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ELECTROCHEMISTRY
BY
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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 (P 2 ) 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 P lt and
hydrogen at P 2 . 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 P 2 . Suppose, now, that B be eliminated from the circuit
by connecting P x 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 P 2 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 P 2 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 P 2 with hydrogen.
The Electrolytic Decomposition of Water. Other
changes, besides the separation of gases, take place at the
plates PI and P 2 , 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 P 2
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 P 2 .
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 P 2 , and partly therein that the solution near
PI contains free acid, and that near P 2 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 P 2 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 P 2 consists in the dissolving of some of
the silver of the electrode PI and deposition of the same
amount of silver on P 2 , and further, the solution near PI
becomes more concentrated, whilst that near P 2 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
(P 2 ), 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 P 2 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 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 10 7 10" (
1 ampere 300 x 10 7 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 P 2 because the positive pole
PI has a higher potential than the negative pole P 2 .
Fall of Potential. In the example quoted it is
customary to speak of a fall of potential * between the poles
PI and P 2 in the solution.
If the potential difference between PI and P 2 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 10 7 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 P 2 a cm. distant it is
t 2 ^)> tnen between the two points there is a fall of temperature of
(*i - * 8 ) ^
-* degrees per cm.
i. CURRENT DENSITY. 7
P 2 , 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 P 2 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 P 2 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 (A1C1 3 ) is 133'5
grams, and one of ferric chloride (FeCl 3 ) 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 SO 4 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 H 2 S0 4 . 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 JH 2 S0 4 .
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 10 7 cm.
dynes = 9'81 X 10 7 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 10 7 = 0-418 X 10 8 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 10 6 dynes per sq. cm.
According to Avogadro's hypothesis (see below), a gram-
molecule of a gas at 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)
V T = 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 10 6 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 v r = 82 T c.c. to v T+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,
f vi
I pdv.
J v
From Boyle's law, pv = p v Qt it follows for a gram-molecule
of .gas that if p = 1 atmo. = 1*014 megadynes per square
centimetre, and if VQ = 82 T c.c.,
Pov =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 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
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 (S0 3 ) 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 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 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 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, M t 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 KN0 3
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 m 2 , 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 ra 2 ,
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^ Cy e 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 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 p t 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 j s ca iied 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 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
143-0
176-5
Potassium hydroxide, KOH
15-0
29-5
64-0
99-2
1400
181-8
223-0
Aluminium chloride, A1CI 3
225
61-0
179-0
3180
Calcium chloride, CaCl 2 .
17-0
39-8
95-3
1666
241-5
3195
Sodium sulphate, Na 2 SO 4 .
Succinic acid, C 4 H 6 O 4 . .
12-6
6-2
25-0
12-4
48-9
24-8
74-2
36-7
48-5
59-7
71-2
Citric acid, C 6 H 8 O 7 . .
Lactic acid, C 3 H 6 O 3 . .
Boric acid, B(OH) 3 . .
7-9
6-5
6-0
15-0
12-4
12-3
31-8 50-0
24 34-3
25-1 38-0
71-1
44-7
51-0
92-8
55-8
65-6
Sulphuric acid, H 2 SO 4
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 (H 2 S0 4 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
(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 (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'p f 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 p a , 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 p R .
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- p ia 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 2H 2 O
and 3H 2 0. 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 (CH 3 OH = 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 (CH 3 OH) 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
(C 2 H 6 = 46)
in benzene.
Cone. Mol.
% weight.
Ace tic acid
(CH 3 COOH = 60)
in benzene.
Cone. Mol.
o/o weight.
Phenol
(C 6 H 5 OH = 94)
in benzene.
Cone. Mol.
% weight.
Ethyl alcohol
(C 2 H 6 = 46)
in acetic acid.
Cone. Mol.
/o weight.
Ethyl alcohol
(C 2 H 6 = 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 combine 1 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
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 H 2 .
