Google
This is a digital copy of a book that was preserved for generations on Hbrary shelves before it was carefully scanned by Google as part of a project
to make the world's books discoverable online.
It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject
to copyright or whose legal copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books
are our gateways to the past, representing a wealth of history, culture and knowledge that's often difficult to discover.
Marks, notations and other maiginalia present in the original volume will appear in this file - a reminder of this book's long journey from the
publisher to a library and finally to you.
Usage guidelines
Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the
public and we are merely their custodians. Nevertheless, this work is expensive, so in order to keep providing this resource, we liave taken steps to
prevent abuse by commercial parties, including placing technical restrictions on automated querying.
We also ask that you:
+ Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for
personal, non-commercial purposes.
+ Refrain fivm automated querying Do not send automated queries of any sort to Google's system: If you are conducting research on machine
translation, optical character recognition or other areas where access to a large amount of text is helpful, please contact us. We encourage the
use of public domain materials for these purposes and may be able to help.
+ Maintain attributionTht GoogXt "watermark" you see on each file is essential for informing people about this project and helping them find
additional materials through Google Book Search. Please do not remove it.
+ Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Do not assume that just
because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other
countries. Whether a book is still in copyright varies from country to country, and we can't offer guidance on whether any specific use of
any specific book is allowed. Please do not assume that a book's appearance in Google Book Search means it can be used in any manner
anywhere in the world. Copyright infringement liabili^ can be quite severe.
About Google Book Search
Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers
discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web
at |http : //books . google . com/|
I
hzrn 3SCi2,?S/2>
SOLUTION AND ELECTROLYSIS.
ilottDott: C. J. CLAY and SONS,
CAMBRIDGB UNIVERSITY PRESS WAREHOUSE,
AYE MARIA LANE.
AND
H. K, LEWIS,
136, GOWER STREET, W.C.
l.(tp)tfl: F. A. BBX)GKHAUS.
^cf» lorft: MAGMILLAN AND GO.
Camtirftifft ^tural ^timtt iWamials!.
* Physical Series.
General Editor: — R. T. Glazeb^ook, M.A., F.R.S.
ASSISTANT DIRECTOR OF THE CAVENDISH LABORATORT,
FELLOW OF TRINITT COLLEQE, CAHBRIDaE.
©
SOLUTION AND ELECTROLYSIS
BY
WILLIAM CECIL DAMPIER ^HETHAM, M.A.
FELLOW OF TBINITY COLLEOE, CAMBRIDGE.
CAMBRIDGE :
AT THE UNIVERSITY PRESS.
1895
[All Rights reserved,]
Che-n-i5Vti^/16".3-
•2
V
y^cn^t^^^cii. irti > ^^ *
(SLamiiriDge:
PRINTED BT J. & 0. F. CLAY,
AT THB UNIVERSITY PRESS.
PREFACE.
TN the foUowiBg account of the phenomena of Solution
-■- and Electrolysis an attempt has been made to separate
the description of the facts of the subject, and of the
necessary theoretical consequences of those facts, from the
consideration of the hjrpotheses which have been framed in
order to explain them. It would be inconvenient, how-
ever, to adhere strictly to such a plan. Many experimental
investigations, which have been undertaken by the light
of the dissociation theory, would, although they may be
explicable in other ways, have merely bewildered the
reader, had he no working hypothesis to guide him through
the maze of their detail. For an account of many such
investigations the last chapter, which deals with theories
of Electrolysis, must, therefore, be consulted. Neverthe- -^f
less, the broad experimental outlines of the subject are
sketched in the earlier part of the book, and theoretical
ideas, except those which necessarily follow from the facts,
are only provisionally introduced.
A considerable part of the matter of the first six chap-
ters has been taken from the second edition of Professor
Ostwald's Lehrhuch der Allgemeinen Chemie, the portion
of which dealing with solutions has been translated into
VI PREFACE.
English by Mr Pattison Muir. For a fuller account of the
developments of the dissociation theory, the reader must
be referred to the second volume of that Lehrbuch, and to
Professor Nemst's Theoretische Chemie, an English trans-
lation of which, by Professor C. S. Palmer, has just
appeared.
A complete description of all work on electrolysia,
which appeared previously to 1883, will be found in
Wiedemann's Electridtdt, and useful summaries appear
in the Reports of the British Association for the years
1885, 1886, 1887 and 1890.
Those wishing to consult the original papers will find
references to them in the following pages. In order to
give clearness to chronological ideas, the date of each
paper is given.
A valuable collection of data on the conductivities
and migration constants of solutions was made by the
Rev. T. C. Fitzpatrick, and published by the British
Association in 1893. By the kind permission of the
author and of the Council of the British Association, I
have been allowed to reprint these tables as an appendix
to this book.
My best thanks are due to Mr R. T. Glazebrook and
Mr J. W. Capstick for their kindness in reading the
proofs, and for the many valuable criticisms and sugges-
tions they have made.
Trinity College, Cambridqe.
May 22, 1895.
CONTENTS.
CHAP. PAGE
I. Introduction X
Properties of Solution. Range of the Subject.
II. Solutions in Gases 8
Solutions of Gases in Gases. Solutions of Liquids
in Gases. Solutions of Solids in Gases.
III. Solutions in Liquids. Solubility .... 10
Solubility of Gases in Liquids. Measurement of
Solubility. Henry's Law. Solutions of Gases in Salt
Solutions. Solubility of Liquids in Liquids. Solu-
bility of Solids in Liquids. Influence of Pressure on
the Solubility of Solids. Influence of Temperature.
Analogy between Solution and Evaporation. Solu-
bility of Mixtures. Solubility in Mixed Liquids.
Table of Solubilities.
IV. Diffusion and Osmotic Pressure , ... 32
General Principles of Difiusion. Osmotic Pressure.
Application of the Gaseous Laws to Solutions. Ap-
plication of Thermodynamics. Diflfusion through
Liquids. Experiments on Diffusion. Dialysis.
V. Freezing Points of Solutions .... 54
Historical. Connection with Osmotic Pressure
and other Theoretical Considerations. Experimental
Methods. Determination of Molecular Weight. In-
fluence of Concentration. Cryohydrates. Melting
Points of Alloys.
VI, Vapour Pressures op Solutions .... 74
Theoretical Considerations. Boiling Points. Ex-
g)rimental Methods. Influence of Concentration,
etermination of Molecular Weights. Solutions of
Gases in Liquids. Solutions of Liquids in Liquids.
VII. The Electrical Properties of Solutions , . 103
Historical Sketch. Faraday's Laws. Polarisation.
Accumulators. Primary Cells. Contact Difference of
Potential. Source of the Energy of the Current, and
Theory of the Voltaic Cell.
VUl CONTENTS.
CHAP. PAGE
VIII. Electrical Properties (continued) .... 127
The Nature of the Ions. Secondary Actions.
Practical Applications of Electrolysis. Complex Ions.
The Migration of the Ions. The Velocities of the
Ions.
IX. Electrical Properties (contimied) .... 143
Resistance of Electrolytes. Experimental Me-
thods. Experimental Results. Consequences of
Ohm's Law. Influence of Concentration on Conduc-
tivity. Dissociatiou Theorjr. lonisation. Influence
of Concentration on lonisation. Resistance of Liquid
Films. Electrical Endosmose.
X. Connection between Electrical and other Pro-
perties 162
Conductivity and Chemical Activity. Conduc-
tivity and Osmotic Pressure.
XI. Theories op Electrolysis 170
Introduction. The Dissociation Theory. Chemical
Properties. Independent Ionic Velocities. Densities
of Salt Solutions. Colours of Salt Solutions. Other
Properties. General considerations. Development
of the Dissociation Theory. Dissociation of Mixed
Solutions. General case of Chemical Equilibrium.
Thermal Phenomena. Difl'usion of Electrolytes in
Solution. Contact Difference of Potential. Dissocia-
tion of Water. Function of the Solvent. Hydrate
Theory of Solution. Conclusion.
Appendix 213
Freezing Points.
Table of Electro-Chemical Properties of Aqueous
Solutions 215
Index 285
On page 28, second line,
for
read
ERROR.
dp 1
dT'\~RT^
dT'p'ET^'
CHAPTER L
INTRODUCTION.
1. Properties of Solution. When common salt
is placed in water, the crystals slowly disappear, and a
solution of the salt in water is formed. The presence
of the salt can easily be recognised by taste, and it
can be regained in the solid form if the water is boiled
away. In presence of the solvent, water, the cohesion of
the molecules of salt in the crystals is in some way
overcome, and they are able to form part of a perfectly
homogeneous liquid. Let us study the changes' which
go on in such a case a little more closely. If we take
a large mass of salt and add only a little water, after
a time no more solid disappears. We now have what is
called a saturated solution. If we apply heat, however, we
shall find that as the temperature increases, the water is
able to dissolve more salt (very little more of the par-
ticular substance we have chosen, but of some things much
more) — thus the solubility depends on temperature. Now
let the solution cool. Little crystals form in the liquid
till, when the temperature has fallen to the point at which
we began, exactly the same amount of salt as at first is
w s. 1
SOLUTION AND ELECTROLYSIS.
[CH. I
dissolved in the water. For each temperature there is a
fixed and definite amount of salt in the same volume of a
saturated solution, however that solution is prepared. It
will be convenient to represent this on a diagram. Let
us divide OX, the horizontal axis of our figure, into 100
equal lengths to represent degrees on the Centigrade ther-
mometric scale, and OT the vertical axis into 100 equal
lengths to represent the parts by weight of salt which will
Fig. 1.
dissolve in 100 parts of water. Let us then make a series
of measurements at intervals of 10 degrees of the mass of
salt in a solution saturated at each temperature. Suppose
we find that at 10° Cent. 35*7 grammes of salt are
dissolved in 100 grammes of water. From the point
marked 10° in the line OX let us draw a straight line
CH. l] INTRODUCTION. 3
vertically upwards, and from the point corresponding to
35*7 in OY a straight line horizontally to the right.
These lines meet in the point P which evidently com-
pletely expresses the amount of salt dissolved by 100
grammes of water to form a saturated solution at 10" C.
If we do the same at temperatures of 20*^, 30°, &c. we get
a series of points, and if these are all joined by a smooth
line, we get what is called a " Solubility Curve" — that is a
curve shmving the way in which the solubility of the salt
varies with the temperature. In the figure three such
curves are given, shewing the solubility in water of the
three substances, sodium chloride (common salt), potassium
chloride and potassium nitrate. It will be seen that the
three curves are very different. Not only are the solu-
bilities of the three salts different at any one temperature,
but the curve for potassium chloride, and still more that
for potassium nitrate, is more steeply inclined than the
curve for sodium chloride, shewing that the solubility of
the two potassium salts increases more for a given rise
of temperature than does that of the sodium salt.
When we dissolve sodium chloride in water an absorp-
tion of heat is observed. That is to say, if both salt and
water when separate are at the temperature of the air,
after the solution is formed its temperature is lower. On
the other ^hand caustic potash gives an evolution of heat
on dissolving and the temperature rises. During solution
there are usually changes in volume. In all but rare cases
contraction occurs, and the volume of the resultant
solution is less than the sum of the volumes of the solvent
and the substance dissolved, or solvend.
1—2
-r
4 SOLUTION AND ELECTROLYSIS. [CH. I
The boiling point of a salt solution is higher than that
of pure water ; and when it is remembered that a liquid
boils when the pressure of its vapour is equal to the
atmospheric pressure acting on it, we see at once that this
statement is equivalent to saying that the vapour pressure
of water is reduced by the dissolved salt. The steam
which comes oflF however is the steam of pure water and
will be found to assume the temperature at which pure
water boils. Thermometers are graduated by marking on
them the places at which the mercury stands at the
freezing point and boiling point of water. It will be now
seen why it is necessary during the latter operation to put
the instrument in the steam and not in the water, which
may contain impurities and be consequently boiling at a
temperature slightly above 100° C. — its normal boiling
point. Closely connected with this lowering of the vapour
pressure is the lowering of the freezing point also pro-
duced by the substance in solution. Thus salt water does
not freeze at a temperature low enough to solidify fresh
water. Here again it is important to observe that the ice
frozen out is the ice of pure water. Sometimes, par-
ticularly if the process of freezing has been rapid, particles
of solid salt are shut in by the ice, and therefore redissolve
when it is melted, but they are quite distinctly separated
from the solid ice and never crystallize out in combination
with it.
Many solutions are found to be good conductors of
electricity, but in all such cases the passage of the current
is accompanied by certain chemical changes, the dissolved
substance being in general decomposed into two parts, one
CH. l] INTRODUCTION. 5
of which is set free at the anode— the place at which the
current enters the liquid — and the other appearing at
the kathode, where it leaves. These liberated components
often attack the solvent, and secondaiy chemical actions
go on, so that the body finally liberated is not always the
same as that primarily formed by the action of the current.
The main body of the solution is apparently unaltered, all
the products of decomposition appearing at the electrodes.
In this book we shall examine in greater detail these
and other properties of solutions, point out how far they
can be correlated and shewn to depend on one another,
and consider their bearing on the question of the nature
of the process.
3. Range of the Subject. The popular use of the
term solution is restricted to the substances formed when
solids dissolve in liquids, but many pairs of liquids will
form mixtures which have properties exactly analogous to
those described in the first section. Thus sulphuric acid
and water are miscible together in all proportions, and the
resultant body can be regarded either as a solution of
sulphuric acid in water or of water in sulphuric acid.
Many gases too are readily absorbed by liquids, and form
solutions in which their properties are to some extent
retained. Examples which will readily occur to everyone
are ammonia and hydrochloric acid ; while the fact that
fish can breathe under water shews that even atmospheric
air is to some extent soluble in that medium.
Many metals, such as silver and gold, will dissolve
in the liquid metal mercury to form amalgams or
alloys which exhibit many of the properties we have
6 SOLUTION AND ELECTROLYSIS. [CH. I
described above as characteristic of solutions, and even
alloys which are solid at ordinary temperatures, such as
compounds of various metals with sodium or with tin,
must be put in the same group.
We can if we like consider mixtures of gases as
solutions of one in the other, thus getting an ideally
simple case, undisturbed by many factors which influence
the properties of the more complicated structures to which
the term solution was at first restricted.
Ostwald defines solutions to be "homogeneous mix-
tures which cannot be separated into their constituent
parts by mechanical means." Unless we read more
meaning into the word "mixtures" than it usually
implies, this would include all chemical compounds, and,
although no definite line can be drawn between the
processes of solution and chemical action, such a result
would be inconvenient for purposes of classification.
Chemical compounds are distinguished by constancy of
composition, and their elements unite in definite propor-
tions. Thus water is produced when two volumes of
hydrogen unite with one of oxygen. If a little oxygen is
present in excess we get, not a new compound, but water
and uncombined oxygen. In the case of solutions how-
ever the constituents need not exist in any particular
proportion. Thus if we have a solution of one molecule
of sulphuric acid in three molecules of water, we can
gradually add either sulphuric acid or water, and get
gradual changes in the properties of the resultant liquid.
This could of course be explained by saying that another
definite compound was formed (say H2SO4 . ^HjO), and that
CH. l] INTRODUCTION. 7
intermediate solutions consisted of mixtures of this with
the original HaS04 SHjO, in the same way that we could
prepare mixtures of water and hydric peroxide whose
percentage composition should be anjrthing we liked
between that of the two oxides of hydrogen. The number
of chemical compounds of two elements is however in
general small, while in the case of solutions (especially of
pairs of liquids miscible in all proportions) we should often
have to suppose that a great many wei^e possible. These
considerations enable us to frame a definition which will,
in the present stage of our knowledge, comprise exclu-
sively those bodies we call solutions.
Definition. Solutions are homogeneous mixtures
which cannot be separated into their constituent parts by
mechanical means, the proportion between the parts being
continuously variable between certain limits^ with a corre-
sponding continuous variation in properties,
. We shall begin by considering solutions in gases, and
then the simpler cases of solution in liquids, leaving till
later an account of the more complicated substances
formed by dissolving mineral salts and acids in water.
This will prevent any attempt to treat the subject his-
torically, for, as is so often the case, the most obvious is
not the most simple, and much trouble was needed, and
many misleading threads were followed, before this
tangled skein shewed any signs of becoming unravelled.
CHAPTER II.
SOLUTIONS IN GASES.
3. Solutions of Gases in Gases. Two gases
which do not chemically interact can always form a
homogeneous mixture with each other in all proportions.
In the ideal case of two perfect gases all the properties
of the mixture would be accurately the sum of those
of the constituents. For instance, if the volume be kept
constant the pressure of the mixture would be equal to
the sum of the pressures exerted by each gas, while if the
pressure be kept constant the resultant volume would be
the sum of the individual volumes. In any real case these
relations are only approximately fulfilled, the deviations
becoming greater as the gases, either by cold or. pressure,
are brought nearer their points of liquefaction. These
gaseous laws are obeyed by any matter existing in a
finely divided state in which the particles are too far
apart to exert any appreciable influence on each other
for the greater part of the time. The physical properties
then depend only on the number of particles and are in-
dependent of their nature. Cases which approach this
will be found in dilute solutions in liquids, though here
the influence of the solvent can seldom be neglected.
CH. Il] SOLUTIONS IN GASES. 9
4. Solutions of Uquids in Gases. When a
liquid evaporates into a space already filled with a gas,
a solution of the vapour in the gas may be supposed to
be present. As an approximate law Dalton found that
the quantity of vapour in a given space was finally the
same as if the space had originally been a vacuum^ so
that the final pressure was the sum of the pressure of
the gas and the vapour pressure of the liquid. Regnault^
Galitzine* and others have shewn that the vapour pressure
of a liquid in a gas is in general less than in a vacuum,
the deviations depending on the nature of the liquid
and gas, as well as on their conditions of temperature,
pressure, &c. Some of the gas may dissolve in the liquid
and lower its vapour pressure, just as any other kind of
dissolved matter — salt for example — would do. This
must also be considered, as well as the forces between
the molecules of the gas and vapour.
5. Solutions of Solids in Gases. Some solids
will sublime without going through a liquid condition,
and it is probable that laws similar to those just de-
scribed hold good in these cases. Sometimes, under the
influence of a gas at high pressure, a solid will sublime
at a lower temperature than that usually necessary, thus
forming a solution of a solid in a gas.
1 MSm, de VAcad. 26, p. 679.
* Dissertation^ Strassburg, 1S90.
CHAPTER III.
*
SOLUTIONS IN LIQUIDS. SOLUBILITY.
6. Solubility of Gases in Uquids. It appears
that every gas is to some extent soluble in every liquid,
though immense differences in solubility occur. When the
amount dissolved has been great, it is generally found that
chemical action has gone on, and the gas cannot be
completely expelled by lowering the pressure, or increasing
the temperature. As an example of this we may take the
case of hydrochloric acid dissolved in water. On the
other hand air, oxygen, hydrogen and other slightly
soluble gases can be completely removed ; the process of
solution seems to be purely mechanical. But even in
these cases the solvent exerts a selective influence, the
gases differing from each other in solubility.
Let us examine these cases in which there seems to be
no chemical action. The mass of a gas like oxygen which
will dissolve in a given mass of water, is proportional to
the pressure of the gas, or since the volume of a given
mass of gas varies inversely as its pressure, the volume
which goes into solution, measured under the pressure to
which it is subject in the liquid, is the same whatever
be the pressure. The reason of this law is at once
CH. Ill] SOLUTIONS IN LIQUIDS. SOLUBILITY. 11
evident if we consider what the mechanism of the process
must be. Molecules of gas must strike the surface of the
liquid and some must be retained, either by molecular
forces or by a process of entanglement or both. When
the number of these becomes great, some of them will
reach the surface from the body of the liquid with such
an energy of motion, and under such conditions, that they
are once more able to fly oflf into the gas. When the number
so leaving the solution in any given time is equal to the
number entering it from without, equilibrium is main-
tained, and the solution has become saturated with the
gas. If the pressure is reduced, the number of gaseous
molecules striking the liquid, and therefore the number
per second retained by it, are reduced in the same pro-
portion, while the rate at which they leave is at first
unchanged. The concentration of the gas in solution is
thus gradually lowered till equilibrium is again attained,
and the concentration bears once more its old relation to
the external pressure. At first sight it would appear that
the solubility of a gas should be unaflfected by an altera-
tion of temperature, since the number of molecules im-
pinging on the surface from within and without would be
changed in the same proportion. But here the influence
of the solvent comes in, and the molecular forces between
it and the gaseous molecules are reduced by increase of
temperature so that the solubility becomes less. It is
found that, in general, the solution of a gas in water, even
when the liquid is nearly saturated, is accompanied by
an evolution of heat. From this it follows by the
principles of thermodynamics (see p. 26), that the solu-
12 SOLUTION AND ELECTROLYSIS. [CH. Ill
bility will decrease with rising temperature. The fact
that heat is evolved in the solution of gases in water is of
great interest, for the state of a substance in solution
more nearly approaches its state when gasified than when
either liquid or solid, so that during the process of solution
of a gas less change goes on in the state of physical
aggregation than in other cases. This has been brought
forward as evidence in favour of the view that solution is
in all cases a chemical process, resulting in the formation
of definite liquid hydrates ^
7. Measurement of Solubility. In an experi-
mental determination of solubility it is necessary to take
precautions to ensure complete saturation, as the process
of diflfusion of matter from one portion of a liquid to
another is very slow. Many forms of apparatus have been
devised, the simplest being that used by Bunsen*, who
placed a measured volume of the gas in a graduated
tube over mercury and added a certain volume of the
liquid. The tube was then shaken in a water bath of con-
stant temperature, the open end being screwed against an
india-rubber plate. By repeatedly opening the end under
mercury and then closing it again and shaking, saturation
was obtained, the solubility being determined by measur-
ing the volume of gas left over, the volume of the liquid,
and the final pressure.
The solvhility of a gas has been defined by Ostwald'
to be the ratio of the volume of gas absorbed to the
^ See Pickering, Watts' Dictionary of Chenmtry, Art. Solution ii.
2 Pogg, Ann, 1865, 93, p. 10.
* Lehrhuch der allg, Chemie.
CH. Ill]
SOLUBILITY.
13
volume of the absorbing liquid, at any specified tempera-
ture and pressure, or
X =
V
V
Bunsen used a more complicated property, which he
called the absorption coefficient It is obtained from
Ostwald's "solubility" by reducing the volume of gas
absorbed to 0° C. at the pressure of the experiment. In
the cases in which no chemical action occurs, we have
seen that the volume of gas absorbed is independent of
the pressure, so that if /8 is Bunsen's absorption coeflR-
cient, and a the coefficient of gaseous expansion
Bunsen and others have determined many absorption
coefficients for water and alcohol. The following are some
of their results ^ :
Temp.
Hydrogen
In In
Water Alcohol
00215 0-0693
0-0190 0-0673
Oxygen
In In
Water Alcohol
0489 0-2337
0-0342 0-2232
Carbon Dioxide
In In
Water Alcohol
1-797 4-330
1002 3-199
8. Henry's I«aw. The law that the mass of a gas
dissolved is proportional to the pressure was given by
Henry*, who established it as an approximation by a series
of experimeuts on five gases at pressures varying from one
to three atmospheres. Buusen made more accurate ob-
servations, both by varying the pressure in his absorpti-
1 Bunsen, Fogg. Ann,, 1865, 93, p. 10. Winkler, Berichte, 1889, 22,
p. 1439. Timofejeff, Zeitschr, /. physikaL Chem, 1890, 6, p. 141.
« Phil Trans, 1803.
14 SOLUTION AND ELECTROLYSIS. [CH. Ill
ometer and by using a mixture of gases. If we have a
volume of gas at atmospheric pressure, consisting of equal
parts of two constituents, the total pressure is obviously
due half to one and half to the other, so that, restricting
our consideration to one gas, the pressure it exerts is half
that of the atmosphere. In this way by using mixtures
in which the proportion of one gas continually diminished,
its pressure could be reduced from one atmosphere to
zero, and it was found that the mass absorbed varied in
the same proportion.
In the case of such very soluble gases as ammonia, the
phenomena are not quite so simple, though at 100° C. the
law of Henry holds good\ If observations be made at
lower temperatures, however, the mass of ammonia ab-
sorbed is not proportional to the pressure, and the curve
drawn to shew the variation of solubility with pressure
when the temperature is kept at 0° C, shews two changes
of curvature. Sulphur dioxide behaves like ammonia,
the law only holding true above 40°. Hydrogen chloride
cannot be entirely removed from solution in water either
by reducing the pressure to zero or by boiling. If aqueous
hydrochloric acid be distilled, its strength will either
increase or diminish till a liquid of a certain composition
remains, which distils over unchanged. This composition
depends on the pressure at which the operation is carried
on; at normal atmospheric pressure the proportion of
hydrogen chloride is 20*24 per cent., at 50 mm. of mercury
pressure the proportion is 23*2 per cent., and at 1800 mm.
it sinks to 18 per cent.
1 Sims, Annalen, 1861, 118, p. 345.
CH. Ill] SOLUBILITY. 15
Thus deviations from Henry's law are found in the
case of gases which are near their points of liquefaction,
and therefore depart from Boyle's law, and also in cases in
which chemical action obviously occurs,
9. Solutions of gases in salt solutions. The
coefficient of absorption for a gas appears to be lowered
when a salt which does not act chemically on the gas
is previously dissolved in the water. In general, however,
chemical action does occur, and the gas dissolved may be
considered to consist of two parts — one being held chemi-
cally by the salt nearly independently of the pressure,
and the other varying with the pressure in accordance
with Henry's law. Good examples of this are seen when
carbon dioxide is dissolved in a solution of sodium car-
bonate or disodium phosphate. Solutions of similar salts
of equivalent strength absorb nearly equal quantities of
carbon dioxide — e,g, the sulphates of zinc and magnesium^.
The eflfect of mixing another liquid with the water is
similar to that of dissolving a salt in it — the absorption
coefficient for a gas is reduced. This holds even with
such substances as sulphuric acid and alcohol, which are
themselves in the pure state as good as or better than
pure water in absorbing power. Thus with sulphuric
acid Setschenoflf found for carbon dioxide a minimum
absorption coefficient when the composition of the liquid
was H2SO4.H2O. His results are as follows.
H2SO4 H2804+iH20 H2SO4+HJO HjS04+2HaO H2SO4 + 68H2O H2O
•923 -719 -666 -705 -857 -923
1 Setschenoff, 1876, Mima, de VAkad, P^tersb., 22, No. 6; 1889, Z.f,
physihal, Chemie, 4, p. 117.
16 SOLUTION ANP ELECTROLYSIS. [CH. Ill
These numbers shew that a mixture of sulphuric acid
and water absorbs less <;arbon dioxide than either liquid
does when pure. Similar relations are found to hold good
for other physical properties, e.g. the electrical resistances
and the viscosities.
lO. Solubility of laiquids in Uquids. When we
pass to the consideration of solutions of liquids in liquids we
find that there are three classes into which pairs of liquids
can be divided. Those in the first class are mutually
soluble in all proportions ; thus mixtures of alcohol and
water, or of water and sulphuric acid, can be prepared of
any composition. Those in the second class are soluble
in each other but not in all proportions ; thus water will
dissolve about ten per cent, of ether, and ether about three
per cent, of water, but if either substance be present in
excess it separates out forming a definite layer. The
third class consists of liquids which are insoluble in each
other, but these are few, and under proper conditions every
liquid appears to be to some extent soluble in every other
liquid. The divisions between these classes are dependent
on external conditions, thus liquids which are only
partially miscible at ordinary temperatures may mix in
all proportions when heated, and it is probable that all
liquids approach the condition of complete miscibility as
they approach their critical points ^
Measurements .of the mutual solubility of liquids have
been made by Alexejeff ', who placed weighed quantities
^ It is stated (Watts' Diet., Art. Solutions i.) that diethylamine and
water, though miscible in all proportions at low temperatures, cease to be
80 when heated.
2 Wied. Ann, 1886, 28, p. 305 ; Chem, Centr(ilbUUt,lSS2, pp. 328, 677, 763.
CH. Ill]
SOLUBILITY.
17
in a sealed tube and noted the temperature at which the
mixture became homogeneous.
The form of the solubility curve for a pair of partially
miscible liquids is shewn in fig. 2, in which the abscissae
represent temperature and the ordinates percentages of
dissolved substances in 100 parts of the solution. The
100%i
60%-
160'
Fig. 2.
curve a represents a solution of water and phenol; the
curve h water and aniline phenolate. At low temperatures
there are two definite states in which equilibrium is
attained — the lower branch of the curve representing a
solution of phenol in water, the upper branch a solution
of water in phenol.
11. Solubility of Solids in Liquids. Great differ-
ences in solubility are presented by various substances in the
same liquid, and bodies which are quite insoluble in one
liquid may be readily soluble in another. No satisfactory
explanation of these difierences can be given, though,
w. s. 2
18 SOLUTION AND ELECTROLYSIS. [CH. Ill
until this is possible, the essential nature of the process of
solution must be regarded as imperfectly understood. It
has been noticed that solution is more likely to occur if
the solvent and solvend are chemically somewhat alike,
than if they diflfer widely in their nature, (thus mineral
salts and acids are in general most readily dissolved by
water, while benzene is a more likely solvent for organic
substances), but even in this sense no general rule can be
framed. We must therefore be content in the present
state of knowledge to study the phenomena of solubility
without reference to the question of its fundamental
nature.
If we have a large quantity of a solid in contact with
a small quantity of liquid, solution will go on till a certain
saturation point is reached. The proportion between
liquid and solid in the solution, is then independent of the
amount of solid which is present in excess, and depends
only on the temperature, and, to a very slight extent, on
the pressure. If there is insufficient solid to produce
saturation, a more dilute solution is of course formed.
On the other hand an abnormally great amount of dissolved
substance can be retained, if the solvent be saturated at a
higher temperature and the clear liquid poured off from
the excess of solid and slowly cooled. We then get what
is called a Supersaturated Solution, If a small crystal of
the dissolved substance be dropped in, precipitation at
once occurs, and a solution saturated at the temperature
of the experiment is left. Any crystal isomorphous with
those of the dissolved body will produce the same eflfect.
The phenomena are well seen in the case of Glauber's salt,
CH. Ill] SOLUBILITY. 19
sodium sulphate, NaaS04 . lOHjO, supersaturated solutions
of which can be obtained of such strength that the
addition of a crystal of the salt causes the whole mass to
solidify, and gives rise to a considerable increase of tem-
perature. If a solution of this body be cooled to a low
temperature, it deposits crystals whose composition is
Na2S04 . 7H9O. If the temperature be still further lowered,
more of these crystals appear, while if it be raised some of
them redissolve. The solution is thus evidently saturated
with regard to them, and a definite equilibrium is at-
tained for each temperature. But the solution is all the
time supersaturated with regard to Glauber's salt, and the
introduction of a crystal of that salt will at once cause
solidification. It is thus clear that the conditions of
saturation involve an equilibrium between the solution
and the solid, so that if one of these be removed the same
conditions no longer hold. Measurements of various
physical properties of non-saturated, saturated and super-
saturated solutions have been made in order to find out
whether any sudden change of properties in the liquid
mark the point of saturation. Determinations of the
electrical conductivity, freezing point, specific gravity,
specific heat, heat of solution, rate of expansion, specific
viscosity, and molecular volume, have shewn that none of
these properties shew any abrupt change as the saturation
point is reached and passed. There is therefore nothing
abnormal in the state of a supersaturated solution as far
as the liquid is concerned. This result confirms our
conclusion that it is the absence of any solid in contact
with the liquid that changes the conditions of equilibrium.
