  the 
deposited  zinc  cannot  re-dissolve,  for  the  copper  ions  only 
diffuse  slowly  to  the  cathode,  and  in  this  way  a  mixed  metal 
is  obtained.  It  is  worthy  of  note  that  brass  can  be  prepared 
in  this  electrolytic  manner.  The  preparation  is  more  suc- 
cessful if  potassium  cyanide  solutions  of  the  two  metals 
be  used,  because  then  their  positions  in  the  electromotive 
series  are  close  together.  A  sufficiently  high  current  density 
(about  O6  amp./sq.  dm.)  must,  however,  be  used  if  equal 
quantities  of  the  two  metals  (zinc  and  copper)  are  dissolved 
in  the  bath,  so  that  the  copper  may  not  be  deposited  in  too 
large  an  amount.  A  piece  of  brass  is  used  as  anode,  and  this 
dissolves  to  replace  the  metals  deposited  from  the  solution. 

Position  of  Hydrogen  in  Deposition.— Since  aqueous 
solutions  are  used  almost  exclusively,  a  secondary  separation 
of  hydrogen  occurs  so  soon  as  a  metal  is  deposited  whose 
solution  pressure  exceeds  that  of  hydrogen  (a  primary 
deposition  also  occurs,  provided  that  no  acid  is  present, 
but  on  account  of  the  low  conductivity  of  water  this  is  very 
small). 

It  is,  therefore,  impossible,  without  some  particular 
device,  to  deposit  the  alkali  metals,  magnesium,  or  aluminium, 
from  aqueous  solution,  and  these  are  consequently  prepared 
from  their  fused  salts.  By  collecting  the  alkali  metals  at  a 


xvi.    ANALYTICAL  SEPARATION  OF  THE  METALS.    281 

mercury  electrode,  a  small  amount  of  the  metal  may  be 
obtained  as  amalgam ;  but  as  soon  as  a  fair  quantity  of  it  has 
separated,  a  secondary  decomposition  of  the  solvent-water 
takes  place,  and  hydroxide  is  formed — a  process  which  is 
used  in  Kellner's  method  of  preparing  hydroxides  of  the 
alkali  metals. 

If  the  solution  pressure  of  the  deposited  metal  (e.g.  zinc 
and  nickel)  is  not  so  high  as  that  of  the  metals  mentioned,  it 
can  be  separated  from  aqueous  solution  (say,  solution  of  the 
sulphate)  without  any  appreciable  disturbance  by  secondary 
processes.  In  technical  work,  however,  the  metal  obtained  in 
these  two  cases  is  frequently  spoiled  on  account  of  the  forma- 
tion of  a  small  quantity  of  oxide,  and  the  nickel  appears 
yellowish  and  the  zinc  spongy.  This  formation  of  oxide  can 
be  prevented  by  addition  of  acid,  which,  however,  must  not 
give  rise  to  a  strong  primary  separation  of  hydrogen.  In  the 
electrolysis  of  nickel  salts,  a  weakly  dissociated  acid  is  added, 
such  as  citric,  lactic,  or  boric  acid  (or  even  phosphoric  acid), 
and  the  nickel  obtained  has  then  a  pure  white  colour.  For  the 
deposition  of  zinc  a  small  amount  of  sulphuric  acid  is  added 
to  the  solution,  about  O'Ol  per  cent.,  or  of  aluminium  sulphate, 
which  is  highly  hydrolysed,  and  a  high  current  density  is 
used  (over  1  amp./sq.  dm.)  in  order  to  avoid  a  secondary 
evolution  of  hydrogen.  If  too  much  hydrogen  does  separate 
in  these  cases,  the  nickel  appears  leafy,  and  the  zinc  is  not 
compact. 

Analytical  Separation  of  the  Metals. — It  has  already 
been  mentioned  (p.  276)  that  the  precipitation  of  copper 
from  an  acid  solution  of  its  sulphate  cannot  be  made  com- 
plete if  other  metals,  particularly  of  the  iron  group  or  zinc, 
are  present.  This  process  cannot,  therefore,  be  used  for  the 
quantitative  separation  of  copper  from  more  positive  metals. 
For  similar  reasons  several  of  the  processes  referred  to  above, 
which  are  quite  good  for  the  deposition  of  the  metal  from  a 
pure  solution,  cannot  be  used  for  the  separation  from  other 
metals.  With  the  electro-analysis  we  therefore  have,  as  a 
rule,  to  combine  the  ordinary  analytical  methods.  For 


282  ELECTRO-ANALYSIS.  CHAP. 

instance,  to  determine  iron  in  presence  of  nickel  or  cobalt, 
both  metals  are  completely  deposited,  and  the  weight  ascer- 
tained ;  the  mixed  metal  is  then  dissolved  in  sulphuric  acid, 
and  by  titration  with  potassium  permanganate  the  quantity 
of  iron  present  is  determined. 

Zinc,  which  under  ordinary  circumstances  cannot  be 
separated  electro-analytically  from  the  metals  of  the  iron 
group,  can  be  separated  (it  deposits  first)  if  we  use  a 
potassium  cyanide  solution.  Zinc,  iron,  nickel,  and  cobalt 
can  be  separated  from  aluminium  and  chromium,  because 
these  two  latter  elements  are  not  deposited  in  the  metallic 
condition. 

In  potassium  cyanide,  double  oxalate,  or  sulphuric  acid 
solution,  cadmium  can  easily  be  separated  from  zinc  (E  =  2*4 
—  3 '6  volts).  Silver  can  be  separated  from  copper  in  nitric 
acid  solution  by  using  an  electromotive  force  of  1*36  volts, 
in  potassium  cyanide  solution  by  using  2*3  —  24  volts. 
Mercury  behaves  similarly  to  silver.  Copper  can  be  sepa- 
rated from  cobalt,  and  nickel  from  copper  in  hot  oxalate 
solution  (60°),  and  from  manganese  in  presence  of  free  oxalic 
acid  (t  =  80°).  Copper  is  deposited  from  sulphuric  acid 
solution  when  the  electromotive  force  is  1/85  volts,  whilst 
cadmium  remains  dissolved.  Mercury  can  easily  be  sepa- 
rated from  iron,  cobalt,  nickel,  zinc,  or  cadmium  in  nitric 
acid  solution. 

Antimony,  in  presence  of  arsenic  (as  arsenic  acid,  into 
which  form  the  arsenic  is  transformed  by  the  current,  pro- 
vided that  alkali  is  present)  and  tin,  are  precipitated 
from  a  concentrated  sodium  sulphide  solution.  Arsenic  can 
best  be  separated  from  tin  by  chemical  means.  These  three 
metals  should  first  be  separated  from  other  metals  by  ammo- 
nium sulphide,  and  the  mixture  then  analysed  by  electrolysis. 

Primary  and  Secondary  Deposition  of  Metal.— 
More  than  forty  years  ago,  Bunsen  observed  that  metals 
deposited  secondarily  have  a  much  more  even  and  brighter 
surface  than  those  which  are  primarily  separated.  It  has 
also  been  observed  that  primarily  evolved  hydrogen  leaves 


xvi.  DEPOSITION   OF   METAL.  283 

the  solution  in  large  .bubbles,  whilst  in  the  secondary 
formation  of  this,,  e.g.  in  the  electrolysis  of  an  alkali  salt 
solution  with  a  mercury  cathode,  a  fine  cloud  of  very  small 
bubbles  is  produced.  This  peculiarity  is  supposed  to  be  due 
to  the  fact  that  the  substance  separates  more  easily  on 
already  present  parts  of  the  same  substance  than  on  foreign 
substances,  on  account  of  the  work  done  in  surface  formation. 
In  an  analogous  way  a  salt,  such  as  Glauber  salt,  may  be 
maintained  in  supersaturated  solution,  so  long  as  crystals  of 
it  are  not  present,  but,  if  these  be  added,  the  salt  deposits  on 
the  crystals.  Consequently,  if  silver  be  primarily  deposited 
from  silver  nitrate  solution,  the  metal  appears  in  a  granular 
crystalline  form,  because  it  tends  to  separate  on  the  already 
formed  crystals  of  metal.  On  the  other  hand,  if  the  silver 
be  deposited  secondarily  from  potassium  cyanide  solution, 
the  positive  ion  of  this  salt,  potassium,  is  primarily  separated, 
and  this  secondarily  precipitates  the  silver.  The  silver  thrown 
out  of  solution  in  this  way  will  naturally  deposit  at  the 
spot  where  the  primarily  separated  potassium  was.  The 
potassium  has  no  reason  for  separating  at  any  particular  spot 
(on  the  silver,  for  instance),  and  therefore  the  deposit  of 
silver  is  more  uniform,  and  a  smooth  film  is  formed  on  the 
electrode.  In  these  cases  the  current  density  does  not 
require  to  be  large ;  indeed,  smaller  current  densities 
frequently  give  better  results.  Thus  in  silvering  with 
potassium  argentocyanide  a  current  density  of  0'15  —  0'5  amp./ 
sq.  dm.  is  used,  and  in  gilding  with  potassium  auricyanide 
0'2  —  0'25  amp./sq.  dm. 

For  the  reasons  given,  a  secondary  deposition  is  almost 
always  used  in  electro-plating  where  the  essential  is  a  uniform 
deposit  of  the  metal.;  the  double  cyanides  are  used  in  the 
cases  of  silver,  gold,  and  copper,  and  the  ammonium  sulphate 
double  salts  in  the  deposition  of  nickel  and  iron.  Particularly 
in  gilding,  the  process  is  often  carried  out  at  a  high  tempera- 
ture, which  aids  the  secondary  deposition. 

It  is  a  matter  of  experience  that  comparatively  small 
amounts  of  organic  substances,  such  as  alcohol,  sugar,  or 


284  ELECTRO-ANALYSIS.  CHAP. 

gelatine,  improve  certain  properties  (density,  lustre,  and 
elasticity)  of  the  deposited  metal.  The  influence  exerted  by 
these  has  not  yet  been  satisfactorily  explained.  Possibly 
they  are  connected,  like  the  cases  previously  mentioned,  with 
surface  phenomena  (see  p.  279). 

Difference  of  the  Temperature  Influence  in  Primary 
and  Secondary  Processes. — As  has  been  repeatedly 
mentioned,  the  velocity  of  a  chemical  reaction  increases 
considerably  with  rise  of  temperature.  As  we  have  seen 
above,  the  secondary  processes  are  of  a  purely  chemical 
nature,  and  an  increase  of  temperature  therefore  promotes 
their  influence.  It  is  true  that  an  exception  is  known  to 
this,  namely,  the  evolution  of  hydrogen  from  an  acid  in  very 
dilute  solution  (01-normal  and  weaker)  by  zinc,  particularly 
at  high  temperature.  However,  so  dilute  solutions  are  seldom 
used  in  practice,  and  we  may  therefore  disregard  this 
deviation  (see  p.  106). 

In  contradistinction  to  the  secondary  processes,  primary 
electrolytic  deposition  depends  solely  on  the  current  strength, 
which  varies  with  the  temperature  only  in  so  far  as  the  resist- 
ance in  the  bath  diminishes  on  heating.  If  a  primary  pro- 
cess is  disturbed  by  a  secondary  one,  the  disturbance  can  be 
increased  or  diminished  by  raising  or  lowering  the  tempera- 
ture. In  the  electrolysis  of  potassium  sulphate  with  a 
mercury  cathode  potassium  is  primarily  deposited  at  the 
mercury  with  formation  of  potassium  amalgam,  from  which 
hydrogen  is  afterwards  evolved  secondarily.  The  higher  the 
temperature  is,  the  sooner  does  this  latter  process  occur. 
When  a  normal  solution  of  potassium  sulphate  was  electro- 
lysed by  using  0*053  ampere  and  a  circular  mercury  cathode 
3*7  mm.  in  diameter,  hydrogen  was  evolved  after  25  seconds 
at  20°,  but  after  7'6  seconds  at  83°. 

These  temperature  relationships  are  of  importance  in 
practice.  Thus,  in  the  deposition  of  bronze  (copper  and  zinc), 
where  the  deposited  zinc  seeks  to  dissolve  and  precipitate 
copper,  the  temperature  must  not,  according  to  Fontaine 
(10),  exceed  36°. 


xvi.        PRIMARY   AND   SECONDARY   PROCESSES.        285 

The  temperature  exerts  no  appreciable  influence  on 
primary  processes  taking  place  with  organic  substances,  as 
Tafel  (11)  has  proved  in  the  case  of  the  electrolytic  reduc- 
tion of  caffein  and  other  difficultly  reducible  substances. 

In  many  cases  it  is  sought  to  favour  the  secondary  pro- 
cess, and  for  this  too  low  a  temperature  must  not  be  chosen. 
Thus,  in  electro-gilding  (with  potassium  auricyanide)  it  is 
recommended  that  the  bath  be  kept  at  70-75°,  and  in  the 
deposition  of  nickel  from  ammonium  nickel  sulphate  the 
temperature  should  be  from  50°  to  90°,  according  to  circum- 
stances. It  has  further  been  found  that  the  optimum 
temperature  for  the  preparation  of  iodoform  from  a  solution 
of  potassium  iodide  and  dilute  alcohol  containing  sodium 
carbonate,  is  about  60° ;  hydriodic  acid  and  carbon  dioxide 
are  also  formed. 

In  the  analogous  preparation  of  chloral  from  potassium 
chloride  and  alcohol  the  temperature  must  be  raised  to  100°. 
Many  other  organic  electrolytic  processes,  of  which  Elbs 
(12)  has  studied  a  large  number,  proceed  best  at  com- 
paratively high  temperatures. 

Occasionally  several  secondary  processes  take  place 
simultaneously,  e.g.  in  the  electrolysis  of  potassium  chloride 
solution  with  a  platinum  anode.  Chlorine  is  primarily 
separated  at  the  anode,  and  this  gives  rise  to  a  secondary 
formation  of  hypochlorite,  chlorate,  and  oxygen.  The  hypo- 
chlorite  is  formed  in  largest  quantity  at  low  temperature, 
the  chlorate  and  oxygen  particularly  at  high  temperature. 

The  relative  quantities  of  the  different  electrolytic  pro- 
ducts can  therefore  be  regulated  by  altering  the  temperature. 

As  a  rule  the  secondary  process  is  favoured  by  stirring 
the  liquid  as  well  as  by  elevating  the  temperature.  The 
effect  of  stirring  is  to  bring  fresh  quantities  of  the  unionised 
substances  into  contact  with  the  ions  primarily  separated  at 
the  electrodes,  and  thus  aid  the  secondary  action.  Since  the 
introduction  of  heat  always  causes  a  stirring  in  the  liquid  of 
the  bath,  the  secondary  process  is  helped  both  by  the  stirring 
.and  by  the  rise  of  temperature. 


286  ELECTRO-ANALYSIS.  CHAP. 

Voltameter. — The  principle  of  the  voltameter,  used  for 
the  measurement  of  current,  is  based  on  the  separation  of 
gases  or  metals.  The  oldest  of  these  instruments  is  the 
electrolytic  gas  voltameter,  in  which  hydrogen  and  oxygen 
are  separated,  and  collected  either  singly  in  calibrated  tubes 
or  together  in  one  tube.  Formerly  the  electrolyte  used  was 
dilute  sulphuric  acid.  Secondary  reactions,  however,  arise 
in  this  case  inasmuch  as,  at  the  expense  of  the  oxygen, 
persulphuric  acid,  ozone,  and  hydrogen  peroxide  are  formed. 
The  sulphuric  acid  was  first  replaced  by  phosphoric  acid,  but 
later,  potassium  hydroxide  solutions  were  introduced,  and  the 
electrodes  were  made  of  nickel  instead  of  platinum.  Using 
sulphuric  acid,  only  the  hydrogen  should  be  collected,  since 
the  disturbances  occur  at  the  pole  where  the  oxygen  is 
separated.  The  gas  volume  must  be  reduced  to  normal 
temperature  and  pressure,  and  due  allowance  made  for  the 
water  vapour  present.  One  coulomb  corresponds  with 
0'174  c.c.  of  electrolytic  gas,  or  0*116  c.c.  of  hydrogen.  One 
ampere  evolves  6*96  c.c.  of  hydrogen  per  minute. 

On  account  of  the  inaccuracies  of  the  electrolytic  gas 
voltameter,  its  place  has  now  been  taken  by  silver  or  copper 
voltameters.  In  the  silver  voltameter  a  platinum  crucible 
is  used  as  cathode,  and  a  rod  of  silver  in  the  centre  serves  as 
anode.  In  order  to  prevent  pieces  (particularly  of  peroxide) 
of  the  anode  from  falling  into  the  crucible,  the  rod  should 
be  wrapped  in  filter  paper,  or  a  small  glass  basin  should  be 
suspended  beneath  it.  The  formation  of  peroxide  can  be  most 
judiciously  prevented  by  adding  some  alcohol  to  the  silver 
nitrate  solution  (15-30  per  cent.)  used  as  electrolyte.  The 
current  density  may  be  very  variable. 

In  the  copper  voltameter  two  thick  copper  plates  serve  as 
anode,  and  a  thin  sheet  of  copper  hung  between  them  is  the 
cathode ;  the  electrodes  are  suspended  in  a  solution  of  about 
15  per  cent,  copper  sulphate,  5  per  cent,  sulphuric  acid,  and 
5  per  cent,  alcohol,  contained  in  a  beaker.  If  the  current 
density  is  less  than  0'4  amp./sq.  dm.,  oxidation  by  the  air  has 
a  disturbing  effect.  When  the  current  density  is  small,  the 


xvi.  VOLTAMETER.  287 

voltameter  should  be  provided  with  a  cover,  and  a  current  of 
hydrogen  passed  over  the  surface  of  the  liquid.  One  coulomb 
corresponds  with  the  deposition  of  I'll 8  milligrams  of  silver, 
or  0*3284  milligram  of  copper.  One  ampere  deposits  0*06708 
gram  of  silver,  or  0'0197  gram  of  copper  in  one  minute  on 
the  cathode,  which  is  weighed  after  being  washed. 