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 (P 4 =; 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, S 8 and P 4 , 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 (FeCl 2 ) and ferric chloride (FeCl 3 ). 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 N 2 0, N 2 3 , and N 2 5 . Besides these, however,
the oxides NO and N0 2 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
Ci2H 22 Oii + H 2 (-J- acid) = C 6 H 12 6 + C 6 Hi 2 6 (+ 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.
7 o 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 + CH 3 .COOC 2 H 5 = CH 3 .COONa + C 2 H 5 OH
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
CH 3 .COOC 2 H 5 + H 2 (+ acid) = C 2 H 5 OH -f CH 3 .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
C 2 H 5 OH + CH 3 .COOH (+ acid) = CH 3 .COOC 2 H 5 + H 2
(+ 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
CH 3 .COOC 2 H 5 + H 2 (+ acid) $ C 2 H 5 OH + CH 3 .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 $ Na 2 Mg(S0 4 ) 2 .4H 2 0+13H 2 O
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
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 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 A 2 , 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.
A 1 + A,= aT [21n + In 7 " 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
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 c 2 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.
C 2 .
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 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
NH 3 + HC1 $ NH 4 C1.
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 3 in the first vessel, and C, C 5 , and (7 6 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 C 3 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 (7 4 and 5 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 5 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
(7 4 to Oi or from 5 to C% in the different cases, the original
condition is established. During this last process the work
done will be
A 1 = RT\n Q and A 2 = 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 = = -
or = *
or G'i X C z = kC a and (7 4 x C 5 = 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 T t and li molecules of substance V, etc.,
the result would be
m]nC P + nlnC q + olnC a + . . . =f In C a 4- g In C r
+ h In C,+ _-.
or- CT X C* q X C\ = kC' s x C g r 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 (7 3 , 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 = kC 3
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=N lt
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
2H 2 $ 2H 2 + O 2 ,
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 C 3 , Ci, and <7 2 , 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
H 2 + I 2 = 2HI,
the values contained in the following table, which apply to
the temperature 440. p denotes the partial pressure of
the hydrogen at the beginning of the experiment, p' 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
N 2 4 ^ 2N0 2 ,
2N0 2 5> 2NO + O a ,
HC1 + (CH 3 ) 2 ^ (CH 3 ) 2 OHC1 (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
CH 3 COOH + C 2 H 5 OH CH 3 COOC 2 H 5 + H 2 0.
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 ~ ET 2
or- d ln p -
dT ' ET 1 '
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
4-5
12-5
15-6
16
1
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 r Ti 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 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
NH 4 C1$NH 3 + 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 p 3
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 C 9 - In C 3 ) _ 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
i m ~H x-^o -r if
vi. CHANGE OF HOMOGENEOUS EQUILIBRIUM. 95
where Kis a constant and C P , 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 P t 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 .o n9 - p( m T J + Ml
when M and i/i are two integration constants, which give the
value of In K and log K at temperature T Q . 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 T , ( ^ - ->_- ) is evidently
\2l Jo 7
negative, and In K greater than M, indicating that, with rising
temperature, the concentrations C P , C v etc., dimmish, whilst
the concentrations C st C T , 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 T .
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, C 8 , C T) or C Y) 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, Q p and the tem-
perature can be represented, according to Kegnault, by the
formula (for 1 gram)
Q p = 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
H P = (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 at temperature T = .. ,... = 715 C.
14-51
matter of fact, the heat of vaporisation becomes equal to
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 Na 2 S0 4 + 10H 2 (the ordinary crystallised Glauber
salt) into the anhydrous salt
Na 2 S0 4 . 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
PbI 2 + K 2 S0 4 $ PbS0 4 + 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
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 + CH 3 COOC 2 H 5 = CH 3 COONa + C 2 H 5 OH.
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-
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 : 2 3 ;
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 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
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 ?r a , then
KTT = 7r ;
or (K -f I)TT, ( = TT ; + TT,,
where K is a constant, i.e. the osmotic partial pressure 7r a of
the molecules which can be attacked stands in a constant
ratio to the osmotic pressure TT* -f ir a 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 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 10 43 water molecules, two are dissociated into
2H 2 and O 2 .