2—2
20 SOLUTION AND ELECTROLYSIS. [CH. Ill
12. Influence of pressure on the solubility
of solids. This is very small, and accurate experimental
determinations are very diflScult. The dynamical theory
of heat indicates that the chief conditions determining the
change of solubility with increasing pressure are the heat of
solution of the salt in the nearly saturated isolution, and the
change in volume on solidification. The few experiments
which have been made seem to confirm this conclusion.
13. Influence of temperature. Many investiga-
tions on the influence of temperature on the solubility of
solids in liquids have been made from the time of Gay
Lussac to the present day. The solubility is usually defined
as the number of parts of the solid which can be dissolved
in 100 parts of solvent. It is determined either by shaking
up an excess of solid with the liquid till no more dissolves,
or by dissolving at a higher temperature, and then al-
lowing the solution to cool in contact with solid to the
temperature at which the measurement is to be made.
The quantity of dissolved substance is then determined
either by evaporating and weighing the residue, or by
chemical analysis. As a general rule solubility increases
with temperature, though several exceptions to this rule
are known, (e.g. calcium hydroxide, and sodium sulphate
between the temperatures of 33° and 100°). It is im-
possible, when studying the influence of temperature on
solubility, to miss seeing the analogy between the solution
of a solid in a liquid and the evaporation of a liquid into
a closed vacuous space. Just as for every temperature
there is a definite quantity of vapour present in the space
CH. Ill] SOLUBILITY. 21
when equilibrium is reached, so there is a definite quantity
of solid dissolved. Increase of temperature causes in the
one case more liquid to evaporate, and in the other more
solid to dissolve, till a new state of equilibrium is reached.
We shall see hereafter that just as a liquid exerts a
vapour pressure, so a solid in solution exerts a solution
pressure which can be recognised and measured by means
of certain phenomena, to which the name of osmose has
been given. The analogy between the two processes seems
thus very close, and this is borne out by the general
similarity of the solubility curves to curves which shew
the variation of vapour pressure with temperature. As
we remarked while studying supersatui'ated solutions, the
equilibrium is between the solid and the solution ; satura-
tion occurs when the number of particles leaving the
solid per second is equal to the number deposited by the
solution. Any change in the nature of the solid, such as
an alteration from the hydrated to the anhydrous form, or
a change in the number of molecules of water in the
hydrated molecule, upsets the equilibrium, and a new
saturation point results.
Thus calcium sulphate, CaS04, is more soluble in
water in the anhydrous form than as hydrated crystalline
gypsum, CaS04 . 2H2O. If we prepare a saturated solu-
tion of gypsum and bring it in contact with the anhy-
drous salt, it takes up more calcium sulphate. It thus
becomes supersaturated with regard to gypsum, and
would crystallise on the addition of a fragment of that
substance.
Now it can be shewn in two ways that the body which
22 SOLUTION AND ELECTROLYSIS. [CH. Ill
exists in solution is exactly the same whether it has been
obtained from crystalline hydrated gypsum, or from
anhydrous calcium sulphate. Firstly, none of the curves
shewing the variation of the different physical properties
(see p. 19) of the solution shew any change of curvature
as the point of saturation for gypsum is passed, so
that no new substance can have been introduced; and
secondly, when a hydrated salt is dissolved, the water of
hydration cannot be distinguished from the rest of the
water by any difference in molecular volume or other
physical property. It also follows from the densities of
solutions and from their thermal capacities (see § 80) that
the salt in solution affects the whole of the water together
and equally. We are thus prevented from supposing that
the solvent which contains as much hydrated gypsum as
it can take up, has still the power of dissolving a cer-
tain quantity of anhydrous salt as such, and of keeping
hydrated and anhydrous molecules simultaneously in
solution. This again drives us back to the view that
saturation is an affair of the solid as well as of the liquid
in contact with it.
A most interesting example of these cases is found in
the variation of the solubility of sodium sulphate with
temperature. The solubility goes on increasing from 0°
to 33°, but beyond that point it diminishes till a tempe-
rature of 100° is reached.
The explanation which was formerly given was that
below 33° hydrated salt ip present in solution, but that
above 33° it is converted into the anhydrous state. No
change in the physical properties of the solution can
CH. Ill]
SOLUBILITY.
23
however be detected, and the truth is that at 33° a change
occurs in the solid which is in contact with the solution.
The solubility up to 33° is that given by the equilibrium
between a solution of sodium sulphate and the crystals
Na^SO* . IOH3O (Glauber's salt), above 33° the solubility
is determined by the conditions of equilibrium between
the solution of sodium sulphate and the solid anhydrous
100l»
Fig. 3.
substance NaaS04. The diagram (fig. 3) thus really
consists of two distinct solubility curves, which cut each
other at 33°. In the case of Thorium sulphate the
hydrates are so stable that the course of both curves can
be traced beyond their point of intersection \
A long series of investigations on the influence of
temperature on solubility has been made by Etard and
Engel^ who find that many other sulphates agree with
1 Zeits. f, phys. Chemie, 1890, 6, p. 198.
s Comp. Rend. 1884-8, 98, pp. 993, 1276, 1432 ; 104, p. 1614 ; 106,
pp. 206, 740.
24 SOLUTION AND ELECTROLYSIS. [CH. Ill
Glauber's salt in having maximum solubilities at definite
temperatures, while certain calcium salts have minimum
values.
If solubility be defined as the parts of salt in 100
parts of solution, instead of 100 parts of solvent, each part
of the curve generally comes out as a straight line. Thus
the curve for copper sulphate consists of three straight
lines which meet at 55° and 105°.
As we have already remarked, the solubility increases
or diminishes with rising temperature, according as heat is
absorbed or evolved when some of the solvend dissolves in
the nearly saturated solution, so that the thermal effect
must change sign where maxima or minima occur in the
solubility curve.
The phenomena of supersaturation are now seen to be
quite comprehensible. When a liquid is cooled in contact
with the solid which would be deposited from it, the
precipitation goes on as the temperature sinks, so that
equilibrium is just maintained. If no solid be present
however, there is no reason for precipitation to occur, as
one of the two bodies which exist in equilibrium in the
usual case is absent. When the molecules of the dissolved
«
substance get so close together that chance aggregations
may produce crystalline structures of considerable size,
spontaneous crystallization may occur. The phenomena
suggest a comparison with the formation of water-drops
in moist air, which has been found by Aitken to require
the presence of dust particles or other nuclei for its
initiation. Surface tension is the cause which retards the
spontaneous formation of minute water-drops in clean air
CH. Ill] SOLUBILITY, 25
saturated with water vapour. This gives to the drops an
amount of potential energy proportional to their areas of
free surface. For a given volume of water, the total
area will be greater the smaller are the drops in which
it is diffused. The precipitation of the excess of water
in a mass of supersaturated air can only begin by the
formation of very minute drops, and consequently the
change might actually involve an increase in the total
potential energy of the system. When this is the case
spontaneous precipitation cannot occur, and the presence
of nuclei is necessary.
The same cause may prevent the formation of per-
manent crystals by the chance aggregations of molecules
of salt in a solution. The surface tension between solid
and liquid may be sufficient to increase the potential
energy and so prevent crystallization. If this explanation
is a true one the surface tension between solid and
liquid should be great in those cases which readily shew
the phenomena of supersaturation^.
14. Analogy between solution and evaporation.
An expression connecting the temperature variation of
vapour pressure with the latent heat of evaporation can be
deduced by the application of the second law of thermo-
dynamics, which states that in any cycle the ratio of
the work done by a reversible heat engine, to the heat
used by it, is the same as the ratio of the range of tem-
^ An account of the principle of minimum potential in its application
to solution and chemical action wiU be found in Liveing's " Chemical
Equilibrium."
26 SOLUTION AND ELECTROLYSIS. [CH.-IIl
perature to the absolute temperature of the source of
heat.
Let us suppose that we have in the cylinder of our
engine some liquid in contact with its vapour at an
absolute temperature = jT. Let it expand isothermally
till the volume has increased by dVy owing to the eva-
poration of one gram of liquid. If p is the vapour
pressure, the work done is pdVy and the heat absorbed is
the latent heat of vaporisation, X. Then let the vapour
expand adiabatically till its temperature sinks to jT — dT.
The pressure will now be ^^ — -^dTy and if we reduce the
volume isothermally at the new temperature to its original
value, the work done will '^ (l> - jm d^j dv. The balance
of effective work done by the engine during the cycle will
therefore be pdv — ip— ^ dT\ dv = ^ dT . dv, and by
the second law of thermodynamics we get
P"""' dT
X T
dT'Tdi (^>'
The general analogy between evaporation and solution
on which stress has already been laid (see p. 20), leads us
to apply this equation to the process of solution. In this
case^ will represent either the solution pressure, which can
be measured by osmosis (see Chap. IV.), or the concentration
which is approximately proportional to it, dv is the volume
CH. Ill] SOLUBILITY. 27
of solution in which olie gram-molecule of the solvend is
dissolved, and \ is the heat of solution of one gram-
molecule in the saturated solution (that is the heat
change involved in the passage of the solution from the
state of saturation at a temperature T — dT to the state
of saturation at a temperature T). Since T and dv are
both positive quantities, it follows from the equation that
dp/dT, the rate of variation of concentration with tem-
perature, and \, the heat of solution, must have the same
sign, so that if the solution of a substance is attended by
an absorption of heat the solubility increases with tempera-
ture, if it is attended by an evolution of heat the solubility
decreases.
This is a special case of the general law that when
a system is controlled by two variables dependent on
each other, a change in one of them produces a change
in the other in such a direction that the change in the
first is resisted.
In dilute solutions we shall find that the molecules of
the dissolved substance obey Boyle's law, that is to say
that the solution pressure which they produce is inversely
proportional to the volume occupied. From the usual
equation for Boyle's law
p X volume = RT,
where -R is a constant, we find that the volume is equal
to RT/p.
If we substitute this value for the volume dv in our
equation
dp ^ X
dfTdv
28 SOLUTION AND ELECTROLYSIS. [CH. Ill
it becomes df'"]RT«
or
^ 1 =
.'. ^0^g«^)=55^2 (2)-
We can thus deduce X, the heat of solution, from the
solubility curve, and Van 't Hoff has given a table which
shews a good agreement with the same constant determined
experimentally. We shall shew in Chapter IV. how to
calculate the value of the constant R for solutions.
calculated r-rrr^ observed
1000 1000
Oxalic acid 8*2 calories 8*5 calories
Potassium bichromate 17*3 „ 17*0
Amylic alcohol - 3*1 „ - 2-8
Phenol 1-2 „ 21
Alum 21-9 „ 20-2
Potassium chlorate 11 „ 10
Borax 27-4 „ 25*8
The solubility curve cannot be deduced conversely
from the heat of solution (though its direction can), for if
we integrate the equation we get
■gy^ + constant (3),
and this constant, which determines the absolute value of
the solubility, remains unknown.
The fact that the solubility of a body is determined by
the properties of the solid in contact with the solution,
suggests that when the temperature is raised above the
l0geP=j--
CH. Ill] SOLUBILITY. 29
melting point of the solid, a difference in solubility may
result. But it can easily be shewn that although a
difference in the direction of the curve may there begin,
at the melting point the solubility of the liquid must be
the same as that of the solid — the two curves must
intersect. At the melting point liquid and solid can exist
in contact at the same temperature. If we suppose one
to be more soluble than the other, it will tend to produce
a stronger solution than the other can support. Matter
will therefore continually dissolve away from the more
soluble body and will be deposited on the less soluble, and
since one of these is solid and the other liquid, differences
of temperature will be produced by the heat effect in-
volved in change of state, in a system which was originally
at a uniform temperature throughout. This is contrary
to experience as formulated in the second law of thermo-
djniamics. Thus at the melting point the solubility of
the liquid must be the same as that of the solid. The
difference between the solid and the liquid state can be
considered as measured by the energy required to pass
from one to the other, i.e. by the heat of fusion. This
suggests that the angle at which the two solubility curves
meet will be greater as the heat of fusion is greater. The
exact relation can be deduced from the equations used
above, and J. Walker^ has confirmed the results experi-
mentally.
15. Solubility of Mixtures. If water be shaken
with a mixture of two salts, the solution when saturated is
1 Zeits, f. physikaZ. Chemie, 1890, 5, p. 192.
30 SOLUTION. AND ELECTROLYSIS. [CH. Ill
in general found to contain less of each substance than it
would have done if the other had been absent, though to
this rule there are many exceptions.
In the case of salts which are not isomorphous and
do not form double salts, the composition of the solu-
tion is independent of the proportion in which the
solids are mixed, and of the method by which the solution
is prepared. In the case of substances which form double
salts, if we add excess of -4 to a saturated solution of B,
the double salt separates out till a solution is formed
which is saturated both as regards A and the double salt,
and is not changed by a further addition of A. The third
case, when the salts are isomorphous and can crystallize
together in all proportions, gives saturated solutions whose
compositions vary continuously with the composition of
the solid mixture. By adding successive quantities of A
it is possible to completely displace the salt B from the
solution. Much experimental work has been done in this
subject by Rudolfs, and Ostwald has pointed out the
analogy between these phenomena and the vapour pres-
sures of mixed liquids, the three cases given above
corresponding to the cases (i) when the liquids do not
mix, (ii) when they are partially miscible, (iii) when they
are miscible in all proportions.
Nemst^ has shewn that the solubility of a slightly
soluble salt like silver acetate must be greater in pure
water than in a solution of any other electrolyte which
contains either silver or the acetate group. A corre-
1 Pogg. Ann., 1873, 148, pp. 466, 556. Wied. Ann,, 1885, 25, p. 626.
2 Zeits.f.physikaL Chemie, 1889, 4, 372.
CH. Ill] SOLUBILITY. 31
sponding phenomenon is observed in the case of gases which,
like the vapour of NH4SH, partially decompose. The
partial pressures of the products of decomposition are less in
the presence of either ammonia or sulphuretted hydrogen.
16. Solubility in mixed liquids. If a liquid is
added to a solution with which it is miscible, the dissolved
substance will be to some extent precipitated if it is
insoluble in the liquid added. Thus copper sulphate or
sodium chloride can be precipitated from their aqueous
solutions by the addition of alcohol. No relation can
however be traced between the amount precipitated and
the quantity of alcohol added.
A dissolved body divides between two solvents in a
constant ratio which is independent of the absolute
concentration. This statement, which is deducible from
the physical theory of solution, was confirmed for the
solution of succinic acid in ether and water by Berthelot
and Jungfleisch\ If the bodies have different molecular
weights when dissolved in the two solvents, like benzoic
acid in benzene and water, different laws hold good and
these were investigated' by Nemst'.
17. Table of Solubilities.
Solability (parts in 100 parts
of solvent)
SubstaDoe
Solvent
At 0°
At 20°
At 100°
Sodium chloride
Water
35-5
36-0
39-2
Silver nitrate
»
121-9
228-0
1111*0
Calcium sulphate
»
0-205
0-23
0-19
Barium chloride
))
31-0
35-7
58-8
1 Ann. de Chimie, 1872, [4], 26, pp. 396. 408.
2 ZeiU, /. physikal. Chemie^ 1891, 8, p. 110.
CHAPTER IV.
DIFFUSION AND OSMOTIC PRESSURE.
18. General Principles of Difflision. When a
mass of gas is placed in an empty vessel, it finally, if the
small effects due to gravity be neglected, distributes itself
equally throughout the volume. This at once follows from
the molecular theory, for the particles of which the gas is
composed are always moving about from one place to
another. If then we suppose that an imaginary partition
is placed anywhere in the gas, the number of molecules
crossing it in one second from left to right will be pro-
portional to the number present in unit volume (i.e. the
concentration) on the left-hand side, and the number
crossing from right to left proportional to the number per
unit volume on the right. If the concentration is greater
on one side than the other, more molecules will leave that
side per second than enter it, and thus the concentration will
be reduced till it is equal on both sides. A similar process
goes on in the case of a substance dissolved in a liquid :
uniformity of distribution is finally reached, though here
the diflBculties put in the paths of the dissolved molecules
CH. IV] DIFFUSION AND OSMOTIC PRESSURE. 33
by the presence of the solvent, prevent their travelling
fast, and make the process of diffusion very slow.
In the case of mixed gases it is found that the final
state of distribution of one gas is not affected by the
presence of the other. Thus the amount of aqueous
vapour which diffuses fi'om water into a vacuum, is
sensibly the same as if the empty space previously con-
tained air, though in this case the process of diffusion
is slower. This too is obviously a necessary consequence
of the molecular theory, for, whether the air be present or
not, equilibrium is reached when the number of molecules
which leave the liquid per second is equal to the number
returning to it from the vapour.
Collisions between the molecules are continually taking
place, and thus the average energy of translation of each
molecule becomes on the whole the same, though some-
times the molecule may be travelling faster and sometimes
slower. This must also hold good even if the molecules are
of different kinds, as in a mass of mixed gas — the average
energy of each is still the same. The kinetic energy being
one-half the mass multiplied by the square of the velocity,
it follows that light molecules must travel faster than
heavy ones and will therefore diffuse more quickly. This
can be shewn by the familiar experiment of filling a closed
porous pot with air and surrounding it by an atmosphere
of hydrogen or coal gas. The molecules of hydrogen enter
more rapidly than the heavier ones of air go out, and a
pressure gauge will shew that the pressure inside the pot
becomes greater than outside. If we could in any way
entirely prevent the air from leaving, we could get a
w. s. 3
84 SOLUTION AND ELECTROLYSIS. [CH. IV
permanent increase of pressure, for the hydrogen would
enter till its concentration was the same within as
without.
19. OBmotic PreBBure. The corresponding pheno-
menon in the case of liquids is shewn by experiments on
what is known as osmotic pressure, Pfeffer^ shewed how
to prepare membranes which readily allow pure water
to pass, but are impervious to certain substances dissolved
in it which do not act on the membrane. These semi-
permeable membranes are made by filling a porous pot
with the solution of a salt such as potassium ferrocyanide,
and surrounding the outside with another solution —
copper sulphate for example — which gives an insoluble
precipitate when in contact with the first. The solutions
gradually diffuse into the walls of the cell, and form an
insoluble membrane on the surface along which they
meet. The solutions are then washed out, and the mem-
brane is complete. Let us place inside a pot so prepared
a solution of some substance — cane sugar for example —
and immerse it in pure water. The molecules of liquid
will strike the walls of the membrane on both sides, but
since there are both sugar and water molecules inside^
fewer water molecules will, in a given time, hit the wall
inside than outside. More water molecules pass in there-
fore, than go out, and, since none of the sugar can escape,
an internal pressure is produced which can be measured
by any convenient gauge. The process will go on until
the pressure due to the water is the same on both sides,
^ Osmotische Untersuchungen, Leipsic, 1S77.
CH. IV] DIFFUSION AND OSMOTIC PRESSURE. 35
and thus the excess of pressure measured is equal to that
due to the sugar alone. The ease of sugar was chosen
because little or no contraction in volume occurs when it
is dissolved, or when the solution is diluted, which makes
the theory of the subject much more simple. Here, at
all events, there is strong evidence to shew that the simple
physical explanation we have given is enough to account
for the phenomena.
In most cases the osmotic pressure, as thus measured,
will include other properties which cause a diminution in
the potential energy of the system on dilution. There
may be, for example, a change of volume, or chemical
action between the solvent and the dissolved substance,
as well as the pressure due to the motion of the molecules
in solution. When equilibrium is obtained the potential
energy of the whole system must have reached a
minimum value.
20. Application of the GaseouB laawB to Solu-
tions. When we measure the numerical value of this
osmotic pressure we find that, in dilute solutions, the laws
which regulate its value are the same as those which
govern the behaviour of gases and vapours. The im-
portance of these results was first pointed out by Van
^t Hoflf^ who called attention to the fact that Pfeffer*s
measurements of the osmotic pressure of cane sugar
proved that the pressure varied as the concentration, i,e.
that it was inversely proportional to the volume occupied
^ PHI Mag,, 18SS, 26, p. 81, or Zeits.f, physikaL Chemie, 1887, 1,
p. 481.
3—2
36
SOLUTION AND ELECTROLYSIS.
[CH. IV
by a given mass of sugar. This exactly corresponds to
Boyle's law for gases. The following are some of Pfeffer's
numbers.
1
Percentage of sugar
Pressure in milli-
Pressure calculated for
in solution
metres of mercury
one per cent, of sugar
1
538
538
1
532
532
2
1016
508
2-74
1513
554
4
2082
521
6
3075
513
1
535
535
The numbers in the last column are constant except
for irregular experimental errors.
In the case of gases, Boyle's law fails to represent the
accurate relation between pressure and volume at very
great pressures, and it also fails fpr solutions when the^
concentration becomes considerable. We should expect
the law of variation to be more complicated for solutions,
since in addition to the intermolecular forces similar to
those brought into play in the case of gases, we shall
here have forces between the dissolved molecules and
the solvent.
For dilute solutions, to which we shall at first restrict
ourselves, the theory shews that the pressure should in^
crease as the temperature rises; and that the variation
should follow the laws of gases and make the pressure
proportional to the absolute temperature. This result
has not been fully confirmed experimentally, but Bonders
CH. IV] DIFFUSION AND OSMOTIC PRESSURE. 37
and Hamburger ^ found that the variation in pressure due
to temperature was independent of the nature of the
dissolved substance. This corresponds to the fact that
the coefficient of increase of pressure is the same for all
gases. The method used was a comparative one, and
shewed that solutions which were isotonic (i.e. gave equal
osmotic pressures) at one temperature, 0°, were also isotonic
at another, 34°.
It is found that the protoplasmic contents of certain
organic cells are surrounded by a membrane which be-
haves like those prepared by Pfeffer in only allowing pure
water to pass. If such a cell be placed in a concentrated
salt solution, the more dilute cell sap parts with water
fester than the external liquid, the contents of the cell
contract and shrink away from the cell walls. If on the
other hand the cell be placed in water, liquid passes in,
and the membrane becomes stretched. By staining the
contents of the cell and having a graduated series of
solutions of varjdng strength, it is easy to find, by observa-
tions with a microscope, what strength of solutions gives
equilibrium with the cell sap, and is therefore isotonic
with it. Solutions of two different substances can thus
be prepared so that both are isotonic with the contents of
^ given kind of cell, and (assuming that two solutions
isotonic with a third are isotonic with each other) we can
find the respective strengths of the two salt solutions
which give equal osmotic pressures. De Vries ^, who was
the first to use this method, employed vegetable cells.
1 ZeiU. f. physikal Chemie, 1890, 6, p. 819.
2 Fringsheim*8 JahrbUcher, 1884, 14, p^ 427.
38 SOLUTION AND ELECTROLYSIS. [CH. IV
and Donders and Hamburger in their investigation on the
influence of temperature used blood corpuscles.
De Vries established the most important generalisa*
tion, that solutions of difierent substances containing the
same number of gram-molecules* in a given volume are
isotonic. This is equivalent to saying that at equal
pressures the solutions of all (non-electrol}rtic) substances
contain, in a given volume, the same number of molecules,
which corresponds to Avogadro's law for gases. Tammann*
confirmed this by allowing a drop of copper sulphate
solution to fall into a solution of a ferrocyanide. A little
membrane is at once formed round the drop, and the
concentrations of the solutions are altered till, when this
is done, no water enters or leaves the cell. Whether any
such passage went on or not was determined by noticing
if there was any change in the index of refraction of the
liquid just outside the little cell.
It is important to observe that in the case of solutions
which are electrolytes (that is to say, which have the
power of conveying a current of electricity and of under-
going simultaneous chemical decomposition), the osmotic
pressure is greater than that given by the solution of a
non-electroljrte containing the same number of gram-
molecules in a given volume. Thus a table of the
"isotonic coefficients" of some indifferent substances
given by De Vries ik as follows, the isotonic coefficient
being a number representing the osmotic pressure when
^ Note — ^A "gram-moleoule** is the molecular weight of a sabstance in
grams.
3 Wied. Ann. 1888, 34, p. 299.
CH. IV] DIFFUSION AND OSMOTIC PRESSURE. 39
that of an equimolecular solution of potassium nitrate is
taken as 3 :
Cane sugar 1*81
Inverted sugar 1*88
Glycerine 1*78
while the coefficients of electrolytic solutions are greater :
Potassium nitrate 3*0
Sodium nitrate 3*0
Potassium chloride 3*0
Potassium sulphate 3'9
Potassium tartrate 3'99
Magnesium chloride 4*33
Calcium chloride 4*33
The importance of this phenomenon we shall examine
in detail later.
When we pass on to the examination of the absolute
value of the osmotic pressure, we find another striking
relation to gaseous properties. We know that one gram of
hydrogen or sixteen grams of oxygen, at normal atmospheric
pressure and 0° C, occupy a volume of about 1116 litres.
Therefore one molecular weight of a gas in grams (2 grams
of hydrogen or 32 grams of oxygen) occupies under these
conditions a volume of 22*32 litres, or if compressed into
one litre would, by Boyle's law, exert a pressure of 22*32
atmospheres. By Avogadro's law the same pressure
would be exerted by any gas or vapour that was a con-
siderable distance from its point of liquefaction.
The absolute values of osmotic pressures have been
found by Pfeffer, Adie * and Tammann. Pfeffer found that
* Chem, 8oc. Jour, Proe. 1891, p. 844.
40 SOLUTION AND ELECTROLTSIS. [CH. IV
at e^^'S a one per cent, solution of sugar gave an osmotic
pressure of 505 mm. of mercury. The molecular weight
of cane sugar (CjjH„0„) is 342. Hence a one per cent.,
solution contains ^f^ of a gram-molecule in one litre. A
volume of hydrogen or of any other gas, which contained
-^ of a gram-molecule in one litre would at 6°'8 exert a
pressure of
10 279*8
760 X prj^ X 22-32 x -zr=^ = 508 mm. of mercury.
342 273 "^
Thus we find that in dilute solutions of indifferent
substances
(i) The osmotic pressure is proportional to the con-
centration, that is, inversely proportional to the volume
occupied by a given mass (Boyle's law).
(ii) The coefficient of variation of pressure with tem-
perature is the same for all substances, and probably
(though this is not fully established by experiment) the
pressure is proportional to the absolute temperature (Gay
Lussac's law).
(iii) Solutions which exert the same pressures contain
the same number of dissolved molecules in a given volume
(Avogadro's law).
(iv) The absolute value of the osmotic pressure of
the solution of a non-electrolyte is the same as that of a
gas or vapour containing the same number of molecules
in a given volume.
Thus we find that the osmotic pressure of dilute
solutions obeys all the gaseous laws, and has the same
absolute value as it would have if the dissolved substance
were transformed into a gas at the same temperature
CH. IV] DIFFUSION AND OSMOTIC PRESSURE. 41
without change of volume. We can therefore apply to
solutions the usual equation which expresses the relation
between the pressure p, and the volume », of a gas, and write
pv^RT,
where T denotes the absolute temperature, and i2 is a
constant whose value can be found as follows. Let us
consider a mass of gas equal to its molecular weight in
grams at 0° C. and 760 mm. pressure. The pressure is
76 X 13*6 X 981 = 1014 x 10* CG.s. units, the volume, as
we have seen on p. 39, is 22320 c.c. and the absolute
temperature is 273°. We therefore get
RsstjZ = 8*290 X 10' ergs per degree centigrade
or dividing by the mechanical equivalent of heat (4*2 x 10')
we get in thermal units
R = 1*974 or nearly 2 calories per degree.
If we define the concentration of a solution to be the
number of gram-molecules per cubic centimetre, it is
equal to l/v, and we can write an equation for osmotic
pressure in the form
p = cRT (4).
The real cause of this remarkable relation is the same
as that which makes the gaseous laws independent of the
composition of the different gases. Both in gases and in
dilute solutions the molecules are in general so tax apart
that they are nearly always out of each other's range of
influence, and only those properties which, like the pressure,
depend on the number and not on the nature of the mole-
cules, are brought into prominence, while those which
42 SOLUTION AND ELECTROliYSIS, [GH. IV
depend on the composition of the molecule tend to disappear.
Properties which depend in this way only on the numb^*
of the particles and not on their nature are called colligcUive
properties. The reason of this importance of the coUiga-
tive properties at great dilution is at once seen if we
remember that while properties which, like the pressure
produced by impact, depend simply on the number of
molecules, must be proportional to the concentration,
properties which depend on the forces between the mole-
cules must be proportional to the square of the concentra-
tion; for a new molecule added not only exerts force ou
others but also allows others to exert force on it. But
any term which is proportional to the square of a quantity
becomes very small, compared with a term depending on
the first power, when the quantity becomes small, so that
the term in the expression for the osmotic pressure which
depends on intermolecular forces must be negligible at
great dilution, compared with the term due to the impact
of the molecules which is proportional to the concentration.
It would be quite possible to explain the fact that the
variation of the osmotic pressure of solutions obeys all the
gaseous laws, by the action of chemical forces between the
dissolved substance and the solvent ^ but on that hjrpo-
thesis there seems to be no particular reason why the
osmotic pressure should assume the same absolute value as
that which the dissolved molecules would give were they
gasified. It is this last fact which seems to shew that in^
dilute solutions of indifferent bodies, the osmotic pressure
is caused by molecular bombardment. The consideration
1 See Fitzgerald, B,A, Report, 1890, pp. 142, add.
CH, IV] DIFFUSION AND OSMOTIC PRESSURE. 48
of the case of salt solutions must be deferred till we have
described the facts of electrolysis.
21. Application of TfaermodynamicB. The
direct determination of osmotic pressure is a very difficult
process, but we shall proceed to shew that there is a
connection between this pressure and other properties of
solutions — their vapour pressures, and freezing points.
This connection is independent of the particular view we
take of the cause of osmotic pressure, and can be deduced
simply from the principles of thermodynamics. For most
purposes therefore it is better to make experimental
determinations of the freezing points, and deduce the
corresponding value of the osmotic pressures. This is
particularly advisable in the case of strong solutions,
which would give osmotic pressures so large that a direct
experimental determination would offer great difficulties-
We shall therefore leave the account of the osmotic
pressures of strong solutions with the deviations from the
gaseous laws which they shew, till we have considered the
freezing point determinations.
Van 't Hoff was the first to point out that the ex*
istence of osmotic pressure, to whatever cause it may be
due, enables the laws of thermodynamics to be applied to
solutions. For imagine the solution of some substance to
be enclosed in a cylinder fitted with a piston, and having
its bottom made of a semipermeable membrane. If it be
placed in water, the volume of liquid inside will increase
until the pressure on the membrane is just equal to the
osmotic pressure, when equilibrium will be attained. If
44 SOLUTION AND ELECTROLYSIS. [CH. IV
in this state we heat the cylinder, the osmotic pressure is
increased, more water will enter, and the piston will rise.