CHAPTER    XVII. 
Development  of  Heat  by  the  Electric  Current. 

Review.  —  When  electricity  passes  through  a  circuit  con- 
sisting of  one  or  several  conductors,  a  quantity  of  heat,  W,  is 
evolved  which  can  be  calculated  from  the  formula  (see 
pp.  11  and  203)— 

W  =  0'24fc  cal. 


where  i  is  the  current  strength  (in  amperes),  and  £  the  poten- 
tial difference  (in  volts)  between  the  two  ends  of  the 
conductor.  If  the  conduction  takes  place  along  a  uniform 
metal  wire,  or  through  a  column  of  liquid,  the  heat  is 
developed  uniformly  throughout  the  conducting  material. 
If  the  circuit  is  not  homogeneous,  i.e.  if  we  have  surfaces  of 
contact  of  different  substances,  then  the  heat  is  not  equally 
distributed  over  all  parts. 

In    the    former   case   the   formula   given    can   also    be 
written  — 

W=Q'2±i*m  =  0-24—  cal. 
m 

where  m  is  the  resistance  between  the  ends  of  the  circuit. 
This  quantity  of  heat,  developed  in  a  uniform  conductor  by 
resistance  analogous  to  friction,  is  called  Joule  heat.  Besides 
this  there  occurs  a  change  of  heat  at  contact  surfaces,  e.g. 
between  metals,  which  is  known  as  the  Peltier  effect,  and 
which  is  measured  by  the  expression  — 

JFi  =  0-247T?:  cal. 
where  ir  is  the  electromotive  force  of  the  Peltier  effect. 


CHAP.  xvn.  ARC   LIGHT.  289 

It  has  also  been  shown  by  Lord  Kelvin  (1)  that  an 
electromotive  force  occurs  between  differently  tempered  parts 
of  the  same  metallic  conductor,  and  this  strives  to  conduct 
heat  from  the  warmer  to  the  cooler  part. 

This  so-called  Thomson  effect  is  very  inappreciable  for 
metals;  it  occurs  in  liquids  and  probably  also  in  gases. 
It  has  not  yet  been  very  thoroughly  investigated,  and  may 
here  be  neglected.  In  galvanic  elements  and  electrolytic 
decomposition  cells,  besides  the  Joule  heat,  a  quantity  of 
heat,  w,  is  evolved  for  each  equivalent  of  substance  taking 
part  in  the  chemical  change,  and  this  is  partially  used  up  in 
doing  work  to  send  the  current  through  the  circuit,  which 
part  is  measured  by  the  expression  23,070P.  (P  denotes  the 
electromotive  force  of  the  element,  or  of  the  decomposition 
cell,  see  p.  205.) 

The  quantity  of  heat — 

Wz  =  w  -  23,070P 

is  termed  local  heat  (or  internal  heat),  and,  like  the  Joule 
heat,  remains  in  the  element  or  vessel  (voltameter)  in  which 
the  electrolytic  process  takes  place. 

In  elements  w  is  generally  positive,  as  also  is  P;  in 
decomposition  cells  it  is  negative. 

Arc  Light. — The  greatest  development  of  heat  takes 
place  when  the  electricity  passes  through  gases.  The  passage 
may  be  disruptive,  as  in  the  spark  discharge  and  outflow  of 
electricity  from  points,  or  it  may  be  continuous  with  forma- 
tion of  an  arc  light.  In  the  former  case  the  quantity  of 
electricity  transported  is  very  small. 

The  arc  light,  or  Volta  arc,  which  is  now  so  much  used 
for  illuminating  purposes,  was  discovered  by  Volta  in 
1808,  and  afterwards  thoroughly  studied  by  several  investi- 
gators. 

Edlund  (2)  showed  that  the  potential  difference  e  between 
two  carbon  points  between  which  the  arc  is  playing  is  given 
by  the  formula — 

£  —  a  -J-  U 

u 


290 


DEVELOPMENT   OF   HEAT. 


CHAP. 


where  a  and  b  are  coefficients  which  gradually  increase  with 
the  current  strength,  and  I  is  the  length  of  the  arc. 

If  /  becomes  very  small  (0*5  mm.),  an  arc  can  be  obtained 
with  a  potential  difference  of  only  25  to  30  volts.  It  is 
difficult,  however,  to  keep  such  an  arc  going.  A  spongy 
elevation  of  carbon,  transferred  from  the  positive  carbon, 
forms  on  the  negative  carbon ;  by  this  loss  the  well-known 
crater-like  depression  is  formed  in  the  positive  carbon.  If 
the  deposit  on  the  negative  carbon  increases  much,  the  two 
carbon  points  come  into  contact,  and,  on  the  other  hand, 
if  it  falls  off,  the  length  I  suddenly  increases,  and  the  arc 
goes  out.  Ordinary  arc  lights  have  a  length  of  at  least  2  mm., 
and  generally  4  to  5  mm.,  and  require  a  potential  difference 
of  40  to  45  volts. 

Arc  lights  produced  by  a  potential  difference  of  only  30  to 
40  volts  do  not  burn  uniformly,  and  make  a  hissing  noise. 

A  certain  minimum  current  strength  is  also  required  to 
produce  a  steady  arc  light.  Arc  lights  have  been  success- 
fully produced  with  1  to  2  amperes  and  40  to  45  volts,  but  a 
very  fine  and  delicate  regulation  of  the  length  is  necessary,  and 
on  this  account  such  small  current  strengths  are  never  used 
in  practice.  To  produce  arcs  with  small  current  strengths  a 
very  good,  hard,  thin  carbon  rod  is  required.  For  arc  lamps 
the  current  strength  used  lies  between  4  and  25,  and  is  most 
frequently  8  amperes,  and  the  potential  difference  is  about 
42  volts,  the  carbon  rods  having  a  diameter  of  8  to  18  mm. 

According  to  measurements  carried  out  at  the  Electrical 
Exhibition  at  Frankfort-a-M.  in  1891,  the  maximum  length 
/  of  an  arc  when  fed  with  a  current  of  i  amperes  is  given  in 
the  following  table : — 


i  amp. 

I  mm. 

i  amp. 

I  mm. 

10 

25 

60 

94 

20 

51 

70 

102 

30 

68 

80 

104 

40 

81 

90 

112 

50 

90 

100 

114 

xvii.  ARC  LIGHT.  291 

The  length  of  the  arc  at  first  increases  rapidly  with  the 
current  strength,  then  more  slowly.  The  carbon  used  is  of 
such  a  size  that  there  is  about  O'l  ampere  per  square  milli- 
metre of  the  section. 

Uppenborn  (J)  determined  a  for  an  arc  between  carbon 
rods  of  12  mm.  diameter  to  be  38  volts,  32-5  for  the  positive, 
and  5'5  for  the  negative  pole ;  for  b  he  found  about  1  volt 
per  millimetre.  From  this  it  can  be  understood  that  the 
greater  heat  development  takes  place  at  the  positive  pole, 
which  radiates  85  per  cent,  of  the  whole  light  emitted. 
Nevertheless,  according  to  measurements  by  Violle  (4)  the 
carbon  cannot  be  heated  above  3500°  at  the  ordinary 
pressure,  for  at  this  temperature  it  volatilises  without 
previous  fusion.  The  glowing  gases  in  the  arc  are  heated 
to  a  greater  extent,  their  temperature  being  estimated  by 
Rosetti  (5)  at  about  4800°. 

Of  the  good  conducting  substances  so  far  investigated, 
carbon  resists  the  heat  best,  with  the  exception  of  some 
oxides  used  in  the  Auer-,  Jablochkoff-,  and  Nernst-lamps ; 
carbon  may  be  heated  to  3000°  without  appreciably  gasifying, 
at  a  somewhat  higher  temperature  it  becomes  soft,  and  may 
be  welded. 

The  arc  light  may  be  interrupted  for  a  short  time,  about 
Ol  second,  without  losing  its  conductivity ;  consequently 
the  arc  may  be  produced  by  an  alternating  current,  which 
is  to  be  preferred  in  electrochemical  practice  when  we  are 
concerned  with  the  production  of  heat.  In  this  case,  of 
course,  the  carbons  are  equally  heated,  and  become  equally 
corroded. 

The  possibility  of  concentrating  the  heat  in  a  small  space 
has  led  to  the  adoption  of  electrical  heating  methods  for  the 
production  of  high  temperatures,  and  by  the  aid  of  these  certain 
reactions  can  be  brought  about  which  only  take  place  when 
the  temperature  is  very  high. 

Influence  of  Temperature  on  Chemical  Reactions. 
— As  has  been  stated  in  previous  chapters,  the  temperature 
exerts  a  double  influence  on  chemical  reactions.  On  the 


292  DEVELOPMENT   OF   HEAT.  CHAP. 

one  hand,  the  velocity  of  reaction  is  generally  very  greatly 
increased  with  rising  temperature.  As  an  example  of  this 
we  may  cite  the  formation  of  water  from  a  mixture  of 
hydrogen  and  oxygen,  which  hardly  proceeds  at  all  at  the 
ordinary  temperature,  but  which  takes  place  with  explosive 
violence  above  580°.  On  the  other  hand,  a  change  of  tem- 
perature causes  a  displacement  of  the  equilibrium  which 
is  established  between  the  components  of  every  chemical 
system.  Again,  we  may  take  water  and  a  mixture  of 
hydrogen  and  oxygen  as  an  example.  Theory  (see  p.  256) 
requires  that  at  20°  a  litre  of  water  contains  0'65  x  10"27 
gram-molecules  of  hydrogen,  and  half  as  many  gram-mole- 
cules of  oxygen.  This  quantity  of  mixed  hydrogen  and 
oxygen  cannot  be  detected  by  chemical  methods,  but  from 
electrical  observations,  such  as  those  of  Helmholtz  (£),  it 
can  be  calculated.  Now,  there  must  be  an  equilibrium 
between  the  water  and  the  mixture  of  gases  dissolved  in  it  — 

2H2+02$2H20. 

If  we  denote  the  concentrations  of  the  three  substances 
by  0H)  Co,  and  (7H2o,  the  following  equations  should  be  valid 
(see  pp.  85  and  94)  :— 


2-3025  x 

where  ju  is  the  quantity  of  heat  which  is  absorbed  when  two 
mols  of  hydrogen  and  one  mol  of  oxygen  combine  to  form 
liquid  water  (  -  136,800  caL). 

The  value  of  K  applies  to  the  temperature  T\.  At  T0> 
log  K=M.  Now,  at  20°,  TQ  =  293  ;  C^  =  55'5  (=  xaon)  ; 
C*  =  0-65  x  10-27;  and  C0  =  0'33  x  10'27.  From  this  we 
obtain  — 

3/=  2  xO-81  -  2  x  28  +  0-51-28-2  x  174  =0-65-  86 


xvn.  CHEMICAL  REACTIONS.  293 

and  — 

136,800  1    (TQ  - 

~  1-99  x  2-3025  '  293  V      TI 

=  Jf+  101-3 


In  the  neighbourhood  of  20°  log  K  increases  for  every 
degree  by   -QQ-  =  0*346,  since    ft^   may  be   regarded  as 


constant,  and  log  K  increases  three  times  as  quickly  as  log 
CH,  consequently  log  C  becomes  greater  by  0*1153  for  each 
degree  ;  CH  therefore  increases  in  the  proportion  1:1-3  per 
degree,  and  reaches  a  tenfold  value  by  raising  the  tempera- 
ture by  7'7°.  At  100°  the  quantity  of  hydrogen  has  risen 
to  115  X  10  "20,  and  at  the  critical  temperature  (365°)  to 
T23  x  10  "9  gram-molecules  per  litre. 

So  long  as  water  is  present  in  the  liquid  condition  there 
is  only  an  exceedingly  small  dissociation  into  hydrogen  and 
oxygen.  From  the  above  formula  it  would  appear  also  that 
log  K  may  never  reach  a  higher  value  than  M  +  101  '3  = 
15'95,  however  high  the  temperature  be  raised,  i.e.  according 
to  the  theory,  even  at  the  highest  temperature  the  dissociation 
cannot  go  beyond  a  certain  limiting  value.  In  this,  however, 
it  is  assumed  that  no  change  of  volume  occurs,  otherwise  the 
pressure  relationships  would  have  to  be  taken  account  of. 
Now,  since  in  the  dissociation  of  water  into  hydrogen  and 
oxygen  two  molecules  give  rise  to  three,  i.e.  the  volume 
increases  (provided  that  the  pressure  is  constant,  and  that  all 
the  substances  are  present  in  the  gas  state),  the  decomposition 
must  increase  when  the  volume  becomes  greater.  If  the 
pressure  be  kept  constant,  the  volume  steadily  increases  with 
rising  temperature.  Consequently  the  gaseous  dissociation 
of  water  vapour  (at  constant  pressure)  increases  with  the 
temperature,  and  the  increase  in  the  degree  of  dissociation 
is  unlimited.  It  has  been  experimentally  found  (Deville) 
that  above  2000°  water  vapour  is  appreciably  dissociated 
(7).  This  dissociation  at  the  high  temperature  is  the  reason 


294 


DEVELOPMENT   OF   HEAT. 


CHAP. 


why,  in  the  explosion  of  a  mixture  of  hydrogen  and  oxygen, 
the  temperature  does  not  rise  so  high  as  would  be  expected 
from  the  calculation. 

As  an  example  of  a  similar,  but  more  thoroughly  studied, 
displacement  of  the  equilibrium  by  temperature  and  pressure, 
we  may  consider  the  decomposition  of  carbon  dioxide  into 
carbon  monoxide  and  oxygen,  which  takes  place  according 
to— 


2C02  $200 


'•2, 


with  evolution  of  136,000  cal.  The  volume  change  is  the 
same  as  in  the  dissociation  of  water  vapour,  and  the  heat 
change  does  not  differ  very  appreciably  from  that  found  for 
water  vapour,  116,000  cal.  The  two  equilibria  must  therefore 
be  similar  in  character,  since  the  dissociations  at  a  correspond- 
ing point  (with  respect  to  temperature  and  pressure)  are  of 
the  same  order  of  magnitude  (at  2000°,  and  1  atmo.  pressure 
carbon  dioxide  is  dissociated  to  the  extent  of  5  per  cent., 
water  to  a  slightly  greater  extent). 

Le  Chatelier  has  calculated  that,  of  100  molecules  of 
carbon  dioxide,  the  following  number  is  dissociated  at  the 
temperature  and  pressure  given : — 


Pressure  in  atmos. 

1000°. 

1500°. 

2000°. 

2500°. 

3000°. 

3500°. 

40003. 

0-001        .       . 

0-7 

7 

35 

81 

94 

96 

97 

0-01    .       .       . 

0-3 

3-5 

18* 

58* 

80 

86* 

90 

0-1      .      .      . 

0-13 

1-7 

10* 

36* 

60 

70 

80 

1  .... 

0-06 

0-8 

5* 

19 

37* 

53 

63 

10  .      .      .      . 

0-03 

0-4 

2-5* 

9 

18* 

32 

45 

100  .... 

0-015 

0-2 

1-2* 

4 

8 

15 

25 

Since  the  heat  of  dissociation  of  water  vapour  is  lower 
(in   the  ratio   12  :  14)   than   that    of    carbon    dioxide,   the 

*  As  in  the  calculations  for  the  temperature  2000°,  an  error  has 
•evidently  been  made  in  the  original  paper,  the  numbers  indicated  by  an 
asterisk  *  are  taken  from  the  curve  given  by  Le  Chatelier  (Zeit.  physikal. 
.y  1888,  2,  785)  instead  of  from  the  table. 


XVII. 


FUSED   ELECTROLYTES. 


-95 


dissociation  of  water  must  increase  more  slowly  (in  the 
ratio  12  :  14)  with  rising  temperature  than  does  that  of 
carbon  dioxide.  Most  substances  (gases)  on  decomposition 
suffer  an  increase  of  volume — the  number  of  molecules,  as 
a  rule,  is  increased  by  the  decomposition — consequently, 
heat,  which  alone  would  not  be  able  to  bring  about  the 
dissociation,  is  frequently  assisted  by  the  simultaneous 
volume  increase  which  takes  place  when  the  temperature 
is  raised. 

From  this  circumstance  it  is  easy  for  us  to  see  that  in  the 
visible  layers  of  the  sun's  atmosphere,  which  possess  a  very 
high  temperature  and  a  relatively  low  pressure,  the  substances 
are  all  decomposed  into  their  ultimate  elements.  The  metals, 
whose  presence  in  the  sun  has  been  detected  by  spectrum 
analysis,  occur  there  in  the  form  of  simple  atoms,  just  as  is 
the  case  with  these  substances  in  solution  at  the  ordinary 
temperature.  In  other  words,  in  the  sun  there  are  formed  as 
many,  and  as  light,  molecules  as  possible.  It  may  well  be, 
however,  that  in  the  interior  of  the  sun,  where  quite  enormous 
pressure  probably  obtains,  compounds  like  water  are  capable  of 
existence. 

Fused  Electrolytes.  Heroult's  Furnace. — For  the 
preparation  of  aluminium 
Heroult  (8)  constructed  a  fur- 
nace which  consists  essen- 
tially of  a  large  iron  crucible, 
Fy  provided  with  plates  of 
carbon,  C  (Fig.  50).  This  is 
filled  with  a  mixture,  B,  of 
two  parts  of  sodium  chloride 
and  one  part  of  cryolite 
(N"a3AlF6),  which  is  fused  by 
being  heated  from  below. 
When  the  mass  has  fused, 
a  bundle  of  carbon  rods,  A,  is 
introduced,  and  this  serves 
as  anode,  the  carbon  plates,  C,  being  used  as  cathode. 