In the same way it can be shown that all possible com-
binations of hydrogen and oxygen, e.g. 0, H, OH, 2 H, 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 2 H 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
2 H does not really exist ; if, for instance, 10 100 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~NT0 3 ), partial exchange takes place, and
there are formed sodium chloride (NaCl) and calcium nitrate
(Ca(N0 3 ) 2 ). Now, if one atom of calcium ( = 2 equivalents)
were not charged with the same quantity of electricity as
two N0 3 radicles, or the two sodium atoms originally com-
bined with these, but had a greater positive charge, the
molecules of calcium nitrate (Ca(N0 3 )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 (Na 2 S0 4 ), or, as he
wrote it, Na^OSOs, the base NaOH collected at the negative
pole, and the acid H 2 S0 4 collected at the positive pole. He
therefore regarded Na 2 and S0 3 as the ions which, with
water, formed 2NaOH and H 2 S0 4 . Others were of the
opinion that the decomposition of Na 2 S0 4 takes place in the
same way as that of copper sulphate, CuS0 4 , namely, into
the metal Na, which, with water, forms NaOH with evolution
vin. COMPOSITION OF THE IONS. 119
of hydrogen, and the acid radicle S0 4 , which, with water,
gives H2S0 4 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. = 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 2 6.
tity of sulphuric acid at the positive.
If Berzelius's view were correct namely, that Na 2 and S0 3
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 (NH 4 ), methylammonium (CH 3 NH 3 ),
phenylammonium (C 6 H 5 NH 3 ), uranyl (U0 2 ), etc., which can
replace a metal, form the positive ions ; and the rest of the
molecule, hydroxyl (OH) in hydroxides, S0 4 in sulphates, N0 3
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 S0 4 , 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 S0 4 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
S0 4 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 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 were contained between the cross
sections. F 2 and Y, if the distance Y 2 Y = 2YiY. In other
words, in the first case the zinc ions which at time 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 S0 4 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 S0 4 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 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
I2 4
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 (ZnS0 4
-f 7H 2 0), 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 A t 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 ZnS0 4 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 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 10 7 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
K V 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 AC y
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 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,
NalTO 3 , CH 3 COOK, iK 2 S0 4 , iMgS0 4 , HC1, iH 2 S0 4 ,
OH 3 COOH, and NH 3 . 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 H 2 S0 4 , and has the specific gravity
1*223. The maximum specific conductivity K max . 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 y o K 18 = 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
3 6
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, X w ,
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 H 2 S0 4 , HC1, MgS0 4 ,
K 2 S0 4 , CH 3 COOK, NaN0 3 , 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
X 10 - X 5 = 4-07 ; for HC1, X 10 - X 5 = 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 X M . 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 X M . 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
X M 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
A oo
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,
A f 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 X M for potassium chloride
evidently represents the sum of the transporting powers of
the K and Cl ions, and since X KCloo = 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 S0 4 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 u c (observed) the observed transport number
of the cation, and under u c (calculated) the value calculated
from Kohlrausch's results for X_ and the Hittorf numbers
Salt.
uc (observed).
Observer.
u c (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
CuS0 4
0-375
Metelka
0-412
BaCl a
0-447
0-465
CdCl,
0-433
0-40
CdI 2
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.
u c
Temperature.
u c
NaCl
AgN0 3
CuS0 4
CdCl,
CdI 2
20
10
15
20
20
0-392
0-470
0-362
0-430
0-360
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 l m 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, NH 4 , Ag, and JS0 4 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, NH 4
63-6 Nitric acid, NO S
61-78
Silver, Ag
55-0 Chloric acid, CIO, 55 5
Barium, JBa
56-6
lodic acid, I0 3
33-87
Strontium, -JSr 53"3
Acetic acid, C 2 H 3 2
33
Calcium, ^Ca
52-3
Sulphuric acid, S0 4
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 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 Cd 3 I 6 , 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 Cd 2 I 6 (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 n c is the transport number for JCd:
V
U C
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 u c remains constant.