If we cool it, the osmotic pressure falls, water is squeezed
out, and the volume inside becomes less. On the other
hand by increasing the pressure on the piston we can force
out water and so reduce the volume, keeping the tempera-
ture constant, or by decreasing that pressure we can draw
water in and make the volume greater. We have evi-
dently a system which is in all respects analogous to a
cylinder containing gas, and by keeping the pressure on
the piston nearly equal to the opposing osmotic pressure,
we can make all the above processes reversible, and obtain
with solutions an apparatus which acts in all respects
like Camot's perfectly reversible heat engine.
This principle can be used to examine the relation
between osmotic pressure and temperature. Beginning
with the ideal machine described above in a state of
equilibrium, let us reduce the pressure on the piston by
an infinitely small amount, and so allow water to enter,
and the piston to slowly rise — the temperature being kept
constant by the addition of a quantity of heat whose
mechanical equivalent is H, If the volume of water
which enters is dv, and we neglect any contraction it
may experience on mixing with the solution, the work
done is p dv, and this must be equal to H, Let the piston
still rise, with no further addition of heat. If the tem-
perature sinks to t — dt the pressure becomes p — ^dt
The piston is then pushed in at this lower pressure till a
change of volume equal to dv is produced, thie heat being
Cy. IV] DIFFUSION AND OSMOTIC PRESSUHE. 46
removed so that the temperature keeps constant. Finally
the removal of heat is stopped, and the piston is further
pushed in till the original temperature and volume are
regained. The work done hy the engine at the higher
temperature is as we have seen jp dVy while that done on it
at the lower temperature is f jp - -^ dn dv, so that the
balance of available work obtained during the cycle is
pdt; — [jp — -^ dtjdv = -^.dtdv.
Now by the laws of thermodynamics we know that the
total amount of heat converted into work by a perfectly
reversible engine, working between the temperatures t and
t'-dtyia to the amount of heat absorbed by the engine at
the higher temperature, as the difference in temperatures
is to the absolute temperature ty
hence the work done ==H -j .
V
We therefore get
H-r^p ,dv ,-r^-¥:.dtdv,
t ^ t dt
or * £ = ^
^^ t dt '
and by integration jp= Ct (5),
where C is the integration constant.
Therefore the osmotic pressure of dilute solutions
should be proportional to the absolute temperature.
22. DiflUBion through laiquids. According to
46 SOLUTION AND ELECTROLYSIS. [CH. JV
the molecular theory then, division is due to the motion
of the molecules of the dissolved substance through the
liquid. These molecules have momentum, and the osmotic
pressure measures the rate at which this momentum is
transferred across unit area. When the osmotic pressure
is uniform throughout, the molecules will he uniformly
distributed, but if the pressure varies from point to point
the concentration will not be uniform. There must thus be
a relation between the rate of change of the concentration
and the variation of osmotic pressure, and this has been
investigated by W. Nemst^ and M. Planck*. Suppose we
have a vertical cylinder with a solution of some non-
electrolyte in its lower part, and pure water at the top.
The dissolved substance gradually makes its way upwards
through the water, and, neglecting the small disturbing
effect of gravity, a uniform solution will finally result.
At a height x in the cylinder let the osmotic pressure
be jp, so that if q be the area of cross section, the
substance in the layer whose volume is qdx, finds itself
under the action of a force equal to — qctp, the negative
sign being taken because the force acts in the direction in
which the pressure decreases. If c be the concentration in
gram-molecules per cubic centimetre, the force which in
this layer acts on each gram-molecule is
q_dp _^ 1 dp
cqdx c dx'
Let k denote the force required to drive one gram-
1 Zeits, /. physikal Chemie, 18S8, 2, p. 616.
^ Wied, Ann,, 1890, 40, p. 561.
CH..IV] DIFFUSION AND OSMOTIC PRESSURE. 47"
molecule through the solution with a velocity of one
centimetre per second ; then the velocity attained is
ck dx'
and if dN be the number of gram-molecules which cross
each layer in a time dt, since the number crossing unit
area per second is proportional to the concentration and
to the average velocity of the individual molecules, we get
dN = f ^qcdt = rQ -J di-
ck dx^ k^ ax
If the solution is dilute, and if there is no poly-
merisation or dissociation of molecules with change of
concentration, we may apply equation (4) for the osmotic
pressure, viz. p = cRT, the value of the constant R corre-
sponding to one gram-molecule being again taken. This
gives
^''—^^i'' <«)•
On the analogy between dififusion and the conduction
of heat Pick^ supposed that the quantity of substance
which diffused through unit area in one second was propor-
tional to the difference of concentration between that area
and another parallel layer indefinitely near it. This
dc
difference in concentration is proportional to — -r- , so that
the quantity crossing an area g in a time dt is
dN=-Dq^£dt (7),
where D is the "diffusion constant," and by comparison
^ Pogg, Ann,y 1856, 94, p. 69.
48 SOLUTION AND ELECTROLYSIS. [CH. IV
RT
with equation (6) is seen to correspond to the term -r- ,
Fick's equation was fully confirmed by the work of H. F.
Weber^ (see p. 49), which therefore also supports the
truth of the theory given above.
Owing to the slowness of the diffusion, the unit of time
genemlly adopted for experimental work is the day instead
of the second, so that the observed difiiision constant K is
given by the expression
dc , . _ 86400 dN
But from equation (6) we see that the force required
to drive one gram-molecule through the solution with a
velocity of one centimetre per second is
86400 RT
.(9).
K
Thus if we know K, the diffusion constant, we can
calculate k, the force required to produce unit velocity.
Voigtlander gives 0*472 as the diffusion constant of formic
acid at 0° C, and from this we can calculate that the force
required to drive one gram-molecule (46 grams) of formic
acid through water with a velocity of one centimetre per
second is equal to the weight of 4340 million kilograms.
The reason such an enormous force is needed is at once
seen if we remember the minute size of the molecules and
1 Wied. Ann., 1877, 2, p. 24.
CH. IV] DIFFUSION AND OSMOTIC PRESSURE. 49
the difficulties they must meet with in struggling through
the liquid.
If the temperature be uniform, a solution will in the
end become homogeneous, but if the upper layers be kept
hotter than those below, in order that the osmotic pressure
should be the same throughout, the concentration in the
lower layers must become greater. This result was ex-
perimentally established by Soret^ and the cause pointed
out by Van 't Hoff ".
23. Erperiments on DlfEliBion. The first to
make a thorough investigation of diffusion •without a
separating membrane was Graham*, who covered a wide-
mouthed bottle containing a solution with a large volume
of water, and after some time measured the quantity of
substance in the water. By this method Graham found
that acids diffused about twice as quickly as normal salts,
and that the rate of diffusion of these salts varied much
according to their composition. Two salts together diffused
independently of each other, so that it was possible to
separate the constituents of some double salts, the alums
for example, which were decomposed by water. The
quantity which diffused was foimd to be nearly pro-
portional to the concentration of the original solution, and
to depend largely on the temperature.
Weber was the first to work out a satisfactory method
of determining the absolute value of the diffusion constant
in Fick's equation. When two plates of amalgamated
1 Ann. Chim. Phys., 1881, 22, p. 293.
2 Zeits.f. phyHkal Chemie, 1887, 1, p. 487.
» Phil Tram., 1860, pp. 1, 806 ; 1851, p. 483.
w. s. 4
50 SOLUTION AND ELECTEOLYSIS. [CH. IV
zinc are placed in two solutions of zinc sulphate of
different concentrations, the solutions being in contact
with each other, a difference of electrical potential is
produced between the plates which is proportional to the
difference in concentration, provided that difference is
small. A concentrated solution of zinc sulphate was
placed in the lower part of a cylindrical vessel, the bottom
of which was made of an amalgamated zinc plate, and a
dilute solution gently poured in on top of the first. The
electromotive force between the lower zinc plate and a
similar plate placed in the topmost layer of liquid was
measured, and found to decrease as the difference in
concentrations became less. If we apply Fick's law to
this case we get an infinite series in the expression for the
electromotive force, but if the time is long, the first term
only is important, and we get, if H is the height of the
vessel, and t the time
E^Ae'^'^^ (10).
The following table gives the observed values of -^ JT,
which should be constant if Fick's law holds good.
Days
4—5
•2032
5—6
•2066
6 7
•2045
7 8
•2027
8 9
•2027
9—10
•2049
10—11
•2049
Mean ^2042
This complete verification of Fick's law also supports
CH. IV] DIFFUSION AND OSMOTIC PRESSURE.
51
the theory of difiusion given on p. 45, since that theory
leads to a similar equation.
Fick's law can be put into another form if we take the
case of a very long cylinder with the concentration at
one end remaining constant. In this case Stefan^ shewed
that the quantity difiusing through an area q should be
a = cq^^.
It
To apply this to a finite cylinder we must imagine
that the amount which would have passed beyond the
limiting layer, is reflected, and added to the quantity
present in the lower layers.
Scheffer" placed a solution underneath a volume of
pure water and measured the quantity of substance which
•diffused upwards. The following are some of his results,
n being the number of molecules of water in which one
molecule of substance is dissolved.
Substance
Temperature
n
K
Hydrochloric acid
11
7-2
2-67
99 9)
11
108-4
1-84
Nitric acid
9
35
1-78
9) 99
9
426
1-73
Sulphuric acid
8
18-8
1-07
Acetic acid
13-5
84
0-77
Potash
13-6
1665
1-66
Ammonia
4-5
16
1-06
Urea
7-5
110
0-81
Mannite
10
220
0-38
1 TTien. Alcad, Ber„ 1879, 79, p. 161.
3 Ber., 1B82-3, 15, p. 788, 16, p. 1903, and Zeits, f. physikaZ, Chemie,
1888, 2, p. 890.
4—2
CHAPTER V.
FREEZING POINTS OF SOLUTIONS.
25. Historical. It has long been known that the
freezing point of a salt solution, such as sea water, is
lower than that of the water when pure, and in 1788
Blagden^ published some observations on the subject,
which shewed that the depression of the freezing point
produced by dissolving a substance in water, was ap-
proximately proportional to the quantity of substance in
solution, except when the concentration became consider-
able.
Further observations were made by RtidorfiF' and
Coppet*. The latter noticed that if the lowering of the
freezing point produced by chemically equivalent quan-
tities of different salts was examined, it was found that
the molecular lowering was nearly equal for salts of
similar chemical constitution.
1 Phil. Trans., 78, p. 277.
> Fogg. Atm.^ 1861, 114 et seq.
s Arm. Chim. Phys., 1871, 2. 28, 25, 26.
CH. V] FREEZING POINTS OF SOLUTIONS. 55
The whole subject has been fully examined by Raoult\
who extended his observations to non-electrolytes, such as
solutions in pure benzene, and solutions of organic com-
pounds in water. He found that the depressions produced
by equi-molecular quantities of different substances were
nearly of the same value.
26. Connection with Osmotic Pressure and
other Theoretical Considerations. Before examining
the results of these experiments in detail, we will shew
how the phenomena are connected with those of osmotic
pressure.
It has already been noticed that the ice which freezes
out from a salt solution is the ice of pure water. Since
this is so, the molecules of dissolved substance, which all
remain in solution, are compressed into a smaller space,
and hence work has to be done in overcoming the osmotic
pressure which tends to increase the volume.
Let us suppose that we have a solvent whose freezing
point is T on the absolute scale of temperature, and whose
latent heat is \. Let some substance be dissolved in
a large volume of it, and let the freezing point of the
solution be T - ST.
Let us force out one gram of the solvent through a
semipermeable membrane at a temperature of T°, If
we neglect any difference in volume between the water
when pure and when in the solution, the quantity of work
done will be pv, where p = the osmotic pressure and v the
volume of the solvent forced out. Then let us abstract a
1 CmwpU rend,, 1882, 94, p. 1517, 95, pp. 188, 1030. Ann. Chim.
Phys., (6), 2, p. 66, (5), 28, p. 187, (6), 4, p. 401.
56 SOLUTION AND ELECTROLYSIS, [CH. V
quantity of heat \ (« latent heat), and so freeze the gram
of solvent If we then cool the system to T - ST, bring
the ice and solution together, again thaw the ice (the water
from which will do no external work in mixing with the
solution), and heat to T, we shall have performed a complete
cycle, and can apply the usual thermodynamic relation,
that the ratio of the work done to the heat absorbed,
is the same as the ratio of the difference in temperature
to the absolute temperature of the system at its hottest.
pv_BT
• * X" T '
'•ST^T^ (11).
Let us take the case of a water solution of any body con-
taining one gram-molecule per litre. We have seen (p. 39)
that the osmotic pressure is the same as the dissolved
molecules would exert in the gaseous state. It is therefore
22-32 atmospheres, or 2232 x 76 x 13-6 x 981 c.G.S. units.
V, the change in volume of the solution when 1 gram of
solvent is frozen, is - , where p is the density, which gives
P
us another form of equation (11)
BT^T^ (12).
\p
For water f) = l, 7=273 and \ = 79'4 calories or
79*4 X 4*2 X 10' ergs or c.G.s. units of energy. If we
calculate BT with these numbers we find that the freezing
point of water should be lowered by one gram-molecule of
dissolved substance per litre, by
.l°-86a
CH. V] FREEZING POINTS OF SOLUTIONS. 57
Raoult^ made many experiments on this subject and
his results give a mean value of
V'85 C.
for the same effect.
It is easier to make a comparison with Raoult's results
by changing the form of our equation, but the effects
of disi§olved bodies on any solvent can be calculated from
(12) by using tlfe values for T and \ given on p. 59.
This is the simplest expression of Van 't HofiTs theory,
and the one which shews most clearly the connection
between the lowering of freezing point and the osmotic
pressure; another form however may be useful.
In our equation (11) let us put, since dilute solutions
obey Boyle's law,
pv = RT.
The expression then becomes
BT = ^. (13).
i2 is a constant whose value for one gram-molecule of any
gas or substance in dilute solution is, as we have shewn
on p. 40,
i2=^ = 8-29x10' ergs,
= 1*976 calories,
taking GriflSth's value for the mechanical equivalent of
heat jr= 4194x10'.
The latent heat of that quantity of solvent in which
one gram-molecule is dissolved is
, ^ lOOOp
n
^ CompU rend,, 1882, 94, p. 1517.
58 SOLUTION AND ELECTBOLTSI8. [CH. V
where n represents the number of gram-molecules per
litre. We then get
gy^ 1-976 2"
L '
0001976 T^w
.(14).
V
In the case of water this gives Sr=l*86°n, and of
course the value for other solvents can%be deduced in a
similar manner.
Raoult expressed the concentrations of his solutions in
terms of the number of gram-molecular weights of sub-
stance dissolved in 100 grams of the solvent. From
observations on more dilute solutions, on the assumption
that the law of proportionality was still applicable, he
calculated the depression of the freezing point which
would be produced by one gram-molecule dissolved in
100 grams of solvent.
We can at once throw our equation (14) into a form
in which comparison with Raoult's results for diflferent
solvents is easy. The volume of 100 grams of solvent is
. We have seen that if we dissolve one gram-molecule
in one litre of soluticm, we get an osmotic pressure of
22'3 atmospheres. If, as a first approximation, we assume
that the density of the solution is the same as that of the
solvent, when we dissolve the same amount in cc, we
P
get a pressure which is greater than that given by one
gram-molecule per litre in the ratio of
1000 : — or 10f> : 1.
CH. V]
FREEZING POINTS OF SOLUTIONS.
59
The value of R becomes lOp times greater than before
and equation (14) assumes the form
BT=
0-00197 y^
1-977* 2T*
^^<*^=iooY*ioox-(^^^-
The comparison between the values calculated from
this equation by Van 't Hoff, and Baoult's observed
numbers is given below.
T
2r«
lOOX
dT
(observed)
Water
273**
79
18-9
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
530
50-0
Nitrobenzene
278-3
22-3
69-5
70-7
The agreement between these results is sufficient to
shew that, at all events in dilute solutions, the theory of
Van 't Hoff, which considers the osmotic pressure to be
the same in its nature as gaseous pressure, leads to results
which agree with observation to a considerable degree of
accuracy.
Baoult stated that one molecule of a substance
dissolved in 100 molecules of solvent always gave a
depression of the freezing point which was approximately
equal to 0*63, and supported this generalization by ex-
periments on solutions in formic acid, acetic acid and
benzene. Our theory gives no theoretical ground for such
an assertion, but if we work out formula (15) for these
60
SOLUTION AND ELECTROLTSIS.
[CH. V
particular cases, we shall find that, as a matter of fact, the
numbers all happen to be nearly what Baoult gave.
If the molecular weight of the solvent be if, the
quantity represented by 100 gram-molecules is M times
that represented by 100 grams, so that the solutions
will be only -jj. as strong as those we dealt with in the
last table. The new depression of the freezing point will
therefore be not
22"
but
2ya
If we divide the
lOOX ™^ lOOXif*
figures given in the table by the molecular weights of
the solvents we get for the depressions
Formic acid = 0-62.
Acetic acid =0-65.
Benzene = 0-68.
The approximate constancy of these numbers is
however a pure accident, and does not hold for other
bodies; thus water gives I'Oo. This point has been fully
examined experimentally by Eykman^ and the following
Obseryed
Van'tHoff'B
formula
Baoalt*B rule
Phenol
Naphthalene
p-Toluidine
Diphenylamine
Naphthylamine
Laurie acid
Palmitic acid
74
69
51
88
78
44
44
77
69-4
49
98-6
102-5
45-2
44-3
58-3
79-4
66-3
104-8
88-7
124
158-7
^ ZeiU. /. physikaL Chtmie, 1889, 3, p. 208.
CH. V] FEEEZING POINTS OF SOLUTIONa 61
table shews his values of the molecular depressions as
given by experiment, compared firstly with the numbers
calculated from Van 't HofTs formula, and secondly with
those deduced from Baoult's empirical rale.
The numbers for lauric and palmitic acids seem quite
conclusive in favour of Van 't Hoff. In Baoult's general-
ization he was misled by a purely accidental agreement of
numbers, and he has since accepted Eykman's results and
the accuracy of Van 't Hoff's formula.
37. Szpeiimental Mettaodi. The best apparatus
for freezing point determi-
nations was introduced by
Beckmann, and is represented
in fig. 4.
The solution to be exam-
ined is placed in a wide test-
tube A, which is surrounded
by a second larger tube B to
serve as an air jacket. This
is placed in a vessel C, into
which a freezing mixture can
be introduced. There is one
stirrer in C, and another, made
of a platinum wire, in A.
A delicate thermometer gradu-
ated to hundredths of a degree,
is also placed, in .4. It has a
little reservoir at the top, into
which some of the mercury psg, 4.
62 SOLUTION AND ELECTBOLTSIS. [CH. V
can be driven, to make the instrument available for
diflferent solvents, which freeze at different temperatures.
It should be remarked however, that for accurate work
the days of the mercurial thermometer are numbered,
and any delicate thermometric measurement should now
be made with one of Callendar's platinum thermometers,
in which the temperature is determined by observing the
electrical resistance of a little coil of platinum wire.
The delicacy of this instrument is very great — ^the
thousandth part of a degree being easily measured — and
its use quite gets rid of irregularities due to the sticking
of the mercury, which is so noticeable when working with
mercurial thermometers.
The method of using Beckmann's apparatus is this.
A weighed quantity of the pure solvent is introduced into
A, and its jfreezing point determined by placing in G some
mixture whose temperature is just below the point to be
reached. The tube A is then removed, and the solvent
melted. A weighed quantity of the substance to be
dissolved is introduced through the side tube D, and the
tube replaced. It is better to cool it slightly below the
temperature at which it will finally stand. This can be
done if it be kept quite at rest. The supercooled liquid
is then stirred by means of the platinum wire, when small
crystals of ice form. The temperature rises to a certain
point, and then keeps stationary. If we go on freezing
the solution however, it will again begin to sink, for
as the solvent is frozen out, the remaining, solution gets
stronger, and so has a lower freezing point. The highest
of these temperatures is therefore the one giving the
CH. V]
FREEZING POINTS OF SOLUTIONS.
63
freezing point of the solution of the calculated concen-
tration.
An immense number of observations have been made
on this subject. The first to investigate it with any
completeness was Raoult, and some of his numbers are
given below. These represent what he calls the molecular
depression, that is the lowering which would be produced
by one gram-molecule of the substance in 100 grams of
the solvent. They are calculated from observations on
solutions of much less concentrations than this, on the
assumption that the law of proportionality is still
applicable,
SoltUions in Acetic Acid.
Van 't HoflTs formula gives 38'8.
Methyl iodide
38-8
Butyric acid
37-3
Ohforoform
38-6
Benzoic acid
430
Carbon disulphide
38-4
Water
33-0
Ethylene chloride
400
Methyl alcohol
35-7
Nitrobenzene
41-0
Ethyl
36-4
Ether
39-4
Amyl „
39-4
Chloral
39-2
Glycerine
36-2
Formic acid
36-5
Phenol
36-2
Sulphur dioxide
38-5
Stannic chloride
41-3
Sulphuric acid 18*6
Hydrochloric acid 17*2
Solutions in Formic Acid,
Van 't HoflTs formula gives 28*4.
Magnesium acetate 18*2
Chloroform
Benzene
Ether
Aldehyde
Acetic acid
26*5
29*4
28*2
26*1
26*5
Potassium formate
Arsenious chloride
28*9
26*6
Magnesium formate 13*9
64
SOLUTION AKD ELECTROLYSIS.
[CH. V
Solutiona in Benzene.
Van 't HoflTs formula gives 53*0.
Methyl iodide
50-4
Chloroform
5M
Methyl alcohol
25-3
Carbon disulphide
49-7
Ethyl
28-2
Ethylene chloride
48-6
Amyl „
39-7
Nitrobenzene
48-0
Phenol
32-4
Ether
49-7
Formic acid
23-2
Chloral
50-3
Acetic „
25S
Nitroglycerine
49-9
Benzoic „
25-4
Aniline
46-3
Solutiona in Nitrobenzene,
Van 't Hoff*s formula gives 69*5.
Chloroform 69 9
Benzene 70*6
Ether 674
Stannous chloride 71-4
Methyl alcohol
Ethyl
Acetic acid
Benzoic „
Solutions in Wat&i\
Van 't Hoflfs formula gives 18 '9.
Methyl alcohol
Ethyl „
Glycerine
Cane sugar
Phenol
17-3
17-3
17-1
18-5
15-5
Formic acid
19-3
Acetic „
190
Butyric „
Oxalic „
18-7
22-9
Ether
16-6
Ammonia
19-9
AnUine
15-3
Hydrochloric acid
Nitric acid
Sulphuric acid
Potash
Soda
Potassium chloride
Sodium
Calcium
Barium „
Potassium nitrate
Magnesium sulphate
Copper
»
>i
»
35-4
35-6
361
37-7
39-1
35-8
38-2
35
36
33
35
49
48'
30-8
19-2
18-0
•3
•2
•6
•1
•9
•6
An examination of these tables at once shews that the
molecular depressions produced by different substances
CH. V] FBEEZING POINTS OP SOLUTIONS. 65
in the same solvent are approximately constant. Leaving
out of consideration for the present solutions in water, we
find that in other solvents, besides a series of normal
compounds, the mean of whose molecular depressions
agrees with the number deduced from Van 't Hoff's
theory, there is in general a series of abnormal substances
which give depressions about half the others. Since on
Van 't HofTs theory the effect is proportional to the
number of dissolved molecules, and independent of their
nature, it is at once suggested, that, in these cases, the
number of molecules is halved by aggregates of two
ordinary molecules being formed, so that the molecular
weight is doubled. This view is strengthened by the fact
that some of the compounds which shew this effect (such
for instance as the acids of the formic acid series, which
give half values when dissolved in benzene or nitro-
benzene) are known to form compound molecules in the
gaseous state, and there is evidence from other sources
(e.g. from the surface tensions) that these acids and also
certain alcohols form polymeric molecules when liquid.
28. Determination of Molecular Weight. It is
evident then, that the determination of the freezing point
of a solution gives a means of controlling the measurement
of the molecular weight of the dissolved substance. If we
do not know whether the molecular weight of a body is M
or riM we can see which of these values we must use
in calculating the molecular depression, in order to get
a number nearly equal to Baoult's mean value for the
constant. It must be noticed that we can only determine
w. s. 5
66 SOLUTION AND ELECTROLYSIS. [CH, V
the molecular weight of a body in a certain solvent, for
the same substance may have different molecular weights
in different solvents (as witness the alcohols in benzene
and acetic acid) and of course these may be all different
from its molecular weight in the gaseous state, though in
general one of them turns out to be the same. The
nature of the solvent may affect the state of molecular
aggregation, just as the conditions of temperature and
pressure affect it when the substance is a gas. The
solvents of the benzene series seem to favour polymeri-
sation, while formic acid and its analogues seem generally
to produce simple moleculea
In the case of aqueous solutions we again have two
series, and, taken alone, we might be inclined to consider
the higher numbers as normal, and to assign doubled
molecular weights to those bodies which give the lower
values. But when we work out Van 't Hoff's formula for
the case of water, it gives, as we have seen, a value 18*9 for
the molecular depression. This at once shews that the
lower numbers are the normal values, and that they can
be explained on Van 't Hoff's theory. It is the higher
series which requires some farther explanation. Are we
to suppose that (as in the case of certain gases at high
temperatures) dissociation occurs, and increases the number
of effective pressure-producing molecules, or are we to
suppose that some new cause is brought into operation ?
In favour of the dissociation hypothesis it may be urged
that the numbers for such salts as KCl, NaCl, &c., —
which can only be dissociated into two parts, never shew
values which are much greater than double the normal.
CH, V] FREEZING POINTS OF SOLUTIONS, 67
while salts such as CaCU, which can be split into three,
sometimes give a molecular depression which is about
three times the normal value. The fuller discussion of
this hypothesis we must defer till we are considering the
electrical properties of solutions, but we will here state
the most important fact that all those substances which
give abnormally great values for the molecular depression
of the freezing point in aqueous solution, form, when
dissolved in water, solutions which are electrolytes. More-
over their electrical conductivities bear a simple relation to
the amount of dissociation which it is necessary to assume
in order to account for the abnormal eflfect on the freezing
point. Whatever is the cause of this abnormally great
molecular depression, is certainly also the cause of
electrolj^ic conductivity.
29. Influence of Concentration. The account
of the subject of freezing points given above does not
apply to strong solutions, for Van 't Hoflf's theory only
holds good when the dilution is so great that the effect of
the forces between the molecules can be neglected. As
the strength increases we get deviations from the law that
the depression is proportional to the concentration. The
depression coefficients of some substances increase, and
of others decrease as concentration gets greater. The
effect of increasing concentration on the freezing points
of indifferent substances (i.e. non-electrolytes) has been
studied by Beckmann* and Eykmanl They find that
^ ZeiU. /. physikal, Chemie, ISSS, 2, p. 715.
^ Ibid., 1889, 4, p. 497.
5—2
68 SOLUTION AND ELECTROLYSIS. [CH. V
in almost all cases the molecular depression changes nearly
in proportion to the concentration, and that it more usually
increases than decreases when a greater quantity of sub-
stance is dissolved. This makes the curves drawn between
the concentrations as abscissse and the molecular depres-
sions as ordinates, nearly straight lines, inclined at a small
angle with the axis of the abscissse. In some cases the
molecular depression decreases faster than the concentra-
tion increases, and, at high concentrations, may even be
reduced to half its former value. If we extend our method
of calculating molecular weights to such solutions, it indi-
cates that the molecular weight has doubled at the high
concentration, so that poljrmerisation must have occurred.
These cases are few ; they include such solutions as those
of acetoxim and other oxims in benzene, and must be
considered analogous to the case of gaseous nitrogen
peroxide at moderate temperatures.
In general the change of molecular depression is far
less than in these oxim solutions, and must be considered
to be analogous to the variation from the usual laws shewn
by gases at high pressures, rather than to a case of gaseous
polymerisation. The best value for the molecular weight
would obviously be obtained by producing the curve
shewing the depression of the freezing point till it cut the
axis of no concentration, and using this value in the
calculation. It is probable that the small deviations of
Raoult's numbers for non-electrolytes from the calculated
values would become still smaller if this correction for
concentration were applied to his observations.
The variation from their ideal laws, of gases at high
CH. V] FREEZIKG POINTS OF SOLUTIONS. 69
pressures can be approximately expressed by Van der
Waal's formula
[p + ^)(v-b) = RT,
where the pressure p is increased by a term proportional
to the molecular attraction (a) and inversely proportional
to the square of the volume, and the volume v is diminished
by a constant b which is equal to four times the actual
volume occupied by the substance of the molecules
themselves and is unaffected by any change in pressure.
An equation of the same nature has been developed by
Ostwald, Bredig and Noyes, taking account of the
molecular volumes of the solvent and of the substance
dissolved, and of the interactions between them. In
general these latter are very small, and on simplification
the formula reduces to
p(v^d)^K ae),
where the constant d expresses a correction for volume,
which depends on the nature both of the solvent and of
the substance in solution. The results deduced fix)m this
equation agree well with observations made by Beckmann
on acetone dissolved in benzene, and on chloral hydrate in
water.
A long series of determinations of the freezing points of
dilute solutions of inorganic and organic bodies dissolved
in water has been made by H. C. Jones^ His results for
organic substances shew that in general the molecular
depression decreases as the concentration increases till a
certain critical concentration, at which the molecular
^ ZeiU.f.phys, Chemie, 1898, 11, pp. 110 aii4 529, 12, p. 623,
70
SOLtJTION AND ELECTROLYSIS.
[CH. V
depression is a minimum, is reached, after which it begins
to increase again as the concentration is made still greater.
This is shewn by the annexed table for cane sugar in
water.
Concentration in
Molecular
Concentration in
Molecalar
gram-moleooles
depression
gram-molecoles
depression
per litre
STIn
9
per litre
STln
000234
2^35
0-117
V94:
•00467
2-36
•154
1-96
•00930
2^29
•203
2-00
•0292
2-27
•585
2-32
•0728
2-08
1169
2^91
•0933
1-99
The kind of variation in this case is obviously the
same as in the case of air at high pressures investigated
by Amagat (see Tait's Properties of Matter § 200) who
found the following results.
Pressure in
atmospheres
pv
Pressnre in
atmospheres
pv
1-00
3167
59^53
73 03
1-0000
•9880
•9815
•9804
94-94
133-51
282-29
400-05
•9814
•9905
10837
M897
We see by equation (11) p. 56 that ST varies as pv, so
that it is analogous to pv in the case of a gas. Thus the
existence of a minimum value of the molecular depression
of the freezing point, is exactly paralleled by the deviation
of air from the gaseous laws.
Ca. v]
FREEZING POINTS OF SOLUTIONS.
71
The behaviour of very much stronger solutions has
been examined by Pickering^ who finds that in such cases
great deviations jfrom the gaseous laws occur. The
following table gives the molecular depression produced
by n molecules dissolved in 100 molecules of solvent.