296  DEVELOPMENT   OF   HEAT.  CHAP. 

When  the  current  has  begun  to  pass  through,  the  heat 
developed  is  sufficient  to  keep  the  whole  mass  molten.  As 
the  aluminium  is  separated,  alumina  (clay  or  bauxite)  or  some 
other  appropriate  material  is  introduced  through  the  openings 
H  and  HI.  The  metal  formed  is  allowed  to  flow  into  the 
receiver  U  from  time  to  time,  through  the  hole  Sy  which  can 
be  closed  by  the  rod  T. 

It  was  soon  found  that  the  aluminium  formed  in  this  way 
was  contaminated  by  particles  of  carbon  from  the  cathode  0. 
In  order  to  prevent  such  contamination,  iron  or  copper  is 
added,  and  this  collects  at  the  bottom,  Ey  of  the  crucible.  In 
this  way  valuable  aluminium  alloys  can  be  obtained.  It  was 
afterwards  found  that  pure  aluminium  could  be  obtained  by 
making  the  melt  more  mobile  in  various  ways,  as  by  the 
addition  of  lithium  fluoride  or  potassium  fluoride  [Hall 
(9)],  or  by  keeping  only  the  central  part  of  the  salt 
fused,  so  that  a  solid,  non-conducting  crust  remains  on  the 
walls  of  the  crucible,  except  at  the  very  lowest  points. 
When  the  latter  device  is  adopted,  a  special  hollowed-out 
copper  cathode  is  set  in  the  bottom  of  the  crucible,  and 
this  is  kept  cool  by  the  circulation  of  water,  so  as  to  prevent 
it  from  fusing  (Borchers).  The  possibility  of  concentrating 
the  heat  in  a  small  part  of  the  mass,  and  thus  avoiding 
contamination  from  the  walls  of  the  crucible,  which  become 
coated  with  a  solid  crust  of  the  electrolyte,  is  one  of  the  most 
important  advantages  which  electrical  heating  possesses  over 
the  ordinary  method ;  this  advantageous  property  of  the 
electric  furnace  has  been  particularly  called  attention  to  by 
Borchers  (10),  who  has  made  much  use  of  it. 

In  order  to  avoid  the  inconvenient  preliminary  heating 
of  the  material,  a  small  quantity  of  the  mixture  is  fused 
in  the  crucible  C,  by  placing  the  anode  A  in  contact  with 
the  bottom  of  the  crucible,  and  fresh  electrolyte  is  then 
added  until  the  whole  is  full.  This  introduction  of  material 
is  occasionally  regulated  by  an  apparatus  similar  to  that 
used  in  arc  lights.  When  the  resistance  between  the 
electrodes  diminishes  the  current  strength  increases,  and  in 


XVII. 


NON-ELECTROLYTIC   PROCESSES. 


297 


o 


order  to  keep  this  approximately  constant  A  is  automatically 
raised. 

Many  arrangements,  similar  to  that  used  in  the  Heroult 
process,  have  been  successfully  employed  in  the  electrolysis 
of  fused  salts.  Thus,  for  instance,  lead  is  used  in  order  to 
take  up  alkali  metals,  and  several  models  of  crucibles  have 
been  constructed  by  Borchers  for  the  preparation  of  the  alkali 
metals  from  the  fused  salts. 

Non-electrolytic  Processes  with  Electrical  Heating. 
Cowles'  Furnace. — So  long  ago  as  1815  Pepys  carried  out 
experiments  on  the  electric  cementation  of  iron  (conversion 
of  iron  into  steel,  by  allowing  carbon  to  diffuse  into  the  iron 
at  a  high  temperature).  In  this  process  the  iron  was  raised 
to  the  necessary  temperature  by  means  of  an  electric  current. 
The  brothers  Cowles  (in  1884)  (11)  were  the  first  to  introduce 
the  extensive  applications  of  the  electric  furnace.  The  furnace, 
named  after  them, 
and  which  is  so 
highly  prized  in  the 
aluminium  industry, 
has  the  construction 
shown  in  Fig.  51.  A 
hollow  block  of  fire- 
proof material,  A,  is 

provided  with  holes,  H  and  H\9  on  opposite  sides ;  through 
these  pass  two  movable  carbon  electrodes,  which,  at  first, 
are  in  contact.  The  crucible  is  furnished  with  an  iron  lid, 
and  gases  can  escape  through  an  opening,  0,  in  this.  The 
carbon  electrodes  generally  consist  of  several  (9)  rods,,  each 
65  mm.  in  diameter,  fastened  together,  and  these,  connected 
by  two  strong  cables  to  the  source  of  the  current,  can  be 
moved  by  means  of  screws.  The  mixture  of  alumina 
(bauxite),  wood,  charcoal  or  coke,  and  copper  or  iron 
clippings  is  placed  round  the  electrodes.  At  first  the 
contact  surface  of  the  electrodes  becomes  warm,  and  these 
are  then  drawn  apart,  so  that  an  arc  is  formed  or  the 
current  passes  through  the  mixture  in  contact  with  the 


FIG.  51. 


298  DEVELOPMENT   OF   HEAT.  CHAP. 

electrodes.  In  any  case  the  mixture  becomes  exposed  to  such 
a  high  temperature,  that  the  iron  or  copper  fuses,  and  the 
alumina  is  reduced  by  the  carbon  to  aluminium,  which  is 
taken  up  by  the  fused  iron  or  copper.  The  electrodes  are 
gradually  drawn  further  and  further  apart,  so  that  the 
current  strength,  read  off  on  an  interposed  ammeter,  remains 
approximately  constant — about  5000  amperes  are  usually 
employed. 

In  the  course  of  some  hours  the  whole  of  the  mixture 
will  have  undergone  reaction;  the  furnace  is  then  allowed 
to  cool,  and  the  melt  withdrawn.  One  disadvantage 
of  the  process  is  that  the  activity  of  the  furnace  is  inter- 
mittent, and  consequently  a  good  deal  of  heat  is  lost  on 
cooling. 

It  has  been  stated  that  the  Heroult  process,  which  is 
in  use  amongst  other  places  at  the  aluminium  works  at 
Neuhausen,  is  more  economical  than  the  Cowles'  process 
which  has  been  introduced  at  the  works  at  Stoke-on- 
Trent. 

In  the  Cowles'  process  direct  currents  can  be  used  just 
as  well  as  alternating  currents  without  in  any  way  inter- 
fering with  the  yield  obtained  from  the  current.  This  shows 
clearly  that  the  electrolytic  process  plays  no  real  part  in  the 
action,  which  depends  only  on  the  high  temperature  (essen- 
tial for  the  reduction  of  the  alumina)  attained  by  means 
of  the  electric  current.  In  such  cases  alternating  currents 
are  to  be  preferred  to  direct  ones,  because  then  the  process 
takes  place  uniformly  at  the  two  poles,  and  alternating 
currents  of  suitable  electromotive  force  and  strength  can 
readily  be  obtained  by  the  use  of  a  transformer.  If  a 
polyphase  current  is  employed,  as  many  electrodes  should 
be  used  as  the  current  has  phases,  e.g.  three  with  a  three- 
phase  current. 

In  the  lighting  of  a  Cowles'  furnace  we  are  reminded  of 
the  lighting  of  an  arc  lamp,  and  Maxim  (1%\  in  the  furnace 
devised  by  him,  has  introduced  lighting  on  the  same  principle 
as  that  made  use  of  in  Jablochkoff's  electrical  candle.  Two 


xvn.  RESISTANCE    FURNACES.  299 

parallel  rods  of  carbon  l  are  placed  near  the  long  side  of  the 
furnace,  and  each  is  connected  at  one  of  the  short  sides  by 
means  of  a  conducting  cable  with  the  source  of  electricity. 
In  the  neighbourhood  of  the  opposite  short  side  the  two 
carbon  electrodes  are  connected  by  a  small  rod  or  a  small 
piece  of  compressed  carbon  powder,  which  is  quickly  used 
up,  and  the  carbon  electrodes  are  gradually  drawn  out  of 
the  furnace  as  the  mass  of  material  suffers  progressive 
reaction. 

Resistance  Furnaces.  The  Carborundum  Process. — 
Instead  of  conducting  the  current  through  the  contents  of 
the  furnace,  and  thus  heating  the  substance  which  is  to 
undergo  reaction,  the  electricity  may  be  passed  through  a 
relatively  large  carbon  resistance,  which  becomes  hot,  and 
passes  the  heat  on  to  the  material  near  it. 

The  simplest  furnace  of  this  type  is  that  designed  by 
Borchers  (10).  A  thin  carbon  rod,  C  (Fig.  52),  lies  between 
two  larger  ones,  A  and  B. 

The     material     to    be    heated       )"          i        II        i          ~ 
surrounds    C,    and    a      strong      W////^///\^^ 
current  is  passed  from  A  to  B. 
A   and  B  should  be  so   thick 
that  the  current   density  does  FIG.  52. 

not  amount  to  more  than  O'l  amp.  /  sq.  mm.  The  size  of 
the  rod  C  depends  on  the  temperature  to  which  it  is  desired 
to  heat  the  mass.  A  red  heat  is  obtained  if  the  current 
density  in  C  amounts  to  0*5  amp.  /  sq.  mm.  If  it  is  ten 
times  as  large,  a  temperature  can  be  attained  at  which 
calcium  carbide  can  be  produced,  and  if  the  current  density 
reaches  10-15  amp.  /  sq.  mm.,  temperatures  of  3000  to  3500° 
can  be  reached.  Borchers  has  stated  that  there  is  no  oxide 
which  can  resist  reduction  when  the  current  density  is 
10  amp.  /  sq.  mm.  The  carbon  electrodes  A  and  B  are 
introduced  through  the  sides  of  the  furnace,  which  is  made 
of  fire-proof  material,  and  is  covered  in  the  usual  way. 

1  When  a  three-phase  current  is  used,  three  electrodes  are  introduced, 
but  otherwise  the  arrangement  is  the  same. 


3°° 


DEVELOPMENT   OF    HEAT. 


CHAP. 


In  the  preparation  of  carborundum  [Miihlhaeuser 
the  two  thick  electrodes,  A  and  B  (Fig.  53),  are  joined  by  a 
train  2  to  3  metres  long  of  coke  powder,  C  (of  4  to  5  mm. 


FIG.  53. 

diameter  granules).  At  the  ends  of  this  train  there  is  placed 
some  finer  coke  powder,  Z>,  in  order  to  ensure  good  contact 
with  the  electrodes.  The  carbon  electrodes  are  embedded, 
by  means  of  asbestos  packing,  in  the  walls  of  the  fire-proof 
furnace  U.  Under  the  influence  of  the  current  the  train  O 
more  or  less  runs  together  to  a  conducting  mass.  The 
mixture  to  be  heated,  which  consists  of  100  parts  of  carbon 
(coke  powder),  100  parts  of  sand,  and  25  parts  of  common 
salt,  is  placed  round  C.  Occasionally  12  parts  of  sawdust 
are  added  to  the  mixture,  and  the  quantity  of  sand  may  then 
be  increased  to  140  parts.  Reaction  occurs  according  to  the 
equation — 

Si02  +  3C  =  SiC  (carborundum)  -f  200. 

The  salt  serves  to  bake  together  the  unattacked  portions 
of  the  mixture.  The  process  is  generally  carried  out  with 
an  alternating  current,  and  when  it  is  finished  it  is  found 
that  round  C  there  is  an  elliptical  mass,  E,  of  crystallised 
carborundum,  but  at  the  ends  of  C  the  substance  is  amorphous. 
Outside  this  kernel  there  remains  a  layer  of  unattacked 
mixture,  and  this  in  turn  is  surrounded  by  a  layer  of  almost 
pure  salt.  Quite  close  to  C  there  is  generally  a  thin  layer  of 
graphite,  which  is  probably  produced  as  a  decomposition 
product  of  the  carborundum  at  the  excessively  high  tempe- 
rature. After  cooling,  the  carborundum  is  removed  from  the 


xvn.  ARC   LIGHT   FURNACES.  301 

furnace  and  freed  from  small  amounts  of  metallic  sulphides, 
phosphides,  and  carbides  by  treatment  with  acid — the  im- 
purities come  from  the  foreign  substances  present  in  the  coke 
and  sand  used. 

Arc  Light  Furnaces. — In  recent  times  the  enormous 
heat  developed  by  the  arc  light  has  been  used  for  bringing 
about  such  chemical  processes  as  require  an  extremely  high 
temperature.  This  was  first  applied  in  the  melting  and 
refining  of  difficultly  fusible  metals.  As  there  is  a  greater 
development  of  heat  at  the  positive  pole  than  at  the  negative 
the  substance  to  be  fused  is  placed  in  direct  contact  with  the 
the  positive  pole.  Many  special  constructions  have  been 
suggested  for  carrying  this  out.  In  many  cases  it  is  necessary 
to  provide  the  electrodes  with  some  form  of  interior  cooler, 
in  order  to  make  them  last  (see  p.  296). 

The  arc  light  furnaces  are,  however,  far  more  important, 
both  in  industry  and  science,  when  so  arranged  that  the 
heat  of  the  arc  itself  is  the  active  factor.  In  such  furnaces 
use  is  made  of  the  property  which  the  arc,  like  all  movable 
conductors  through  which  a  current  is  passing,  possesses 
of  being  influenced  by  an  electro-magnet.  A  conductor 
through  which  a  current  is  passing,  and  which  is  perpen- 
dicular to  the  lines  of  force  of  a  magnetic  field,  moves  so 
as  to  cut  the  lines  of  force  from  right  to  left  as  seen  by  a 
person  supposed  to  be  swimming  in  the  direction  of  the 
current,  and  facing  in  the  direction  opposite  to  that  of  the 
lines  of  force. 

If  the  magnetic  field  is  very  strong,  and  the  current 
producing  the  arc  light  comparatively  weak,  the  arc  may 
be  so  much  affected  by  this  attraction  that  it  goes  out. 
(Tesla's  method  of  preventing  a  series  of  consecutive 
electric  sparks  from  following  a  track  is  based  on  this 
phenomenon.) 

The  electromagnet  is  so  arranged  that  the  arc  is  attracted 
downwards,  and  thus  comes  into  contact  with  the  material 
to  be  heated.  The  longest  path  through  which  the  arc  is 
deflected  is  met  with  in  Zerener's  "  electric  blowpipe "  (14), 


302 


DEVELOPMENT   OF    HEAT. 


CHAP. 


where  a  strong  current  circulating  between  two  carbon  poles, 
A  and  B  (Fig.  54),  is  so  influenced  by  an  electromagnet,  E, 
fixed  perpendicularly  to  the  plane  in  which  A  and  B  lie,  that 
a  pointed,  highly  deflected  arc,  L,  is  formed.  The  point  of 
this  arc  is  directed  against  the  substance  S,  which  is  con- 
tained in  the  fire-proof  furnace  U.  This  principle  has  been 
used  by  Lejeune  and  Ducretet  in  the  furnace  constructed  by 
them  (Fig.  55).  In  this  furnace  any  gas  may  be  introduced 


FIG.  54. 


FIG.  55. 


through  the  side  tube  R ;  it  is  provided  on  two  sides  with 
mica  windows,  so  that  the  process  taking  place  inside  may 
be  observed.  The  crucible  is  filled  through  the  opening  0, 
which  can  be  closed  by  the  plug  P.  The  crucible  U,  con- 
taining the  reaction  mixture,  can  be  moved  up  or  down 
by  means  of  the  screw  V.  The  arc  formed  between  A 
and  B  is  directed  by  the  aid  of  an  electromagnet  placed 
outside. 

Moissan's  furnace  (1-5)  differs  from  the  one  just  described, 
inasmuch  as  the  carbon  electrodes  are  placed  horizontally, 
and  the  charge  can  be  introduced  through  a  slightly  bent 
carbon  tube,  which  is  fixed  on  the  side  of  the  furnace,  whose 
walls  are  made  of  lime. 

Zerener's  electrical  blowpipe  was  originally  constructed 
for  soldering  and  welding,  but  in  recent  times  it,  as  well  as 


xvii.        PRODUCTION   OF   CALCIUM    CARBIDE.          303 

the  other  two  furnaces  mentioned,  has  been  an  important 
piece  of  apparatus  in  the  laboratory.  In  this  connection  we 
need  only  recall  Moissan's  comprehensive  investigations,  in 
which  he  has  succeeded  for  the  first  time  in  producing 
several  metals  and  carbides  in  a  pure  state. 

Production  of  Calcium  Carbide. — Within  the  last  few 
years  calcium  carbide,  used  in  the  preparation  of  acetylene, 
has  obtained  an  ever-increasing  economic  importance.  The 
calcium  carbide  industry  has,  no  doubt,  a  great  future  before 
it,  especially  in  countries  where  water-power  is  easy  to 
obtain. 

Calcium  carbide  is  produced  by  heating  a  mixture  of  56 
parts  of  lime  and  36  parts  of  coal  to  a  temperature  of  about 
2000°.  The  reaction  takes  place  according  to  the  equation— 

CaO  +  3C  =  CaC2  (Calcium  carbide)  +  CO. 