In a O'l -normal solution of copper sulphate, the transport
number for the anion S0 4 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 1 M 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 .
HC0 2
59-6
Acetic acid . .
Propionic acid .
CH 3 C0 2
C 2 H 5 C0 2
46-0
41-6 ~ Q
Butyric acid .
C 3 H 7 C0 2
37-8 **
Valerianic acid
C 4 H 9 C0 2
35-7 -K
Caproic acid .
Succinuric acid
Phthalouric acid
C 5 H 2 N 2 4
N 2 H 7 C 9 4
34-2
33-4
31-2
Phthalanilic acid
NH 10 C 14 3
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 (K 4 Fe(CN) 6 ), sodium platinichloride
(Na 2 PtCl 6 ), and sodium aurichloride (N"aAuCl 4 ), 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 A M 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 1 M for the
mobilities of the ions, however, we can easily calculate the
value of A M . From what has been said, it follows that
A^ is made up of the sum of the mobilities of the two
ions Moo and l Aoo of the salt MA ; thus, at 18 for potassium
chloride, A M = / 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 l Kco is subtracted, and that of
l ttoa 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, PP l 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 6 f f' 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 V t 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
N0 3
640
NH 4
Ag
660
570
CH 3 C0 2
C 2 H 5 C0 2
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
10 7 ergs is required to transport 1 coulomb against this
potential difference. Inversely, if the fall of potential is
1 volt per centimetre, then 10 7 dyne-cms, (ergs) are
required to transport 1 coulomb through 1 cm. against this
fall, i.e. the force necessary for 1 coulomb is 10 7 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
10 5
1 cm. per second must be ^= times greater, i.e. it must be
983,000 x 10 5
>- = 302 x 10 6 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
NH 4
H .
1490 ! Cl .
302
Ag. . 1725 N0
1450 | OH . . 552
1435 ! CH 3 C0 2 . 2810
1536 C 2 H 5 C0 2 . 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
3 1
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 . . .
S0 4 , C0 3 , 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 (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 P 2 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 10 6 kilograms, and that of P 2 for Cl, 1450 X 10
kilograms ; therefore for sodium chloride (NaCl) P = P\ 4- P 2
= 3630 x 10 6 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 10 4 ). We then obtain for sodium chloride at 18-
N = 49 > 289 x 8'64 x 10 4 -, .-, ,-
3,630 x 10 6
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 NaN0 3 . .... 1-03 1-15
HN0 3 2-22 2-32 | NaC 2 H 3 2 . . . 0-78 0-84
KOH ..... 1-85 2-07 NaCHO, .... 0-95 1-02
NaOH 1-40 1-55 ! NaC 6 H 8 SO s . . . 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
NH 4 C1 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
AgN0 3 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 '0034 at 18, and of PI
and P 2 , 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(NH 2 ) 2
CC1 3 CH(OH) 2
8 GO
. 10 165
2,500x10 kg.
3,800
Mannitol . . .
CH M 6
26 182
5,500
Cane sugar . .
Gum arable .
Qi2"-2?Pn
(C a H 10 O fi )
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 10 6 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.
KCaH 3 02.
iBa01 2 .
*K 2 S0 4 .
iZnS0 4 .
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
i 5 8
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, l m , 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 K 2 S0 4 =
2K + S0 4 ,?i= 3; for K 4 (CN) 6 Fe = 4K + (ClS T ) 6 Fe, = 5),
and if a 2 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 a 2 undissociated
molecules and atfi ions, which are to be regarded as free
molecules. From every gram-molecule, therefore, we obtain
1 a 2 4- na% = 1 -f (n I)a 2 molecules, and the observed
freezing point A must be greater than that calculated
1 oc
according to the chemical formula - ~~ in this ratio (/).
That is to say
_f A . 18*6 ,
/-> 4-r -y 1 +(,<- IK
from which a 2 can be calculated.