Substance
n=l
5
10
50
100
300
1000
2000
Solvent = Water
Methyl alcohol
Ethyl „
Acetic acid
1-05
1-06
1-05
1-03
0:826
1-10
1-06
1-15
0-816
0-548
1-04
0-944
0-865
0-52
Solvent = Benzene
Methyl alcohol
Ethyl „
0-6
0-6
0-31
0-33
0-22
0-22
0-077
0-10
0066
0-076
0-042
0-067
0-040
0-044
0-031
0038
Thus in all cases the molecular depression gets less
when the concentration is increased. This is contrary to
Jones' result for fairly strong solutions, but if we expressed
Pickering's numbers in gram-molecules per 100 cubic
centimeters of solution, instead of in 100 gram-molecules
of solvent, the value of n would be less, and that of ST/n
increased, and this diflference would increase as the
concentration increased. The densities of mixtures of
ethyl alcohol and water are known, and if we calculate the
molecular depression (n = number of gram-molecules per
100 c.c. of solution) for the mixture under the column 100
we get S2yn = l'38 instead of 0*548, and this is greater
than the value when n = 1 viz. 1-10.
1 Chem, Sac. Jour, Trans. 1893, 63, p. 998.
72 . SOLUTION AND ELECTROLYSIS. [C5. V
The difference between the results obtained by measur-
ing the concentration by the number of gram-molecules
per litre, and measuring it by the number of gram-
molecules to 1000 grams of solvent, is well shewn by the
tables and diagrams given by Abegg^ who has determined
the freezing points of many concentrated solutions. A.
higher value for the molecular depression is always
obtained by using the former method, and as the concen-
tration increases the difference becomes very great indeed,
30. Ciyohydratei. Since the solubility of a solid
usually increases as the temperature rises, the solution
which is just saturated at the freezing point can retain all
its contents at higher temperatures. If such a solution
is cooled, it again becomes saturated when the freezing
point is reached, and as ice is frozen out, solid must be
deposited, because there now remains insufficient solvent
to keep it in solution. The ice and dissolved substance
will therefore be deposited in the proportion in which they
exist in solution, and since the concentration of the
remaining liquid keeps unchanged, the temperature will
be constant till all has solidified. The ice and salt are not
deposited in combination, but only side by side, for they
never form clear definite crystals, and alcohol will dissolve
out the ice, leaving a framework of solid salt. Owing
to the constancy in the melting points and composition
of such bodies, they have been regarded by Guthrie
and others as definite chemical compounds. The applica-
tion of our present knowledge of the properties of solu-
^ Zeit9, f. phynkal, Ckemie, 1S94, 15, p. 209.
CH. V] FREEZING POINTS OF SOLUTIONS. 73
tions however will, as shewn above, completely expla^
their existence, without the need of such an assumptioiL'
31. Melting points of Alloys. If metals are
dissolved in mercury, they produce depression of the
melting point, just as bodies dissolved in water produce
depression of the freezing point. Tammann examined
solutions of potassium, sodium, thallium and zinc, and
found Raoult s laws approximately true. These metals
seem to form monatomic molecules.
Heycock and Neville^ used sodium and tin as solvents,
and found the following values for the atomic depressions :
Solutions in Sodium,
Gold 4-50— 4-87 Cadmium 3-17— 3-92
Thallium 4-27— 473 Potassium 3-34— 3*85
Mercury 4*37— 453 Indium 3-37— 3-77
Solutions in Tin,
Silver 2-93 Cadmium 2-43
Gold 2-93 Mercury 2-39
Copper 2-91 Calcium 2*40
Sodium 2*84 Indium 1-86
Magnesium 2*76 Aluminium 1*25
Lead 276
Indium and Aluminium thus shew a tendency to form
more complex molecules when dissolved in tin.
The chief interest of these experiments lies in their
influence on our views as to the nature of alloys, which
must now be considered as solutions of one metal in
another.
1 Chem, Soc, Joum. 1889, 1890.
CHAPTER VI.
VAPOUR PRESSURES OF SOLUTIONS.
32. Theoretical Confiderationi. If any non-
volatile substance be dissolved in water, it will be found
that the boiling point is higher than that of the pure
solvent. A liquid boils when its vapour pressure is equal
to the pressure of the atmosphere, and we see from the
above statement that the effect of the dissolved substance
is to make it necessary to heat the liquid to a higher
temperature in order to reach such a pressure, that is to
say, that at any given temperature the vapour pressure is
reduced. This effect of decreasing the vapour pressure
obeys much the same laws as those which govern the
depression of the freezing point. The experimental diffi-
culties of determining it are however much greater. Let
us first examine its connection with the osmotic pressure,
to which it must evidently be related, since the air over
an evaporating liquid acts as a semipermeable membrane
in allowing the solvent, but not the dissolved substance, to
escape. A thermodynamic investigation similar to that
applied on p. 56 to freezing points, was given by Van 't
Hoff, but a more direct method due to Arrhenius will be
reproduced here.
CH, Vt] VAPOUR PRESSURES OF SttLUTIONS.
75
Suppose that a long tube, open at the top and closed
below by a semipenneable mem- ^^,^^
braoe, is filled with the solution ""^^^
of some non-volatile, indifferent
substance, and placed in an ex-
hausted bell-jar with its lower
end dipping in water. Water
will enter or leave the apparatus
till the level of solution in the
tube is such that the potential
energy of the system is at a mini-
mum value, so that any farther
rise would involve an increase in
the potential energy. We may
then say that the pressure due
to the colunm of liquid is equal
to the osmotic pressure of the
solution, if we understand the
term osmotic pressure to include all those properties
which cause the potential energy of the solution to
increase when the concentration gets greater, whether
they are due to the movement of the dissolved molecules,
to volume changes on dilution, to chemical action between
the dissolved substance and solvent, or to other causes.
If A is the height of the column of liquid in centi-
metres, p its density, and a the density of mercury, the
osmotic pressure when there is equilibrium is
I* ■= mm. or mercury.
The bell-jar has become filled with the vapour of the
Fig. S.
76 SOLUTION AND ELECrBOLYSIS. [CH. VI
solvent, and at the level a, at which the liquid stands in
the tube, the pressure of this atmosphere of vapour must
be equal to the vapour pressure of the solution. If this
were not so there could not be equilibrium, and vapour
would continually leave the solution at a, or condense
there; water would at the same time enter or leave
through the membrane to compensate for this process,
and a continuous, automatic circulation would be set up.
Since by the principles of thermodjoiamics we know this
to be impossible, the vapour pressure of the solution must
be less than that at the surface of the pure solvent by the
pressure due to a column of vapour of height h. If, for a
first approximation, we assume that the density of the
vapour is uniform throughout that column we get
, 10 htr
TT =7r ,
8
where ir represents the vapour pressure of the solvent,
tt' that of the solution, and a the density of the vapour.
Fs
But A =
lOp'
... ^'«^«:?? (17),
P
so that the lowering of the vapour pressure is Pa/p, or
the osmotic pressure multiplied by the density of the
vapour under its existing pressure and divided by that
of the solution-
The density of the vapour may be considered to be
proportional to the pressure, and for very dilute solutions,
when the column h is short, we may treat the pressure as
CH. n] VAPOUR PRESSURES OF SOLUTIONS. 77
everywhere equal to ir. If the density of the vapour at
760 mm. is a^ we have
The density of the vapour will also be inversely pro-
portional to the absolute temperature, but since the osmotic
pressure P is directly proportional to the same thing, the
correction goes out, and our result will be independent
of temperature.
We thus get
, Pa Po-qIt
(18),
•• IT 760/>
which gives us the ratio of the decrease in the vapour
pressure, to the vapour pressure of the solvent.
Let us take the case of one gram-equivalent of some
indiflferent substance dissolved in water, in such a way
that the volume of the solution is one litre. This, as we
have seen, gives an osmotic pressure equal to 22*3 atmo-
spheres or
22*3 X 760 mm. of mercury,
da, the density of water vapour at normal temperature and
pressure is 9/11160, and />, the density of the solution
when it is dilute, can be put equal to that of water,
viz. unity. Thus we get
^-^' _ 22-3 X 760 X 9 _
~1t 760 X 11160 -00180.
Raoult determined the decrease of vapour pressure of
water caused by the solution of various bodies in it. He
found that if different bodies were dissolved in the pro-
78 SOLUTION AND ELECTROLYSIS. [CH. VI
portion of their molecular weights, the lowering of vapour
pressure was the same for all. For a strength of solution
represented by 1 molecule in 100 molecules of solvent he
found that the mean value of the ratio of the decrease
of pressure to the whole pressure, when water was the
solvent and indifferent bodies were dissolved, was 00102.
If instead of this strength, we have one gram-molecule in
one litre of solution or (which is the same thing for very-
dilute solutions) one litre (that is 1000 grams) of water,
we have reduced the mass of solvent in the ratio of
18 X 100 : 1000 (since 18 is the molecular weight of water)
and so increased the concentration in the ratio of 10 : 18.
The result of Raoult s experiments then is to shew that
in a dilute solution containing one gram-molecule per litre
the relative lowering of the vapour pressure is
00102x1-8 = 00184,
a number almost identical with that deduced from the
osmotic pressure.
This expression has been obtained by assuming that
the density of the vapour in our exhausted bell-jar (see
p. 75) is everjrwhere uniform. Such an assumption is only
justified if the column of vapour of height h is very short,
that is if the osmotic pressure, and therefore the concen-
tration of the solution, is exceedingly small. Where this
is not the case we must divide the height of vapour h into
a number of parts each equal to dh and put
dir = — o" . dhy
8
, 10 CToTT ,,
• '^'^""T-Teo'^^'
CH. Vl] VAPOUR PRESSURES OF SOI4UTIONS. 79
. ,, _ 5 760 dir
10 Co TT
By integrating from to A we get
A =
760 «
'*(S'
lOcTo
TTo being the pressure at the level of the water, i.e, the
vapour pressure of the pure solvent, and tt^ the pressure
at the height h, i,e. the vapour pressure of the solution.
Ps
Now A =
.-.log. (5)
10/)'
(19).
PcTo
760p
This equation gives a necessary relation between the
osmotic pressure and the lowering of the vapour pressure
of any solution, and is quite independent of the view we
take as to the real cause of osmotic pressure. Whatever
the cause of it may be, we know that osmotic pressure
exists, and it therefore follows that the vapour pressure
must be lowered by the amount shewn in our equation.
The value of the osmotic pressure can thus be deduced
from observations on the diminution of the vapour pressure,
just as it can from observations on the lowering of the
freezing point.
It is easy to transform our equation into a form which
gives the concentration of the solution in terms of the
ratio of the number of molecules of dissolved substance
to the number of molecules of solvent, which was Raoult's
method. The osmotic pressure P is 22*32 x 760 mm. of
mercury for a strength of 1 gram-equivalent in 1000 cc.
80 SOLXmON AND ELECTROLYSIS. [CH. VI
and so for a strength of n gram-equivalents in Fee. its
value is
P _ 2232 X 760 n
Now the mass of the solvent is NMy where N is the
number of gram-molecules and M its molecular weight,
and the volume is the mass divided by the density
or Kas ,
p
p _ 22-32 X 760 x 1000 x np
(To the density of the vapour under normal conditions of
temperature and pressure is
M
^' 22-32 X 1000 '
assuming that the molecular weight of the vapour has the
same value as we have taken for it in the liquid condition.
We thus get by substituting in equation (18) —
TT — tt' n
If we treat equation (19), which gives the strict relation
with the osmotic pressure, in the same way, assuming
as before that P is proportional to the concentration, we
get
Now loge [ — ?) can be written as
CH. Vl] VAPOUR PRESSURES OF SOLUTIONS. 81
and since ir — ir' is small compared with tt' this may be
developed in a series
ir — n/ . (I T — ir\
-IP — *l~;7~j+
All except the first term will be small, so that we may put
as a fair approximation —
adding 1 to each side
ir'
~N'
IT
N
•
• <
IT —
7r'~ n'
B
IT
N + n
IT
-ir'
~ n '
•
TT —
tr m
(20),
which is the exact expression deduced empirically by
Raoult from the results of his experiments.
But this result, unlike our equation (19) on p. 79, has
been deduced by making an assumption which is only true
for dilute solutions, namely that the osmotic pressure is
proportional to the concentration. It therefore gives
results which fail to represent the truth when the concen-
tration becomes considerable.
Thus for solutions of turpentine in ether
^ 0627 1377 -3055 5504 9194 1-817,
N
log. (5) •
0619 1278 -2473 391 576 '865.
For dilute solutions however it gives good results and has
a great advantage over the other equation, inasmuch as it
shews that if solutions be prepared which contain the same
w. s. 6
82 SOLUTION AND ELECTROLYSIS. [CH. VI
number of molecules of dissolved substance in the same
number of molecules of solution, the relative lowering of
the vapour pressure will be the same for all.
Thus if we have solutions in each of which there is
one molecule dissolved in 100 molecules of solvent, that is
in 101 molecules of solution,
^?^^^' = ^ =00099.
IT 101
Raoult first shewed that if the same number of gram-
molecules of various indifferent substances were dissolved
in water, or other solvents, the relative lowering of the
vapour pressure was very nearly constant. He then took
twelve solvents and, dissolving many bodies in each, proved
that for a strength of solution of 1 molecule in lOO
molecules the relative lowering of pressure was nearly
constant and equal to 0*0104.
In 1890 however he shewed^ that when acetic acid
was used as a solvent, the number obtained was 0*0163.
This seems not to agree with the results of our equations,
but in deducing them it must be remembered that (on
p. 80) we assumed that the molecular weight of the vapour
was the same as that which we took for the liquid. Now
in preparing the solution the normal value of the molecular
weight was of course assumed for the liquid, and it is
known that at moderate temperatures the vapour density
of acetic acid is abnormal, shewing that its molecular
weight is also abnormal. At the boiling point 118° C,
the ratio of the actual to the theoretical vapour density
^ Baoult and Beconra, Compt, Rend, 1890, 110, p. 402.
CH. Vl]
VAPOUR PRESSURES OF SOLUTIONS.
83
is 1*64, which makes our theoretical number 0*0162.
This indicates that we must always correct our theoretical
number in this way by multipljdng it by the ratio of the
actual to the theoretical vapour density. Raoult gave
the following numbers for six solvents —
Solvent
Temperature
n
N+n
(correoted for
vapour density)
(observed)
Water
Ethyl alcohol
Ether
Carbon bisulphide
Benzene
Acetic acid
100
78
20
24
80
118
00102
0-0101
0-0103
0-0100
0-0101
0-0162
0-0102
0-0101
0-0104
0-0099
00101
0-0163
Thus, as in the case of the depression of the jfreezing
point, we have a satisfactory theory of the lowering of
vapour pressure for the case of dilute solutions. For
stronger solutions variations appear, as we observed in the
case of jfreezing points. There is a simple method of con-
necting the two effects, which are evidently related since
we have deduced both of them jfrom the osmotic pressure.
Suppose we have lowered the temperature of some
pure water to its jfreezing point, and allowed ice to separate.
The ice is in equilibrium with the liquid, and unless heat
be added to or taken away from the mixture, there is no
tendency for the quantity of ice to increase or diminish.
It follows that the ice and the water at the freezing point
must have the same vapour pressure, otherwise if we had
6—2
84 SOLUTION AND ELECTROLYSIS. [CH. VI
ice and water in a closed vessel, vapour would pass away
from the body with the higher pressure, and condense on
that which had the lower pressure, and the quantity of
ice would increase or diminish. By the same reasoning
we can shew that at the freezing point of a solution, when
it can exist in equilibrium with ice, its vapour pressure
must equal that of the ice. If then we know how the
vapour pressure of ice varies with the temperature, we can
find what decrease of temperature is necessary to reduce
the vapour pressure by the same amount as the dissolved
substance decreases that of the water, and this gives the
lowering of the freezing point.
This shews that whatever the variations in the lowering
of the freezing point at great concentrations, there must
be a corresponding variation in the diminution of vapour
pressure at the freezing point which can at once be
calculated, but as most of the observations on vapour
pressures have been made at higher temperatures, various
approximate assumptions have to be made in order to
correlate the two series of results.
The following investigation of this connection is taken
from Ostwald's Lehrbuch.
The relation between the quantity of heat \ required
to evaporate unit mass of liquid, the vapour pressure ttq,
and the volume of the saturated vapour F, is as we have
seen on p. 26 —
\ _ d7ro j^
T^dT
CH. VI] VAPOUR PRESSURES OF SOLUTIONS. 85
A similar expression holds good for ice, but in this
case the heat of evaporation, Xj, is greater, for the heat
required to melt the ice must be added to that required
to vaporise the water.
Xi _ rf ,
where pi is the vapour pressure of ice ; the difference is
RT^ dT V ^ 7ro>
But Xi — Xq is the heat of fusion of ice, which has the
value (7904 H- "49^), t denoting the temperature in degrees
jfrom the Centigrade zero.
,, TTi (7904 + -490,^
Taking the value of It which corresponds to one gram of
water (viz. 2/18 calories per degree, see p. 41), treating T^
as constant in the denominator, and neglecting t^ we get
log -' « 00954^.
Wo
33. Boiling Points. It is more convenient in
some cases to measure the boiling point of a solution than
its vapour pressure at some other temperature. Since
the effect of the dissolved substance is to reduce the
vapour pressure at any given temperature, it must raise
the boiling point, and the relation between the two is
easily found. Let IIIX be a portion of the vapour pressure
curve of a solvent and II'IT a portion of that of a solution.
If the solution is dilute, so that the change in the vapour
pressure is small, we may consider the part of the curve
for the pure solvent that we want to use to be a straight
86
SOLUTION AND ELECTROLYSIS.
[CH. VI
line. Any vertical line cutting nn in A and IITI' in B
will represent the change in vapour pressure at a certain
temperature, and CB drawn horizontally from the point B to
cut nn in'C, will represent the change in boiling point, ST.
00
m
s
o
>
Temperaturca
Fig. 6.
Now whatever be the direction and form of the solu-
tion curve n'n', AB = CB tan ACB,
,\ir-ir' = STta.nACB
dir
= ST.
dT
(21).
If we observe hT and know dTr/dT for the pure solvent, we
can at once calculate tt — tt'. The value of dirjdT can be
experimentally determined by measuring the boiling point
of the solvent first when the barometer is high and then
when it is low, and dividing the difference in pressure by
the difference in temperature.
CH. Vl] VAPOUR PRESSURES OF SOLUTIONS. 87
Another method of getting dir/dT is to use Clausius'
equation which we deduced from the principles of thermo-
dynamics on p. 26 and used on p. 84.
dir ^ \
df''{V-v)T'
where \ = latent heat, V the volume of the saturated
vapour and v the volume of the liquid. If we assume
that the vapour obeys the gaseous law irV=RT, we get,
since v is small,
dir _ Xir
dT'RT^'
Xtt
7r-7r' = Sr
RT
2
V^ = «^^2^ w
Now for 1 gram-molecule of the vapour the value of
-B is 1*974 calories : calling this 2 we can put
^ = «2'^. (23).
From this expression the relative lowering of vapour
pressure can be calculated from observations on the rise of
boiling point.
In order to examine the validity of our theory, let us
calculate BT for special cases. Baoult, assuming that the
law of proportionality still held, found that for a strength
of solution of 1 molecule in 100 molecules of solvent
(tt — 7r')/7r was equal to '01 (see p. 82), so that for this
concentration our equation gives
88
SOLUTION AND ELECTROLYSIS.
[CH. VI
The following table gives the calculated values of
'02Ty\ and the mean results for the molecular rise of
boiling point, deduced from observations on very dilute
solutions in different solvents by Beckmann's method.
•02r» ,
Solvent
dT (observed)
•
— r— ^ (calculated)
A
Water
4 to 5
5-2
Alcohol
10 to 12
11-6
Acetone
17 to 18
16-7
Ether
21 to 22
2M
Carbon bisulphide
22 to 24
23-7
Acetic acid
25
25-3
Ethyl acetate
25 to 26
26-0
Benzene
25 to 27
26-7
Chloroform
35 to 36
36-6
34. Experimental Methods. Determinations of
the vapour pressures of solutions have been made by
Faraday, Wiillner, Tammann, Emden, Raoult, Walker,
Beckmann, and others. Raoult^ was the first to examine
solutions of indiflferent substances, and to use solvents
other than water. His method consisted in comparing
the heights of three mercurial barometric columns, the
space over one being empty, and the others containing the
vapours from the pure solvent and from the solution
respectively. The depressions of these Columns as
compared with the first gave the vapour pressure of the
solvent and of the solution. Raoult found that
1 Compt. Bmd. 1886-7, 103, p. 1125; 104, p. 1430.
CH. VI] VAPOUR PRESSURES OF SOLUTIONS. 89
(i) The relative lowering of the vapour pressure
(tr — 7r')/Tr is independent of temperature.
(ii) For dilute solutions (tt — 7r')/7r is proportional
to concentration, but as the solutions get stronger it is
more nearly represented by n/(N'+n), where n and N are
the numbers of molecules of dissolved substance and of
solvent respectively.
(iii) The molecular lowering of vapour pressure
(i.e. the lowering produced by 1 gram-molecule in 100
grams of solvent) is independent of the nature of the
dissolved substance. Thus for ethereal solutions he found
Molecular
weight
Molecular
lowering
Carbon hexachloride
237
•71
Turpentine
Cyanic acid
Benzaldehyde
136
43
106
•71
•70
•72
Aniline
43
•71
Antimony chloride
228-5.
•67
(iv) When the ratio of the number of molecules of
the dissolved substance to the number of molecules of the
solvent is made the same, the lowering of vapour pressure
is independent of the nature of the substance and of the
solvent. (For table see p. 83.)
We have already seen that all these laws can be
deduced from the theory of dilute solutions. Stronger
solutions shew deviations in their vapour pressures as in
their osmotic pressures and freezing points, under which
latter heading the influence of increasing concentration
has been discussed from the point of view of the theory.
90 SOLUTION AND ELECTROLYSIS. [CH. VI
There are several objections to the barometric method.
The quantity of vapour is so small that any more volatile
impurity in the liquid would produce a large error, and
since evaporation only occurs at the surfece, the upper
U,.r. of '.h, soMo/g,. .tronger ..d give ^ JJ a
vapour pressure. Beckmann* improved the method by
allowing the solution to evaporate into a small flask. He
then calculated the quantity of vapour produced from
the decrease in weight of the solution, which was con-
tained in a weighed bulb.
A method applicable to low temperatures has been
introduced by Ostwald and Walker^ A current of air is
passed through two bulbs containing the solution, and is
thus saturated with its vapour. It is then led through
another bulb containing pure water. Since this gives a
higher vapour pressure, the air takes up more water and
again becomes saturated. Finally the whole of the
aqueous vapour is extracted by passing the air through
pumice moistened with sulphuric acid. The gain in
weight of the sulphuric acid gives the whole quantity
of vapour evaporated, and the loss in weight of the water
bulb gives the difference between that furnished by it
and that furnished by the solution. Thus the ratio
(tt — 7r')/7r is at once found.
Beckmann has also used the boiling point method. It
is necessary to measure the temperature of the solution,
and not the temperature of its vapour which is the same
as that of the pure solvent. To prevent "bumping" a
1 Zeits.f.phys. Chemie, 1889, 4, p. 632.
2 Ibid,, 1888, 2, p. 602.
CH. Vl]
VAPOUR PRESSURES OF SOLUTIONS.
91
piece of platinum wire is sealed through the bottom of
the flask. Boiling then takes place exclusively jfrom the
end of this, and a constant and uniform stream of bubbles
is given off.
Tammann^ has measured vapour pressures at 100° by
noticing what decrease of external pressure was required
to make the liquid boil at that temperature. He gives
an immense number of figures shewing the diminution
of vapour pressure in millimetres of mercury, due to the
solution of n gram-molecules in 1000 grams of water. We
select a few of them to which we shall have occasion to
refer.
n=0-6
1
•
2
3
4
5
6
Potassium chloride
12-2
24-4
48-8
74-1
100-9
128-5
162-2
Sodium „
12-3
25-2
52-1
80-0
111-0
143-0
176-5
Potash (KOH)
15-0
29-5
64-0
99*2
140-0
181-8
223-0
Aluminium chloride
22-5
61-0
179-0
3180
Calcium „
17-0
39-8
95-3
166-6
241-6
319-6
Barium „
16-4
36-7
77-6
Succinic acid
6-2
12-4
24-8
36-7
48-6
69-7
71-2
Citric „
7-9
15-0
31-8
60-0
71-1
92-8
Lactic „
6-5
12-4
240
34-3
44-7
56-0
65-6
If we calculate the theoretical depression for a con-
centration of 0*5 gram-molecule in 1000 grams of water
from equation (20) on p. 81
TT — TT
TT
n
N+n
0-5
we get TT — tt' = 760 x ^^^ — j^;^ = 6*8 mm. of mercury.
^ Mim, Acad. Pdterab,, 1887, 35, No. 9. Table in Ostwald's
Lehrhuch,
92 SOLUTION AND ELECTROLYSIS. ^ [CH. VI
Thus we see that bodies like lactic and succinic acids give
a result which agrees well with theory, while metallic
salts are abnormal. Salts like potassium chloride^ ECl,
give numbers nearly double the figure deduced from
theory, calcium and barium chlorides, CaCU and BaCls,
produce nearly three times, and aluminium chloride,
AlCls, nearly four times the normal effect.
As in the case of the depression of the freezing points,
these exceptions to the usual law are all electrolytes. It
is also important to note that ECl contains two atoms,
CaClj three atoms and AlCls four atoms. The lowering
of the vapour pressure by electrolytes seems then to be
proportional to the number of atoms in the molecule.
The discussion of these relations must be postponed for
the present.
35. Influence of Concentration. Tammann's
results shew that in general the lowering of vapour
pressure increases faster than the concentration for
metallic salts, but appears to be nearly proportional to it
for indifferent substances. The concentration of Tam-
mann's solutions is expressed in terms of the number
of gram-molecular weights of salt dissolved in 1000
grams of water. If we convert it into the number of
gram-molecules in a litre of solution, the result will be to
make the molecular lowering of vapour pressure increase
faster as the concentration gets greater (see p. 71).
36. Determination of Molecular Weights. Like
the depression of the freezing point, the lowering of
vapour pressure has been used to determine the molecular
CH. Vl] VAPOUR PRESSURES OF SOLUTIONS. 93
weight of bodies in solution. It can be used for high tem-
peratures, and for cases (such as for solutions in alcohol)
when the freezing point method is not applicable. In this
way Beckmann obtained the molecular weights of iodine,
phosphorus and sulphur in solution. It was found that
1*065 grams of iodine, dissolved in 3014 grams of ether,
raised the boiling point by 0'296°. This concentration
corresponds to (1065 x 7400)/(3014 x M) gram-molecules
of iodine in 7400 grams (100 gram-molecules) of ether.
Now it can be proved either by experimenting with a body
of known molecular weight, or by calculation from our
formulae, that 1 gram-molecule of any indifferent substance,
dissolved in 100 gram-molecules of ether, gives a change
in the boiling point of 0*284°. The above strength of
solution must therefore be 296/284 gram-molecules.
1065 X 7400 _ 296
'• 3014 Jf "284*
.*.Jf= 250*3.
The atomic weight of iodine is 127, so that in ethereal
solution the molecule consists of two atoms.
In a similar manner it was shewn that the molecule of
phosphorus in carbon bisulphide contains 4 atoms, as it
also does in the state of vapour, but that in the same
solvent the molecule of sulphur consists of 8 atoms,
whereas the vapour density gives a formula Se.
The vapour pressures of amalgams have been ex-
amined by Ramsay* who found that in nearly all cases
the loweriDg of vapour pressure corresponded to that
^ Chem. Soe, Journal Trans,, 1889, p. 621.
94 SOLUTION AND ELECTROLYSIS. [CH. VI
which would be produced by monatomic molecules. The
value deduced for the molecular weight of potassium
however is less than its atomic weight (29*6 instead of
39'1) and the numbers for calcium and barium (19'1 aud
75*7) correspond to half their atomic weights. What this
means it is as yet impossible to say. Aluminium and
antimony tend to form more complex molecules.
37. Solutions of Gases in Liquids. We have
already seen (p. 10) that, with reference to their solubility
in liquids, gases can be divided into two classes: firstly
those which are completely removed by boiling the liquid
or decreasing the pressure, and secondly those which
cannot be so removed.
In the first case, where the dissolved gas obeys
Henry's law that the mass dissolved is proportional to
the pressure, the laws of the vapour pressure are very
simple. Let us consider the case of a mass of air
saturated with water vapour over a saturated solution
of air in. water. We know that if the external pressure
be reduced, some air will at once come out of solution,
while if the pressure be increased more goes in. If we
have then some water with air dissolved in it over the
mercury in a barometer tube, air will be expelled till
its pressure in the barometric vacuum is equal to the
pressure of that dissolved, and whatever changes may
occur in order that there may be equilibrium, the
water must always keep saturated with air under the
existing conditions of temperature and pressure. The
pressure of aqueous vapour from the solution will obey
CH. VI] VAPOUR PRESSURES OF SOLUTIONS. 95
the usual laws, and will therefore be less than that from
pure water in accordance with our equation
TT — TT n
~m' WTn'
or 7r' = 7r (1 - ,^ . ),
for the air in solution will exert osmotic pressure just like
other substances. The total vapour pressure of the
solution will be the sum of this and of the pressure due to
the air, which, as we have seen, equals that in the
vacuous space. This latter will depend on the relative
volume of the solution and of the vacuous space, which
takes air from the solution till there is equilibrium, so the
measured vapour pressure would depend on the dimen-
sions of the apparatus. We can however calculate the
total vapour pressure in any given case if we know the
concentration of the solution. Thus if there are n gram-
molecules of gas dissolved in JV gram-molecules of solvent,
the diminution of the pressure of aqueous vapour (due to
osmotic pressure) is
or for dilute solutions
If we know \ the solubility of the gas at 760 mm.
pressure and 0° C, we can find the vapour pressure of the
dissolved gas, for
0"~ TT'
96 SOLUTION AND ELECTROLYSIS. [CH. VI
where Vq is the volume of gas dissolved under normal
conditions and V the volume of the solution.
In a volume Vq c.c. there are t;o/22320 gram-molecules.
Let us call this number n©, then by Henry's law
n _ p
no"760'
where p is the pressure of gas.
Hiyr. w "760 X 22320 n
Vp
V, the volume of the solvent, contains -r~ gram-molecules,
where M = molecular weight and p the. density of the
solvent,
' P =
P
760 X 22320 p n
This gives the increase in the total vapour pressure due
to the gaseous pressure, so the total increase in the vapour
pressure is
„ /760 X 22320 p \n
In the second case of gases dissolved in liquids we
have a substance like an aqueous solution of hydrochloric
acid gas, which on distillation grows either richer or poorer
in HCl till a certain strength of solution is reached.
The solution then distils over unchanged. This is exactly
analogous to the solution of one volatile liquid in another
80 we need not consider it separately.
CH. Vl] VAPOUR PRESSURES OF SOLUTIONS.
97
38. Solutiong of Iiiquids in Iiiquidg. When we
were considering solubility, we found that pairs of liquids
must be divided into three classes — (i) those which will
not mix at all, (ii) those partially soluble in each other,
(iii) those soluble in each other in all proportions. The
laws of vapour pressure are different for each case.