Instead  of  lime,  an  equivalent  quantity  of  limestone 
(CaC03)  may  be  used,  since  at  the  high  temperature  this  is 
dissociated  into  lime  and  carbon  dioxide.  If  an  insufficiency 
of  coal  be  taken,  metallic  calcium  is  formed,  and  this,  dis- 
solving in  the  carbide,  gives  rise  to  certain  difficulties.  On 
the  other  hand,  an  excess  of  coal  contaminates  the  carbide 
and  hinders  its  proper  fusion.  Furthermore,  the  lime  used 
should  be  almost  free  from  sulphates  and  phosphates,  other- 
wise sulphides  and  phosphides  are  formed,  which  render 
the  acetylene  prepared  from  the  carbide  impure,  and  must 
be  removed.  The  presence  of  magnesia  in  the  lime  also 
interferes  with  the  fusion  of  the  carbide.  If  the  furnace 
used  is  first  coated  with  coal,  this  is  partially  attacked,  and 
10  per  cent,  less  coal  is  introduced  into  the  charge;  the 
charge  is  put  into  the  furnace  in  the  form  of  small  lumps  of 
coal  and  lime  about  the  size  of  a  hazel-nut. 

Calcium  carbide  is  comparatively  easy  to  prepare,  and  a 
number  of  types  of  furnace  for  its  production  have  been 
invented,  amongst  which  is  the  resistance  furnace  of  Borchers 
mentioned  above.  The  furnace  constructed  by  Eathenau 
(16)  consists  of  a  containing  vessel,  UU  (Fig.  56),  provided 


304 


DEVELOPMENT   OF   HEAT. 


CHAP. 


with  carbon  plates,  A  ;  a  thick  carbon  rod,  K,  stands  upright 
in  the  middle,  and  is  surrounded  by  the  carbon  plates  B  and 
B\.  The  charge  S  is  introduced  between  K  and  B,  and  it 
gradually  sinks  as  it  is  transformed  into  a  liquid  mass,  T,  by 


FIG.  56. 

the  action  of  the  arc  light  /.  The  large  quantity  of  gas 
evolved  escapes  through  the  channels  V  and  V\  between  A 
and  BBi. 

If  the  fused  carbide  is  not  run  off  at  a  tap-hole,  the 
molten  mass  must  be  allowed  to  cool  after  some  time,  and 
the  process  thus  becomes  discontinuous.  As  the  melting 
point  of  the  carbide  is  high,  and  its  heat  conductivity  is 
small,  it  is  extremely  difficult  to  prevent  stopping  up  of  the 
tap-hole. 

Furnaces  have  been  constructed  which  can  be  continu- 
ously worked,  although  they  theoretically  functionate  dis- 
continuously.  King's  furnace  is  of  this  type ;  in  it  the 
hearth  consists  of  an  iron  box,  covered  inside  with  plates 
of  carbon,  and  mounted  on  wheels  which  run  on  rails.  A 
receiver  of  this  sort  forms  one  of  the  poles,  and  it  is  run  in 
under  the  other  pole  consisting  of  a  bundle  of  carbon  rods, 
which  are  then  lowered  so  as  to  form  an  arc.  The  charge 
is  introduced  through  channels  into  the  carriage,  and  is 
gradually  transformed  into  carbide.  When  the  carriage  is 
full  it  is  removed,  and  its  place  taken  by  a  fresh  one. 
The  whole  apparatus  is  set  in  a  large  furnace  built  of 
fire-proof,  bad-conducting  material,  and  provided  with  an 


xvn.          SILENT   ELECTRICAL   DISCHARGES.  305 

opening  for  the  receiver  to  pass  through.  This  process  is 
carried  on  with  success  in  the  works  at  Niagara. 

Another  type  of  furnace  worthy  of  attention  is  that 
devised  by  Memmo  (17).  The  space  in  which  the  fusion 
takes  place  consists  of  a  prismatic  iron  receiver,  A,  covered 
inside  with  plates  of  carbon,  and  closed  at  the  bottom  by  a 
plate  of  graphite,  B,  resting  on  an  iron  plate ;  the  bottom 
can  be  raised  or  lowered  by  means  of  a  toothed- wheel 
arrangement.  Two  electrodes,  CC  (with  a  three-phase 
current  three  electrodes  are  used),  are  so  placed  in  the  walls 
of  the  iron  receiver  A  that  an  arc  light  is  formed  between 
them  immediately  above  the  plate  B.  The  charge  is  put 
into  a  chimney  arrangement,  D,  above  A,  and  is  lowered  into 
the  receiver  as  required  by  a  scoop-shaped  feeder.  In  the 
path  of  the  arc  some  carbide  is  formed,  and  this  flows  over 
the  graphite  plate  and  gradually  solidifies  as  B  is  lowered. 
A  fresh  charge  is  then  introduced,  and  in  this  way  there  is 
an  almost  continuous  production  of  carbide  between  the 
electrodes  CC.  A  solid  column  of  carbide  is  formed,  the 
upper  level  of  which  is  kept  at  a  constant  height.  When 
the  bottom  plate  B  has  been  lowered  to  a  certain  depth, 
the  top  part  of  the  column  is  supported  by  a  plate  intro- 
duced from  the  side,  and  the  lower  portion  is  then  cut  out. 
When  this  lower  portion  has  been  removed,  the  plate 
B  is  pushed  up,  the  side  support  withdrawn,  and  the  process 
continued. 

The  carbon  monoxide  which  is  evolved,  and  the  air 
which  is  heated  by  the  hot  carbide,  are  each  led  up  through 
a  tube  into  D,  and  thus  the  charge  is  preliminarily  heated 
before  being  introduced  into  the  furnace.  The  same  gases 
may  also  be  used  for  heating  the  space  A,  in  which  the 
fusion  takes  place. 

Silent  Electrical  Discharges. — If  the  conductor  of 
a  Holtz  electrical  machine  be  connected  to  a  point,  the 
electricity  flows  out  through  this,  and  a  so-called  electrical 
wind  is  formed. 

In  a  dark  room  a  small  ball  of  light  can  be  seen  at  the 

x 


306  DEVELOPMENT   OF   HEAT.  CHAP. 

point,  which  may  assume  the  form  of  a  brush  (aigret)  if  there 
be  a  sufficient  outflow  of  positive  electricity.  The  discharge 
is  discontinuous,  as  can  easily  be  proved  by  making  use  of 
a  rotating  mirror ;  the  hissing  noise  also  indicates  that  the 
discharge  is  discontinuous.  When  the  discharge  takes  place 
in  the  air  a  smell  of  ozone  becomes  perceptible  ;  many  other 
chemical  actions  are  also  brought  about  by  this  action  of 
points.  For  instance,  in  the  air  some  oxidation  products  of 
nitrogen  are  formed  as  well  as  ozone ;  in  acetylene,  benzene 
is  formed ;  in  an  atmosphere  of  carbon  monoxide  and  water 
vapour  combination  takes  place,  and  formic  acid  is  produced, 
if  carbon  dioxide  is  used  oxygen  is  evolved  (this  reaction 
corresponds  with  the  process  of  vegetation) ;  nitrogen  and 
hydrogen  give  ammonia,  which  is  again  partially  decom- 
posed ;  sulphur  dioxide  and  oxygen  give  sulphur  trioxide ; 
cyanogen  and  hydrogen  give  hydrocyanic  acid ;  and  nitrogen 
and  oxygen,  in  presence  of  water,  give  ammonium  nitrate, 
a  compound  whose  presence  has  also  been  detected  after 
lightning. 

The  same  reactions  can  also  be  brought  about  by  a  spark 
discharge,  which  only  differs  from  the  "  silent  "  or  "  dark  " 
discharge  in  its  greater  intensity.  A  gas  may  be  brought 
to  the  glowing  point  when  it  is  enclosed  between  two 
condenser  plates  separated  by  an  insulator  (e.g.  glass),  when 
these  are  connected  with  the  poles  of  a  high  tension  alternat- 
ing current  machine.  In  this  case  there  is  formed  a  com- 
paratively large  quantity  of  ozone,  as  in  the  discharge  from 
the  poles  of  a  Tesla  alternating  current  machine. 

The  most  remarkable  method  of  bringing  about  chemical 
actions  by  the  silent  discharge  is  that  found  by  Berthelot 
(18).  The  apparatus  devised  by  him  is  shown  in 
Fig.  57.  Two  thin- walled  glass  tubes,  a  and  I,  are  arranged 
concentrically  one  within  the  other.  The  outer  tube  1)  is 
furnished  at  its  upper  end  with  side  tubes,  c  and  d,  and 
immediately  above  these  it  is  sealed  on  to  a.  The  tube  a  is 
filled  with  sulphuric  acid,  and  b  is  immersed  in  a  cylinder 
filled  with  the  same  liquid.  When  solid  substances  are  to 


xvn.        THERMIC   AND   CHEMICAL   ACTIONS.          307 

be  investigated  they  are  introduced  into  c  (between  a  and  b)  ; 
gases  are  introduced  through  c  or  d.  (A  later  construction, 
in  which  d  is  continued  into  the  apparatus  and  ends  near  e, 
is  evidently  more  suitable  when  gases  are  used.)  The  inner 

and    outer    layers   (sulphuric    acid)    of    this  + 

Leyden  jar  are  connected  each  with  one  pole 
of  a  galvanic  battery.  After  introducing  the 
substance  to  be  investigated,  c  and  d  are 
closed. 

Berthelot  succeeded  in  bringing  about  quite 
remarkable   actions  with   a   potential   differ- 
ence between  the  two  acids  of  only  8  volts, 
although  a  single  experiment  required  several 
months.    The  apparatus  was  afterwards  used  by 
others,  but  much  higher  potential  differences         FlG-  57> 
or  high-tension   alternating   currents   were   invariably   em- 
ployed. 

Electrothermic  and  Electrochemical  Actions. — All 
the  conditions  of  experiment  mentioned — except  those 
applied  by  Berthelot,  the  actions  of  which  have  not  yet  been 
explained — agree  in  this  respect,  that  for  an  exceedingly 
short  time  a  gas  is  heated  to  the  glowing  point  and  then 
cools.  Judging  from  the  spectra  of  gases  glowing  under  the 
influence  of  action  of  points,  sparks,  or  electrical  oscillations, 
the  temperature  at  certain  times  is  much  higher  than  that  of 
the  arc  light.  This  is  concluded  from  the  fact  that  the  spark 
spectrum  excels  the  arc  spectrum  in  number  of  lines  and 
brilliancy  just  as  the  arc  spectrum  excels  that  obtained  with 
a  Bunsen  burner.  Of  course,  quantitative  differences  exist 
between  the  phenomena  of  the  action  of  points,  spark  dis- 
charge, and  vibrations  in  the  ether,  in  so  far  as  the  heat 
effect  is  concerned,  according  to  the  greater  or  smaller 
quantity  of  energy  possessed  by  the  discharge ;  but  all  must, 
as  the  spectra  prove,  produce,  during  a  very  short  time,  a 
higher  temperature  than  the  arc  light. 

At  these  high  temperatures  chemical  reactions  proceed  in 
quite  a  different  direction  from  that  taken  at  the  ordinary 


308  DEVELOPMENT   OF   HEAT.  CHAP. 

temperature,  and  the  velocity  is  also  much  greater.  During 
the  extremely  short  time  of  heating,  the  gas  pressure  cannot 
come  into  equilibrium  with  that  of  the  surrounding  atmo- 
sphere, and  it  is  assumed  that  the  pressure  of  the  gas  stands 
in  about  the  same  ratio  to  that  of  the  surrounding  atmosphere 
as  the  corresponding  absolute  temperatures  do  to  each  other, 
i.e.  about  20  : 1.  After  the  short  heating  a  sudden  cooling 
takes  place,  so  that  the  products  of  the  reaction  are  pre- 
vented from  passing  back  into  the  original  condition  during 
the  cooling  interval.  The  conditions  striven  after  by  Sainte 
Claire-Deville  and  his  pupils  by  other  methods  ["the  hot 
and  cold  tube  "]  (19),  are  in  these  cases  fulfilled  to  a  large 
extent,  namely,  heating  the  substance  to  a  very  high  degree, 
and  suddenly  cooling,  so  that  further  reaction  with  total 
decomposition  is  prevented. 

Besides  the  electrothermic  process,  others  of  a  truly 
electrochemical  character  take  place.  In  1849,  Perrot 
showed  that  a  series  of  sparks  from  an  induction  machine  can 
electrolyse  water  vapour  so  that  oxygen  collects  at  the  anode 
and  hydrogen  at  the  cathode,  and  indeed  in  the  proportions 
required  by  Faraday's  law.  This  observation  has  been 
recently  confirmed  by  Liideking  (20)  and  by  J.  J.  Thomson 
(21).  An  electrothermic  decomposition  also  takes  place 
so  that  electrolytic  gas  (a  mixture  of  hydrogen  and  oxygen) 
is  produced  at  both  poles.  The  electrothermic  evolution  of 
electrolytic  gas  is  often  much  greater  than  the  electrolytic, 
and  can,  of  course,  be  distinguished  from  this. 

I  (22)  have  shown  that  gases  are  often  electrolytically 
dissociated,  as  in  the  case  of  the  vapours  produced  from 
alkali  salts  in  a  Bunsen  burner.  All  salts  of  the  same  metal 
conduct  equally  well ;  probably  on  account  of  the  large 
amount  of  water  vapour  present  the  salts  are  as  good  as 
completely  converted  into  hydroxides.  With  respect  to  con- 
ductivity, the  series  is  :  thallium,  lithium,  sodium,  potassium, 
rubidium,  and  caesium,  of  which  the  last  is  the  best  conductor. 
The  rubidium  and  caesium  (hydroxide)  vapours  are  so  strongly 
dissociated  that  their  conductivity  at  extreme  dilution  can 


xvn.  PRODUCTION   OF   OZONE.  309 

be  calculated;  these  compounds  follow  exactly  Ostwald's 
dilution  law.  This  is  also  the  case  for  the  other  salts  whose 
conductivity  is,  therefore,  proportional  to  the  square  root  of  the 
concentration.  Two  metal  poles  (of  nickel,  copper,  iron,  or 
platinum)  placed  in  a  flame  containing  such  a  vapour  showed 
a  potential  difference  which  approximated  to  that  which 
would  be  obtained  in  an  aqueous  solution.  No  polarisation 
could  be  observed,  which  is  probably  due  to  the  strong  "  polar- 
isation current ; "  quite  the  same  observation  is  made  with 
fused  electrolytes  and  glowing  oxides.  For  small  electro- 
motive forces  (up  to  0*5  volt)  the  current  strength  is  nearly 
proportional  to  this  force,  but  it  afterwards  increases  much 
more  slowly,  probably  on  account  of  an  insufficiency  of 
gaseous  ions.  Besides  the  electrolytic  conduction,  there  is 
also  a  so-called  connective  conduction  through  the  particles 
which  become  charged  at  one  electrode  and  are  discharged 
at  the  other.  In  the  case  of  the  salts  of  the  alkaline  earth 
metals  this  convective  current  is  much  greater  than  the 
electrolytic,  and  with  other  salts  the  electrolytic  conduction 
in  the  Bunsen  flame  cannot  be  detected. 

At  the  ordinary  temperature  gases  assume  an  electrolytic 
conductivity  under  the  influence  of  ultraviolet,  Eontgen,  or 
Becquerel  rays.  So  far  as  the  investigations  on  this  subject 
go,  it  has  been  found  that  here,  too,  the  laws  of  electro- 
motive effect  between  two  metals,  Ostwald's  dilution  law, 
etc.,  apply  just  as  well  as  for  electrolytes  in  solution.  The 
electrolytic  conductivity  of  gases  is  not  yet  of  any  practical 
interest. 

Production  of  Ozone. — The  production  of  ozone  by  the 
silent  electrical  discharge  is  of  practical  importance.  This 
substance  is  frequently  found  at  the  anode  of  an  electrolytic 
bath.  Thus,  McLeod  (23)  found  that  by  working  with  an 
extremely  high  current  density  he  obtained  an  anode  gas 
containing  up  to  17 '4  per  cent,  of  ozone  ;  the  anode  consisted 
of  a  so-called  Wollaston  point,  i.e.  a  fine  platinum  wire  fused 
into  a  glass  tube  so  that  only  the  end  remained  free.  Traces 
of  ozone  are  found  in  the  arc  light  in  which  a  number  of  gas 


310  DEVELOPMENT   OF   HEAT.  CHAP. 

reactions  can  be  realised  which  are  characteristic  of  the  silent 
electrical  discharge. 

The  ozoniser  devised  by  von  Babo  (24)  has  the  form 
shown  in  Fig.  58.  Metal  wires  are  inserted  into  glass  tubes 
sealed  at  one  end,  and  they  are  alternately  connected  with 
the  poles  of  an  induction  coil.  When  the  coil  is  in  action, 
electrical  oscillations  arise  in  the  capillary  spaces  between 
the  glass  tubes,  and  these  ozonise  the  air.  A  current  of  air 
passed  through  a  tube  containing  the  wires  is  therefore 
ozonised.  From  a  large  number  of  experiments  with  ozon- 
isers  of  this  type  it  has  been  found  that  the  presence  of  a 


Aif  Air  and  ozone 

FIG.  58. 

small  quantity  of  water  vapour  favours  the  production  of 
ozone,  whilst  a  large  quantity  (or  carbon  dioxide)  has  a  dis- 
turbing effect.  The  air  to  be  ozonised  is,  therefore,  dried  with 
some  not  too  hygroscopic  substance  (sulphuric  acid  at  the 
ordinary  temperature,  or  calcium  chloride  at  temperatures 
below  0°).  Low  temperature  favours  the  formation  of  ozone 
because  the  amount  formed  is  not  then  so  easily  decomposed 
as  at  higher  temperatures.  The  air  should  be  free  from  dust, 
as  the  ozone  in  oxidising  this  is  destroyed.  The  yield  of 
ozone  diminishes  with  decreasing  pressure;  since  ozone 
occupies  f  of  the  volume  of  the  oxygen  from  which  it  is 
formed,  increase  of  pressure  must  favour  its  formation  (see 
p.  99). 