Non-electrolytes.
Bases.
Acids.
Methyl alcohol
ai 2
0-00 0-06
a l "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.
C 1
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 (7 AB = C' A x C K
where K is a constant.
If we dissolve an electrolyte, for instance, acetic acid,
it partially dissociates into the ions H and CH 3 C0 2 , 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 = C B ,
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 (7 AB = <7 A x C B = (-) 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 C 8 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
H 2 S0 4 = H + HS0 4 .
As the solution is diluted, the HS0 4 ions suffer further
dissociation
HS0 4 = H + S0 4 .
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 (CH 2 C1COOH) is considerably stronger than
acetic acid (CH 3 COOH); dichloracetic acid (CHC1 2 COOH)
is stronger than monochloracetic acid ; and trichloracetic acid
(CC1 3 COOH) 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
CH 3 COOH CH 2 C1COOH CHC1 2 COOH CC1 3 COOH
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).
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),
S b = 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, AiK 2 , A 2 Ki, and A 2 K 2 , 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 AiK 2 is the same as the
difference between the salts A 2 Ki and A 2 K 2 . We may put
this in the form
xi. SPECIFIC GRAVITY OF SOLUTIONS. 171
AJ^ - A 2 K! = AiK 2 - A 2 K 2 .
If we arrange a series of m negative ions, AI, A 2 , . . .
A, H , in a horizontal row, and a series of n positive ions, BI,
B 2 , . . . B f0 in a vertical row, then by combination of
these ions mn salts AB can be obtained, as the following
scheme shows :
Ax
A 2 . .
. A m
Bl
AiBi
A 2 Bi . .
. AJfc
B 2
AiB 2
A 2 B 2 . .
. A,, 4 B 2
B w AiB M A 2 B W . . . A m B
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 - AiB 2 = A 2 Bi - A 2 B 2 = . . . 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'
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 :
NH 4 K Na Li JBa JSr JCa JMg pin Zn
289 238 78 735 500 280 210 356 410
JCd JPb JCu Ag H Cl Br I N0 3 iS0 4
606 1087 434 1061 16 373 733 163 206
C 2 H 3 O 2 OH
- 15 20
The specific gravity of, e.g. a 3n JCaBr 2 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.
NH 4 .
A.
Li.
A.
K.
A.
Na.
I. .
954
14
940
8
932
8
924
NO 3 .
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.
C10 3 .
HOg.
C10 4 . H 2 P0 4 .
C 2 H 3 2 .
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 = N x + (a + V)x
we can calculate the refractive index n of a salt solution if
the normality (x) be known ; N x 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
H a , D, H^, and H y lines of the spectrum :
X.
H a . D.
H/3 .
H 7 .
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
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 H a :
= 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,.
*S0 4 .
iCO a .
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
m t = m (l - 0-00325 t)
where t is the temperature (centigrade), and m t and m 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,
Mn0 4 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, K 2 (CN) 4 Hg, 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 8 4
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
H 2 S0 4
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
C 2 H 5 COOH ....
C 3 H 7 COOH .
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
C 2 H 4 (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 NH 4 C1. 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
(NH 3 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,
10 4 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
10 4 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 10 4
volts, and e denotes the number of coulombs with which
the chlorine ions are charged, here equal to ^ 1 (T0 96,500=48 < 2,
since the cubic centimetre of the solution contains -
gram-ions. The force acting is therefore (see p. 6)
48-2 x 10 4 volt-coulombs per cm. = 48'2 x 10 11 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 at A.
According to p. 26, this is for the temperature 18
= 291 abs.-
84,688 x 291 X *& = 2*42 x 10 7 dynes.