(i) With immiscible liquids the vapour pressure is
equal to the sum of those of the constituents. This can
be proved by passing the vapour of one boiling liquid into
the other and examining the vapour which comes through,
for in it the two substances will obviously be present in
the ratio of their pressures. The sum of the two pressures
will, at the boiling point of the mixture, be equal to the
atmospheric pressure, so the boiling point must be lower
than that of either constituent, but this is usually
masked, for if one liquid forms a layer over the other, the
mixture bumps violently if the more volatile liquid be
below, while, if the positions are reversed, it is only the
upper liquid which evaporates.
(ii) The behaviour of partially miscible liquids has
been studied by Konowaloff\ who
found by experiment that the solu-
tion of a liquid A saturated with a
liquid B exerts at a certain tempera-
ture the same vapour pressure as
that which a solution of B saturated
with A exerts at the same tempera-
ture. This can also at once be proved
from theoretical considerations. For if we have an arrange-
1 Wied. Ann,, 1881, 14, p. 219.
W. S. 7
N
/ ^
^^
— ~ ""
b
-=W
Fig. 7.
98
SOLUTION AND ELECTROLYSIS.
[CH. VI
ment like that in fig. 7 with a saturated solution of £ in
A at a, and a saturated solution of ^ in £ at 6, the vapour
over each must have the same pressure and composition,
or else distillation or diffusion would go on in the
upper space; this would be compensated by diffusion
through the liquids, and so a perpetual circulation would
be kept up, which is impossible. Eonowaloff measured the
vapour pressures of mixtures of two liquids of varying
composition and at different temperatures. The general
result of his observations is shewn by the form of the
89^
100
Fig. 8. Peroentage of aloohoL
curve in fig. 8, which gives the relation between percentage
composition (abscissae) and vapour pressure (ordinates)
of a mixture of water and isobutyl alcohol at 89° and 60"*.
While the percentage of alcohol is less than that required
to saturate the water, the vapour pressure of the solution
increases with the percentage of alcohol. When the
solution is saturated, the vapour pressure is independent
of the excess of alcohol present. Such a mixture has
then a constant boiling point, and the composition of
CH. VI]
VAPOUR PRESSURES OF SOLUTIONS.
99
the vapour is always the same. This constant vapour
pressure is found to be smaller than the sum of those of
the two constituents. When the percentage of alcohol is
so large that all the water present can dissolve in it, the
vapour pressure again alters with the composition of the
solution, and fitially sinks to its value for the pure
alcohol. If a mixture represented by any point on either
of the inclined portions of the curve be distilled, the
composition of the vapour and the boiling point will
gradually alter till the liquid present in large excess is
finally lefb nearly pure. But as long as a heterogeneous
mixture is present, the curve is a horizontal straight line,
and the composition of the vapour and the boiling point
remain constant
(iii) The vapour pressures of mixtures of liquids which
are soluble in each other in all proportions give curves which
Fig. 9. Water and propyl alcohol.
gradually change fix)m a form very like those given above
to one quite different. The following curves are taken
from Ostwald's Lehrbmh, and were drawn from Konowaloff*s
7—2
100
SOLUTION AND ELECTROLYSIS.
[CH. VI
numbers. They at once shew how the mixtures will
behave on distillation. The tendency is (since there is no
Fig. 10. Water and ethyl alcohol.
constancy in the composition of the vapour) for that
particular mixture which has the greatest vapour pressure,
and therefore the lowest boiling point, to come off first in
greatest quantity, and therefore by repeatedly redistilling.
Fig. 11. Water and methyl alcohol.
we at last get a distillate which has the composition
corresponding to this lowest boiling point. Thus with
water and propyl alcohol, which mixture has a maximum
CH. Vl]
VAPOUR PRESSURES OF SOLUTIONS.
101
vapour pressure when the percentage of alcohol is about
75, the final distillate obtained will have that com-
position.
The curves for water with ethyl alcohol and with
methyl alcohol shew that in these cases no maxima are
reached, so that by repeated distillation we get a nearly
pure alcohol in the receiver, and pure water is left in the
retort after the first boiling. It is much easier to get
<^<
42®
Fig. 12. Water and formio acid.
water free from alcohol than alcohol free from water,
because the influence of a little alcohol on the boiling
point of water is so much greater than that of a little
water on the boiling point of alcohol. This case is of
great importance in practice, for by such means mixed
liquids of different boiling points are separated in the
chemical laboratory by the process of "fractionation."
We now see that this can only give perfect separation
when the type of the vapour pressure curve is that shewn
in figs. 10 and 11.
A mixture of water and formic acid shews the effect of
considerable interaction between the constituents. The
102 SOLUTION AND ELECTROLYSIS. [CH. VI
vapour pressure of the mixture is lower than that of
either constituent, and reaches a minimum at a percentage
of alcohol of about 73. All other proportions will there-
fore tend to distil over sooner than this, and finally we
shall get a residue left in the retort containing 78 per
cent, of alcohol. This will then distil ovar unchanged.
The last case really includes such liquids as an
aqueous solution of nitric or hydrochloric acid, which were
once thought to shew definite chemical combination in
the proportions of the mixture which finally distilled over
unchanged. Roscoe^ however proved that the composition
of this distillate varied with change of pressure, and the
facts are fully explained by the vapour pressure curves
given above.
^ Quart. Joum, Chem*^ xn. p. 128, or Treatise on Chemistry, Vol. i.
p. 138.
CHAPTER VII.
THE ELECTRICAL PROPERTIES OF SOLUTIONS.
39. Historical Sketch. As soon as the discovery
of Volta's pile in the year 1800 became generally known,
many investigations were made on its eflfects. The pile
consists of a series of little discs of zinc, copper and
blotting-paper moistened with water or brine, placed one
on top of the other in the order zinc, copper, paper, zinc,
&c., finishing with copper. Such an arrangement is really
a primitive primary battery, each little pair of discs
separated by moistened paper acting as a cell, and giving
a certain difference of electric potential, the differences
due to each little cell being added together and producing
a considerable difference of potential or electromotive
force between the zinc and copper terminals of the pile.
Another arrangement was the crown of cups, consisting
of a series of vessels filled with brine or dilute acid, each
of which contained a plate of zinc and a plate of copper.
The zinc of one cell was fastened by a screw to the copper
of the next and so on, the isolated copper and zinc plates
in the first and laist cups forming the terminals of the
battery.
104 SOLUTION AND ELECTROLYSIS. [CH. VII
Using a copy of Volta's original pile, Nicholson and
Carlisle^ found that when two brass wires leading from
its terminals were immersed near each other in water,
there was an evolution of hydrogen gas from one, while
the other became oxidised. If platinum or gold wires
were used, no oxidisation occurred, but oxygen was evolved
as gas. They noticed that the volume of hydrogen
was about double that of oxygen, and since this wa» the
proportion in which these gases are contained in water,
they explained the phenomenon as a decomposition of
water. They also noticed that a similar kind of chemical
action went on in the pile itself, or in the cups when that
arrangement was used. Cruickshank^ soon afterwards
decomposed the chlorides of magnesia, soda and ammonia,
and precipitated silver and copper from their solutions.
He also found that the liquid round the pole connected
with the positive terminal of the pile became alkaline and
the liquid round the other pole acid. In 1806 Sir
Humphry Davy' proved that the formation of the acid
and alkali was due to impurities in the water. He had
previously shewn that decomposition of water could be
effected although the two poles were placed in separate
vessels connected together by vegetable or animal sub-
stances, and established an intimate connection between
the galvanic effects and the chemical changes going on in
the pile. The identity of "galvanism" and electricity,
which had been maintained by Volta, and had formed the
1 Nicholson's Joumaly 1800, 4, p. 179.
2 Ihid,, 4, p. 187.
« Bakerian Lecture for 1806, Phil, Trans.
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. 105
subject of many investigations, was finally established in
1801 by WoUaston, who shewed that the same effects
were produced by both. In 1804 Hisinger and Berzelius^
stated that neutral salt solutions could be decomposed by
electricity, the acid appearing at one pole and the metal at
the other, and drew the conclusion that nascent hydrogen
was not, as had been supposed, the cause of the separation
of metals from their solutions. Many of the metals then
known were thus prepared, and in 1807 Davy decomposed
potash and soda, which had previously been considered to
be elements, by passing the current fi:om a powerful
battery through them when in a moistened condition, and
so isolated the metals potassium and sodium.
The difference between the conduction of electricity
through such bodies as these, and through metals and
other solids, early engaged the attention of observers, and
for some time the presence of water was thought to be
necessary for electrolytic conduction, Faraday* however
shewed that many bodies, including nearly all fusible salts
which were non-conductors when solid, became electrolytes
when fused, and just recently J. J. Thomson'^ and others
have shewn that the passage of electricity through gases
is an electrolytic action accompanied by chemical decom-
position. The conditions necessary for electrolytic con-
duction in solutions will be discussed later.
The remarkable fact that the products of decomposition
appear only at the poles, was perceived by the early
^ Ann. de Chimie, 1804, 51, p. 167.
^ Experimental Researches, Vol. i. 1833.
' Recent Researches in Electricity and Magnetism, 1893.
106
SOLUTION AND ELECTROLYSIS. [CH. VII
experimenters on the subject, who suggested various
explanations. Grotthus^ in 1806 supposed that it was
due to successive decompositions and recompositions in
the substance of the liquid. Thus if we have a compound
AB in solution, the molecule next the positive pole is de-
composed, the B atom being set free. The A atom attacks
a:b
A|B
I
. — 1...
AjB
a:b
A:B
I
Fig. 13.
the next molecule, seizing the B atom and separating it
from its partner which attacks the next molecule and so on.
The last molecule in the chain gives up its B atom to the
A atom separated from the last molecule but one, and
liberates its A atom at the negative pole. Grotthus, and
in fact nearly all the pioneers in the subject, thought that
the decomposition was due to a direct attraction exerted
by the poles on the opposite constituents of the de-
composing compound, which varied as the square or some
other power of the distance. This view was finally
disproved by Faraday" who shewed that the electrical
forces were the same at all positions between the
poles, by placing two platinum strips, kept at a constant
difference apart and connected through a galvanometer,
at different positions in a trough of dilute acid through
^ AnnaUs de Chimie, 1806, 58, p. 64.
* Experimental Researches, 1833.
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. 107
which a current was flowing. He also shewed that
chemical decomposition could be produced without the
presence of any metallic pole. An electric discharge
from a sharp point connected with a Mctional machine,
was directed on to a strip of turmeric paper moistened
with sulphate of soda solution, the other end of the paper
being joined to the other terminal of the machine.
Alkali appeared on the paper opposite to the discharging
point. Another experiment shewed that insoluble hydrate
of magnesia was produced at the junction between a
strong solution of sulphate of magnesia and pure water
when a current was passed across it. Faraday accepted
the idea of Grotthus* chain, but held that there were
chemical forces between atoms of opposite kinds in
neighbouring molecules as well as in the same molecule,
and that when the electric force was added to these they
became strong enough to overcome the attractions between
the atoms in the same molecule, so that a transfer of
partners occurred. We shall see later that transfers of
partners are probably always going on in solutions, whether
a current is passing or not, and that the function of the
electric forces is merely directive, but Faraday's account
of the consequences of this interchange still holds good.
He pointed out how it explained all the facts, including
the passage of acids through alkalis under the influence
of the current, a phenomenon which had created such
surprise when discovered by Davy. Faraday shewed that
the presence of the alkali not only facilitated the passage
' of the acid, but was even necessary, for, without something
with which to combine on its way, the acid would be
108 SOLUTION AND ELECTROLYSIS. [CH. VII
unable to travel. Thus Faraday's view amounts to
supposing a constant stream of acid in one direction and
of alkali in the other.
Faraday introduced a new terminology which is still
used. Instead of the word pole which implied the old
idea of attraction and repulsion, he used the word
electrode, and called the plate by which the current enters
the liquid the anode, and that by which it leaves the
kathode. The parts of the compound which travel in
opposite directions through the solution he called ions —
kations if they went towards the kathode and anions if
they went towards the anode. He also introduced the
words electrolyte, electrolysey &c., which we have already
used.
Faraday clearly pointed out that the diflference between
the effects of a frictional electric machine and of a voltaic
battery lay in the fact that the machine produced a very
great difference of potential, but could only supply a
small quantity of electricity, while the battery gave a
constant supply of an enormously larger quantity, but
only produced a very small difference of potential.
40. Faraday'g Iiawg. Davy had prevpusly shewn
that there was no accumulation of electricity in any part
of a voltaic circuit, so that a uniform flow or current must
be everywhere going on, and Faraday set himself to
examine the relation between the strength of this current
and the amount of chemical decomposition. He first
proved by observations on the decomposition of acidulated
water, that the amount of chemical action in each of
CH. Vll] ELECTRICAL PROPERTIES OF SOLUTIONS. 109
several cells was the same when the cells were joined
together and a current passed through them all in series,
even if the sizes of the platinum plates were different in
each. The volume of hydrogen was unchanged even if
electrodes of different materials — such as zinc or copper
— were used. He then divided the current after it had
passed through one cell into two parts, each of which
passed through another cell before they were reunited.
The sum of the volumes of the gases evolved in these
two cells was equal to the volume evolved in the first cell.
The strength of the acid solution was then varied, so that
it was different in the different cells in one series, but the
chemical action still remained the same in all. Thus the
deduction was made that the amou/nt of decompositUm was
proportional to the quutntity of electricity which had passed.
An apparatus for the decomposition of water can there-
fore be used to measure the total quantity of electricity
which has passed round a circuit. Such instruments are
termed voltameters.
The same law was then shewn to be true for solutions
of various metallic salts, and also for salts in a state of
fusion — the weight of metal deposited being always the
same for the same quantity of electricity. A second law
also was discovered, namely that ike mass of an ion
liberated by a definite quantity of electricity is proportional
to its chemical equivalent weight In the case of elementary
ions this equivalent weight is the atomic weight divided
by the valency, and in the case of compound ions it is the
molecidar weight divided by the valency.
It was then proved that the mass of zinc consumed
4 I
110 SOLUTION AND ELECTROLYSIS. [CH. VII
in each cell of the battery was the same as that deposited
by the same current in an electrolytic cell placed in the
external circuit.
These results may be grouped in one statement which
is known as Faraday's law of electrolysis.
The mass of an ion liberate by a current is proportional
to the whole quantity of electricity which passes amd to the
electro-chemical equivalent of the ion, the electro-chemical
equivalent being proportional to the chemical equivalent
weight
By later investigations it has been found that the
mass of hydrogen liberated by one electro-magnetic unit
of electricity is 1*0352 x 10"* gram. The electro-chemical
equivalent of any other ion can be found by multiplying
this figure by its chemical equivalent weight. By mea-
suring the quantity of electricity which passes in electro-
magnetic units and calling it q, we can therefore write an
expression for the mass liberated
m= 1-0352 xlO-*€g,
where e is the chemical equivalent weight.
Faraday's law has been confirmed in the case of silver
to a great degree of accuracy by Lord Rayleigh and
Mrs Sidgwick^, who gave the value 0*0111795 for its
electro-chemical equivalent, and in the case of copper by
W. N. Shaw". In the latter case small variations occurred
on altering the intensity of the current, but they were
traced to the action of the copper sulphate solution in
1 Phil, Tram,, 1884, (2), p. 411.
^ British Association Report^ 1886, p. 318.
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. Ill
dissolving the newly precipitated copper. Faraday him-
self considered that in certain cases a small current could
leak through electrolytes without chemical decomposition^
but it is very doubtful whether such can be the cafte.
One or two consequences of these laws must now be
traced. Since many elements (iron for example) have
different equivalents in their different series of com-
pounds, their electro-chemical equivalents must also
vary. Thus if a current be sent through two cells in
series, one containing the solution of a ferrous and the
other the solution of a ferric salt, the quantity of iron
liberated in the first cell will be proportional to 56/2
or 28, and the quantity liberated in the second will be
proportional to 56/3 or 18*7, since the atomic weight of
iron is 56.
Since unit quantity of electricity in passing through
an electrolyte always decomposes a mass of the substance
equal to 1'0352 x 10"^e, it follows that a definite quantity
of electricity is always associated vdth the same number
of equivalents. We can in fact represent electrolytic con-
duction as a process of convection, a positive charge being
carried by the kations in one direction, and a negative
charge by the anions in the other, and it follows that the
charge on a univalent ion is always the same whatever
be the nature of the ion, and the charge on a divalent
ion is twice, and that on a trivalent ion three times
that carried by a univalent ion. From the equation on
p. 110 we see that the charge carried by the number
of the two opposite univalent ions contained in one
^ Exp, Researches 1 1834, series 8, §§ 970, 984.
112 SOLUTION AND ELECTROLYSIS. [CH. VII
gram-equivalent of a simple binary compound like NaCl,
is (since m = e)
1
?=!:;
10352 X 10-* 1? '
where 17 is the electro-chemical equivalent of the standard
substance hydrogen.
41. Polarisation. It was soon observed that a
single cell of Volta's crown of cups was not able to de-
compose water, and that a certain considerable difference
of potential had to be kept up in order to drive a per-
manent current through an electrolytic apparatus. This
subject was investigated by Faraday, who referred the
effect to the chemical affinity between the parts of the
water, which needed a force greater than that affinity in
order to separate them. If we use a sufficient electro-
motive force, and send a current between platinum plates
in acidulated water, the plates will be found to be in
a peculiar condition (which is known as polarisation) and
to have acquired the power of driving a current for some
time in the reverse direction, if they are disconnected
from the primary battery and joined to each other
through a galvanometer. If the electromotive force
between the polarised plates be determined, it will be
found to be 1*47 volts, and this may be taken to measure
the affinity of hydrogen and oxygen, so that no primary
battery or other source of electrical energy is able to send
a permanent current through acidulated water unless the
electromotive force that it gives is at least 1*47 volts, and
it is important to observe that the effective electromotive
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. 113
force acting round such a circuit is that of the battery
less 1*47 volts. This reverse electromotive force must
always be taken into account in calculating the strength
of a current, when there is any polarisation in the
circuit. If the applied electromotive force is less than
the critical value, some current will at first pass, but this
gradually becomes less, and finally nearly vanishes as the
electrodes become polarised. A very small current always
appears to leak through, but whether this is due, as
Faraday supposed, to some conduction without decomposi-
tion is extremely doubtful. It must be remembered that
both oxygen and hydrogen are to some extent soluble in
water, so that some of the gases set free are dissolved, and
may so escape into the air and make room for more. In
other cases, in which bodies like chlorine are evolved, the
products of electrolysis may meet by diffusion of one or
both through the solution and recombine; a little more
decomposition would then go on to supply their place, and
so a permanent, though very small, leakage current would
be kept up. The accurate measurement of the reverse
electromotive force of polarisation presents some difficulty.
It rapidly falls off in intensity and the reversal of the
connections must be quickly made in order to get its
maximum value. Raoult* found that a speed of reversal
equal to 100 per second was enough to secure this.
42. Accumulators. Polarisation is the principle
which underlies the action of all secondary cells or accumu-
lators. If an ordinary water voltameter, with the platinum
» Ann. de Chimie et de Phys,, 1864, [4], 2, 326.
W. S. 8
114 SOLUTION AND ELECTROLYSIS. [CH. VII
electrodes resting partly in the solution and partly in the
evolved gases, be connected with a galvanometer, we shall
find that a reverse current is set up, and will continue to
flow as long as any of the evolved gases (which will
gradually disappear) remain. This is Grove's gas battery.
If two lead plates be immersed in dilute sulphuric acid
and a current passed between them, the anode becomes
coated with brown dioxide of lead, and spongy metallic
lead is deposited on the kathode. The reverse electro-
motive force of this arrangement is about 2*0 volts. For
practical purposes the cells are much improved if currents
be passed through them for some time as a preliminary,
first in one direction and then in the other. This treat-
ment increases the effective area of the lead plates, and
so enables them to store a larger amount of chemical
energy. These lead cells, originally due to Plants (1860),
are universally employed in one of their many forms. The
modifications which have been introduced have mainly
been directed to increasing the effective area of the
plates by making them in the form of a lattice-work or
by coating them with red lead.
43. Primary Cells. Just as polarisation is set up
in an electrolytic apparatus placed in the external circuit,
so it is produced in the cells of the battery itself, when
these consist pf a plate of zinc and a plate of platinum or
copper placed in acidulated water. Bubbles of hydrogen
appear at the platinum plate, and the reverse electro-
motive force which they set up soon causes the current to
decrease in strength. Many forms of cell have been de-
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS, 115
vised to obviate this. In some, oxidising agents such as
bichromate of potash are added to the liquid, while in
others the platinum plate is put inside a porous pot, and
surrounded by oxidising agents (such as nitric acid in
Grove's cell), or by a solution of copper sulphate which
causes copper to be deposited on the electrode: in this
case itself of copper (Daniell's cell). By some such
device a fairly constant electromotive force can be ob-
tained. It is worthy of note that if a current be forced
through a DanielFs cell against the electromotive force of
the cell, copper will redissolve to form copper sulphate,
while zinc will be deposited on the zinc electrode from the
zinc sulphate solution. The processes which go on in
DaoieU's cell are therefore perfectly reversible.
It is interesting to examine the conditions necessary
for the solution of zinc. Pure zinc, or ordinary zinc which
has been amalgamated with mercury, will not dissolve in
dilute sulphuric acid, but if a piece of another less oxidis-
able metal like platinum be put into the liquid in contact
with the zinc, solution at once begins, zinc sulphate is
formed and hydrogen is evolved at the surfece of the
platinum. A complete voltaic circuit is thus necessary,
and a quantity of electricity equivalent to the amount of
chemical action, flows round it. If a piece of pure zinc
be placed in a neutral solution of zinc sulphate, no action
occurs even in presence of platinum, but solution at once
begins if a few drops of acid be added. Ostwald^ observed
that if the zinc and platinum were separated by a porous
partition, and connected by a wire outside the solution of
1 PUl, Mag,, 1S91, 32, p. 145.
8—2
116 SOLUTION AND ELECTROLYSIS. [CH. VII
zinc sulphate, no action occurred if acid was added to the
vessel containing the zinc, but that the zinc was at once
attacked if the acid was put into the vessel containing
the platinum. In the first case, supposing the zinc re-
places the hydrogen in the acid, the hydrogen must
again form sulphuric acid in contact with the zinc sulphate
round the platinum plate, and zinc must be there de-
posited. There is thus no resultant chemical action, and
no supply of energy to keep up the current. In the
second case, however, hydrogen is evolved at the plati-
num, being replaced in the sulphuric acid by zinc from
the zinc sulphate. This action gives a supply of energy,
and can therefore go on spontaneously.
44. Contact Difference of Potential. The source
of the energy of a voltaic cell is unquestionably the
chemical action which goes on, but much discussion has
taken place about the exact seat of the difference in
potential. Volta thought that it was produced at the
contact between the pair of metals, and arranged his pile
in the order zinc, copper, paper, zinc... on this supposition.
If a piece of zinc connected with one pole of an electro-
meter be put in contact with a piece of copper connected
with the other, a difference of potential is certainly
observed, and this may amount to about 0*8 volt. It
must be remembered, however, that the apparatus is in
contact with air, which may exert an oxidising action, and
experiments conducted in absence of air, or in artificial
atmospheres of other gases, have led to no definite results,
probably owing to the difficulty of getting rid of the last
traces of air. An indirect method of measurement, used
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. 117
by Jahn^ avoids this difficulty. Peltier found that when
a current of electricity was passed across the junction
between two metals, a reversible evolution or absorption of
heat occurred. By the principles of thermodynamics it
follows that an electromotive force must reside there, and
by measuring the strength of the current and the total
thermal evolution its value can be calculated. Jahn*s results
shewed that it was always small, and rarely amounted
to more than a few thousandths of a volt. This appears
to disprove the existence of any difference of potential
of the order of 0*8 volt, and, though some doubt has
been thrown on the validity of the reasoning, it is im-
probable that the great electromotive force observed by
the other method could be so nearly balanced as to
disappear in the Peltier effect.
Faraday's work led many people to believe that the
true seat of the difference in potential, like the source
of the energy of the current, was to be found at the
junction between inetal and liquid, and this appears to be
the more probable view. This again is a difficult thing
to observe, for, in order to get the potential of the liquid
by any of the ordinary methods, we must introduce a wire
leading to an electrometer, which gives a new surface
of contact, and therefore another difference of potential.
The only way in which this difficulty has been surmounted
is due to Lippmann*. It is found that when the surface
of separation between mercury and dilute sulphuric acid
is increased, a current is produced, and conversely if an
^ WiedemanrCs Annalerif 188S, 34, p. 755.
2 Pogg. Ann,, 1873, 149, p. 561 ; Arm, de Ghim,, 1875, [5], 5, p. 494.
118
SOLUTION AND ELECTROLYSIS. [CH. VII
^
external electromotive force be applied by passing a
current across it, that the area of the surface tends to
alter, owing to a change in the eflFective surface tension
caused by the polarisation at the junction. These
phenomena have been utilised by Lippmann in the
construction of electrometers. Several forms are used^ —
in one a vertical glass tube is drawn
oflF to a very fine capillary the end
of which is bent upwards. This
apparatus is filled with mercury, and
the lower part immersed in a vessel
of dilute sulphuric acid whose bottom
is covered with a layer of mercury.
The capillary forces tend to depress
the mercury surface in the little tube,
and are balanced by the pressure of
the long column. When the mercury
in the vertical tube, and the mercury
in the bottom of the vessel of acid,
are kept at diflFerent potentials, the
surface tension at the junction be-
tween mercury and acid in the
capillary tube changes, and the level
of the junction is altered. A microscope is arranged to ob-
serve this, and for small differences, the change in the level
is found to be proportional to the difference of potential.
These phenomena have been explained by von Helm-
holtz*. The difference of potential between a metal and
Fig. 14.
^ See Ostwald's Physico-Chemical Mecisurements,
« Wied, Ann., 1882, 16, p. 35.
I
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. 119
an electrolyte must cause an electrification over the
boundary between them, positive electricity accumulating
on the mercury surface, and negative electricity on the
acid. Each side of this " double layer of electricity " will
try to increase its area owing to the repulsion between
the different portions of the similar charge, so that the
effect of the double layer will be opposite to that of the
surface tension, which tends to diminish the area. If
then we have mercury in contact with dilute sulphuric
acid, and increase the difference of potential between
them by external means, the surface tension will be still
further reduced. If, however, we reverse our external
electromotive force, so that we make the mercury less
and the acid more positive, the effect of the natural
double layer will be reduced, and the surface tension will
increase. This will go on until the external potential
difference is equal and opposite to that of the natural
double layer, when the surface tension will be a maxi-
mum. Beyond this another double layer will be formed
of opposite sign — the mercury becoming negative and the
acid positive — and a reduction in surface tension will
again take place. Thus by measuring the external
difference of potential required to give the surface tension
its maximum value, the difference of potential due to the
natural double layer formed on contact was found by
Lippmann to be about 0*9 volt.
This has been confirmed in two ways. If the surface
of contact be increased by mechanical means, the double
layer will be stretched, the potential difference will be
reduced and a current will flow, in order to again increase
120 SOLUTION AND ELECTROLYSIS. [OH. YII
it to its normal value. But if the potential difference
be destroyed by an external electromotive force, this will
cease to hold, and no current will be observed on increasing
the surface. Pellat^ found that the current ceased to be
produced when an external electromotive force of about
I'O volt was applied.
When mercury is dropped from a fine orifice in a glass
vessel the lower part of which is placed in an electrol3rte,
it must in the end assume very nearly the potential of the
liquid ; for as each drop falls, it will form a double layer
round it, and in order to do this, it must take positive
electricity from the stock of mercury, and so reduce its
potential nearly to that of the liquid. It will never quite
reach that value, because it is all the time trying to set
up the usual difference of potential by contact, but by
making the formation of the drops rapid, the discharge of
electricity from the stock of mercury can be made nearly
perfect. In this way Ostwald* obtained a difference of
potential between the drops and the mercury at rest of
about 081 volt.
The maximum value of the surface tension, produced
by applying an external electromotive force sufficient to
destroy the double layer, is the real surface tension free
from all electrical disturbances, and this was found by
Ostwald to be independent of the nature of the electro-
lyte, while the natural value as usually measured varies
greatly.
When we know the true difference of potential
1 Comp, Rend., 18S7, 104, p. 1099.
2 ZeiU,f. physikal, Chemie, 1887, 1, p. 683.
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. 121
between mercury and any given electrolyte, we can find
the value for a surface between that electrolyte iand any
other metal, by measuring the electromotive force of the
combination mercury-electrolyte-metal. Assuming that
the effect at the junction of the metals is small, this
gives the sum of the effects at the junctions mercury-
electroljiie and electrolyte-metal, and from this the latter
can be found by subtraction. The following table gives
the potentials of different metals in normal solutions, the
potential of the electrolyte being put equal to zero.
HOI
HBr
HT
HjSO^
Zn
-0-54
-0-46
-0-30
-0-62
Cd
-0-24
-0-18
-008
-0-22
Sn
+ 0-02
+ 0-12
-f.0-28
-0-02
Pb
-f 003
+ 0-10
+ 0-26
-0-04
Cu
+ 0-35
+ 0-35
-f.0-36
+ 0-46
Bi
+ 0-41
-f.0-47
+ 0-60
+ 0-46
Sb
+ 0-51
+ 0-60
-f.0-54
+ 0-48
Ag
+ 0-57
-f.0-51
-f.0-45
-f.0-73
Hg
+ 0-57
+ 0-50
-f.0-44
+ 0-86
Thus the initial electromotive force of a zinc-copper couple,
108 volt, is produced by a difference of potential of 062
between the zinc and acid and of 0*46 between the acid
and copper.
The cause of these differences of potential has been
explained by W. Nemst on the supposition that each metal
in contact with a given electrol)rte possesses a certain
*' solution pressure," analogous to the vapour pressure of
122 SOLUTION AND ELECTROLYSIS. [CH. VII
a liquid, by reason of which ions are detached from it,
and go into solution carrying their charges with them and
leaving the metal oppositely electrified. The development
of this idea will be described when we are considering the
Dissociation Theory in Chapter XI.
It is worthy of note that cells with diflferent positive
terminals (copper, platinum, &c.) give different electromo-
tive forces, although the chemical actions are the same,
consisting in each case of the solution of zinc and the
evolution of hydrogen. The differences arise from the
fact that, in order to set free the hydrogen, different
electromotive forces have to be overcome at the electrode,
so that different fractions of the whole energy are used to
keep up the electromotive force.
45. Source of the Energy of the Current^ and
Theory of the Voltaic Cell. As we have already
remarked, the supply of energy necessary to drive the
current is drawn from the chemical energy liberated by
the actions which go on in the cell.