Working  at  the  pressures  and  temperatures  given  in  the 
table,  Hautefeuille  and  Chappuis  (,?-5)  obtained  the  following 
percentages  by  weight  of  ozone  : — 


XVII. 


PRODUCTION   OF   OZONE. 


Pressure  of 
the  oxygen. 

Temperature. 

mm.  Hg. 

-23°. 

0°. 

20°. 

100°. 

760 

21-4 

14-9 

10-6 

380 

20-4                 15-2 

12-5 

1-17 

300 

20-1                 15-2 

11-2 

— 

225 

19-1                 15-3 

10-4 

1-18 

180 

18-1 

13-7 

8-9 

— 

The  presence  of  chlorine  or  oxidation  products  of  nitrogen 
hinders  the  formation  of  ozone.  Presence  of  hydrogen  pro- 
motes the  yield,  if  formation  of  water  be  rigidly  avoided  (i.e. 
if  the  tension  is  not  too  high).  Silicon  fluoride  greatly  aids 
the  formation.  If  an  induction  apparatus  be  used,  the 
current  must  not  be  made  and  broken  too  many  times  per 
second,  otherwise  it  is  not  possible  to  keep  the  air  sufficiently 
cool.  Shenstone  (26)  recommends  16  breaks  per  second  ; 
but,  of  course,  if  the  air  be  changed  rapidly  this  number  may 
be  increased. 

The  Siemens  and  Halske  ozoniser  consists  of  two  con- 
centric tubes,  coated  inside  and  outside,  separated  by  a 
thin  mica  plate  placed  close  to  the  inside  of  the  outer  tube, 
and  by  a  narrow  space  through  which  the  air  to  be  ozonised 
must  pass.  The  apparatus  is  very  similar  to  the  Berthelot 
tube.  It  works  with  an  alternating  current  of  6500  volts ; 
the  yield,  i.e.  the  quantity  of  heat  consumed  in  the  ozone 
formation  (36,000  cal.  for  48  grams)  corresponds  with  only  2*2 
per  cent,  of  the  electrical  energy  spent.  The  yield  is,  how- 
ever, nine  times  as  great  as  that  calculated  on  the  assumption 
that  the  process  is  an  electrolytic  one  which  follows  Faraday's 
law.  The  inner  tube  of  the  ozoniser  is  kept  cold  by  a  current 
of  water. 

Andreoli  (27)  has  recently  described  an  ozoniser  which 
is  said  to  give  a  yield  of  ozone  about  five  times  as  great  as 
the  apparatus  of  Siemens  and  Halske,  namely,  up  to  120 
grams  of  ozone  per  kilowatt-hour.  The  apparatus  consists  of 
a  number  of  square  aluminium  plates  of  about  70  cm.  length 


312  DEVELOPMENT   OF   HEAT.         CHAP.  XVH. 

of  side.  Alternate  plates  are  smooth,  and  the  others  are 
in  the  form  of  a  grid,  made  up  of  80  pieces  of  notched 
aluminium  strips,  each  of  which  possesses  111  points.  The 
smooth  and  grid  plates  are  separated  by  thin  plates  of  glass. 
Five  pairs  of  these  are  combined  to  one  system.  A  combina- 
tion of  eight  such  systems,  when  actuated  by  an  induction 
coil  whose  primary  current  was  5*9  amperes  at  a  tension  of 
85  volts — i.e.  absorbed  500  watts — and  whose  secondary 
current  was  at  a  tension  of  3000  volts,  gave  60  grams  of 
ozone  per  hour.  The  air  is  blown  through  the  various 
systems ;  on  account  of  the  small  amount  of  energy  trans- 
formed, no  particular  cooling  apparatus  is  said  to  be 
required. 


LITERATURE    REFERENCES. 


CHAPTER  II. 

{1}  Faraday  :  Ostwcdd's  Klassiker,  No.  87. 

(£)  Hittorf  :  Ostwald's  Klassiker,  Nos.  21  and  22. 

(3)  Helmholtz  :  Faraday  Lecture,  •"  On  the  Modern  Development  of 

Faraday's  Conception  of  Electricity."     J.  Chem.  Soc.,  1881, 

39,  277. 


CHAPTER  III. 

(1)  De  Vries:  Zeit.  phys.  Chem.,  1888,  2,  414. 

(2)  M.  Traube  :  Arch.f.  Anatomie  und  Physiologic,  1867,  87. 
(3}  Pfeffer :  "  Osmotische  Untersuchungen,"  Leipsic,  1877. 

(4)  van't  Hoff :  Ostwald's  Klassiker,  No.  110. 

(5)  Ramsay  :  Phil.  Mag.,  1894,  38,  206.     See  also  Arrhenius  :  Zeit. 

phys.  Chem.,  1889,  3,  119. 

(6)  Hamburger  :  Zeit.  phys.  Chem.,  1890,  6,  319. 

(7)  Hedin:  Zeit.  phys.  Ch,em.,  1895,  17,  164;  1896,  21,  272. 

(8)  Tammann  :   Wied.  Ann.,  1888,  34,  229. 

(9)  Adie  :  J.  Chem.  Soc.,  1891,  59,  344. 

(10)  Koppe  :  Zeit.  phys.  Chem.,  1895,  16,  261;  1895,  17,  552. 


CHAPTER  IV. 

(1)  van't  Hoff.     See  (4),  Chap.  III. 

(2)  Arrhenius  :  Zeit.  phys.  Chem.,  1889,  3,  115. 

(3)  Raoult:  Zeit.  phys.  Chem.,  1888,  2,  353. 

(4)  van't  Hoff:  Zeit.  phys.  Chem.,  1887,  1,  481. 

(5)  Tammann:  Mem.  Acad.  Peterb.,  1887,  35,  (9). 


CHAPTER  Y. 


(/)  Guldberg:  Compt.  rend.,  1870,  70,  1349. 
(2)  van't  Hoff.     See  (4),  Chap.  III. 


3H  LITERATURE    REFERENCES. 

(3)  Juhlin  :  Stockholmer  Akad.  Bihang,  1891,  17,  (I),  1. 

(4)  Beckmann:  Zeit.  phys.  Chem.,  1888,  2,  638,  715. 

(5)  Beckmann  :  Zei£.  phys.  Chem.,  1889,  4,  543;  1891,  8,  223. 

(6)  Eykmann:  Zeit.  phys.  Chem.,  1888,  2,  964;  1889,  3,  113,  203; 

1889,  4,  497. 

(7)  Raoult :  Compt.  rend.,  1882,  94,  1517  ;  1882,  95,  188.  Ann.  Chim.. 

Phys.,  1884  (vi),  2,  66. 

(8)  Beckmann  :  Zeit.  phys.  Chem.,  1890,  6,  439. 

(9)  See  Walden  and  Centnerszwer  :  Zeit.  phys.  Chem.,  1902,  39,  558- 

565. 

(10)  Beckmann  :  Zeit.  phys.  Chem.,  1888,  2,  715. 

(11)  Ramsay:  J.  Chem.  Soc.,  1889,  55,  521;  Zeit.  phys.  Chem.,  1889, 

3,  359. 

(12)  Tammann  :  Zeit.  phys.  Cliem.,  1889,  3,  441. 

(13)  Hey  cock  and  Neville  :  J.  Chem.  Soc.,  1889,  55,  666 ;  1890,  57,  376, 

656 ;  1892,  61,  888  ;  1897,  71,  383. 

(14)  Roberts- Austen  :  Proc.  Roy.  Soc.,  1896,  59,  283;  Phil.   Trans., 

1896,  187,  383. 

(15)  G.  Meyer :  Wied  Ann.,  1897,  61,  225. 

(16)  See  van  Bijlert :  Zeit.  phys.   Chem.,   1891,  8,   343;  Beckmann: 

Zeit.  phys.  Chem.,  1897,  22,  609. 

(17)  van't  Hoff :  Zeit.  phys.  Chem.,  1890,  5,  322. 

(18)  Bruni :  Atti.  R.   Acad.   Line.  Roma,  1898  (v),  7,  166.     See  also 

Bruni  and  Gorn-i :  Atti.  R.  Acad.  Line.  Roma,  1899  (v),  8, 
454,  570 ;  1900  (v),  9,  151. 

(19)  Beckmann:  Zeit. phys.  Chem.,  1890,  6,  437. 

(20)  Beckmann  :  Zeit.  phys.  Chem.,  1890,  5,  76;  1895,  17,  107. 

(21)  Biltz  and  V.  Meyer  :  Zeit.  phys.  Chem.,  1888,   2,  920.     >SV  «/*<> 

Biltz  and  Preuner  :  Zeit.  phys.  Chem.,  1901,  39,  323. 

(22)  Hamburger.     See  (6),  Chap.  III. 

(23)  Dieterici :  Wied.  Ann.,  1891,  42,  513 ;  1893,  50,  47. 

(24)  Nilson  and  Pettersson :  Zeit.  phys.  Chem.,  1888,  2,  657. 


CHAPTER  VI. 

(1)  Reicher  :  Zeit.  Kryst.  Min.,  1884,  8,  593. 

(2)  W.  Gibbs  :  Trans.  Connecticut  Acad.,  1874-1878,  III,  108,  343. 
(5)  van'fc  Hoff.     See  (4],  Chap.  III. 

(4)  Berthelot  and  Jungfleisch :    Ann.  Chim.   Phys.,    1872  (iv),   26, 

396,  408. 

(5)  See  Nernst :  Zeit.  phys.  Chem.,  1891,  8,  110. 

(6)  Nernst :  Zeit.  phys.  Chem.,  1890,  6,  16. 

(7)  Guldberg  and  Waage  :  Oswald's  Klassiker,  No.  104. 

(8)  Lemoine  :  Ann.  Chim.  Phys.,  1877  (v),  12,  145. 

(9)  Berthelot  and  P^an  de  St.  Gilles :  Ann.  Chim.  Phys.,  1862,  65  ; 

1862,  66;  1863,  68. 


LITERATURE   REFERENCES.  315 

(10)  van'tHoff:  Ber.,  1877,  10,  669. 

(11)  van't  Hoff :  Kongl.  Svenska.  Akad,  Handl,  1886,  38. 

(12)  Nordenskiold  :  Pogg.  Ann.,  1869,  136,  309. 

(13)  van't  Hoff :  Zeit.  phys.  Chem.,  1889,  4,  62. 

(14)  Etard  and  Engel :  Compt.  rend.,  1884,  98,  993,  1276,  1432;  1887, 

104,  1614  ;  1888,  106,  206,  740. 

(15)  Troost  and   Hautefeuille :    Compt.   rend.,   1871,   73,   563;    Ann. 

Chim.Phys.,  1876  (v),  9,  70. 

(16)  Ditte  :  Compt.  rend.,  1872,  74,  980. 

(17)  Kniipffer:  Zeit.  phys.  Chem.,  1898,  26,  255. 

(18)  A.  Klein  :  Zeit.  phys.  Chem.,  1901,  36,  360. 

(19)  Bunsen  :  Pogg.  Ann.,  1850,  81,  562. 

(20)  Tammann:   Wied.  Ann.,  1897,  62,  280;  1898,  66,  473;  1899,  68, 

553,  629.     Drud.  Ann.,  1900,  2,  1,  3,  161. 

(21)  F.  Braun  :  Zeit.  phys.  Chem.,  1887,  1,  259. 


CHAPTER  VII. 

(1)  V.  Meyer:  Lieb.  Ann.,  1892,  269,  49;  Zeit.  phys.  Chem.,   1893, 

11,  28;  Ber.,  1893,  26,  2421. 

(2)  Wilhelmy  :  Ostwald's  Klassiker,  No.  29. 

(3)  Madsen  :  Zeit.  phys.  Chem.,  1901,  36,  290. 

(4)  Noyes  and  Whitney :  Zeit.  phys.  Chem.,  1897,  23,  689.  i  See  aUo 

Bruner  and  Tolloczko :  Zeit.  phys.  Chem.,  1900,  35,  283. 
Zeit.  anorg.  Chem.,  1901,  28,  314. 

(5)  Tammann :  Zeit.  phys.  Chem.,  1897,  24,  152 ;  1898,  25,  441 ;  1898, 

26,  307 ;  1899,  29,  51. 
(6')  H.  A.  Wilson  :  Phil.  Mag.,  1900  (v),  50,  238. 

(7)  Arrhenius  :  Zeit.  phys.  Chem.,  1889,  4,  226. 

(8)  Ericson-Aure'n  :  Zeit.  anorg.  Chem.,  1898,  18,  83 ;  1901,  27,  209. 

Ericson-Auren  and  Palmaer  :  Zeit.  phys.  Chem.,  1901,  39,  1. 
(9}  Bothmund  :  Zeit.  phys.  Chem.,  1896,  20,  170. 

(10)  Guldberg  and  Waage  :  J.  pr.  Chem.,  1879,  19,  83. 

(11)  Ostwald  :  J.  pr.  Chem.,  1885,  31,  115.     See  also  Arrhenius :  Zeit. 

phys.  Chem.,  1899,  28,  317. 

(12)  Tammann  :  Zeit.  phys.  Chem.,   1892,  9,  106.     See   also  Steiner  : 

Wied.  Ann.,  1894,  52,  275.  Gordon  :  Zeit.  phys.  Chem.,  1895, 
18,  1.  Roth  :  Zeit.  phys.  Chem.,  1897,  24,  114.  Euler  :  Zeit. 
phys.  Chem.,  1900,  31,  360.  Bothmund  :  Zeit.  phys.  Chem., 
1900,  33,  401. 


CHAPTER  VIII. 

(1)  Gubkin  :   Wied.  Ann.,  1887,  32,  114. 

(?)  Buff:  Lieb.  Ann.,  1853,  85,  1;  1855,  94,  1. 


316  LITERATURE   REFERENCES. 

(3)  Helmholtz:     Sitz.   Ber.  Berl   Acad.,    1883,    I,    660.      See    «!*<> 

Arrhenius  :  Zeit.  phys.  Chem.,  1893,  11,  826. 
(Jf)  Faraday  :  Ostwald's  Klassiker,  Nos.  81,  86,  and  87. 

(5)  Kohlrausch :  Wied.  Ann.,  1886,  27,  1. 

(6)  Lord  Rayleigh  and  Mrs.  Sidgwick :  Phil.  Trans.,  1884,  175,  411. 


CHAPTER  IX. 

(1}  Horsford :  Pogg.  Ann,,  1847,  70,  238. 

(£)  Fuchs:  Pogg.  Ann.,  1875,  156,  159. 

(3}  Bouty  :  Ann.  Chim.  Phys.,  1884  (vi),  3,  433. 

(4}  Kohlrausch.     See  Kohlrausch  and  Holborn :  "  Leitvermogen  der 

Elektrolyte,"  Leipsic,  1898. 

(5)  Lummer  and  Kurlbaum  :  Verhandl.  der  Phys.  Gesellsch.,  1895. 
(6}  Hopfgartner  :  Zeit.  phys.  Chem.,  1898,  25,  115. 
(7)  Hifctorf.     See  (2},  Chap.  II. 

(8}  Kohlrausch  :   Wied.  Ann.,  1879,  6,  145 ;  1885,  26,  161,  213. 
(9)  Jahn  :  Zeit.  phys.  Chem.,  1901,  38,  673. 
(10}  Bein  :   Wied.  Ann.,  1892,  46,  29. 
(11}  Hittorf :  Pogg.  Ann.,  1859,  106,  543. 
(12}  Lenz  :  Pogg.  Ann.,  1877,  160,  425. 
(13}  Goldhaber  :  Zeit.  phys.  Chem.,  1901,  37,  701. 
(IJf)  Ostwald :  J.  pr.  Chem.,  1885,  31,  433.    Zeit.  phys.  Chem.,  1888,  3, 

170,  418. 

(15}  Bredig  :  Zeit.  phys.  Chem.,  1894,  13,  191. 
(16}  Schrader :  Zeit.  Electrochem.,  1897,  3,  501. 
(17}  Arrhenius  :  Zeit.  phys.  Chem.,  1892,  9,  501. 
(18}  Walker  and  Hambly  :  J.  Chem.  Soc.,  1897,  72,  61. 
(19}  Kablukoff :  Zeit.  phys.  Chem.,  1889,  4,  429. 
(20}  Lodge  :  Brit.  Assoc.  Report,  1887,  393. 
(21}  Whetham  :  Zeit.  phys.  Chem.,  1893,  11,  220.     Phil.  Trans.,  1893, 

184,  337  ;  1895,  186,  507.    Phil.  Mag.,  1894,  38,  392. 
(22)  Vollmer  :  Wied.  Ann.,  1894,  52,  328. 
(23}  Carrara :  Zeit.  phys.  Chem.,  1896,   19,  699.     Gazzetta,  1896,  26, 

119;  1897,  27,  207. 

(24}  Euler :  Zeit.  phys.  Chem.,  1899,  28,  619. 

(25}  Walden  :  Ber.,  1899,  32,  2862.  Zeit.  anorg.  Chem.,  1900,  25, 209  ; 
1902,  29,  371.  See  also  Bouty  :  Compt.  rend.,  1888,  106, 
595,  654.  Cady  :  J.  Physical  Chem.,  1897,  1,  707.  Whetham: 
Phil.  Mag.,  1897,  44,  1.  Dutoit  and  Aston  :  Compt.  rend., 

1897,  125,   240.     Dutoit  and  Friderich  :  Bull.  Soc.  Chim., 
1898  (iii),  19,  321.      Schroder:  J.  Buss.  Phys.  Chem.  Soc., 

1898,  30,  333.     Franklin  and  Kraus  :  Amer.  Chem.  J.,  1898, 
20,  820 ;  1899,  21, 1 ;  1900,  23,  277  ;  1900,  24,  83.    Tolloczko: 
Zeit.  phys.  Chem.,  1899,  30,  705.     Bruni  and  Berti :  Rend. 