The force is therefore 2 x 10 5 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~ 7 th 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 10 13 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 F B . Then if = *, no change
PA PB
in the dissociation will occur when the two solutions are
mixed. For if 7T A 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 F A to F" A + F B . Consequently, after mixing,
we have
r B )
CHAP. xii. PRECIPITATION. 189
If Pi ^ ^ fa Q 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, KN0 3 , Nad,
and NaN0 3 , present in the quantities M\, M 2 , M 3 , and M,
and whose degrees of dissociation are ai, a 2 , a s , and a 4 , there
exists the following relationship :
aii X a = a z z 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(AgCH 3 COO). 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' (Ag) x 6' (CH 3 COO) = K x C'(AgCH 3 COO),
and after the addition
Ci(Ag) x ft(CH 8 COO) = K* tf(AgCH 8 COO).
C'(AgCH 3 COO) is the same in both cases. On the other
hand, Ci(CH 3 COO) is greater than <7 (CH 3 COO) on account
of the addition of CH 3 COO ions from sodium acetate
or other compound. Consequently (7 2 (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, K y
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\ 7 ric 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
i 9 4 EQUILIBRIUM BETWEEN ELECTROLYTES. CHAP.
From the electromotive force of the element H 2 (Pt) |
Base | Acid | H 2 (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. 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 + H 2 0-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 H 2 0. 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
20 3 = 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 A 4) , 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 X M (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 A 9 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
HN0 3
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 | H 2 S0 4 | 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 | ZnS0 4 | CuS0 4 | 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, F 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 F , 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 = 10 7 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(F - 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 F - 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 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
H 2 S0 4 + 100 aq 1 CuS0 4 1 Cu 25065
1-00
1-00
Zn
H 2 S0 4 | CdS0 4 | Cd ... 8295 0-33
0-33
Zn
HC1 1 A<rf!l 1 Acr - 9704-0 1-08
1-06
Zn
H 2 S0 4
HN0 3 1C...
48040
1-92
1-86
Zn
H 2 S0 4
HN0 3 + 7H 2 | C
41405
1-65
1-69
Cu
Cu
H 2 S0 4
H 2 S0 4
K 2 Cr 2 7 + H 2 S0 4 | C
HN0 3 1C...
49895
22995
1-99
0-92
1-85
0-88
Cu
H 2 S0 4
HNO, + 7H 9 1 C
16340
0-65
0-73
Fe
FeCl 2 | Fe 2 Cl 6 | 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 (HN0 3 + 7H 2 0) 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 T y 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 (273 absolute).
Element.
23070P-W.
P.
23070P. W.
Obs.
Gale.
Cu
Cu
CuS0 4
+ 100H 2 | ZnS0 4 + 100H 2 | ZQ .
1302)2 + 100H 2 | Pb(C 2 H 3 2 )2
1-096
25263 ! 25035
208
214
+ 1001:
2 | pb
0*476
10980 ' 8261
2718
2422
Ag | AgCl
ZnCl 2 + 100H 2 | Zn . . . . .
1-031
23753 26085
-2330
-2574
Ag | AerOl
ZnCl 2 + 50H 2 1 Zn
1-017
9.-U48
24541
-1093
-1322
tf
AgCl
AgBr
ZnCl 2 + 25H 2 | Zn
0-974 22454
0'841 19386
23573
19963
-1169
582
-1270
667
ZnBr 2 + 25H 2 I Zu
Ag
AgNO
1 PhfWOY^ Ph .
0*932 25435
914.QO
39 7 K
3945
AC
AgNOo 1 OiifTCOo^ Ou
0-458 15090 10560 4460
4460
4
H g2
| 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 = I 1 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 S0 4 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 | CuS0 4 | CuS0 4 CuS0 4 | Cu,
2 x 96,500 coulombs (because a mol of CuS0 4 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 CuS0 4 \,
(1 - m) S0 4
mCu
mS0 4
CuS0 4 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
S0 4 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, Jf 2 , 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. M 2 dil. sol. M x cone. sol.
| c, TT, v | (1 - m)CuS0 4 | c + dc, TT + d-rr, v -dv \ .
214 ELECTROMOTIVE FORCE. CHAP.
In the first place, we force through M 2 towards the left
(1 m)dv c.c. of water. This process takes place against an
osmotic excess pressure which rises from 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
dA l = l ~- m dv . d(RTci).