When a quantity of electricity q passes round the-
circuit, the total amount of energy liberated by the
chemical action which goes on can be calculated from the
heats of formation of the various chemical compounds
produced, which have in most cases been experimentally
determined by Thomsen and others. If fi* be the heat
(measured in mechanical units) which would be liberated
if all the energy produced when one unit of electricity
passes, assumed the thermal form, then the total energy is
qH, and if all this energy were used iu forcing the current
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. 123
round the circuit, we should have the equation which Lord
Kelvin* deduced from Joule's principle .
qH = qE or H^E,
where E is the electromotive force. In nearly all cases
however the electromotive force of a cell changes with
temperature, and if this is the case it is easy to shew from
the principles of thermodynamics that a reversible heat
evolution or absorption will occur on the passage of a
current. In order to prevent this from producing changes
in temperature, heat must be supplied or abstracted, and
one side of our equation must be increased or diminished
by the mechanical equivalent of this heat.
The relation is at once deducible if we imagine a cell,
in which the chemical processes are all reversible, put
through a thermodynamical cycle of changes. Let us
begin by supposing that we place our cell in an enclosure
whose temperature is T and that we let pass a quantity of
electricity q through the cell in the direction of the
electromotive force. The cell will do a quantity of work
Eq. Suppose that in order to keep its temperature constant
we supply hq units of heat. Then let us put the cell into
a second enclosure which is at a temperature T— BT, very
slightly lower than the first. If the electromotive force is
unchanged, the work done on the cell in forcing q units
of electricity through it against the electric forces, will
be Eq, so that the whole gain of work throughout the
cycle is nil, and no heat is required to keep the temperature
constant. If, however, E changes with the temperature
^ Philosophical Magazine, 1851, [4], 2, p. 429.
124 SOLUTION AND ELECTROLYSIS. [CH. VII
SO that dEjdT represents its rate of change, we shall have
for the electromotive force of the cell at a temperature
T-ZT
so that the work done will now be
dE
{^-p^y
We now have the cell in exactly the same state as at first,
for forcing the q units backwards through it has reversed
all the chemical changes. We can therefore apply the
principles of thermodynamics, and are able to use the
ordinary relatioD that the effective gain of work during
the cycle is to the amount of heat absorbed in the hot
enclosure as the difference in temperature is to the
absolute temperature. Now the gain of work is evidently
and so we get
dT '^ BT
hq T'
dE
.\h^T
dT'
which gives the mechanical equivalent of the heat
necessary to keep the temperature constant when one
unit passes. Since T is always a positive quantity, it
follows that the sign of h is the same as that of dEjdT y
and so, if the electromotive force increases as the
CH. VIl] ELECTRICAL PROPERTIES OF SOLUTIONS. 125
temperature rises, the sign of h is positive and heat must
be supplied to the cell. If the electromotive force de-
creases as the temperature rises, heat must be taken
from the cell.
Thus the chemical energy of the materials has other
work to do than was at first supposed, and we must put
dT
or E=H-T^ (24),
an equation for the electromotive force of a cell first
given by von Helmholtz^, and experimentally confirmed
by Czapski^ and Jahn^
Let us calculate by this method the electromotive
force of a Daniell's cell. When unit quantity of electricity
passes, the chemical changes are these: — 32*5x10352
X 10~* grams (the electro-chemical equivalent) of zinc
dissolve in dilute acid, the hydrogen evolved from this
(1-0352 X 10-* gram) displaces 316 x 10352 x lO""* grams
of copper from copper sulphate, and this same amount
of copper is liberated. The heats of formation are given
in any book on chemistry — we shall take them from
Ostwald's Lehrbach, When zinc sulphate is formed from
its elements, the amount represented in grams by the
formula ZnS04 evolves 230000 calories of heat, and its
solution in water 18500 cals. In the same way the heat
^ BerU Ber.t 1S82, pp. 22, 825, and Wissenschaftliche Abhandlungen,
2, p. 962.
2 Wied, Ann., 1884, 21, p. 209.
s Wied. Ann., 1886, 28, pp. 21, 491 and 1888, 34, p. 755.
126 SOLUTION AND ELECTROLYSIS. [CH. VII
of fonnation of sulphuric acid, H8SO4, is 193100 cais. and
its heat of solution 17800 cals. The net result of. the
action Zn + H2SO4 = ZnS04 + Hg is therefore the evolution
of 37600 cals. of heat Finally we have the action
Ha + CUSO4 = H3SO4 + Cu. Now the heat of formation
of CUSO4 is 182600 cals. and its heat of solution 15800.
The net result of the change is got by subtracting from
the sum of these the sum of the corresponding numbers
for sulphuric acid : it comes out — 12500 cals. . Since the
CUSO4 is not formed but decomposed^ we must subtract
this from the 37600 cals. to get the total change
throughout the cell, which equals 50100 cals. This is
the heat change corresponding to the solution of 65 grams
of zinc, so that when one electro-chemical equivalent is
dissolved the thermal evolution is
50100 X 32-5 X 10352 x 10-* „ ^^« ,
w;i = 2-592 cals.
00
The temperature coefficient of a Danieirs cell is very
small, so that dEjdT can be neglected, and equation (24)
becomes
JS^=2-592 J
= 2-592 x 4-2 X 10'
= 1*09 X 10® electro-magnetic units
= 1-09 volts,
a number agreeing extremely well with observation.
CHAPTER VIII.
ELECTRICAL PROPERTIES (continued),
46. The Nature of the Ions. The work of
Berzelius, beginning in 1804, on the electrolytic de-
composition of neutral salts, led him to frame a theory
which regarded all chemical action as brought about by
the electric forces between oppositely charged atoms.
When two atoms united, he supposed that the charges
wei:e not exactly neutralised, and the group of atoms was
left with a balance of positive or negative electricity, and
so could still combine with other atoms or groups of
atoms. He regarded each chemical compound as formed
by the union of an electro-positive group with an electro-
negative group, and held that the action of the electric
current in producing acid round the anode, and alkali
round the kathode of a neutral salt solution, was to be
explained simply as a direct separation of the salt into
acid and base. When the attention of chemists began
to be directed more to organic chemistry, the dualistic
ideas of Berzelius had to be abandoned, and even from
the physical side objections were soon raised. Thus
128 SOLUTION AND ELECTROLYSIS. [CH. VIII
Daniell^ shewed that in the electrolysis of a solution of
sodium sulphate an equivalent of hydrogen was produced
as well as an equivalent of acid and base. This is at once
reconciled with Faraday's law if we suppose that the parts
of the salt, from an electrolytic point of view, are Na
and SO4, and that the hydrogen results from a secondary
action of the sodium on the water of the solution.
In some cases, the phenomena of electrolysis give
valuable information about the nature of the body in
solution. We are able, for instance, to distinguish be-
tween double salts and salts of compound acids. Thus
Hittorf shewed that when a current was passed through
a solution of potassium platinichloride, the platinum
appeared at the anode. The salt must therefore be
derived from a compound acid, and have the formula
NaaPtCl«, the ions being sodium and PtCle, for if it were
a double salt it would decompose as a mixture of sodium
chloride and platinum chloride, and both metals would go
to the kathode.
47. Secondary Acttons. Owing to these secon-
dary actions it is often difficult to determine what are the
real ions in any given case of electrolysis, for the parts
into which the electrolyte is primarily resolved, and which
travel through the solution, when they reach the electrode
and are set free, may attack the substance of the
electrode, or some constituent of the solution, and form
secondary products. Thus the final products of the
decomposition are often quite different from the ions,
1 Phil. Trans, 1839, 1, p. 97 and 1840, 1, p. 209.
CH. VIIl] NATURE OF THE IONS. 129
and chemical analysis of the solution round the electrodes
then gives only indirect evidence as to their nature. In
the case of a solution of potash, for example, the ions are
K and OH. When the kation K reaches the electrode,
instead of being set free in the metallic state, it attacks
the water, liberating hydrogen and again forming potash,
and the anion OH produces water and oxygen at the
anode. Thus the final products are the same as though
water had been directly decomposed.
This leads us to examine more closely the part played
by water in electrolysis. It was at first thought to be
the only active body, and to be necessary in every case
of electrolytic decomposition. The dilute acid or alkali
which was always added when water was to be decom-
posed, was supposed merely to allow the passage of
* the current by reason of its conductivity, and it was
imagined that the current then directly decomposed
the water. Now pure water is known to be a very
bad conductor, though when great care is taken to
remove all dissolved bodies, there is evidence to shew
that some part of the small trace of conductivity
remaining is really due to the water itself. Thus F.
Kohlrausch^ has prepared water whose conductivity in
C.G.s. units was 1*8 x 10"" at 18° C. Even here some
little impurity was present, and Kohlrausch estimates
that the conductivity of chemically pure water would be
0-36x10-" at 18° C. As we shall see later, the con-
ductivity of very dilute salt solutions is proportional to
the concentration, so that it is probable that in most
1 See § 78.
w. s. 9
130 SOLUTION AND ELECTROLYSIS. [CH. VIH
cases practically all the current-carrying is done by the
salt. It seems probable then that what is called the
decomposition of water is really a secondary effect due to
the presence of the acid. Thus, if sulphuric ^id is used,
the primary ions are probably hydrogen and sulphion, SO4.
This latter, instead of being set free, decomposes the water,
again forming sulphuric acid and liberating oxygen.
This reasoning is confirmed by the fact that if the acid
is strong, sulphur dioxide is evolved — if the water were
the active agent it would still furnish the final product,
even when present in very small quantities. The same
kind of thing occurs with hydrochloric acid dissolved in
water. While the solution is strong, hydrogen and
chlorine are evolved, but as it becomes dilute the
chlorine is gradually all taken up by the water, oxygen
being liberated. The part played by the water will be
again considered in Chapter XI.
The electrolysis of mixed solutions is probably another
case of secondary action. When two salts are dissolved
together in water, and a current passed through the
liquid, it is generally found that, unless the current is
very strong, the less oxidisable metal is alone deposited
at the kathode. But if we imagine the ions to convey
the current by a process of convection, we must suppose
that the ions of both salts are travelling through the
liquid, since the electric forces act on both alike. This
was experimentally confirmed by Hittorf^ by measure-
ments of the conductivity of a mixed solution. When
the more oxidisable metal reaches the kathode, however,
^ Poggendorf*s Annalen^ 1868, ciii. p. 48.
CH. VIIl] NATURE OF THE IONS. 131
it acts on the solution and replaces the less oxidisable
metal, just as a strip of zinc placed in copper sulphate
solution precipitates the copper. When the current is
increased, and the chemical action is rapid, there is no
time for this process to take place, and both metals
appear on the electrode. The readiness with which an
ion acts on the solution, when it is liberated at the
electrode by the electric forces, has been taken advantage
of by Becquerel and others in order to prepare many new
and interesting chemical compounds.
48. Practical Applications of Electrolysis. In
this book any detailed account of the practical applications
of electrolysis would be entirely out of place, but it is
interesting to remark that just as the strength of current
used may influence the secondary actions which go on, so
it may also influence the physical state in which a metal
is deposited. This explains why in the processes of
electroplating, &c. it is necessary to carefully adjust the
current density (that is the strength of the current per
unit area of the electrode) in order to prevent the deposit
from being crystalline, or from being deposited so fast
that it only loosely adheres to the plate.
The fact that the less oxidisable metal is usually first
deposited from solution has often been used to effect the
separation of metals, and the process has lately been
developed on the large scale for the deposition of pure
copper from an impure solution of its salts.
49. Complex Ions. In a normal case of electro-
lysis, such as that of an aqueous solution of potassium
9—2
132 SOLUTION AND ELECTROLYSIS. [CH. VIII
chloride, it is probable that the primary ions are the
simple bodies K and CI, but in a few cases, such as that
of cadmium iodide dissolved in alcohol, very great
changes of strength occur in the solution near the
electrodes (see p. 135), and it seems necessary to suppose
that some unaltered salt is attached to the anion. The
ions will then be Cd and Ia(Cdl2), the latter being
complex. It has even been suggested that molecules of
the solvent may also be attached to ions, and be dragged
along by them under the influence of the electric forces \
50. The Migration of the Ions. Having obtained
some idea of the nature of the ions, we must now enquire
whether it is possible to obtain any information about the
velocity with which they travel through the solution.
If we pass a current from copper plates through a
solution of copper sulphate, we shall notice that the
colour of the liquid in the neighbourhood of the anode
becomes deeper, and in the neighbourhood of the kathode
lighter in shade. This is well seen if the electrodes are
arranged horizontally with the anode underneath. When
the electrodes are of copper, the quantity of metal in solu-
tion remains constant, since it is dissolved from the anode
as fast as it is deposited at the kathode, but if we use
platinum electrodes, the quantity in solution becomes con-
tinually less, and in this case more salt is taken from the
neighbourhood of the kathode than from near the anode,
and the colour of the solution, therefore, becomes pale more
rapidly near the kathode than near the anode.
^ See W. N. Shaw on Electrolysis, B, A, Report 1S90, p. 201.
CH. VIIl]
MIGRATION OF THE IONS.
133
Two explanations of this seem possible.* The first
is to suppose that (as in the case of cadmium iodide in
alcohol) the ions are really complex, unaltered salt being
attached to the anion or solvent to the kation, so that salt
is drawn to the anode or solvent to the kathode. The
second explanation (due to Hittorf*), is that the velocity
of the ions is different — the anion, in the case of copper
sulphate, travelling faster than the kation.
Let us develope the consequences of Hittorf s hypo*
8S888S888888
ooooo oooooooo
88880808000000
Fig. 16.
thesis by the method given by Ostwald. In fig. 15 the
black dots represent the one ion, and the white circles the
other. Let the black ions move to the left twice as fast
as the white ions move to the right. While the black
ions move over two of our spaces, the white ones move
over one. Two of these steps are represented in the
diagram. At the end of the process it will be found that
six molecules have been decomposed, six black ions being
liberated at the left and six white ions at the right.
Looking at the combined molecules, however, we see that
while five remain on the left side of the middle line, only
three are still present on the right. Thus the left-hand
1 Pogg. Ann,, 1863—9, 89, p. 177, 98, p. 1, 108, p. 1, 106, pp. 887, 618.
134 SOLUTION AND ELECTROLYSIS. [CH. VIII
side, towards which the faster ions moved, has lost two
combined molecules, while the right-hand side, towards
which the slower ions travelled, has lost four — just twice
as many. Thus we see that the ratio of the masses, of salt
lost by the two sides is the same as the ratio of the veloci-
ties of the ions leaving them. Therefore, by analysing the
contents of a solution after a current has passed, we can
calculate the ratio of the velocities of its two ions. A long
series of measurements of this kind has been made by
Hittorf ^ Loeb and Nemst^ and others, who used various
forms of apparatus arranged so as to enable the anode and
kathode solutions to be separately examined after the
passage of the current. Hittorf called the phenomenon
the " migration of the ions," and expressed his results in
terms of a migration constant which gives the amount of
salt taken from the neighbourhood of one electrode as a
fraction of the whole amount decomposed. It also ex-
presses the ratio of the velocity of one ion to the sum of
the opposite ionic velocities. All known results on the
subject have been collected by T. C. Fitzpatrick in his
tables of ''The Electro-Chemical Properties of Aqueous
Solutions," published in the British Association Report
for 1893, and reprinted by permission in the appendix
to this book. From these tables the following numbers
are selected. They represent the migration constant for
the anions. Thus CuSOi '638 means that the velocity of
the SO4 ion is to the sum of the two velocities as "638 : 1,
and is therefore to the velocity of the Cu ion as 'QS8 : '362.
1 Pogg. Ann., 1853—9. Vol. 89, p. 177, 98, p. 1, 103, p. 1, 106, pp.
337, 513.
s Zeits.f, phyHkaL Chemie, 1888, 2, p. 948.
CH. VIIl]
VELOCITIES OF THE IONS.
Migration Constants,
135
Substance
Conoentration of
solution in gram
equivalents per litre
Migration constant
for anion
Hydrochloric Acid
•0128
•33
•210
•161
2^64
•193
7-34
•319
Potassium Chloride
•03
•503
2-55
•516
Sodium Chloride
•162
•628
Sodium Nitrate
•125
•615
35
•600
Sulphuric Acid
iH,SO,
•126
3-48
10-8
•206
•174
•288
Sodium Sulphate
•276
118
•634
•641
Copper Sulphate
•0846
•692
•638
•675
1-962
•724
Cadmium Iodide in
1 part in M07.
2^102
Alcohol
„ „ 3723
1318
The migration constant for cadmium iodide dissolved in
alcohol shews that some unaltered salt must be conveyed
through the solution, and has led to the supposition of
the existence of complex ions.
51. The Velocities of the Ions. Thus from
Hittorf 's migration constants we can find the ratio of the
velocities of the two ions in any given case, but in order
to find'the absolute value of these velocities we must get
some other relation between them. F. Kohlrausch
pointed out^ that such a relation could be deduced from a
knowledge oFthe conductivity of the solution.
1 Wied. Ann., 1879, 6, pp. 1, 145, 1885, 26, p. 161 and 1898, 50, p. 385.
136 SOLUTION AND ELECTROLYSIS. [CH. VIII
Let u and v be the ionic velocities of the kation and
anion respectively,* so that u + v \b their relative velocity,
that is the velocity with which they are dragged past each
other by a certain electric force. This force will be
measured by the rate at which the electric potential falls
off per unit of length as we go from one electrode to the
other — by what we may call the potential gradient, dVjdx.
If there are N gram-equivalents of electrolyte in one
cubic centimetre, when the ions travel past each other
with a speed u + Vy they cause a total quantity of
electricity of N{u + v)/i) (see p. 112) to flow in one second
across unit area normal to the direction of motion. But
this is equal to the current per unit area, and since Ohm's
law holds good for electrolytes (see p. 143) we can also put
the current equal to k.dV/dx where k denotes the con-
ductivity, i.e. the reciprocal of the specific resistance.
.N ,dV
^ ^1/ dx
vk dV .^..
^^ ^+^=lv^-dS (^^>-
f), the electrochemical equivalent of hydrogen, is 1*0352
X 10"^ ; for a potential gradient of one volt per centimetre
(which is the unit most often used) we must put
^- = 10® cas. umts,
cLx
k
so that for this gradient w + v = 1*0352 x 10* -^^ .
If n is the number of gram-equivalents per litre,
n = 1000iVand
u + V = 10352 X 10' - (26).
In order to find k/n, which he called the molecular
CH. VIIl]
VELOCITIES OF THE IONS.
137
conductivity, Kohlrausch made a long series of deter-
minations of the specific electrical resistances of salt
solutions. These will be fully described later (p. 145).
At present we need only notice that, as the dilution
increased, the values of kjn rose, approached a limiting
value, and finally at very great dilution became constant.
For very weak solutions, then, the value of i^ + t; is a
constant. Now if we know w 4- v, and also the ratio ujvy
we can get absolute values for both velocities, and at
great dilution these will be constants, independent of
the concentration. Kohlrausch found, if he calculated
the values of this limiting velocity for any one ion from
observations on the solutions of two or more substances
containing it, that they came out the same. Thus the
velocity of the chlorine ion was, at great dilutions, the
same in solutions of the chlorides of potassium, sodium
and lithium. This is shewn by the following table.
Ionic Velocities in 10""* cms. per sec. at 18* C. calctdated
for a potential gradient of 1 volt per cm.^
KOI
NaCl
Li 01
n
M + t;
u
660
V
690
u+v
u
V
u-\-v
u
360
V
690
1350
1140
450
690
1050
0-0001
1335
654
681
1129
448
681
1037
356
681
0-001
1313
643
670
1110
440
670
1013
343
670
0-01
1263
619
644
1059
415
644
962
318
644
0-03
1218
597
621
1013
390
623
917
298
619
0-1
1153
564
589
952
360
592
853
259
594
0-3
1088
531
557
876
324
552
774
217
557
1-0
1011
491
520
765
278
487
651
169
482
3
911
442
469
i 582
206
376
463
115
348
5-0
438
153
285
334
80
254
10-0
1
117
25
92
1 Wied, Ann, 1893, 50, p. 385.
138
SOLUTION AND ELECTROLYSIS. [CH. VIII
This fact enabled Kohlrausch to assign specific ionic velo-
cities to many ions — velocities which depended only on the
ion and the solvent through which it was travelling, and
were independent of the nature of the other ion present.
A list of Kohlrausch's latest values for these is given below.
It shews the velocities with which the ions move through
an infinitely dilute aqueous solution at 18° C, under a
potential gradient of one volt per centimetre.
cms.
cms.
Na
Li
•?•
Ag
66 X 10"* per sec.
45 „
36 „
66 „
320. „
57 „
CI
I
OH
C.H3O.
ChH.O.
69x10"* per sec.
69
64
182
36 „ „
33
It is interesting to calculate the magnitude of the
forces required to drive the ions with a certain velocity.
If we have a potential gradient of one volt per centimetre,
the electric force is lO® in C.G.S. units. The charge
of electricity on one gram-equivalent of any ion is
l/'000103o = 9653 units, hence the mechanical force
acting on this mass is 9653 x 10® dynes. This, let us say,
produces a velocity u, then the force required to produce
unit velocity is
„ 9-653 X 10^^ , 9-84 x 10» , ., . , ,
Fj^ = dynes = -^ kilograms-weight.
u
u
If the ion have an equivalent weight A, the force
producing unit velocity when acting on one gram is
10*
Pi = 9*84 X -J- kilograms-weight.
CH. VIIl]
VELOCITIES OF THE IONS.
139
Thus, in order to drive one gram of potassium ions with
a velocity of one centimetre per second through a very
dilute solution, we must exert a force equal to the weight
of 38 million kilograms.
Kilograms Weight
Kilograms Weight
Pa
Pi
Pa
Pi
K
15 X 10«
38 X 10'
CI
14 X 10«
40 X 10*
Na
22 „
95 „
I
14 n
11 »
Li
27 „
390 „
NO,
15 „
25 „
NH,
15 „
83 „
orf
5-4 „
32 „
H
3-1 „
310 „
C.H.O,
27 „
46 „
Ag
17 „
16 „
oXo,
30 „
41 »
Since the ions move with uniform velocity, the frictional
forces brought into play must be equal and opposite to
the driving forces acting, and therefore these numbers
also represent the ionic friction coefficients in very dilute
solution at 18° C.
From a table of ionic velocities, we can, by the help
of equation (26), calculate the molecular conductivity of
any given solution, and the agreement with observation
of numbers so deduced gave the first confirmation of
Kohlrausch's theory. Instead of using the ionic velocities
deduced from the limiting values of the molecular
conductivities, we can calculate them for solutions of finite
strength, and as long as the solutions are fairly dilute, the
numbers so obtained for any one ion, though less than
the limiting values, will still be sensibly the same for all
solutions containing that ion. We can then calculate the
conductivity of any given solution of the same concen-
140 SOLUTION AND ELECTBOLYSIS. [CH. VIII
tration and compare the result with observation. Thus
Kohlrausch gives a table of velocities of ions in solutions
containing one tenth gram-equivalent of electrolyte per
litre, and then calculates the conductivity of different
solutions of that strength containing those ions. The
numbers all agree with observation for well conducting
solutions like those of mineral salts and acids, but in the
case of substances whose molecular conductivity varies
greatly between a strength of one tenth gram-equivalent
per litre and infinite dilution, the effect of concentration
is so great that no agreement is obtained; thus acetic
acid should give a value of 3168 x 10"^', while the
observed number is 46 x 10~" for this strength, and only
rises to 1386 x 10~" for a strength of one hundred
thousandth of a gram-equivalent per litre.
If we examine Kohlrausch's theory in order to find
some explanation of this discrepancy, it appears that it
could be due to one of two causes. Either the velocities
of the ions must be much less in these solutions than in
others, or else only a fractional part of the number of
molecules present can be actively concerned in conveying
the current. We shall return to this point later.
The first direct experimental determination of the
speed of an ion was made by Oliver Lodge*. A horizontal
glass tube was filled with agar-agar jelly, in which sodium
chloride was dissolved, with just enough caustic soda
added to make it alkaline and bring out the red colour
of a little phenol-phthallein. The ends of the tube were
immersed in two vessels containing dilute sulphuric acid,
^ B.A. Report J 1886, p. 393.
CH. VIIl]
VELOCITIES OF THE IONS.
141
A current of electricity was then passed from one vessel
to the other through the tube. The hydrogen ions of the
sulphuric acid travel with the current, and when they
enter the tube, displace the sodium ions, which are also
moving in the same direction, and form hydrochloric acid.
This decolourises the phenol-phthallein, and thus the
motion of the hydrogen along the tube can be traced.
Lodge found, as the results of three experiments, that the
velocity of the hydrogen ion came out 0*0029, 0*0026 and
0*0024 cms. per second, under a potential gradient of one
volt per centimetre. If these numbers are compared
with Kohlrausch's calculated values 0*0032 for infinite
dilution, or 0*0028 for a decinormal solution, it will at
once be seen how striking the agreement is.
The present writer* has determined the velocity of a few
other ions by another method. Suppose
we have two solutions like copper chloride
and ammonium chloride, containing one ion
in common, and having nearly equal con-
ductivities. Let one solution be coloured,
and have a density diflFerentfrom that of the
other. The denser solution is first poured
into the longer arm of a kind of U tube
(see fig. 16), and then the other is allowed
to flow gently on to its surface from the
shorter arm. If a current is passed across
the junction between the two solutions, it
carries the copper and ammonium ions
with it, and drives the chlorine ions in
1 Phil Trans,, 1893, A. p. 337.
Fig. 16.
142 SOLUTION AND ELECTROLYSIS. [CH. VHI
the opposite direction. Since the colour depends on the
presence of the copper ions, the boundary will travel with
the current, and, by measuring its velocity, the speed of the
ions under unit potential gradient can be calculated. The
specific ionic velocities of copper and of the anion of
potassium bichromate (the group CrjOy), determined in
this way, were found to agree with the values deduced
from Kohlrausch's theory. Measurements were also made
with alcoholic solutions, the conductivities of which are
much less than those of aqueous solutions of corresponding
strength, and again a satisfactory agreement with theory
was observed. The velocity of the hydrogen ion through
sodium acetate has also been determined by a modification
of Lodge's method^ In this case the hydrogen ion forms
acetic acid as it travels, and it was found that, when
travelling through a solution of sodium acetate in agar
jelly of strength 0*07 gram-equivalent per litre, its ionic
velocity was about 0000065 cms. per second. This
great reduction in the speed of hydrogen shews that
the ionic velocities are reduced in these abnomuil cases in
about the same ratio as the condvctivity. Our equation on
p. 136 will therefore always give the conductivity of any
solution, if we know the proper values to assign to the
velocities of the ions.
1 Phil. Mag, 1894, 2, p. 392.
CHAPTER IX.
ELECTRICAL PROPERTIES (continued),
52. Resistance of Ellectrolytes. The investi-
gation of the laws which govern the passage of currents
through electrolytes, and of the relation between current
and electromotive force, offers some difi&culties owing to
the phenomena of polarisation. In the case of metallic
conductors, it is found that the current produced is
proportional to the electromotive force applied, and is
given by i = EjR where i2 is a constant for any given
conductor under fixed conditions, called its resistance.
This is Ohm's law, which is proved by shewing that the
measured resistance of a conductor is independent of the
strength of the current passing through it. Now we have
seen that no permanent current will flow through an
electrolytic cell unless the electromotive force applied
exceeds a certain critical value, so that it appears at first
sight that Ohm's law cannot hold. But, in order to
apply the law, we must consider the effective electromotive
force acting round the circuit, which is equal to the
difiFerence between the external applied electromotive
^
144 SOLUTION AND ELECTROLYSIS. [CH. IX
force and the reverse electromotive force due to the
polarisation of the electrodes. When this is done, Ohm's
law is found to still hold good.
5 3 . Elxperimental Methods. Many attempts were
made to measure the resistances of electrolytes before a
satisfactory method was discovered. Horsford* passed
a current between two electrodes in a rectangular trough,
then moved them nearer together, and determined the
resistance of a wire which, when interposed in the circuit,
reduced the current to its former value. Assuming that
the polarisation is the same in the two cases (which,
owing to migration, is difi&cult to insure) the resistance
of the wire is the same as that of a column of solution
equal in length to the diflference of the distances between
the electrodes in the two positions. The method was im-
proved by Wiedemann, who used as electrodes plates of the
metal present in solution, and thus reduced polarisation.
Beetz^ used an ordinary Wheatstone bridge arrange-
ment, getting rid of nearly all polarization by making his
electrodes of amalgamated zinc placed in a neutral
solution of zinc sulphate.
Since the electromotive force between any two points
of a given circuit is proportional to the resistance be-
tween them, the resistance of two parts of a circuit
can be compared by comparing the electromotive forces
between their ends. In this way Bouty' examined
many solutions ; he placed them in the inverted U tubes
1 Poflfflf. Ann,y 1847, 70, p. 238. « p^gg^ ^^„^ 1352, 117, p. 1.
3 Aiva. de Chemie et de Physique 1884, iii.
CH. IX]
CONDUCTIVITY OF ELECTROLYTES.
145
a and b (fig. 17), the legs of which dipped in larger volumes
of the same solutions placed in porous pots. These
porous pots were immersed in larger cells filled with zinc
sulphate solution, and connections were made mth siphons
a
Fig. 17.
filled with the same liquid, as shewn in the diagram. The
main electrodes E and J^ were of amalgamated zinc, and a
curi'ent was passed between them. Two tapping electrodes
were constructed, each consisting of a zinc rod in sulphate
of zinc solution placed in a WoulflFe*s bottle, with a thin
siphon tube coming out of one neck to make connection
with the liquid in either of the cells. In this way the
electromotive forces between the ends of a and h were
compared. The only polarisation is at the contact of the
different solutions outside and inside the porous pots.
The best measurements of the resistances of electro-
lytes hitherto made are due to Kohlrausch\ In order to
avoid the effects of polarisation, alternating currents
(that is currents whose direction is constantly being re-
1 Pogg, Ann,, 1869, 138, pp. 280, 870 ; 1873, 148, p. 148 ; & 1874, J. p. 290.
W. S. 10
146 SOLUTION AND ELECTROLYSIS. [CH. IX
versed) axe used. The electromotive force of polarisation
is thus rapidly reversed, and never reaches its full magni-
tude. Still, unless proper precautions are taken, polari-
sation is produced by such a small amount of chemical
decomposition that, even with alternating currents, its
efiTect is important, and the resistance as measured is
found to depend on the rate of alternation. It was found
that the products of the decomposition of -^ milligram
of water on two platinum plates, each having an area of
one square metre, gave an electromotive force of about one
volt, and that the electromotive force of polarisation was
proportional to the surface density of the deposit : it can
therefore be made as small as we please by increasing the
area of the electrodes. The effective area can be made
much larger by coating the electrodes with platinum-
black This is done by passing a current backwards and
forwards between them through a dilute solution of
platinum chloride containing free nitric acid.
It has been usual to employ the alternating currents
given by a small induction coil, and to adjust a Wheatstone's
bridge till the sound given by the telephone, used as indi-
cator, was a minimum. Various disturbing causes must,
however, in that case, be taken into account or eliminated.
Thus the self-induction of the circuit produces an effect.
This is opposite to that of polarisation, and, by proper
adjustments, can be made to balance it^. The electro-
static capacity of the apparatus is also of importance^
1 Ene, Brit,, Art. ** Electricity," or B, A, Report, 1886, p. 384.
3 See Chaperon, Compt. Rend, 1889, 108, p. 799, and Eohlrausch,
ZeiU.f, phyaikal. Chem. 1894, 15, p. 126.