LITERATURE    REFERENCES.  317 

Acad.  Lined,  1900,  9,  321.    Centnerszwer  :  Zeit.  phys.  Chem., 
1901,  39,  217.     Kahlenberg  :  J.  Physical  Chem.,  1901,  5,  384. 
Walden  and  Centnerszwer  :  Zeit.  phys.  Chem.,  1902,  39,  513. 
Nernst:  Zeit.  phys.  Chem.,  1888,  2,  613. 
(27)  Euler:   Wied.  Ann.,  1897,  63,  273;  Zeit.  phys.   Chem.,  1898,  25, 
536. 


CHAPTER  X. 

CO  See  Kohlrausch  and  Holborn :  (4),  Chap.  IX. 

(£)  Arrhenius:  Zeit.  phys.  Chem.,  1887,  1,  631. 

(3}  Jones  :  Zeit.  phys.  Chem.,  1893,  11,  110,  529 ;  1893,  12,  623. 

(4)  Nernst  and  Abegg  ;  Zeit.  phys.  Chem.,  1894,  15,  681. 

(5)  Loomis  :   Wied.  Ann.,  1894,  51,  500 ;  1896,  57,  495  ;  1897,  60,  523. 
(6}  Hausrath  :  Inaugural-Dissertation,  Gottingen,  1901. 

(7)  van't  Hoff  and  Reicher :  Zeit.  phys.  Chem.,  1888,  2,  781. 

(8)  Ostwald  :  Zeit.  phys.  Chem.,  1888,  2,  36,  270. 

(9)  Ostwald  ;  Bredig.     See  (IJf)  and  (15},  Chap.  IX. 
(10}  Rudolph! :  Zeit.  phys.  Chem.,  1895,  17,  385. 
(11}  van't  Hoff :  Zeit.  phys.  Chem.,  1895,  18,  300. 

(12}  Storch:  Zeit.  phys.   Chem.,   1896,    19,   13.      See   also   Bancroft 

Zeit.  phys.  Chem.,  1899,  31,  188. 
(13}  Arrhenius:  Zeit.  phys.  Chem.,  1899,  31,  211. 
(14)  Ostwald.     See  (IJf),  Chap.  IX. 


CHAPTER  XI. 

(1}  Valson:  Compt.  rend.,  1871,  73,  441;  1873,  77,  806. 

(#)  Rontgen  and  Schneider:   Wied.  Ann.,  1886,  29,  165;  1887,  31, 

1000;  1888,  33,  644  ;  1888,  34,  531. 
(3}  Reyher:  Zeit.  phys.  Chem.,  1888,  2,  744. 

(4)  Bender:  Wied.  Ann.,  1890,  39,  89. 

(5)  Le  Blanc:  Zeit.  phys.  Chem.,  1889,  4,  558. 
(6}  Jahn:  Wied.  Ann.,  1891,  43,  280. 

(7)  G.  Wiedemann:  Pocjg.  Ann.,  1865,  126,  1  ;  1868,  135,  177.     See 
also  Henrichsen:   Wied.  Ann.,  1888,  34,  180;  1892,  45,  38. 

(8}  du  Bois  and  Liebknecht :  Ber.,  1899,  32,  3344  ;  1900,  33,  975. 

(9)  Oudemans:  Lieb.  Ann.,  1879,  197,  48,  66;  1881,  209,  38.     Eec. 
Trav.  chim.  Pays  Bas,  1886,  4,  166.      See  also  Tykociner: 
Eec.  Trav.  chim.  Pays  Bas,  1883,  1,  144. 
(10}  Landolt:  Ber.,  1873,  6,  1073. 

(11)  Ostwald:  Zeit.  phys.  Chem.,  1892,  9,  579. 

(12)  Arrhenius  :  Inaugural-Dissertation,  Stockholm,  1884.    Zeit.  phys. 

Chem.,  1887,  1,  631. 

(13)  Gore  :  Proc.  Roy.  Soc.,  1865,  14,  213.    Phil.  Trans.,  1869,  159, 173. 


318  LITERATURE    REFERENCES. 

(14)  Kahleiiberg  and  Austin:  ,7.  Physical  Chem.,  1900,  4,  553. 

(15)  Loeb:  Pfluger's  Arch.,  1897,  69,  1;  1898,  71,  457. 

(16)  Paul  and  Kronig:  Zeit.  phys.  Chem.,  1897,  21,  414. 

(17)  Ostwald:  J.  pr.  Chem.,  1883,  28,  449;  1884,  29,  385;  1884,  30, 

93.     See  also  Arrhenius :  Inaugural-Dissertation,  1884,  Part 
II,  60. 

(18)  Arrhenius:  Zeit.  phys.  Chem.,  1889,  4,  244. 

(19)  Palmaer :  Zeit.  phys.  Chem.,  1894,  22,  492. 
(20}  Reicher:  Lieh.  Ann.,  1885,  228,  257. 


CHAPTER  XII. 

(1)  van't  Hoff:  Zeit.  phys.  Chem.,  1889,  3,  484. 

(2)  Euler:  Zeit.  phys.  Chem.,  1900,  31,  360. 

(3)  Rothmund :  Zeit.  phys.  Chem.,  1900,  33,  401. 

(4)  Thomsen:  ' '  Thermochemische  Untersuchungen,"  1882-1886. 

(5)  Ostwald:  J.  pr.  Chem.,  1877  (ii),  16,  396. 

(6)  Berthelot :  Ann.  Chim.  Phys.,  1862,  65,  66  ;  1863,  68. 

(7)  Arrhenius.    See  (12],  Chap.  XI. 

(8)  Shields :  Zeit,  phys.  Chem.,  1893,  12,  167. 

(9)  Arrhenius:  Zeit.  phys.  Chem.,  1893,  11,  805. 

(10)  Wijs:  Zeit.  phys.  Chem.,  1893,  11,  492;  1893,  12,  514. 

(11)  Ostwald:  Zeit.  phys.  Chem.,  1893,  11,  521. 

(12)  Bredig  :  Zeit.  phys.  CJiem.,  1893,  11,  829. 

(13)  Kohlrausch  and  Heydweiller :  Zeit.  phys.  Chem. ,  1894,  14,  317, 

(14)  Arrhenius:  Zeit.  phys.  Chem.,  1889,  4,  96;  1892,  9,  339. 

(15)  J.  J.  Thomson:  Phil.  Mag.,  1893,  36,  320. 

(16)  Nernst:  Zeit.  phys.  Chem.,  1894,  13,  531. 
(77)  Planck:   Wied.  Ann.,  1887,  32,  494. 

(18)  Fanjung :  Zeit.  phys.  Chem.,  1894,  14,  673. 

(19)  Drude :  Zeit.  phys.  Chem.,  JL897,  23,  265. 

(20)  Ratz:  Zeit.  phys.  Chem.,  1896,  19,  94. 


CHAPTER  XIII. 

(./)  Helmholtz  :   "  Erhaltung  der  Kraft,"  Berlin,  1847. 

(2)  Lord  Kelvin :  Phil.  Mag.,  1851  (iv),  2. 

(3)  Thomsen:   Wied.  Ann.,  1880,  11,  246. 

(4)  Edlund:  Pogg.  Ann.,  1869,  137,  474;  1871,  143,  404,  534. 

(.5)  Braun:   Wied.  Ann.,  1878,  5,  182  ;  1882,  16,  561;  1882,  17,  593. 

(6)  Gibbs :    "  Thermodynamische  Studien,"   German   translation  by 

Ostwald,  Leipsic,  1892,  p.  407. 

(7)  Helmholtz:  Sitz.  Ber.  Berl.  Akad.,  1882. 

(8)  Jahn :   Wied.  Ann.,  1886,  28,  21,  491. 

(9)  G.  Meyer:  Zeit.  phys.  Chem.,  1891,  7,  477. 


LITERATURE    REFERENCES.  319 

(10}  See  (11),  (12),  (13),  (14),  and  (15),  Chap.  V. 

(11)  Helmholtz:   Wied.  Ann.,  1878,  3,  201. 

(12)  Jahri:  Zeit.  phys.  Chem.,  1900,  33,  545. 

(13)  Nernst :  Zeit.  phys.  Chem.,  1888,  2,  613  ;  1889,  4,  129.     See  also 

Planck:  Wied.  Ann.,  1890,  40,  561. 

(14)  Nernst :  Zeit.  phys.  Chem.,  1889,  4,  129. 

(15)  Moser:   JFieti  Ann.,  1878,  3,  216  ;  1881,  14,  62. 

(16)  Nernst:  Zeit.  phys.  Chem.,  1889,  4,  155,  161. 

(17)  von  Tiirin:  Zeit.  phys.  Chem.,  1890,  5,  340. 

(18)  Ostwald:  "  Lehrbuch  der  allgemeinen  Chemie,"  1893.     Ghemiache 

Energie,  p.  852. 

(19)  Planck  :   JFierf.  ^ww.,  1890,  40,  561. 

(20)  Negbaur:   Wied.  Ann.,  1891,44,  767. 


CHAPTER  XIV. 

(1)  Helmholtz:  Wied.  Ann.,  1879,  7,  340. 

(2)  Lippmann :  Ann.  Chim.  Phys.,  1875  (v),  5,  532.      Compt.  rend., 

1876,  83,  192. 

(3)  Konig:  Wied.  Ann.,  1882,  16,  1. 

(4)  Helmholtz:     Gesammelte    Abhandl.,    I,    934.      Monatsber.    Berl. 

Akad.,  Nov.,  1881. 

(5)  Paschen:   Wied.  Ann.,  1890,  41,  42. 

(6)  Nernst:  Beilage  zu  Wied.  Ann.,   1896,  10.    Zeit.   phys.   Chem., 

1898,  25,  265-268. 

(7)  Palmaer:  Zeit. phys.  Chem.,  1898,  25,  265  ;  1899,  28.  257. 

(8)  Brown:  Phil.  Mag.,  1878,  6,  142;  1879,  7,  108;  1881,  11,  212. 

(9)  Pellat:  Compt.  rend.,  1889,  108,  667. 

(10)  Ostwald:  Lehrb.  d.  allg.  Chem.;  Electrochemie,  944.     Zeit.  phys. 

Chem.,  1900,  35,  337. 

(11)  Edlund:  Pogg.  Ann.,  1869,  137,  474. 

(12)  Streintz:  Siiz.  Ber.  d.  Wien.  Akad..  1878  (ii),  77,  21. 


CHAPTER  XV. 

(1)  Becquerel:  Ann.  Chim.  Phys.,  1823,  23,  244. 

(£)  Bancroft:  Zeit.  phys.  Chem.,  1892,  10,  394.     See  also  Neumann 

Zeit.  phys.  Chem.,  1894,  14,  193. 
{3)  Meidinger:  Pogg.  Ann.,  1859,  108. 

(4)  Ostwald:  Zeit.  phys.  Chem.,  1893,  11,  521. 

(5)  Lalande  and  Chaperon :  Elektr.  Zeitschr.,  1890,  377. 
{6)  Helmholtz:  8itz.  Ber.  Berl.  Akad.,  1882,  834. 

(7)  Clark  :  J.  Soc.  Tel.  Eng.,  1878,  7,  53. 

(8)  See  Jaeger  and  Lindeck:  Drud.  Ann.,  1901,  5,  1. 

(9)  Smale :  Jahrb.  Electrochem. ,  1894,  36. 


320  LITERATURE    REFERENCES. 

(10}  Bose  :  Zeit.  phys.  Chem.,  1900,  34,  701. 

(11)  Helmholtz.     See  (3),  Chap.  VIII. 

(12}  Jahn:  "  Orundriss  der  Elektrochemie,"  1895,  252. 

(13}  Le  Blanc :  Zeit.  phys.  Chem.,  1891,  8,  299  ;  1892,  12,  333. 

(14}  Oberbeck:   Wied.  Ann.,  1887,  31,  337. 

(15)  Grove:  Phil.  Mag.,  1842.     Phil.  Trans.,  1843,  91;  1845,  351. 

(16)  Planter  Pogg.  Ann.,  I860,  109. 

(17)  Faure  :  German  Patent,  8th  Feb.,  1881. 

(18)  Sellon  and  Volckmar.    See  Nature,  1882,  25,  561. 

(19)  Darrieus :  Bidl.  Soc.  intern,  des  Electriciens,  9,  205.    IS  Electricien, 

1894,  237  and  321;  1895,  81  and  306.      See  also  Elbs  and 
Schonherr:  Zeit.  Electrochem.,  1894,  1,  473;  1895,  2,  471. 

(20)  Streintz:  Wied.  Ann.,  1892,  46,  454. 

(21)  Dolezalek:  Zeit.  Electrochem.,  1897,  4,  349;  Wied.  Ann.,  1898, 

65,  894. 

(22)  Graetz  :  Zeit.  Electrochem.,  1897,  4,  67.     See  also  Pollack  :  Compt. 

rend.,  1897,  124,  1443.     E.   Wilson:  Proc.  Roy.  Soc.,  1898, 
63,  329.     Kallir:  Zeit.  Electrochem.,  1898,  16,  602,  613. 


CHAPTER  XVI. 

(1)  Erdmann:  Ber.,  1897,  30,  1175. 

(2)  Kohlrausch  and  Rose :  Wied.  Ann. ,  1893,  50,  136.  • 

(3}  Behrend  :  Zeit.  phys.  Chem.,  1893,  11,  466;  1894,  15,  498. 

(4)  See   Classen :    "  Quantitative  Analyse   durch  Electrolyse"  Berlin, 

1897. 

(5)  Ulsch :  Zeit.  Electrochem.,  1897,  3, 546.     See  also  Ihle  :  Zeit.  phys. 

Chem.,  1896,  19,  572. 

(6)  Neumann  :  Zeit.  Electrochem.,  1898,  4,  316. 

(7)  Forster  and  Seidel:  Zeit.  anorg.  Chem.,  1897,  14,  106. 

(8)  Oettel :  Chem.  Zeitung,  1893?  543. 

(9)  Freudenberg:  Zeit.  phys.  Chem.,  1893,  12,  97., 

(10)  Fontaine:  "Electrolyse,"  1892,  146. 

(11)  Tafel:  Ber.,  1899,  32,  3206;  1900,  33,  2209.     Zeit.  phys.  Chem., 

1900,  34,  187. 

(12}  See  Lob :  "  Unsere  Kenntnisse    in   der    Electrolyse   und   Elektro- 
synthese  organischer  Verbindungen,"  Halle  a.  S.,  1899. 


CHAPTER  XVII. 

(1)  Lord  Kelvin:  Phil.  Trans.,  1856. 

(2}  Edlund:  Pogg.  Ann.,  1867,  131. 

(3)  Uppenborn:  Central- Blatt  f.  Elektrotech.,  1888,  10,  102. 

(If)  Violle:  Compt.  rend.,  1892,  115,  1273. 


LITERATURE   REFERENCES.  321 

(o)  Rosetti:  Atti  d.  Inst.   Venet.  (v),  5,  1.     BeiU.  zu  Wied.  Ann., 

1879,  3,  821 ;  1880,  4,  134. 
(6}  Helmholtz.     See  (3),  Chap.  VIII. 

(7)  Deville:  Compt.  rend.,  1863,  56,  195,  322. 

(8)  Heroult:  Eng.  Patent,  7426  (1887). 

(9)  Hall :   U.S.A.  Patent,  400664  and  400766. 

(10)  Borchers:   "  Elektrometallurgie"  Brunswick,  1896. 

(11)  Cowles:  Eng.  Patent,  9781  (1885). 

(12)  Maxim :  EMJ.  Patent,  4075  (1898).   Zeit.  Electrochem.,  1899,  5.  430. 

(13)  Muhlhaenser :  Zeit.  angew.  Ghem.,  1893,  485,  637. 

(14)  Zerener:  Jahrb.  Electrochem.,  2,  113. 

(15)  Moissan:  "  Le  Four  fflectrique,"  Paris,  1897. 

(16)  Rathenau:  Ger.  Patent,  86226. 

(17)  Memmo:  Zeit.  Mectrochem.,  1898,  5,  197.     Eng.  Patent,  14022. 

and  24077  (1897). 

(18)  Berthelot:  Compt.  rend.,  1876,  83,  677;  1877,  85,  173;  1878,  87y 

92.     Ann.   Ghim.  Phys.,  1877  (v),  10,  55,  63,  75;  1878  (v)T 
12,  463. 

(19)  Deville:    " Lecons  sur  la  Dissociation,"  1864.     See  also  Perrot : 

Ann.  Chim.  Phys.,  1861,  61,  161. 

(20)  Ludeking :  Phil.  Mag.,  1892  (v),  33,  521. 

(21)  J.  J.   Thomson :   "  The  Discharge  of  Electricity  through   Gases" 

London,  1898.    Proc.  Roy.  Soc.,  1893,  53,  90. 

(22)  Arrhenius  :  Wied.  Ann.,  1891,  42,  18. 

(23)  McLeod:  J.  Ghem.  Soc.,  1886,  49,  591. 

(24)  von  Babo:  Splb.  zu  Lieb.  Ann.,  1863,  2,  265. 

(25)  Hautefeuille  and  Chappuis :  Compt.  rend.,  1880,  91,  228. 

(26)  Shenstone  and  Priest:  J.  Ohem.  Soc.,  1893,  63,  938.      See  also 

de  Hemptinne:  Bull.  Acad.  Roy.  Belg.,  1901,  612. 

(27)  Andreoli:  J.  Soc.  Ohem.  Ind.,  1897,  16,  87. 