2i
Now let MI be removed, and so much water forced from right
to left as was contained between M 2 and M b 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
dA 1 + dA z = (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 c
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|Iv01 mC1
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 p z
or = 86T . 10-" !LT- . i n & = 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, NH 4 C1
0-366
0-019
0-0183
0-0004
0-0211
0-0011
NH 4 C1, NaCl
0-218
0-0098
0-0126
KC1, HC1 . . .
- 0-688
- 0-0357
- 0-0397
KOI, HN0 3
0-719
0*0378
0*0414
KC1, H0 3 SC 9 H n ....
- 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 CuS0 4 | concentrated CuS0 4 | 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.ln P ~,
P*
T997MO * pi
or TT = - log .
n * p 2
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 + 7T 2 = ~ . - - . 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
P lBSir .+ 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 AgN0 3 | 0-01 AgN0 3 | 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 c a 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.
c x .
C 2 .
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
NH 4 C1
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 + 7T 2 = 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 CuS0 4 , and not only, as the
above formula gives us, their sum.
In order to obtain some analogy with the other formulae,
the form
TTO + 7r a = 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 ^ - _
* = ;r9poo ' ln F = -ir - 1 V 2 '
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\, q 2) 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 c 2 , 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 ^^ log 51 .
u + v c 2
A further simplification occurs when ^ = c 2 , *.. when the
total concentration is the same on both sides of the contact
surface. In this case we have
ri Ei + F 2
" Fx + ^ 2
and TT = 1-99 . 10~ 4 . T . log * "j" !1 2 -
r i -f- C/2
For a solution of one electrolyte, U\ = up, and V\ = vp ;
and for that of another electrolyte, Z7 2 = MI#>, and F 2 = 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
2 3 2
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 "
2 34
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, Hg 2 , 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 | Hg 2 S0 4 in H 2 S0 4 . 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 | Hg 2 S0 4 in rc-H 2 S0 4 = -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 | Hg 2 S0 4 in H a S0 4 (7i) | ZnS0 4 ( | Zn.
The electromotive force of this element has been found
to be 1*514 volts. If we subtract from this - 99 volt
for Hg | w-H 2 S0 4 , we obtain as remainder O524 volt for
Zn | ZnS0 4 . (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 | ZnS0 4 is taken as equal to 0*518
volt : see p. 240)
Magnesium
Zinc
10 18
Aluminium
Cadmium . .
Iron .
.... 10 13
10 3
Nickel .
Zn
ZnS0 4
MgS0 4 | Mg
Volls.
= -0-725
.'. Mg
I MgS0 4 =
Volts.
1-243
Zn
ZnS0 4
CdS0 4 j Cd
= 0-360
.'. Cd
j CdS0 4 =
0-158
Zn
ZnS0 4
FeS0 4
Fe
= 0-440
.'. Fe
FeS0 4 =
0-078
Zn
ZnS0 4
PbAc 2
Pb
= 0-607
/. Pb
PbAc 2 ^
-0-089
Zn
ZnS0 4
CuS0 4
Cu
= 1-100
.-. Cu
CuS0 4 =
-0-582
Zn
ZnS0 4
Ag 2 S0 4
Ag
= 1-539
/.Ag
Ag 2 S0 4 =
- 1-024
Zn
ZnS0 4
H 2 S0 4
H 2 (Pd)
= 0-760
/.H 2
H 2 S0 4 =
-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 = '000774 volt; for
Copper | Copper sulphate, '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 | CuS0 4 | ZnS0 4 [ Zn. In this there occur four potential
differences, namely
Zn | Cu,
Cu | CuS0 4 ,
CuS0 4 I ZnS0 4 ,
ZnS0 4 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 P 2 and p- 2>
the total electromotive force is given by -
1-99 X 10-V/i Pi , P a \
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.