CJH. IX] CONDUCTIVITY OF ELECTROLYTES. 147
A modification of the method, described by Fitzpatrick^
^nd now in constant use at Cambridge, eliminates all such
periodic disturbances. The current fix)m one or two
Leclanch6 cells is led to an ebonite drum, which is kept
revolving at a very uniform rate by means of a turbine.
This is driven by a water supply carefully kept at constant
pressure. On the drum are fixed brass sectors, with wire
brushes touching them in such a manner that the current
is reversed several times in each revolution. The wires
from the drum are then led to an ordinary resistance box,
and connected in the same way as the battery wires of a
Wheatstone's bridge. A reflecting galvanometer is used
^is indicator, and, on the back of the drum, there is
another set of sectors, arranged to periodically reverse the
galvanometer connections, so that any residual current
always flows through it in the same direction. These
sectors are rather narrower than the others, so that the
galvanometer circuit is made just after the battery circuit
is made, and broken just before the battery circuit is
broken. The needle of the galvanometer is loaded with
lead ; its moment of inertia is therefore considerable, and
its period of vibration very long compared with the period
of alternation of the current. This prevents the slight
residual effects of polarisation, and of other periodic dis-
turbing causes, from sensibly affecting the galvanometer.
When the measured resistance keeps the same on in-
creasing the speed of the turbine and changing the
ratio of the arms of the bridge, the disturbing effects may
be considered to be eliminated.
^ B. A, Report, 1886, p. 828.
10—2
148
SOLUTION AND ELECTKOLYSIS.
[CH. IX
Various shaped vessels are used to contain the electro-
lytes ; a convenient form is represented in fig. 18. A glass
r
Fig. 18.
tube, about an inch or an inch and a half in diameter, has
a tube sealed in at one side through which a thermometer
can be inserted, and a stout platinum wire carrying a
platinum plate sealed through each end. Little tubes to
hold mercury are fixed over the protruding ends of these
wires, and, in this way, connection is easily made with the
Wheatstone's bridge. The constant of the cell is deter-
mined once for all by measuring in it the resistance of a
standard solution. From the observed resistance of any
solution in the cell, we can then calculate the resistance
of a centimetre cube, which is called the specific resistance.
The reciprocal of this, the specific conductivity , is a more
generally useful constant. As the temperature coefficient
is large (it is about two per cent, per degree for moderately
dilute aqueous solutions of common salts or acids), it is
necessary to keep the cell in a paraffin bath, and observe
the temperature with some accuracy.
CH. IX] CONDUCTIVITY OF ELECTROLYTES. 149
54. Elxperimental Results. Kohlrauscb expressed
his results in terms of molecular conductivity, that is the
conductivity (k) divided by the number of gram-equi-
valents of electrolyte per litre (n). He finds, that, as the
concentration diminishes, the value of k/n approaches a
limit, and, if the dilution is pushed far enough, becomes
constant, that is to say, that at great dilution the con-
ductivity is proportional to the concentration. Kohlrausch
established this by preparing very pure water by careful
distillation. He found that the resistance of the water
continually increased as the process of purification pro-
ceeded. The conductivity of the water, and of the slight
impurities which must always remain, was subtracted firom
that of the solution, and the result, divided by n, gave the
molecular conductivity of the substance dissolved. This
appears justifiable, for, as long as conductivity is pro-
portional to concentration, it is evident that each part of
the dissolved matter produces its own independent eflFect,
so that the total conductivity is the sum of those of the
pai-ts, and when this ceases to hold, the conductivity of the
solution has, in general, become so great that that of
the solvent is negligible.
The general result of these experiments can be
graphically represented by plotting k/n as ordinates, and
w* as abscissae; n^ is a number proportional to the re-
ciprocal of the average distance between the molecules —
to which it seems likely that the molecular conductivity
will be closely related. The general form of the curves
for a neutral salt, and for a caustic alkali or univalent
acid (like HCl) are shewn in fig. 19. The curve for
150
SOLUTION AND ELECTROLYSIS.
[CH. IX
the neutral salt comes to a limiting value, while that
for the acid attains a maximum at a certain (verj^
small) concentration, but when the dilution is pushed
to extreme limits, it falls again. This Kohlrausch con-
sidered to be due to chemical action between the acid
■**.
t
■•««.
^^
'^^9'
n*
Fig. 19.
and the residual impurities in the water, which, at such
great dilution, are present in quantitiq^ quite comparable
with the amount of acid. He therefore considered the
maximum value to be the limit in the case of acids. It
will be seen from our tables in the appendix that the
values of the molecular conductivities of all neutral salts
are, at great dilution, of the same order of magnitude,,
while those of acids at the maximum are about three
times as great. The influence of increasing concentration
is greater in the case of salts containing divalent ions than
for those composed only of univalent ions, and greatest
of all in such cases as ammonia and acetic acid, which
hardly conduct any better in strong solutions than in weak.
CH. IX] CONDUCTIVITY OF ELECTROLYTES. 151
The most important results of Kohlrausch's work are —
1. The proof of Ohm's law for electrolytes.
2. The fact that the conductivity of dilute solutions
can be represented as the sum of two independent factors,
each of which depends on one of the ions only, and the
consequent possibility of determining the ionic velocities
by the method described in Chapter VIII.
55. Consequences of Ohm's Law. A direct
proof of Ohm's law for electrolytes has also been given by
Fitzgerald and Trouton^ who shewed that the measured
resistance was independent of the strength of the current.
The agreement with the law is a fact of great interest.
Since any electromotive force, even if very small, must be
able to produce a corresponding current, there can be no
appreciable reverse electromotive forces in the interior of
an electrolyte, and no appreciable amount of chemical work
can be there done by the current. It follows either that
the function of the current is merely directive — that it
controls the direction of the motions of the ions which it
already finds continually interchanging their partners— or
else that the work done in tearing one molecule asunder
is exactly equal to that given back in the formation of the
next.
The first of these h3^otheses was advanced by
Clausius' to explain the facts of electrolysis, and, as it is
the one generally adopted, we will examine 'the evidence
for it in some detail. If two solutions containing the salts
^ B, A. RepoH, 1886, p. 312.
2 Pogg, Ann., 1867, 101, p. 338.
152 SOLUTION AND ELECTROLYSIS. [CH. IX
AB and OD are mixed, double decomposition is found to
occur — AD and CB being formed. This goes on till a
certain part of the first pair of substances has been
transformed into an equivalent amount of the second pair.
The proportions between the four salts AB, CD, AD and
CB, which finally exist in solution, are found to be the
same whether we begin with AB and CD or with AD and
CB, The phenomena were found by Guldberg and Waage
to be fully represented by a theory which supposed that
both the change fi'om AB and CD into AD and CB, and
the reverse change firom AD and CB to AB and CD were
alwajrs going on, the quantities transformed per second
being proportional to the product of the active masses of
the original substances and to a coefiicient k, which ex-
presses the afiinity producing the reaction. If the active
masses of AB, CD, AD, CB are p, q, p\ q' respectively, and
k and kf the two coefficients of affinity, we get for the
rate of transformation ot AB and CD into AD and CB
kpq,
and for the velocity of the reverse change
kyq\
When there is equilibrium, these two rates of trans-
formation must be equal and opposite, and we get
Jfcpj = &>Y (2'7).
The results of this equation have been experimentally
confirmed for many cases, and the view here taken of
double decomposition is universally admitted to be a true
one. But in order that this process of chemical change
CH. IX] CONDUCTIVITY OF ELECTROLYTES. 153
in opposite directions should continually go on, it is
obviously necessary that perfect freedom of interchange
should exist between the parts of the molecules, so that,
here again, we are forced to believe that a series of
perpetual separations and reunions is going on among
them. This hypothesis was first advanced from the
chemical side by Williamson* in order to explain the
process of etherification.
A study of chemical changes shews us that it is always
the electrolytic ions of a salt that are concerned in the
reactions. The tests for a salt, potassium nitrate for
example, are the tests not for KNOg, but for its ions K
and NOs, and in cases of double decomposition, it is always
these ions that it exchanges for those of other substances.
That this is the case is shewn by the fact that, if an
element is present in a compound otherwise than as an
ion, it is not interchangeable, and cannot be recognised
by the usual tests. Thus neither the chlorates, which
contain the ion CIO,, nor monochloracetic acid, shew the
reactions of chlorine, although of course it is present in
both ; and the sulphates do not answer to the usual tests
which indicate the presence of sulphur as sulphide.
It seems certain, then, that the parts of the molecules
in solution are continually changing partners, that the
electrolytic ions are also the parts which enter into
chemical combinations, and that the effect of a current
is merely so to control the direction of these decom-
positions and recompositions, that, on the whole, a stream
of positively electrified ions travels in one direction, and
1 Cheni. Soc, Journal, 1852, 4, 110.
154 SOLUTION AND ELECTROLYSIS. [CH. IX
a stream of negatively electrified ions in the other. As
far as we have gone, there is no evidence to shew that the
ions remain dissociated for any appreciable time, the
reasoning given above only goes to prove that there is
freedom of interchange. This freedom may only exist in
the case of those molecules which the kinetic theory
teaches ufc will, at any instant, happen to be moving with
a velocity so much greater than the average, that, on col-
liding with another molecule, the impact is violent enough
to produce dissociation, and make rearrangement possible.
So much seems to follow from the truth of Ohm's
law and the phenomena of chemical action. There is
further evidence, which we shall discuss later (see Chap.
XI.), that the ions remain dissociated, or at all events
keep a certain amount of freedom, throughout a con-
siderable fractional part of their existence.
56. Influence of Concentration on Conduc-
tivity. The tables given in the appendix shew at once
that the molecular conductivity of solutions falls off as
the concentration increases, that is to say, the conductivity
does not increase as fast as the concentration, so that the
eflfect of each successive increase in the amount of salt
dissolved becomes less. How are we to explain this ? It
follows from the experimental determination of the velocity
of the hydrogen ion in acetic acid solutions, described on
page 142, that the immediate cause of the reduction in
molecular conductivity is a reduction in the velocities
of the ions. It is true that the viscosity of a solution
increases with the concentration, so that the frictional
CH. IX] CONDUCTIVITY OF ELECTROLYTES. 155
resistance to the motion of the ions may become greater^
but this is a small change, insufficient to explain the
marked decrease in molecular conductivity, and Arrhe-
nius^ has shewn that, at any rate in many cases, there
is no proportionality between viscosity and electrical re-
sistance. We can, however, imagine another way in which
the average velocities of the ions might be reduced : viz.
by supposing that the ions are only able to move during a
part of their time, so that each molecule in solution
becomes in turn active and inactive.
57. Dissociation Theory. A theory of electro-
lysis, which has been framed by Arrhenius, Ostwald and
others, supposes that a substance is chemically active only
when dissociated, in which state the ions are to some
extent free from each other. In the language of this
" Dissociation Theory " the freedom of interchange which
we know to exist among the ions, is secured, not by the
momentary dissociation and consequent rearrangement at
the instant of collision of the molecules, as described on
page 154, but by the continued freedom of the ions for a
considerable part of their existence. Dissociation and re-
composition are continually going on, and a substance is
active only while its ions are dissociated and able to move.
An ion will, at one instant, be combined with another, form-
ing an inactive molecule, at another, be travelling freely
through the liquid under the influence of the electric forces,
and, at a third, combined with a fresh one of the opposite
kind to form a new inactive molecule. Dissociation is
^ B. A. Rep<yrt, 1886, p. 344.
156 SOLUTION AND ELECTROLYSIS. [CH. IX
possibly caused by collisions as Clausius supposed, but
Arrhenius says that the ions do not at once recombine with
others as the older theory imagined. We shall see later
(§ 79) that the forces between atoms are much reduced by
solution in a solvent of high specific inductive capacity,
which will give greater freedom, and that there is some
reason to suppose that the ions, when free from each
other, are combined with the solvent molecules, which
pass them on from one to the other through the liquid.
58. lonisation. The dissociation theory will be
considered in greater detail later, it is only introduced
here to give some idea of how ions can be in turn active
and inactive. But though the most obvious, it is not the
only way in which such a result could be secured. The
activity of a molecule might be due to a particular ar-
rangement of complex structures formed with other mole-
cules, either of the substance dissolved or of the solvent,
in which state alone transference of ions could occur, or it
might be that the contact of two molecules in a particular
position was the necessary condition for interchange of their
ions. In either of these ways it could be managed that a
part only of the dissolved substance should be at any
moment in a state of electrolytic activity, which is all that
is necessary to produce the diminution of ionic velocity
which we require. Instead of using the word "dissociation '*
to express the active state of a molecule, we shall use, at
Fitzgerald's suggestion \, the term " ionisation." Even if
the process of ionisation does consist in giving a certain
1 B. A, Report, 1890, p. 142.
CH. IX] CONDUCTIVITY OF ELECTROLYTES. 157
amount of freedom from chemical chains to the parts of a
molecule, it is certain that the ions so produced are not in
the same electrical or chemical state as the elements
would be if they were dissociated from each other by
ordinary chemical processes, and it would be better to
restrict the term "dissociation" to such cases as the
resolution by heat of solid ammonium chloride into
gaseous ammonia and hydrochloric acid.
59. Influence of Concentration on lonisation.
We have now found a way in which the ionic velocities,
and consequently the molecular conductivity, of a solution
may be reduced, and we can, therefore, return to the con-
sideration of the effect of increasing concentration. In the
normal case, in which the molecular conductivity tends to
a limiting value at great dilution, we can suppose we have
got all the contents of the solution in a state of activity. As
the concentration increases, and the molecular conductivity
gets less, the proportion of active molecules continually
decreases, so that the ratio of the number of active to the
whole number of molecules is the same as the ratio of the
molecular conductivity at the given concentration to that
at infinite dilution. This ratio (a) can be called the
coefficient of ionisation, and its value, for any given
solution, is
a==
oc
where /a represents the molecular conductivity of the
solution, and ji^ its value at infinite dilution. The
following table gives Kohlrausch's results for a solution
of potassium chloride.
158
SOLUTION AND ELECTKOLYSIS.
[CH. IX
n
fixKfi
a
0^0
1296
1-00
•0001
1285
•99
•0006
1275
•98
•001
1268
•98
•006
1235
•95
•01
1219
•94
•03
1178
•90
•1
1113
•86
•5
1018
•78
1^0
977
•75
30
879
•68
60. Resistance of Liquid Films. Beinold and
Riicker^ have investigated the electrical resistance of thin
soap films. By examining the effect on interference
phenomena of passing one of the interfering rays of light
through a tube across which several films were stretched,
they were able to measure the thickness of the films with
considerable accuracy. This method assumes that the
index of refi*action of a film is the same as that of the
liquid in bulk, but reasons are given to justify this
assumption. It was found that, when films were prepared
which, like the central spot of Newton's rings, looked
black by reflected light, the thickness was constant for any
given liquid. If some salt was added to the liquid, the
thickness decreased; thus the following table shews the
thickness in micro-millimetres (metre x 10~^^), of films
of 1 part of hard soap in 40 parts of water with varying
amounts of potassium nitrate.
1 Phil Trans,, 1893, 1, p. 606.
CH. IX] ELECTRICAL ENDOSMOSE. 159
Optical Method.
Percentage of KNO3 3 1 0*5
Thickness in fifi 12-4 13-5 14-5 32-1
If the specific resistance of the film is the same as that
of the liquid in bulk, we ought to be able, by measuring
the resistance of a film of known size, to get values for the
thickness, agreeing with these numbers. It was found
that, as long as the amount of salt present was greater
than 3 per cent., the results of the two methods agreed,
but if the proportion was less than this, the electrical
method gave a greater value than the optical.
Electrical Method,
Percentage of KNO3 3*2 1 050
Thickness in /x/x 10-6 12-7 24-4 26-5 154
Thus the conductivity of a thin film is much greater
than that of the liquid in bulk when the concentration
is very small, but, as the concentration increases, the
conductivity more and more nearly approaches the normal
value, which it reaches when the strength of solution
is about two or three per cent.
We cannot explain this phenomenon by supposing
that the surface tension increases the ionisation, because
it is in the case of very dilute solutions, where the
ionisation is already nearly complete, that the eflfect is
most marked. The ionic friction may, however, be less,
and the ionic velocities greater, in the surface layer than
in the bulk of the liquid.
6 1 . Electrical Endosmose. If we pass an electric
current through a cell divided into two compartments by
160 SOLUTION AND ELECTROLYSIS. [CH. IX
means of a porous partition and filled with some solution,
we shall, in general, find that, as well as alterations in the
contents of the solutions round the electrodes, there is a
bodily transfer of the liquid — usually in the direction of
the current — through the porous plate. To this pheno-
menon the name of electric endosmose is given. It has
been experimentally studied by Wiedemann^ and Quincke^.
If the pressure be kept the same on both sides of the
partition, the volume of liquid which flows through, as
measured by the overflow, is proportional to the whole
quantity of electricity which has passed, and is inde-
pendent of the area and thickness of the porous plate ; it
varies much with the nature of the solution, being greater
with liquids of high specific resistance, and, in solutions
of any one substance of different strengths, is approxi-
mately proportional to the specific resistance.
If we do not allow the liquid to overflow, but measure
the final pressure reached, we find that this pressure
varies directly as the strength of the current, inversely
as the area of the porous wall, and directly as its thickness.
In this case, the flux of liquid due to the electric forces
must be equal and in the opposite direction to that caused
by the difference in hydrostatic pressure.
A mathematical theory of the subject has been given
by von Helmholtz*, on Quincke's assumption of a constant
difference in potential at the surface of contact between
the liquid and the walls of the little tubes which run
through the porous partition.
1 See Elektricitdt, Bd. II., p. 166. « p^gg^ ^„„,^ iggi^ 113^ p 513^
3 Wied. Ann, , 1879, 7, p. 337.
CH. IX] ELECTRICAL ENDOSMOSE. 161
Such a discontinuity in potential must produce an
^'electrical double layer'* — that is a charge of one kind
of electricity on the walls of the tube, and an equal
charge of the opposite kind on the nearest film of liquid.
The latter charge is acted on by the external electric forces,
and the liquid is dragged through the tube by its skin.
When a difference of pressure is allowed to develop, one
current of liquid is dragged forward along the walls, and
another flows back down the centre of each little tube,
and, when a stationary state is reached, the volumes
flowing in these two currents are equal and opposite.
From these ideas Helmholtz deduced all the observed
laws of electric endosmose, and calculated that the contact
differences of potential, which would produce the observed
effects, are comparable with the electromotive force of a
Danieirs cell. A modification of Helmholtz's theory has
been given by Lamb^ allowing for some slight slip between
the liquid and the walls of the tubes.
A similar contact difference of potential will explain
the motion of fine particles of clay or other material
through water or other liquids under the influence of an
external electromotive force. Details of observations on
these phenomena will be found in the fourth chapter of
the second volume of Wiedemann's " Elektridtdt"
1 B, A, Report, 1887, p. 496.
M^. S. 11
CHAPTER X.
CONNECTION BETWEEN ELECTRICAL AND OTHER
PROPERTIES.
62. Conductiyity and Chemical Activity. It
was noticed by Hittorf that there was a very close
connection between chemical activity and electrical con-
ductivity, but the exact numerical agreement was first
pointed out by Arrhenius^
It is found that the constant k, which we have used
on p. 152 to express the "affinity" determining the rate
of transformation of two compounds AB and CD into
AD and CB, and likewise the constant A/, which controls
the reverse action, can each be considered as the product
of two factors, one measuring a characteristic property
of each of the reacting bodies. This leads to the idea of
" specific coefficients of affinity," which is of the utmost
importance in the modem theory of chemistry, and is
based on the fact that the relative affinities of different
acids are the same, whatever the nature of the action by
which they are compared.
By measuring the heat evolved during the action,
Thomsen determined how much of the sodium salt of one
^ **Recherches sor la conductivity galvanique des Electrolytes,' '
Stockholm, 1SS3. Abstract in B, A. Report, 1886, p. 357.
CH. X] CONNECTION BETWEEN PROPERTIES. 163
acid was decomposed by another, which gives the ratio in
which the base is shared by the acids. Ostwald* investi-
gated the relative affinities of acids for potash, soda, and
ammonia, and proved them to be independent of the base
used. The method employed was to measure the changes
in volume caused by the action. His results are given
in column I. of the table on p. 164, the affinity of
hydrochloric acid being taken as one hundred.
Another method is to allow some acid to act on an
insoluble salt, and to measure the quantity which goes
into solution. Determinations have been made with
calcium oxalate CaCgOi + HjO, which is easily decomposed
by acids, oxalic acid and a soluble calcium salt being
formed. The affinities of acids relative to that of oxalic
acid are thus found, so that the acids can be compared
among themselves. Their relative affinities as thus
measured are given in column II. of the table.
If an aqueous solution of methyl acetate is allowed
to stand, a very slow decomposition into alcohol and acid
goes on. This is much quickened by the presence of a
little dilute acid, though the acid remains unchanged. It
is found that the influences of diflferent acids on this action
are proportional to their specific coefficients of affinity.
The results of this method are given in column" III.
Finally in column IV. the electrical conductivities of
normal solutions of the acids have been tabulated. A
better basis of comparison would be the ratio of the actual
to the limiting conductivity, but, since the conductivity
^ Lehrbueh der Allg, Chemie.
11—2
164
SOLUTION AND ELECTROLYSIS.
[CH. X
of acids is chiefly due to the hydrogen, its limiting value
is nearly the same for all, and the general result of the
comparison would be unchanged.
The feet, which we have already noticed, that the
electroljrtic conductivity of solutions of mineral acids
attains a maximum value, shewing that the ionisation is
complete, corresponds to the phenomena observed in the
case of their chemical aflSnities. The value of these for
hydrochloric, nitric and other strong acids is practically
the same, and cannot by any means be increased. Thus
Ostwald has found that the introduction of oxygen,
sulphur or a halogen, which increases the affinity of a
weak acid (compare acetic acid with the three chloracetic
acids), has no eifect on the affinity of these strong acids.
The limit has evidently been reached, and the whole
substance obtained in a state of activity. In each column
of the following table the number for hydrochloric acid
has therefore been made equal to 100.
Acid
I
II
III
IV
Hydrochloric
100
100
100
100
Nitric
102
110
92
99-6
Sulphuric
68
67
74
65-1
Formic
4-0
2-5
1-3
1-7
Acetic
1-2
1-0
0-3
0-4
Propionic
11
0-3
0-3
1 Monochloracetic
7-2
51
4-3
4-9
Dichloracetic
34
18
23-0
25-3
Trichloracetic
82
63
68-2
62-3
Malic
3-0
5-0
1-2
1-3
Tartaric
5-3
6-3
2-3
2-3
Succinic
0-1
0-2
0-5
0-6
CH. X] CONNECTION BETWEEN PROPERTIES. 165
It must be remembered that, the solutions uot being
of quite the same strength, these numbers are not strictly
comparable, and that the experimental difficulties in-
volved in the chemical measurements are considerable.
Nevertheless, the remarkable general agreement of the
numbers in the four columns is quite enough to shew the
intimate connection between chemical activity and electrical
conductivity. We may take it, then, that only that portion
of a body is chemically active which is electrolytically
active — that ionisation is necessary for chemical activity
just as it is necessary for electrolytic conductivity.
63. Conductivity and Osmotic Pressure. During
our examination of the phenomena of osmotic pressure
and its consequences — the lowering of vapour pressure,
and the depression of the freezing point — we noticed
that the values for solutions of electrolytes were in
all cases abnormally great. As more investigations have
been made on the depression of the freezing point than
on the other correlated properties, and as the experi-
mental error is probably less in this case, we shall at first
confine ourselves to it. In order to shew the intimate
relation which exists between the abnormal osmotic
pressures, as measured by the depression of the freezing
point, and the electrical conductivity, we must suppose
that every electrolytically active molecule produces an
abnormally great osmotic pressure, and that its eflfect is
proportional to the number of ions into which it can be
resolved. Thus the effect of an active molecule of KCl is
twice that of an inactive one, and the effect of a molecule
166 SOLUTION AND ELECTROLYSIS. [CH. X
of H2SO4 (which gives two H ions and one SO4 ion) is,
when in a state of ionisation, three times as great as that
of the normal. If then, in a certain solution, we have m
inactive and n active molecules, each of the latter giving
k ions, the total osmotic pressure produced will be propor-
tional to m + kn, whereas the normal osmotic pressure
would be proportional to m + w. By measuring the con-
ductivity we can (see p. 157) find the fractional number of
molecules which is at any moment active. Let us call it a.
Now a =
m + w'
so that, if the ratio of the actual osmotic pressure to
the normal is called ^,
This same ratio can also be found by direct experiment
on the depression of the freezing point, for by Van 't
HoflTs equation (14 on p. 57) we know the normal value,
and if t be the observed depression for a solution of one
gram-equivalent per litre,
t
^ =
1-89 •
We can thus compare the value of i as directly
determined by observations on the freezing point, with its
value as calculated from the conductivity. The following
table is part of that given by Arrhenius* for aqueous
solutions.
1 ZeiU, farphysikal, Chemie, 1887, ii., p. 491.
Substance dissolved
No. of gram-
equivalents
i observed
from freez-
i calcu-
lated from
conduc-
tivities
a coeffi-
cient of
per litre
ing points
ionisation
A. N(m-C<ynductor8,
Methyl alcohol |
CH3OH "j
0-1
0-485
0-97
0-97
0-96
1-00
\
\
Ethyl alcohol f
0125
0-62
1-24
0-97
1-01
1-05
Phenol
0-101
0-216
0-558
0-00234
0-0445
0-96
0-96
0-93
1-2671
1-08
- 1-00
>■
Cane sugar J
0-0947
Ml
C12H22O11
0-316
1-12
V
0-809
1-34
1-01
1-43
/
)
B. Mectrol^/tes,
Lithium hydrate j
LiOR I
0-127
1-98
1-90
-90
0-317
1-89
1-86
-86
. Acetic acid J
CH3COOH ]
0-135
0-337
0-842
1-05
1-04
1-01
1-01
1-01
1-00
•01
•01
-00
Phosphoric acid J
HsP04 t
0-077
0-146
1-38
1-27
1-32
1-25
•11
•08
0-319
1-22
1-20
•07
'
0-0467
2-00
1-88
•88
Sodium chloride
0-117
1-93
1-84
•84
NaCl
0-194
1-87
1-82
-82
i
0-539
1-85
1-74
•74
Silver nitrate J
AgNOj 1
0-056
0-140
2-02
1-90
1-86
1-81
-86
•81
0-341
1-77
1-73
•73
'
0-0364
2-68
2-45
•72
Potassium sulphate
0-091
2-35
2-33
•66
K2SO4
0-227
2-21
218
•69
,
' 0-465
2-04
2-06
•53
'
0-0476
2-74
2-52
•76
Calcium chloride
0-119
2-62
2-42
•71
CaCla
0-199
2-66
2-34
•67
I
0-331
2-73
2-24
•62
/
0-0393
1-33
1-41
•41
0-112
1-15
1-34
•34
Copper sulphate
0-254
1-03
1-27
•27
0-523
0-94
1-22
•22
>
0-973
0-92
1-18
•18
1 Jones. ZtiU, fUrphyaikal. Chemie, 1893, 12, p. 642.
168
SOLUTION AND ELECTROLYSIS.
[CH. X
Another way of tracing the connection between the
two eifects is to compare the coeflScient of ionisation
calculated from the depression of the freezing point with
its value as found from the conductivity. The following
table is given by H. C. Jones \
Coefficient of Ionisation
Concentration
Snbstanoe
in gram-
molecoles
per litre
Kohlrausch's
result from
conductivity
Jones' result
from depression
of freezing
point
I
0-002
1-00
0-984
HC1(m.=3455) \
001
0989
-968
(
01
0-939
-886
(•
0003
0-898
-860
Hi!SO4 0».=3342) \
0-005
0-854
•838
(
0-06
0-623
•607
f
0-002
1-00
•984
HNO3 0*.=3448) ]
0-01
0-985
-968
(
0-1
0-935
-878
H,PO,(m.=977) j
0-002
0-01
0-878
0-635
-862
•688
KOH0i.=2141) J
0-002
1-00
•984
0-01
0-992
•937
0-1
0-928
•831
/
0-002
0-989
•984
NaOH(/i„ = 1880) \
-01
0-995
•937
-05
0-904
•884
(
0006
0166
•111
NHiOH0..=7O0) ]
•01
0130
•069
\
-06
0-061
•038
/
0-003
0-920
•966
K»C03(m. = 1222) \
-005
0-886
•960
\
-06
0-719
•776
{
0003
0-914
•963
Na2C03(;i. = l746) ]
•006
0-860
•959
^
•06
0-650
•730
Loomis" finds that the molecular depression of the
1 Zeits.furphysikaL Chemie, 1893, 12, p. 689.
2 Wied, Ann, 1894, 51, p. 500.
CH. X] CONNECTION BETWEEN PROPERTIES. 169
freezing point, agrees with that calculated from the con-
ductivity in the case of solutions of sodium chloride, but
that solutions of sulphuric acid and magnesium sulphate
shew deviations from the theoretical results greater than
can be accounted for by experimental errors.
The general agreement between the observed and
calculated results is, however, quite enough to shew the
intimate connection of the electrical conductivity with the
abnormal depression of the freezing point. The cases
in which the conductivity is very low, such as solutions
of ammonia and acetic acid, are most interesting, for it is
in these also that the abnormal increase in the depression
of the freezing point is very small. It seems certain that
whatever is the cause of the conductivity of electroljrtes
is also the chief cause of the increase in the osmotic
pressure.
CHAPTER XL
THEORIES OF ELECTROLYSIS.
64. Introduction. In the preceding pages an
account has been given of the experimental facts of our
subject, and of those theoretical deductions which seem to
necessarily follow from them. We have seen that an
intimate relation exists between the conductivity of
electrol3rtes and their other physical and chemical pro-
jperties. The quantitative agreement between the mole-
(cular conductivities, the abnormal value of the osmotic
Ipressures, and the specific chemical affinities of electro-
lytes, certainly shew that the peculiar condition which we
have termed " ionisation " is the chief cause of them all.
We shall now proceed to examine the theories which have
been advanced in order to explain what is the real
physical meaning of ionisation, but it should be remarked
that no hypothesis advanced merely to explain observed
facts, rests on the same sure ground as a theoretical idea
which is a necessary consequence of those fects. Never-
theless, a theory, from which deductions can be made
agreeing in all respects with the observed phenomena,
may continually increase the amount of evidence in its
CH..XI] .THEORIES OF ELECTROLYSIS. I7l
favour, and, even if it does not represent the actual
physical truth, must certainly be based on a deep-seated
analogy, so that it cannot fail to throw new light on the
subject and point the way for further investigation.
65. The Dissociation Theory. The theory of
electrolytes which has been worked out in the greatest
detail is certainly that founded by Arrhenius, Kohlrausch,
Ostwald and Nemst on Van *t Hoff 's view of the nature
of solutions. The fact that an indiflTerent substance exerts
in solution the same pressure as in a gaseous state leads,
as we have seen, to the idea that the osmotic pressure,
like that of a gas, is mainly due, in dilute solutions,
to molecular impacts.