INDEX   OF   AUTHORS1    NAMES, 


ABEGG,  101,  198 

Adie,  38 

Ampere,  21 

Andreoli,  311 

Arrhenius,  31,  39,  55,  105,  150, 

159, 179, 182, 183, 193, 196, 197, 

308 

Auer,  291 
Avogadro,  25 


BABO,  von,  309 

Bancroft,  244 

Barnes,  161 

Beccaria,  16 

Beckmann,  51,  52,  63,  65 

Becquerel,  244 

Behrend,  269 

Bein,  141 

Bender,  174 

Bergman,  73,  192 

Bergmann,  273 

Berthelot,  73,  80,  89, 192,  306, 307 

Berzelius,  18,  19,  20,  21,  22,  117, 

118 

Biltz,  65 

Blanc,  Le,  174,  257 
Bogdan,  141 
Bois,  du,  176 
Borchers,  296,  299,  303 
Bose,  254 
Bouty,  129 
Boyle,  25 
Braun,  99,  207 
Bredig,  145,  158,  163,  194 


Brown,  236 

Bruni,  63 

Bucholz,  224 

Buff,  114 

Bugarzsky,  209 

Bunsen,  99,  249,  256,  282 


CARLISLE,  17 
Carrara,  152 
Chaperon,  250 
Chappuis,  310 
Chatelier,  Le,  294 
Clapeyron,  48,  90 
Clark,  5,  124,  252 
Classen,  273 
Clausius,  114,  116,  136 
Coppet,  de,  55 
Coulomb,  4 
Cowles,  297 


DALTON,  32 
Daniell,  5,  119,  251 
Darrieus,  263 
Davy,  17,  18,  117 
Deimann,  16 
Deville,  293,  308 
Dieterici,  65 
Ditte,  98 
Dolezalek,  265 
Bonders,  35,  65 
Drude,  200 
Du  Bois,  176 


3H 


INDEX   OF   AUTHORS'   NAMES. 


Ducretet,  302 
Dutrochet,  32 


EDLUND, 200, 240,  289 
Elbs,  285 
Engel,  97 
Erdmann,  208 
Ericson-Auren,  100 
^tard,  97 

Euler,  152,  155,  190 
Exner,  207 
Eykman,  55 


FAN JUNG, 199 

Faraday,  4,  7,  22,  39,  110,  112,  i 

117,  119 
Faure,  261 
Fechner,  22 
Fontaine,  284 
Forster,  277 
Fresenius,  273 
Freudenberg,  279 
Fuchs,  129 


GALVANI,  17 
Gay-Lussac,  25 
Gibbs,  73,  207 
Goldhaber,  144 
Gore,  180 
Graetz,  267 
Graham,  155 
Grotthuss,  21, 110 
Grove,  249,  260 
Gubkin,  113 
Guldberg,  49,86,89,  100 


HALL,  290 
Halske,311 
Hamburger,  35,  36,  65 
Hausrath,  162,  216 
Hautefeuille,  98,  310 
Hedin,  36,  38 


Helmholtz,  22, 116,  201,  205, 207, 

209,  212,   230,  233,  251,  255, 

264,292 

Henry,  77,  79,  255 
Heroult,  295 
Heycock,  62,  212 
Heydweiller,  194 
Hisinger,  18 
Hittorf,  22,  119,  139,   141,  143, 

144,  145 
Hoff,  van't,  30,  39,  42,  49,  55,  59, 

60,  63,  71,  72,  80,  89,  92,  102, 

110,  162,  165,  190 
Hoitsema,  63 
Hopfgartner,  139 
Horsford,  125 


JABLOCHKOFF,  291,  298 

Jahn,  141, 174,  209,  215,  257,259 

Jones,  161 

Joule,  206,  288 

Juhlin,  49 

Jungfleisch ,  80 


KABLUKOFF,  151 

Kahlenberg,  181 

Kellner,  281 

Kelvin,  Lord,  205,  289 

King,  304 

Kirchhoff ,  129 

Klein,  98 

Kniipfer,  98 

Kohlrausch,  113,  117,  119,  129, 

131,  132,   140,  141,  158,  159, 

194,  248,  269 
Konig,  233 
Koppe,  38 
Kronig,  181 
Kurlbaum,  132 


LALAKDE,  250 
Landolt,  177 
Landsberger,  53 


INDEX   OF   AUTHORS'   NAMES. 


325 


Le  Blanc,  174,  257 
Le  Chatelier,  294 
Leclanche,  249 
Legrand,  39 
Lejeune,  302 
Lemoine,  88 
Lenz,  144 
Liebknecht,  176 
Lippmann,  232 
Lodge,  151 
Loeb,  181 
Loomis,  161,  216 
Liideking,  308 
Lummer,  132 


MADSEN,  102 
Magnus,  22 
Mariotte,  25 
Maruni,  van,  16 
Maxim,  298 
Maxwell,  115 
McLeod,  309 
Meidinger,  245 
Memnao,  305 
Metelka,  141 
Meyer,  G.,  63,  210 
Meyer,  V.,  65,  100 
Miesler,  223 
Moissan,  302 
Moser,  223 
Miihlhaeuser,  300 


NEGBAUR,  229 

Nernst,  83,  154,    161,  198,    200, 

201,   218,   220,    223,  226,   227, 

228,  233,  291 
Neumann,  276 
Neville,  62,  212 
Nicholson,  17 
Nollet,  de,  33 
Nordenskiold,  93 
Noyes,  103 


OBERBECK,  260 

Oettel,  278 

Ohm,  5,  120 

Ostwald,  107,  144,  158,  162,  163, 
167,  177,  182,  183,  191,  194, 
199,  226,  233,  237,  238,  239, 
244 

Oudemans,  177 


PAETS  VAN  TROOSTWYK,  16 

Palmaer,  183,  234, 

Paschen,  233 

Paul,  181 

Pe'an  de  St.  Gilles,  89 

Pellat,  236 

Pepys,  297 

Perrot,  308 

Pfeffer,  28,  29,  30,  33 

Planck,  199,  227,  240 

Plante',  261 

Poggendorff,  249 

Pollak,  250 

Priestley,  16 


RAMSAY,  31,  61 

Raoult,  42,  43,  44,   54,  56,  159, 

161,  205,  206 
Rathenau,  303 
Rayleigh,  Lord,  117 
Regnault,  26,  96,  97 
Reicher,  71,  184 
Reyher,  173 
Ritter,  17,  253 
Rive,  de  la,  22 
Roberts-Austen,  63 
Rontgen,  172 
Rose,  269 
Rosetti,  291 
Rothmimd,  106,  190 
Rudolphi,  164 
Riidorff,  55 


326 


INDEX   OF   AUTHORS'   NAMES. 


SCHNEIDER,  172 
Schonbein,  22 
Schrader,  146 
Schweigger,  19 
Sellon-Volckmar,  261 
Shenstone,  311 
Shields,  193 
Siemens,  4,  123,  311 
Smale,  253,  256,  260 
Storch,  165 

Streintz,  241,  264,  265,  267 
Stroud,  132 


TAFEL,  285 

Tammann,  37,  45,  62,  65,  99,  104, 

109,  212 
Tesla,  301 
Thompson,  242 
Thomsen,  Jul.,  92,  97,  191,  197, 

205,  263,  264 
Thomson,  J.  J.,  198,  308 
Thomson,  W.     See  Lord  Kelvin. 
Topler,  37 
Traube,  28 
Troost,  98 
Tudor,  262 
Tiirin,  von,  224 


ULSCH,  275 
Uppenborn,  291 


VALSON,  171 

Violle,  291 

Vollmer,  152 

Volta,  17,  235,  251,  289 

Vries,  De,  27,  35,  55 


WAAGE,  86,  89,  106 
Waals,  van  der,  26,  61 
Walden,  152 
Walker,  53,  150 
Watt,  11 
Weston,  124,  252 
Wheatstone,  129 
Whetham,  151 
Whitney,  103 
Wiedemann,  175 
Wijs,  193 

Wilhelmy,  100,  107 
Wilson,  104 
Wright,  242 


ZERENEE,  301 


INDEX   OF    SUBJECTS. 


ABNORMAL  transport  numbers,  143 
Absolute  temperature,  11 
units,  4 

velocity  of  ions,  147 
zero,  11 
Absorption  of  light  by  salt  solutions,  177 

spectra,  177 
Accumulator,  261 

capacity  of,  263 
efficiency  of,  264 
Acetylene,  303,  306 
Action  at  a  distance,  111,  244 

of  neutral  salts,  109,  183 
Active  molecules,  105 
Additive  properties,  168 
Affinity,  19,  73 
Air  as  an  insulator,  235 
Alcohols,  molecular  weight  of,  57,  59 
Alkali,  application  of,  in  elements,  250 

metals,  conductivity  of  vapour  of,  308 
deposition  of,  280 
preparation  of,  297 
Alloys,  61 
Aluminium  alloys,  296 

deposition  of,  274,  280 
electrodes,  267 
preparation  of,  295 
separation  of,  282 
Amalgams,  62,  211,  224 
Ammonia,  formation  of,  275,  306 
Ammonium  chloride,  chemical  equilibrium  of,  84,  185 

use  of,  in  elements,  250 
nitrate,  formation  of,  306 
Ampere,  4,  123 


328  INDEX   OF   SUBJECTS. 

Ampere-hour,  203 

Ampere's  electrochemical  theory,  21 
Analysis  by  electrolysis,  268,  270,  279,  281 
Analytical  chemistry,  179 
Anion,  4,  120 
Anode,  4,  120 

slime,  276 

Antimony,  deposition  of,  274 
separation  of,  282 
Arc  light,  289 

furnace,  301 

heat  and  temperature  of,  291 
length  of,  and  current  strength,  290 
reactions  in,  301 
Arsenic,  separation  of,  282 
Association,  57,  59 
Atmosphere,  13 
Atomic  charge,  22,  23 
magnetism,  176 
weight,  8 

Attackable  molecules,  105 
Attraction  between  molecules,  26,  61 
Avidity,  191 

Avogadro's  hypothesis,  25 
law,  13,  25 


BACTERIA,  action  of  poisons  on,  181 

osmotic  pressure  of,  36 
Battery  plates,  ''forming"  of,  261 
Beckmann  thermometer,  52 
Becquerel  rays,  309 

Benzene  derivatives,  constitutive  influences,  167 
electrolysis  of,  23 
formation  of,  306 
as  a  solvent,  57,  59 

Beryllium,  behaviour  on  electrolysis,  274 
Berzelius'  electrochemical  theory,  19 
Bimolecular  reaction,  102 
Bismuth,  deposition  of,  273 
Blowpipe,  electric,  301 
Boiling  point,  47 

apparatus,  52 
molecular  raising  of,  64 
raising  of,  63 
Borcher's  furnace,  299 


INDEX   OF   SUBJECTS.  329 


Bound  energy,  210 

Boyle's  law,  25 

Brass,  electrolytic-  preparation  of,  280 

Bronze,  deposition  of,  284 

Bugarzsky's  element,  209 

Bunsen  flame,  307,  308 

Bunsen's  element,  203,  249 

CADMIUM,  deposition  of,  273 

element,  124,  252 

iodide,  transport  number  of,  143 

separation  of,  282 
Calcium  carbide,  303 
Calorie,  11 

Caoutchouc  as  semi-permeable  membrane,  32 
Capacity  of  accumulator,  263 

resistance  vessel,  132 
Capillarity,  172 
Capillary  electrometer,  232 
Carbide,  303 

Carbon  dioxide,  dissociation  of,  294 
Carborundum,  299 
Catalysis,  71,  182 
Cathode,  4,  120 
Cation,  4,  120 
Cementation,  297 
Chaperon's  element,  250 
Charge,  atomic,  23 

ionic,  118,  185 
Charging  current,  116 
Chemical  equilibrium,  69 

garden,  33 

properties  of  ions,  113,  178 
Chloral,  preparation  of,  285 
Chlorate,  preparation  of,  285 
Chromium,  deposition  of,  274 
Clapeyron's  formula,  48,  50,  90,  91,  93 
Clark's  element,  5,  124,  203,  252 
Clausius'  hypothesis,  114,  136 
Cobalt,  deposition  of,  273 
separation  of,  282 
Coefficient  of  diffusion,  153 
distribution,  81 
friction,  153 
isotonic,  37 
Coexisting  phases,  49,  73 


330  INDEX   OF   SUBJECTS. 

Colloids,  molecular  weight  of,  155 
Colour  of  salts,  178 
Commutator,  electrochemical,  267 
Complete  reaction,  71 
Complex  ions,  146 

molecules,  58 
Compressibility,  172 

Concentration,  deviations  at  high,  44,  46,  58,  61 
element,  202,  210,  212,  220,  245 
influence  of,  on  E.M.F. ,  241 
unit  of,  10 

Condensed  systems,  72 
Condenser,  electrolytic,  235,  307 
Conduction,  convective,  309 

metallic,  120 
Conductivity  of  electrolytes,  125 

application  in  analysis,  268 

equivalent,  128 

of  glowing  gases,  308 

maximum,  134 

molecular,  128,  162 

specific,  127 

of  water,  196 

unit  of,  128 

vessel,  132 

capacity  of,  132 
Constant,  dielectric,  58,  198 

dissociation,  86,  157 
Convective  conduction,  309 
Cooling  of  electrodes,  296,  301 

in  gas  reactions,  306,  308,  3J1 
Copper,  deposition  of,  273 
element,  250,  266 
refining  of,  276 
separation  of,  281 
voltameter,  286 
Coulomb,  4 
Cowles'  furnace,  297 
Cryohydrate,  74 
Crystallisation,  velocity  of,  104 
Current,  charging,  116 

density,  7,  250,  262,  273,  277 
local,  250,  266 

polarisation,  1,  253,  256,  309 
strength,  253,  256 
Cyanide  solution,  243 


INDEX   OF   SUBJECTS.  331 

D  ALTON'S  law,  32 

Daniell's  element,  5,  123,  204,  206,  240,  251,  265 

Davy's  electrochemical  theory,  18 

Dehydrating  agents,  46 

Density,  current,  7,  250,  262,  273,  277 

Depolarisation,  249,  253 

Deposition  of  metals,  268,  279,  281,  282 

Depression  of  freezing  point,  54 

solubility,  83,  189, 190 
vapour  pressure,  39 
Deviations  from  the  law  of  dilution,  164 

van't-Hoff,  57,  59,  60,  76,  110,  158,  183 
Dielectric  constant,  58,  198 
Diffusion,  152,  185,  234,  245,  251,  253 

coefficient,  153 
Dilute  solution,  ideal,  77 
Dilution,  law  of,  163,  309 
Discharge,  silent,  305 
spark,  306 
Dissociation  constant,  86,  157 

degree  of,  137,  157,  159 
electrolytic,  59,  90,  184 
electrolytic,  of  gases,  308 

water,  87,  116,  193,  256,  292 
heat  of,  194 

influence  of  solvent  on,  152 
ordinary  (thermal),  84,  185 
volume,  191 

Distance,  chemical  action  at  a,  111,  244 
Distribution  coefficient,  81 
law,  80 
of  a  base  between  two  acids,  191 

substance  between  two  solvents,  81 
Divalent  acids,  166 
Double  cyanides,  274,  283 
layer,  electrical,  230 
molecules,  58 

salts,  application  of,  in  electro- analysis,  273,  274,  279,  282 
Dropping  electrodes,  233 
Ducretet's  furnace,  302 
Dyne,  11 


EFFICIENCY  of  accumulators,  264 
Electric  blowpipe,  301 

charge  on  an  ion,  118 


332  INDEX   OF   SUBJECTS. 

Electric  double  layer,  230 
furnaces,  295-305 
spark,  306 
vibration,  307,  311 
wind,  305 
work,  6,  204 

Electro-analysis,  268-287 
Electrochemical  commutator,  267 
equivalent,  7,  117 
series,  20,  236 
theory  of  Ampere,  21 
Berzelius,  19 
Davy,  18 
Helmholtz,  22 

Electrodes,  cooling  of,  296,  301,  306,  308,  311 
dropping,  233 

non-polarisable,  113,  221,  251 
normal,  260 
Electrolysis,  3, 16,  111 

analysis  by,  268,  270,  279,  281 
primary,  3,  19 
secondary,  3 
Electrolytes,  23, 110 

conductivity  of,  125 
degree  of  dissociation  of,  137,  157,  159 
equilibrium  of  several,  188-200 
fused,  295 

strong  and  weak,  147,  157,  158,  162,  193 
Electrolytic  condenser,  235,  307 

dissociation,  59,  90,  184 

of  gases,  308 

polarisation,  1,  23, 131,  133,  232,  249,  253 
solution  pressure,  226 
Electrometer,  application  of,  as  indicator,  269 

capillary,  232 

Electromotive  force,  5,  111,  123, 185,  201,  218,  230,  237,  240,  264,309 
influence  of  pressure  on,  254 
unit  of,  6,  123 
series,  Volta's,  17,  236 
Electroplating,  283 
Electrostriction,  200 
Electrothermic  actions,  307 
Elements,  atomic  and  equivalent  weights  of,  8 
galvanic,  202 
Bugarzsky's,  209 
Bunsen's,  203,  249 


INDEX   OF   SUBJECTS.  333 

Elements,  cadmium,  124,  252 

Clark's,  5,  124,  203,  252 
concentration,  202,  210,  212,  220,  245 
copper,  250,  266 