S0 4
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 p t 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 | ZnS0 4 | 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 K 2 (CN) 4 Cu 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 10 207 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 SnCl 2 | NaCl | aCl + Br 2 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 | NaN0 3 | AglST0 3 | 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 | K0 3 Ka | N0 3 Ag | Ag,
(2) Ag | AgCl | NaN0 3 + NaN0 3 | 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 | S0 4 X | S0 4 Zn | Zn,
where X is divalent, hydrogen (H 2 ) or zinc in the Daniell
element, magnesium in Meidinger's element. On account
of the passage of the current, the chemical reaction
CuS0 4 + Zn = Cu + ZnS0 4
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,
SnCl 2 in KOH | SnCl 2 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.
SnCl 2 inKOH . . . .
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 ....
SnCl 2 inHCl
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
NaHS0 3
H 2 S0 3
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 H 2 S0 4 '
Potassium ferrioxalate . .
Potassium ferricyanide . .
Potassium bichromate . .
Potassium nitrite in H 2 S0 4 .
Chlorine in KOH ....
Nitric acid
KC10 4 inH 2 S0 4 . . . .
Br 2 in KOH
H 2 Cr 2 7
KC10 8 in H 2 S0 4 . . . .
Br 2 in KBr
. KI0 3 in H 2 S0 4 . .
Mn0 2 in HC1
C1 2 in KC1
KMn0 4 inH,S0 4 . . . .
Cu 2 Cl 2
Na 2 S 2 3
Na 2 S0 3
Na 2 HP0 3
FeS0 4
Hydroxylamine in HC1
Neutralisation Element. In the following element
electrical energy is produced on account of the neutralisation
process which takes place :
PdH | OHK | N0 3 K | X0 3 H | HPd.
It gives
Pd | H 2 | KN0 3 | KN0 3 | HHPd,
and therefore the process consists of the transformation of
248 OXIDATION AND REDUCTION ELEMENTS. CHAP.
KOH + HN0 3 into KN0 3 + H 2 0. 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 p a and C a 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 C a is known, the value of C b 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 KN0 3 , and at that
between KN0 3 and HN0 3 , 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 | H 2 S0 4 | Pt, we find that it gives
rise to a current which, however, soon ceases because H 2 is
xv. IRREVERSIBLE ELEMENTS. 249
deposited at the platinum electrode, and we then really have
the element
Zn | ZnS0 4 | H 2 S0 4 | H 2 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 | HaS0 4
| HN0 3 | 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 P = 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)
9T 7
dE = . In 1000 = 0-0879.
A molecule of hydrogen (H 2 ) 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 + dE l = 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- 4 log/,
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. e cE
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 (H 2 and
C1 2 ), hydrobromic acid (H 2 and Br 2 ), hydriodic acid (H 2
and I 2 ), 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 2 and H 2 , 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.
2 59
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 2 I 2' Ilorma l 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 S0 4
at the anode, and this latter, by reaction with the water, gives
H 2 S0 4 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 | CuS0 4 .
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 Pb0 2 + 2H 2 S0 4 + aq = 2PbSO, + 2H 2 + 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
w r hen 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 (H 2 S0 4 ) 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, Mn 3 4 , 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
Cu 2 S0 4 + H 2 ^ Cu 2 + H 2 S0 4
(or 2C + u + H 2 ^ Cu 2 + 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'2i*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
2H 2 +0 2 $2H 2 0.
If we denote the concentrations of the three substances
by H) Co, and (7 H2 o, 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 T 0>
log K=M. Now, at 20, T Q = 293 ; C^ = 55'5 (= xaon) ;
C* = 0-65 x 10- 27 ; and C = 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 (T Q -
~ 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
C H , consequently log C becomes greater by 0*1153 for each
degree ; C H 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
2C0 2 $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.
4000 3 .
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"a 3 AlF 6 ), 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 S y 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, E y 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
Si0 2 + 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),
3 02
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 = CaC 2 (Calcium carbide) + CO.
Instead of lime, an equivalent quantity of limestone
(CaC0 3 ) 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, 87 y
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 AUTHORS 1 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. 3 2 9
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."
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