Daniell's,  5,  123,  204,  206,  240,  251,  265 
gas,  253 
Grove's,  249 
Helmholtz's,  212,  251 
hydro,  202 
irreversible,  202,  248 
Lalande  and  Chaperon's,  250 
Leclanche's,  203,  249,  250,  265 
liquid,  218 
Meidinger's,  245 
Meyer's,  210 
neutralisation,  247 
normal,  5,  251 
oxidation,  240 
PoggendorflTs,  249 
Pollak's,  250 
reduction,  240 
regenerative,  250 
reversible,  202,  251 
secondary,  253 
von  Tiirin's,  224 
Weston's,  124,  252 
Endothermic  reaction,  98 
Energy,  bound  and  free,  209 

transformation  of,  in  the  element,  203,  244 
Equilibrium  between  several  electrolytes,  188-200 
complete,  71,  72 
heterogeneous,  73 
homogeneous,  73,  84 
incomplete,  71 
influence  of  pressure  on,  98 

temperature  on,  93,  193,  291 
maximum  and  minimum,  96 
mobile,  82 
Equivalent,  chemical,  7,  118 

electrochemical,  7,  117 
weight,  8 
Erg,  11 

Ester,  equilibrium  in  hydrolysis  of,  70,  89 
saponification  of,  70,  102,  182,  193 
Ethyl  acetate,  equilibrium  in  solution  of,  89 

saponitication  of,  70,  102,  182,  193 


334  INDEX    OF    SUBJECTS. 

Ethyl  ether,  vapour  pressure  of,  43 
Exothermic  reaction,  98 


FARADAY'S  law,  4,  7,  22,  117,  120,  270,  308 

Force,  electromotive,  5,  111,  123,  185,  201,  218,  230,  237,  240,  300 
"  Forming  "  of  battery  plates,  261 
Franklin's  plate,  230 
Free  energy,  209 
ions,  114 
valency,  24,  66 
Freezing  point,  49 

apparatus,  51 
depression  of,  54 
molecular  depression  of,  56,  159 
Friction,  action  of  non-electrolytes  on,  150 

coefficient  of,  153 

galvanic,  122 

internal,  150,  172 

of  the  molecules,  155 
Furnace,  arc  light,  301 

Borchers',  299 

Cowles',  297 

Ducretet's,  302, 

Heroult's,  295 

King's,  304 

Lejeune's,  302 

Maxim's,  298 

Memmo's,  305 

Moissan's,  302 

MiihlhaeuserV  300 

Rathenau's,  303 

resistance,  299 

Zerener's,  301 
Fused  electrolytes,  295 

GALVANIC  elements,  202 

of  the  Daniell  type,  205 
friction,  122 
Gas  element,  253 

evolution  during  electrolysis,  1,  253,  257 
ideal,  77 
voltameter,  286 
Gases,  electrolytic  dissociation  of,  308 

electromotive  action  of,  309 
Gay-Lussac's  law,  13,  25,  30 


INDEX   OF   SUBJECTS.  335 

Gibbs'  phase  rule,  73 
Gilding,  283,285 
Gold,  deposition  of,  274 
Gram-equivalent,  9 
Gram-ion,  9 
Gram-molecule,  9 
Grotthuss'  chain,  21,  110,  113 
Grove's  element,  249 
Guldberg  and  Wciage's  law,  86 

HEAT  of  dissociation,  194 

of  water,  194,  294 
ionisation,  238 
Joule,  206,  277,  288 
local,  206,  240,  289 
mechanical  equivalent  of,  11 
of  neutralisation ,  196 
solution,  92,  239 
vaporisation,  48,  49,  90 
Helmholtz's  calculation  of  E.M.F. ,  207 

concentration  element,  212,  251 
electrochemical  theory,  22 
Henry's  law,  77,  255 
Heroult's  furnace,  295 
Heterogeneous  equilibrium,  72 

system,  69 
Hoffs,  van't;  law,  31,  39,  60,  76,  77,  110,  226 

deviations  from,  57,  59,  60,  76,  110,  158,  183 
Homogeneous  equilibrium,  70,  84 

system,  69 

Hydriodic  acid,  dissociation  of,  88 
Hydrochloric  acid  methyl  ether,  dissociation  of,  89 
Hydrocyanic  acid,  formation  of,  306 
Hydrodiffusion,  152 
Hydro  elements,  202 
Hydrogen  selenide,  dissociation  of,  98 
Hydrolysis,  193 
Hydroxyl  ions,  150,  182,  193 
Hygroscopic  substances,  vapour  pressure  of,  46 
Hypochlorite,  manufacture  of,  285 
Hypothesis  of  Avogadro,  25 

Clausius,  114,  136 

IDEAL  dilute  solution,  77 
gas,  77 


33<$  INDEX   OF    SUBJECTS. 

Incomplete  reaction,  71 
Indicators,  178 

electrometer  as  an,  269 
Indium  chlorides,  68 
Insulators,  235 
Internal  friction  of  salt  solutions,  150,  172 

pressure,  27 
International  ohm,  123 
Inversion  of  sugar,  69,  100,  182 
lodoform,  preparation  of,  285 
Ions,  4,  113,  118,  137,  225 

absolute  velocity  of,  147 
in  chemistry,  118,  178 
coloured,  178 
complex,  146 
concentration  of,  242 
negative,  4 
organic,  144 
positive,  4 

Ionic  charge,  118,  185 
migration,  138 

in  mixed  solutions,  145 
mobility,  140,  144 
lonisation,  heat  of,  238 
Iron  chlorides,  67 

deposition  of,  273 
separation  of,  282 
Irreversible  elements,  202,  248 
Isohydric  solutions,  188 
Isothermal  expansion,  15 
Isotonic  coefficients,  37 
solutions,  27 


JABLOCHKOFF  lamp,  291,  298 
Joule  heat,  206,  277,  288 
Julien  metal,  266 


KELLNER'S  process,  281 

Kilogram-metre,  203 

Kilowatt,  11 

Kinetic  considerations,  82,  86,  105,  114,  121 

King's  furnace,  304 

Kirchhoffs  law,  129 

Kohlrausch's  law,  140 


INDEX   OF    SUBJECTS.  337 


LALANDE  and  Chaperon's  element,  250 
Law  of  Avogadro,  25 

Boyle,  25 

constant  and  multiple  proportions,  23 

Dalton,  32 

dilution,  163,  308 

distribution,  80 

Faraday,  4,  7,  22,  117,  120,  270,  308 

Gay-Lussac,  13,  25,  30 

Guldberg  and  Waage ,  86 

Henry,  77 ,  255 

Hoff,  van't,  31,  39,  60,  76,  77,  110,  226 

Kirchhoff,  129 

Kohlrausch,  140 

mass  action,  86 

moduli,  172 

Ohm,  5,  120 

Ostwald,  163,  309 

Oudemans,  177 

Raoult,  42 

van  der  Waals,  26 
Lead,  deposition  of,  274 
accumulators,  261 
Leafy  metallic  deposit,  282 
Leclanche"s  element,  249,  250,  266 
Legal  ohm,  123 
Lejeune's  furnace,  302 
Ley  den  jar,  307 

Light,  absorption  of,  by  salt  solutions,  177 
arc,  289 

furnace,  301 

refraction  of,  by  salt  solutions,  173 
Limit  of  reaction,  71 
Liquid  cells,  218 
Local  current,  250,  266 

heat,  206,  240,  289 
Lowering  of  freezing  point,  50 

molecular,  56,  159 
vapour  pressure,  39 

relative,  41 


MAGNET,  action  of,  on  arc  light,  301 
Magnetism,  atomic,  176 

molecular,  175 


338  INDEX   OF   SUBJECTS. 

Magnetic  rotation  of  solutions,  174 

Manganese,  deposition  of,  274 

Mass  action,  law  of,  86 

Maxima  and  minima  in  equilibria,  90 

Maxim's  furnace,  298 

Maximum  conductivity,  134 

work,  207 
Mechanical  equivalent  of  heat,  11 

work,  11 
Megerg,  13 
Megohm,  13 

Meidinger's  element,  245 
Membrane,  semi-permeable,  28,  34,  84,  115 
Memmo's  furnace,  305 
Mercury,  deposition  of,  273 
separation  of,  282 
as  a  solvent,  61 
surface  tension  of,  231 
Metals,  deposition  of,  270,  280,  282 

molecular  weight  of,  61,  62,  66,  212 
replacement  in  salts,  20,  192 
solution  pressure  of,  225,  238 
Metallic  conduction,  120 

Methyl  ether  hydrochloride,  dissociation  of,  89 
Meyer's  concentration  element,  210 
Microvolt,  13 
Migration,  ionic,  138 

velocity,  138 

Mixed  solutions,  migration  in,  145 
Mixture  of  electrolytes,  conduction  by,  125 
equilibrium  of,  188 
Mixtures  of  solvents,  150 
Mobile  equilibrium,  82 
Mobility  of  the  ions,  140,  144 
Moduli,  Valson's,  172 
Moissan's  furnace,  302 
Mol,  9 
Molecular  conductivity,  128,  162 

depression  of  freezing  point,  56,  159 

dimensions,  231 

magnetism,  175 

normal  solution ,  10 

rise  of  boiling  point,  64 

weight  determinations,  42,  54,  57,  59,  61,  83,  155 
Monomolecular  reaction,  102 
Muhlhaeuser's  furnace,  300 


INDEX   OF   SUBJECTS.  339 

NEGATIVE  bodies,  20 

ions,  4 

Neutral  salts,  action  of,  109,  183 
Neutralisation,  195 

element,  247 

heat  of,  196 

volume,  198 
Nickel,  deposition  of,  274,  281 

separation  of,  282 

Nitric  acid,  reduction  of,  to  ammonia,  275 
Non-conductors,  23,  150,  235 
Non-polarisable  electrodes,  113,  221,  251 
Normal  elements,  5,  124,  251 
Normality  of  solutions,  10 

OHM,  4 

international,  123 

legal,  123 

Siemens',  4,  123 
Ohm's  law,  5,  120 
Oil,  electrolysis  of,  23 
Optical  properties  of  salt  solutions,  173 
Organic  ions,  mobility  of,  144 
Osmotic  pressure,  28,  31,  33,  38,  55,  107,  109,  110,  115,  183 

work,  75 

Ostwald's  law,  163,  309 
Oudemans'  law,  177 
Oxidation  elements,  240 

Oxide  formation  in  metallic  deposition.  272,  274 
Ozone,  16,  306,  309 
Ozoniser,  309,  310,  311 


PALLADIUM,  273 

as  semi-permeable  membrane,  31 
Partial  pressure,  31 
Peltier  effect,  206,  239,  240,  288 
Peroxide  precipitation,  274 
Phase  rule,  73 
Phases,  coexisting,  49,  73 
Physiological  measurement  of  osmotic  pressure,  35 

properties  of  ions,  180 
Planck's  formula,  227 
Plasm oly sis,  28 
Platinum,  273 


340  INDEX   OF    SUBJECTS. 

Platinum,  black,  132 

electrode,  132 
PoggendorfFs  element,  249 
Points,  action  of,  306 
Poisons,  physiological  action,  180 
Polarisation  current,  1,  253,  256,  309 

electrolytic,  1,  23,  129,  131,  133,  232,  249,  253,  259 
anodic,  260 
cathodic,  260 
maximum,  259 
Pollak's  element,  250 
Polyphase  current,  299 
Positive  bodies,  20 

ions,  4 
Potassium  cyanide  solution,  243 

nitrate,  osmotic  pressure  of,  29 
Potential,  5,  112 

difference,  6,  230 
fall  of,  6 

Precipitation,  189 
Pressure,  influence  of,  on  E.M.F.,  254 

equilibrium,  98 
reaction  velocity,  106 

osmotic,  28,  31,  33,  38,  55,  107,  109,110,  115,  183 
solution,  225,  238 
vapour,  39 
Primary  electrolysis,  3,  19 

metal  deposition,  280,  282 
Principle  of  maximum  work,  206 
Protoplasm,  28 


RATHENAU'S  furnace,  303 
Raoult's  law,  42 
Reaction,  bimolecular,  102 

complete,  71 

endothermic,  98 

exothermic,  98 

incomplete,  71 

limit  of,  71 

monomolecular,  102 

reversible,  71 

secondary,  258,  282 

velocity,  69,  100 

influence  of  pressure  on,  106 
specific,  101 


INDEX   OF    SUBJECTS.  341 


Reactivity,  179 
Reduction  elements,  244 

of  organic  compounds,  285 

oxides,  300 

Refilling  of  copper,  270 
Refraction  of  light  by  salt  solutions,  173 
Regenerative  element,  250 
Resistance.     See  Conductivity. 
Resistance  furnace,  299 
Reversible  element,  202,  251 

reaction,  71 
Rontgen  rays,  309 
Rotation,  magnetic,  174 

optical,  176 
Rule,  phase,  73 

Thomson's,  204,  208,  210 


SALTS,  action  of  neutral,  109,  183 
difficultly  soluble,  242,  269 

Saponification  of  ethyl  acetate,  70,  102,  182,  193 
Saturated  compounds,  23 
Secondary  deposition  of  metals,  282 
electrolysis,  3 
elements,  253 
reaction,  258,  282 

Semi-permeable  membranes,  28,  34,  84,  115 
Siemens'  unit,  4,  123 
Silent  discharge,  305 
Silver,  deposition  of,  274 
separation  of,  282 
voltameter,  280 
Solid  solution,  63 
Solution,  heat  of,  92,  239 
ideal  dilute,  77 
isohydric,  188 
isotonic,  27 

pressure  of  the  metals,  225,  238 
solid,  63 
Solubility,  82 

depression  of,  83,  189,  190 
influence  of  temperature  on,  91,  97 
Solvent,  influence  of,  on  dissociation,  152 

electrolytic  friction,  150 
Spark  discharge,  306 
Specific  conductivity,  127 


342  INDEX    OF    SUBJECTS. 

Specific  gravity,  109 

reaction  velocity,  101 
Spectra  of  gases,  307 

solutions,  177 
Spectrum,  absorption,  177 
Speed  of  ions,  138 

reaction,  69,  100 

in  heterogeneous  systems,  103 
Standard  of  E.M.F.,  123 

resistance,  123 
Streak  apparatus,  37 
Strength  of  acids  and  bases,  192 
Strong  electrolytes,  46,  133-138,  157,  164,  193-195 
Substitution,  166 
Succinic  acid,  distribution  of,  80 
Sugar,  inversion  of,  69,  100,  182 

osmotic  pressure  of,  29,  61 
Sulpho-salts,  274 
Sulphuric  acid,  formation  of,  306 
Sun,  condition  of  matter  in  the,  99,  295 
Surface,  nature  of,  in  metallic  deposits,  278,  281,  284 

tension  of  mercury,  231 

work  done  in  formation  of,  283 
System,  condensed,  72 

heterogeneous,  69 

homogeneous,  69 


TEMPERATURE, 6, 10 

absolute,  11 

coefficient  of  conductivity,  122,  141,  142,  198 
dielectric  constant,  198 
diffusion,  154 
E.M.F.,208,  238 
magnetism,  176 
osmotic  pressure,  30 
velocity  of  reaction,  104,  284 
influence  of,  on  equilibrium,  93,  193-198,  291 
metal  deposition,  271,  284 
molecular  weight,  65,  66  , 

solubility,  91,  97 
transport  number,  141 
velocity  of  reaction,  104,  284,  291,  308 
Tension,  solution,  225,  238 
Thermometer,  Beckmann's,  52 
Thomson  effect,  289 


INDEX   OF    SUBJECTS.  343 


Thomson  rule,  204,  208,  210,  264 
Three-phase  current,  299 
Tin,  deposition  of,  274 
separation  of,  282 
Transition  point,  72 
Transport  number,  138 

abnormal,  143 

Turpentine,  electrolysis  of,  23 
Turin's,  von,  element,  224 

ULTRA-VIOLET  rays,  309 
Units,  absolute  system  of ,  4 

Siemens',  4, 123 

Unpolarisable  electrodes,  113,  221,  251 
Unsaturated  compounds,  23 
Uranium,  deposition  of,  274 

VALENCE  charge,  23 
Valency,  doctrine  of,  66,  146 

free,  23,  66 
Valson's  moduli,  171 
Vaporisation,  heat  of,  48,  49,  90 
Vapour  pressure,  lowering  of,  39 

relative,  41 

Vegetation  process,  306 
Velocity  of  crystallisation,  104 
ions,  138 

absolute,  147 
migration,  138 
reaction,  69,  100 

influence  of  pressure  on,  106 
in  heterogeneous  systems,  103 
and  osmotic  pressure,  107,  182 
Vibrations,  electric,  307,  311 
Volt,  5,  123 
Volt-ampere,  11 
Volt-coulomb,  11,  203 
Volta  effect,  23,  235 
Voltaic  arc,  289 

pile,  17,  202 
Voltameter,  copper,  286 
gas,  286 
silver,  286 

Volume  change,  work  done  by,  12 
neutralisation,  198 


344  INDEX    OF    SUBJECTS. 

WATER,  conductivity  of,  196 

dissociation  of  vapour  of,  87,  292 

electrolytic  dissociation  of ,  87,  116,  193,  256,  292 

heat  of,  294 
power,  303 
Watt,  11 
Watt-hour,  264 

Weak  electrolytes,  147,  157,  158,  162,  193-195 
Weston  element,  124,  252 
Wheatstone  bridge,  129 
Wind,  electric,  305 
Wollaston  point,  309 
Work  done  by  change  of  volume,  12 

gas  evolution,  12 
electric,  6,  204 
maximum,  2C7 
mechanical,  11 
osmotic,  75 


ZERENER'S  electric  blowpipe,  301 
Zero,  absolute,  11 
Zinc,  deposition  of,  274 

separation  of,  282 

velocity  of  solution  of,  106 


THE  END. 


PRINTED  BY   WILLIAM   CLOWES   AND  SOXS,   LIMITED,   LONDON  AND  BECCLKS. 


UNIVERSITY  OF  TORONTO 
LIBRARY 


Acme  Library  Card  Pocket 

Under  Pat.  "Ref.  Index  File." 
Made  by  LIBEAEY  BUREAU,  Boston