It has been noticed already that solutions of salts,
acids and alkalies, give greater values for the osmotic
pressure and its consequences — the lowering of vapour
pressure and the depression of the freezing point — than
do the solutions of non-electrolytes. This, it must be
noticed, is the case even in dilute solutions, where the
intermolecular forces must be small. It seems natural
to attempt to explain these abnormal results by an
extension of the ideas which have already proved so
satisfactory in the normal cases. But, if we again refer
the pressure to molecular impacts, we must still suppose
that each molecule produces the same effect as before, so
that, in the case of electrolytes, we must have in solution
a number of effective pressure-producing particles greater
than that indicated by the concentration. If we follow
this line of argument, we are brought to the idea that a
172 SOLUTION AND ELECTROLYSIS, [CH. XI
large part of the number of molecules in solution must be
dissociated, so that the number of eflTective particles is
increased. Baoult found that, whereas the molecular de-
pression of the freezing point for dilute aqueous solutions
of indifferent substances was 18*9, the result for potassium
chloride was 33*6. If we are to explain this by means
of molecular impacts, we must imagine that about 78 per
cent, of the potassium chloride is dissociated into two
parts. Substances which, like barium chloride (BaCla),
can dissociate into three parts, give, in general, a de-
pression of the freezing point nearly three times the
normal. Thus barium chloride gives 48*6 — corresponding
to a dissociation of 79 per cent. By examining Eaoult's
table on page 64, it will be seen that no substance
gives a value which exceeds that calculated from com-
plete dissociation by more than an amount so small that
it might be due to secondary effects or experimental
errors.
Exactly the same phenomenon is found in the case of
direct determinations of osmotic pressure, and of the
lowering of vapour pressure. Here again, in order to
explain the behaviour of electroljrtes by the theory of
molecular bombardment, we have to imagine a certain
part of the molecules to be dissociated. The percentage of
dissociation calculated from these effects agrees fairly well,
in most cases, with that deduced from the freezing points.
Differences occur, especially in stronger solutions, but it
must be remembered that the experimental investigation
of either of these phenomena presents greater difficulties
than the determination of the freezing point. In the direct
CH. XI] THEORIES OF ELECTROLYSIS. 173
measurement of osmotic pressure, besides uncertainties
already mentioned, the membrane may not be quite im-
pervious to the salt\ This would result in the measured
pressure being too low. In the determination of vapour
pressure, the temperature is, in general, diflTerent from that
of the freezing point, and, in the theory of the subject, we
have assumed certain relations which are only approxi-
mately true.
66. Chemical Properties. When we pass to the
consideration of the chemical properties of solutions, we
are forced by the facts of double decomposition to admit
that interchanges among the parts of the molecules are
always going on, so that, at all events, temporary dis-
sociation must occur. It does not of course follow that
the parts remain free for any considerable time — but
freedom of interchange is certainly necessary.
67. Independent Ionic Velocities. Turning to
the electrical phenomena, we are met at the outset by
Kohlrausch's law of the independent velocities of the ions.
This is not a proof that the ions are permanently dis-
sociated, but it is certainly evidence in favour of that view
in the case of dilute solutions, for, if the motions of the
ions were produced by taking advantage of interchanges
at the instants of collision, it seems likely that the average
velocity of an ion would depend on the nature and, still
more, on the number of the other ions present. Since an
ion could, on this hypothesis, only take a step forward
when the molecule of which it formed part collided with
1 See Tammann, ZeiU, fiir physikal, Chemiey 1892, 9, p. 97.
174 SOLUTION AND ELECTROLYSIS. [CH. XI
another molecule, we should expect the velocity with
which the ions worked their way through the solution to
increase with the concentration, and the conductivity to
increase faster than the concentration. The fact, then,
that, in dilute solutions of good electrolytes, the con-
ductivity is proportional to the concentration, and the
molecular conductivity constant, is evidence in favour of
the permanence of the dissociation.
The mutual independence of the ions is also suggested
by the observation that, while the properties of the
solutions of indifferent substances are determined by the
constitutioD and bear no definite relation to the properties
of the components, the properties of the solutions of
electrolytes are additive — that is, can be represented as
the sum of those of their parts.
68. DensitieB of Salt SolutionB. Yalson^ found
that the specific gravities of salt solutions could be
calculated from a table of moduli of the elements of the
substance dissolved, the modulus for each element being
experimentally determined. The relation is better in-
vestigated, however, by considering the specific volume
instead of its reciprocal the specific gravity, and Groshaus^
found that the molecular volume of the dissolved salt was,
in dilute solution, the sum of two constants, one determined
only by the acid and the other only by the base.
The following table gives the volume-change in cubic
centimetres for one gram-equivalent of substance in 10
litres of water:
1 CampL rend. 1874, 73, p. 441.
a Wied. Ann, 1888, 20, p. 492.
H
Na
K
NH4
18
-5-8
3-6
18-3
16-6
26-9
37-4
290
28-0
38-5
48-2
16-2
6-4
15-7
24-2
CH. XI] THEORIES OF ELECTROLYSIS. 175
OH
CI
NO3
Thus the solution of 40 grams of NaOH in 10 litres of water
involves a contraction of 5*8 cc, so that the volume of the
solution (viz. 9994*2 cc.) is actually less than the volume
of solvent used. With other solvents increases in the
total volume may occur; thus a mixture of 100 cc. of
alcohol and 100 cc of carbon bisulphide occupies a
volume of 202 cc.
Ostwald^ has measured the volume-changes accom-
panying the neutralisation of bases by acids, and shewn
that, here again, additive relations appear. Normal
solutions of strong acids and strong bases give, on
neutralisation, a constant volume change, equal to a
contraction of 20 cc per litre. The subject has been
fully discussed by NicoP.
69. Colours of Salt Solutions. Similar relations
hold good with regard to the colour of a salt solution*,
which is obtained by the superposition of the colours of the
ions and the colour of any undissociated salt. Anhydrous
cobalt chloride is blue, while in cold aqueous solution
all cobalt salts are red. Red, then, is the colour of the
cobalt ion, and only appears when the salt is more or less
dissociated. If cobalt chloride is dissolved in alcohol, the
1 Z.fUrprakt, Chemiey 1878, 18, p. 358.
2 Phil Mag., 1883-4, 16, p. 121 and 18, p. 179.
^ Ostwald's Lehrbuck.
176 SOLUTION AND ELECTROLYSIS. [CH. XI
conductivity is very low, shewing very incomplete ioni-
sation. The colour is, accordingly, the blue of the un-
dissociated salt. If we slowly add water to this solution,
the ionisation gradually increases, and the colour changes
to purple and then red. If an aqueous solution be boiled
with potassium cyanide, it is decolourised, for a cobalti-
cyanide, K8Co(CN)e, has been formed; the ions of this
compound are 3K and Co(ON)g; the free cobalt ions no
longer exist, and the solution ceases to respond to the
usual tests for cobalt. That the red colour is really due
to the ionisation, and not to a hydrate formed between
the cobalt salt and the solvent, is indicated by the additive
nature of the phenomena, for, like other properties, the
colour of non-electrolytes depends on the constitution and
is not additive. The use of indicators, which shew the
presence of acids or bases by a change in colour, is a
phenomenon of similar character. Thus para-nitrophenol
is a weak acid, very little dissociated. The addition of an
alkali, soda for example, causes the corresponding salt to
be formed. This is largely dissociated, and the intensely
yellow colour of the ion C«H4N02 . is at once seen.
We shall see reasons later (see p. 193) for supposing
that, in most cases, a rise of temperature reduces the
dissociation of a salt in solution, and increases the number
of combined molecules — the increase of conductivity being
brought about by a still greater reduction in the viscosity
which the solution opposes to the motion of the ions.
We should expect, therefore, that, on heating a coloured
solution, the colour would become more like that of the
undissociated salt. Thus anhydrous copper chloride is a
CH. Xl] THEORIES OF ELECTROLYSIS. 177
yellow solid, and the combination of this with the blue
of the copper ion produces the green colour of the strong
solution. On adding water the colour gets more blue,
but on heating it goes back to green. Many similar
cases will be found described by J. H. Gladstone \ If the
absorption spectra of salt solutions are examined, the^j
additive character of the colour is well seen, the absorption
bands due to each constituent being unaffected by the
presence of the other. The transmitted light is therefore
composed of all those rays which have been absorbed by
neither constituent.
70. Other Properties. Similar additive relations-
have been traced in the refraction coefficients, which were
found by Gladstone to be an additive property for the case
of solutions of active — i,e. dissociated — salts, in the optical
rotatory powers, in the surface tensions, and in the viscosities
of salt solutions, while Perkin, from the phenomena of
magnetic rotation, considered, without reference to the
dissociation theory, that salts were dissociated into acid
and base. The thermal capacities are complicated by the
fact that a change of temperature causes, in general, a
change in the state of dissociation to an amount dependent
on the nature of the substance, but, in coihpletely dis-
sociated solutions, the thermal capacity is also an additive
property^
The following table gives the change in thermal
1 PUL Mag,, 1857, (4), 14, p. 423.
2 Ostwald's Lehrlmch.
8 Marignac, Ann. Ckim, et Phys.j 1876, (6), 8, p. 410.
w. s. 12
H
Na
E
NH4
18
-27
-38
-28
-16-3
-30
-13
-10-7
- 8-7
-16
7
9
-25
-36
-16
178 SOLUTION AND ELECTROLYSIS. [CH. XI
capacity which 10 litres of water undergo when one gram-
equivalent of the substances indicated are dissolved.
OH
CI
NO3
iso.
Thus the thermal capacity of a solution of 40 grams of
NaOH in 10 litres of water is 9973 — less than that of the
water alone.
71. Gteneral considerations. That substances,
which shew great chemical stability when solid, are largely
dissociated when dissolved, is at first sight rather a
startling statement. We must remember, however, that
it is precisely these bodies which shew the greatest
amount of chemical activity, that is to say, more readily
exchange their ions with those of other molecules. The
fact that a solution of potassium chloride does not shew
any of the properties of the elements potassium and
chlorine, though it has been urged as an objection, is not
a conclusive argument against the theory of dissociation,
for the ions are certainly under chemical and electrical
conditions very diflferent from those under which the
elements can exist in their usual forms. Without entering
into the still uncertain question as to the exact relation
between the ions and the electric changes they carry, we
are at least certain that the ion has to give a certain
definite charge of electricity (whatever that may exactly
mean) to the electrode before it can be liberated from the
CH. Xl] THEORIES OF ELECTROLYSIS. 179
solution in a normal chemical state. The amount of
energy possessed by an ion must therefore be very
diflferent from that belonging to the same quantity of
substance when liberated from solution, and there is no
reason to suppose that their properties would be identical.
Another objection which has been brought forward is that
the two ions would diffuse at diflFerent rates, and be
therefore separable. But, as soon as an ion got separated
from the mass of the substance, it is obvious that electric
forces would be brought into play tending to draw it
back, and these would increase, as more ions wandered
away, till they prevented further diflfusion. Still, some
separation would occur, and a volume of water, in contact
with the solution of an electrolyte, is found to take a
potential of the same sign as that of the more diffusible
ion, leaving the solution to assume a potential correspond-
ing to that of the less diffusible ion. (See p. 197.)
Further evidence is given by the behaviour of semi-
permeable membranes. A membrane of copper ferro-
cyanide can be prepared which will allow potassium
chloride in solution to pass through it, but is quite
impermeable to barium chloride. Now, on the theory of
free ions, some of the chlorine will again pass, since it
could do so in the first case, but the electric forces will pre-
vent any considerable separation from taking place. But if
we place some substance like copper nitrate on the other
side of the membrane, the chlorine ions, which diflFuse in
one direction, are replaced by nitric acid ions, which diffuse
in the other, and this process will continue till we soon
find nitrate mixed with the barium chloride, and chloride
12—2
180 SOLUTION AND ELECTKOLYSIS. [CH. XI
mixed with the copper nitrate. The salts cannot have
directly reacted with each other, for neither alone can pass
through the membrane, but the phenomenon is readily
explained on the hypothesis of free ions\
72. Development of the Digsociation Theory.
The ordinary laws of chemical equilibrium have been
applied to the case of the dissociation of a substance into
its ions. Let c be the number of molecules which disso-
ciate per second when the number of undissociated mole-
cules in unit volume is unity, then cp is the number when
the concentration is p. Recombination can only occur when
two ions meet, and since the frequency with which this
will happen is proportional to the square of the ionic con-
centration, we shall get for the number of molecules
re-formed in one second
where q is the number of dissociated molecules in one
cubic centimetre. When there is equilibrium
cp = c'g'l
If /L6 be the molecular conductivity, and /a^ its value at
infinite dilution, the fractional number of molecules dis-
sociated is /Lc//A^, and the number undissociated 1 — fi/fi^,
so that, if V is the volume of the solution containing ona
gram-molecule of the dissolved substance, we get
3 = i(^)and;, = |(l-ii).
00' -^ r-QO*
c
V
00' r- 00
^ Ostwald, B,A. Report, 1890, p. 332.
CH. Xl]
THEORIES OF ELECTROLYSia
181
t^'
f^'
^Moo (A*ce - M)
.(29).
Let) us put fi/fi^ » a ; then a, which we have called the
coefficient of ionisation (p. 157), measures both the mole-
cular conductivity referred to its limiting value as unity,
and also the fractional number of molecules dissociated.
The equation then becomes
q2 q
=—— = - =s constant = h
F (1 — a) c
(30).
This should represent the eflfect of dilution on the
molecular conductivity of binary electrolytes, and Ostwald*
has confirmed it by observation on an enormous number
of acids.
Cycmdcetic acid.
V
/*
100^
Jc
16
78-8
21-7
0-00376
32
105-3
29-1
373
64
139-1
38-4
374
128
176-4
48-7
361
256
219-1
60-5
362
512
260-9
72-0
361
1024
297-3
82-1
368
Formic acid
''ife= -0000214
Propionic i
acid
•0000134
Acetic „
•0000180
Butyric
»
•0000149
Monchloracetic
„ -00155
Isobutyric
})
•0000144
Dichloracetic
„ -051
Isovaleric
»
•0000161
Trichloracetic
„ 1-21
Caproic
>»
•0000145
1 Zeits.fUr physikal Chevfuey 1888, ii. p. 270; 1889, iii. pp. 170, 241,
369.
182 SOLUTION AND ELECTKOLYSIS. [CH. XI
The value of k, however, does not keep so satis&cto-
rily constant in the case of strong acids, and, though the
experimental error may be rather larger, no good ex-
planation of this discrepancy has yet been given.
If we put a equal to ^ in equation (30), we find that
the value of k is ^^. Thus, 2k measures the concentration
at which the electrolyte is just half dissociated. Ostwald
considers that this constant, k, gives the "long sought
numerical value of the chemical affinity."
If we choose states of dilution V^ and V^ for two
diflferent substances, such that the products VJc^ and VJc^
are equal, then :j— — , and therefore a, must be the same
for both. If we alter both dilutions in the same ratio,
the products Viki and VJc2 are still equal, so that the
dilutions at which two substances are dissociated to the
same extent are always proportional, whatever the ab-
solute values of the dilution. This was experimentally
discovered by Ostwald before he had applied the theory
of dissociation to electrolytes.
In the case of substances like ammonia and acetic
acid, where the dissociation is small, 1 — a is nearly equal
to unity, and only varies slowly with dilution. The
equation then becomes
^-k
or a = VF^ (31),
so that the molecular conductivity should be proportional
to the square root of the dilution. If we determine a for
CH. Xl] THEORIES OF ELECTROLYSIS. 183
a number of solutions of diflferent strength, and use our
results to calculate A, the values obtained should be
constant. The following table is given by Ostwald for
acetic acid:
V
M
a
k
8
4-34
-0119
•0000180
16
6-10
•0167
179
32
8-65
•0238
182
64
12-09
•0333
179
128
16-99
•0468
179
256
23-82
•0656
180
512
32-20
•0914
180
1024
46 00
•1266
177
Fis the number of litres containing one gram-molecule,
fi the molecular conductivity (in mercury units), a the ratio
of this to the maximum, fi^ = 864. This maximum value
is calculated from the velocities of the acetic acid ion and
of hydrogen, determined by Kohlrausch from the con-
ductivity of sodium acetate and mineral acids.
If we have once determined the constant k for any
electrolyte, we can, by the help of the equation, calculate
its conductivity for any dilution.
This account of dissociation applies only to substances
which yield two ions, but similar expressions can be
deduced for other cases. Thus for a body which gives
three ions like BaCU or HaS04, the frequency with which
recombination will occur will be proportional to the cube
of the ionic concentration, so that we get for equilibrium
184 SOLUTION AND ELECTROLYSIS. [CH. XI
which leads to the equation
a^
and if a is small a^V V^k.
In the case of weak polybasic acids, succinic for example,
the dissociation at first obeys the law for monobasic acids,
and varies as the square root of the dilution. This shews
that the ions are H and HA^^ instead of H, H and A".
When about half the molecules are dissociated, some
generally begin to give rise to three ions, and the
variation with concentration gradually becomes normal.
In the case of strongly dissociated bodies the three ions
are always produced.
73. Dissociation of Mixed Solutions. Let us
consider, for the sake of example, two simple electrolytes
containing one ion in common. We get for our equations
of equilibrium
and C2 ^ = C2 'tt • w 9
where a is the fraction dissociated, and V the volume
containing one gram-molecule.
If we mix the two solutions, the volume becomes
Fi + Fg. The concentrations of the undecomposed por-
1 — ft 1 — ff-
tions become ^ ^ and ^ ^ . Those of the unlike
CH. Xl] THEORIES OF ELECTROLYSIS. 185
ions fall to -^f — ^5^ and -^ — tf > and that of the common
ion will be -^ — ^ . We thus get
r 1 + K J
^ !-«! ^/ Oi a, + «i
ana c, ,p^-j-^^ - c, prij^^^- T^+F;-
Dividing each of these into the corresponding equation of
the upper pair we get
y^^y. _ y^^y^ (r. + F,)a,
F, - F, • F,(a, + a,)
„r.H Zl±Zj-Zl±Z? T^i+^. (F. + F,) a,
F, ^ F, • F, • F,(a, + a.) '
r
Dividing the second of these equations by the first we
obtain
V," Vr OL,' " a," V, ^""^^^
so that, in order that no change in the number of free ions
should occur on mixing, the dissociated portions of two
electrolytes must be proportional to the dilutions.
The equation can also be written in the form
Y^ = Y^ -(SS).
which shews that the concentration of the ions must be
the same in both solutions.
The most important application of this piinciple is to
the case of two acids. In order that no change in the
states of dissociation should occur on mixing, it is necessary
186 SOLUTION AND ELECTROLYSIS. [CH. XI
that the concentration of the hydrogen ions should be the
same in both solutions. Such solutions were called by
Arrhenius^ isohydric.
Any two solutions, then, will so act on each other when
mixed that they become isohydric. Suppose we have one
very active acid like hydrochloric, in which dissociation is
nearly complete, and another like acetic, in which it is
very small. In order that the solutions of these should
be isohydric and the concentrations of the hydrogen ions
the same, we must have a very large quantity of the feebly
dissociated acetic acid, and a very small quantity of the
strongly dissociated hydrochloric, and in such proportions
alone will equilibrium be possible. This explains the
action of a strong acid on the salt of a weak acid.
Suppose we act on dilute sodium acetate with dilute
hydrochloric acid. Some acetic acid is formed, and this
process will go on till the solutions of the two acids are
isohydric: that is till the dissociated hydrogen ions are
in equilibrium with both. In order that this should hold,
we have seen that a considerable quantity of acetic acid
must be present, so that a considerable quantity of the
salt will be decomposed, the quantity being greater the
less the acid is dissociated. This "replacement" of a
" weak " acid by a " strong " one, is a matter of common
observation in the chemical laboratory.
Nemst ' has pointed out that it follows from this theory
that, when a salt is dissolved in the saturated solution of
^ M6m. pr^sent^ k TAcad. des Soienoes de Su^e le 6 Juin, 1883.
Account in B.A, Report, 1886, p. 357.
2 ZeiU. filr phynkdl. Chemie, 1888, iv. p. 372.
CH. Xl] THEORIES OF ELECTROLYSIS. 187
another slightly soluble salt, two principles must hold.
The quantity of undissociated salt with which the solution
is saturated must keep constant, and the product of the
numbers of the opposite ions in solution must also
keep constant. Thus, if \ and \' be the solubilities of
two salts in pure water, X and X' their solubilities when
both are present together, and «©> oio'j «> aiid a' the corre-
sponding values of the dissociation, we get
\,(l-Oo) = X(l-a)
Xo'(l-ao') = V(l-aO,
and from the second principle
Xo^ao* = Xa (Xa + XV)
V'Oo'' = XV (Xa + XV).
By means of these equations, the dissociation can be cal-
culated from the solubilities, and Noyes and Abbot ^ have
found that, in the cases of three slightly soluble salts of
thallium, it agrees with the value obtained from the con-
ductivity.
74. General case of Chemical Equilibrium.
Suppose we have four solutions of the substances AiBi,
A1B2, A2B1 and A2B2, so adjusted that solutions containing
a common ion are isohydric. Let a, 6, c and d be the
relative volumes in which, if the four solutions are mixed,
no change occurs, and let /3, y, S and ^ be the undissoci-
ated quantities of the four substances. Since we must
have, in all cases, equal concentration of the ions, the
dissociated quantities can be represented as ha, hb, he and
^ ZeiU. fUr physikal. Chemie, 1895, xvi. p. 125.
188 SOLUTION AND ELBCTBOLYSIS. [CH. XI
hd. The equations of dissociation of the solutions thus
become
/3 , fhaV 7 , /hb
-rrigf— J and ^ = A;4
hdy
d) '
or fi^k^h^ay y^k^h% S-k^h^c and l^^kji^d.
If the four volumes are mixed, new equations will hold
P _r. h(a-\-b)(a-\-c) .
a + b-^-c + d^ \a + b + c + dy '^^''"
which reduce to the form
^^ a + b + c + d
kji^ (6* + a6 + 6rf + ad) p
7= ^ 5 5 ^&a...
a + 6 + c+a
Dividing the corresponding equations by each other
we get fh)m each pair
ad = 6c (34),
from which we see that the products of the volumes of
such pairs of solutions as contain no common ion must be
equal to each other.
Now the volumes a, 6, c and d are proportional to the
active (or dissociated) portions of the four substances
present. Hence the values a, 6, c and d are equal to
aii>i, ^P2i «8?i and 04^2 respectively, where j^i, p^y q\
CH. Xl] THEORIES OP ELECTROLYSIS. 189
and ^2 represent the total quantities of the four substances
present We thus get from equation (84)
ai;>i . Ml = «2i^9 • «4?a (35).
This expression represents Guldberg and Waage's formula
for chemical equilibrium, which has been fully confirmed
by observation, and also shews that, as Ostwald has
observed, the constants ki and k^ in their equation
are made up of two fectors, each of which depends only on
the nature of one substance.
Many observed fiawts, before inexplicable, follow at
once from our equation. Thus the active portion of
slightly dissociated acids must be reduced by the presence
of their normal salts, which themselves famish a supply of
the same ions. Such mixtures are found to have less
activity than the amount of acid in them would possess
alone.
75. Thermal phenomena. The theory gives an
immediate explanation of Hess' law of thermoneutrality,
which expresses the fact that, in general, no heat change
occurs when two neutral salt solutions are mixed. Since
the salts, both before and after mixture, exist mainly as
dissociated ions, it is obvious that large thermal effects
can only appear when the state of dissociation of the
products is very different from that of the reagents.
Let us now consider the case of the neutralisation of a
base by an acid in the light of the dissociation theory.
In dilute solution, such substances as hydrochloric acid
190 SOLUTION AND ELECTROLYSIS. [CH. XI
and potash are almost completely dissociated, so that,
instead of representing the reaction as
HCl + KOH = KCl + H,0,
we must write
H + Cl + K + OH^K + Cl + H^O.
The ions K and CI suffer no change, but the hydrogen of
the acid and the hydroxyl (OH) of the potash unite to
form water, which is only very slightly dissociated. The
heat liberated, then, is almost exclusively that produced by
the formation of water from its ions. An exactly similar
process occurs when any strongly dissociated acid acts on
any strongly dissociated base, so that in all such cases the
heat evolution should be approadniately the same. This is
fully borne out by the experiments of Thomsen, who
found that the heat of neutralisation of one gram-
molecule of a strong base by an equivalent quantity
of a strong acid was nearly constant, and equal to 13700
or 13800 calories.
In the case of weaker acids, the dissociation of which
is less complete, divergences from this constant will occur,
for some of their molecules have to be separated into their
ions. For instance, sulphuric acid, which, in the fairly strong
solutions used by Thomsen, is only about half dissociated,
gives a higher value for the heat of neutralisation, so that
heat must be evolved when it is resolved into its ions.
The heat of formation of a substance from its ions is
of course very different from that evolved when it is made
from its elements in the usual way, since the energy
CH. Xl] THEORIES OP ELECTROLYSIS. 191
associated with an ion is different from that possessed by
the atoms of the element in their normal state. The heat
of neutralisation of weak acids can be represented, when
the resultant salt is highly dissociated, by
where A and B depend on the states of dissociation of the
acid and base respectively.
We can calculate the heat of formation of any substance
from its ions by applying the same thermo-dynamical
principles as in the case of vapour pressure or osmotic
pressure. Suppose we have an electrolyte which dissociates
into two ions. We have shewn (p. 180) that the equation
of equilibrium is
cp = c V
where p and q are the concentrations of the undissociated
molecules and of the ions respectively. Since the con-
centrations are proportional to their partial pressures,
we get, if ^ and q represent these pressures,
i-=zA-, = constant = K,
p c
We can now apply the thermo-djniamical equation (2)
already used on p. 33. It here takes the form
dhgeK _ 7
dt RT^
(36),
where 7 denotes the heat of formation of one gram-
molecule from its ions.
From experimental determinations of the temperature
192
SOLUTION AND ELECTROLYSIS.
[CH. XI
coefficient of dissociation of aqueous solutions, Arrhenius ^
has calculated the heats of formation of various molecules
from their ions by means of this equation. It is important
to observe that his results only apply to solutions in water.
Substance
7 at 21-5
y at 35°
Acetic acid CH.COOH
Propionic acid CgH^COOH
Butyric acid C H,COOH
Phosphoric acid HgPO^
Hydrofluoric acid HE
Hydrochloric acid HCl
Nitric acid HNO3
Soda NaOH
Potassium chloride KCl
Barium chloride BaCl,
Sodium butyrate CgHyCOONa
+ 28
- 183
- 427
-2103
-3200
- 386
- 557
- 935
-2458
-3549
-1080
-1362
-1292
- 362
- 307
+ 547
The numbers for strongly dissociated bodies are calcu-
lated from observations on decinormal solutions.
From this table, by adding to the heat of formation of
water from its ions that caused by the completion of the
dissociation of the acid, Arrhenius has calculated the total
heats of neutralisation of soda by different acids.
Substance
Calculated
Observed
Hydrochloric acid HCl
13447
13740
Hydrobromic „ HBr
13525
13750
Nitric „ HNO,
13550
13680
Acetic „ CHCOOH
13263
13400
Phosphoric „ HgPO^
14959
14830
Hydrofluoric „ HF
16320
16270
1 Zeits. fur phyHkal Chemie, 1889, iv. p. 96; 1892, ix. p. 339.
CH. XI] . THEORIES OF ELECTROLYSIS. 193
Thus the divergences from the constant value are
likewise explicable by this theory.
From equation (36) on page 191 it follows that, if the
heat of formation is negative, that is, the heat of dis-
sociation positive, the value of d log« Kjdt is also negative,
and the dissociation must become less with increasing
temperature. The conductivity is dependent on two
factors, (1) the dissociation, and (2) the frictional resist-
ance offered by the solution to the passage of an ion
through it. If we call the reciprocal of this resistance
the ionic fluidity of the solution, the molecular conduc-
tivity will be proportional to the dissociation and to the
ionic fluidity. At infinite dilution the dissociation is
complete, and the ions are so far apart that no change in
temperature can affect the state of dissociation. Any alter-
ation in conductivity with change of temperature must
then be due to an alteration in fluidity, and, therefore,
the temperature coefficient of fluidity can be determined
by measuring the temperature coefficient of conductivity
at a dilution so great that the molecular conductivity has
reached its limiting value. Now the table on page 192
shews that the heats of formation from the ions have
invariably a greater negative value at the higher tempe-
rature. From equation (36) it follows that the rate of
decrease of dissociation with increase of temperature must
therefore increase as the temperature rises. If the
temperature coefficient of fluidity either decreases with
rise of temperature, keeps constant, or increases more
slowly than the negative coefficient of dissociation, it
is clear that a maximum conductivity must be reached
w. s. 13
194 SOLUTION AND ELECTROLYSIS. [CH. XI
at a certain temperature, beyond which any further
heating will decrease the dissociation more than it
increases the fluidity, and so, on the whole, diminish the
conductivity.
Arrhenius calculated, from deductions from the equa*
tioh, that solutions of the two slightly dissociated
bodies, hypophosphoric and phosphoric acids, should have
maximum values for the conductivity at 57° and 78°^
respectively. He then experimentally determined their
conductivities at different temperatures, and actually
found maxima at 55° and 75°. More recently Sack^,
by measuring the conductivity of copper sulphate solu-
tions in closed vessels, found a maximum at 96° for a 0*64
per cent, solution. Calculation by Arrhenius* method
gives 99° for a solution of this concentration.
These results must be considered, not only as a
confirmation of the values found for the heat of formation
of molecules from their ions, but also as evidence in
fevour of the general ideas of the dissociation theory.
76. Difllision of Electrolsrtes in Solution. A
theory of the diffusion of dissolved substances has been
worked out by W. Nemst ' and M. Planck » on the lines of
the dissociation hypothesis. In our account of osmotic
pressure we shewed how the laws of the diffusion of
non-electroljrtes could be deduced. We have now to
1 Wied..Ann, 1S91, zuii. p. 212.
* Zeits. fur physikal Chemie, 1888, ii. p. 613, or Nemst's ** Theo-
retisohe Chemie."
s Wied, Ann, 1890, xl. p. 561.
CH. XI] . THEORIES OF ELECTROLYSIS. 195
extend the reasoning to cases in which free ions are
present.
If the osmotic pressure-gradient were the only driving
force, as in the first case, the different mobility of the two
ions (e.g. H and 01) would cause separation between them.
Thus suppose we had a solution of hydrochloric acid
in the bottom of a tall glass cylinder, with pure water
lying above it. The hydrogen ions travel faster than the
chlorine, and carry their positive charges with them,
leaving the lower layers negatively charged. Thus an
electrostatic force is set up, which prevents the process
of separation going far, and keeps the number of opposite
ions in each part of the system very nearly the same.
Nevertheless some separation does occur, and this
explains the fact that water, in contact with an aqueous
«
solution of an electrolyte, takes, with regard to it, a
positive or negative potential as the positive or negative
ion travels the faster.
The presence of a substance like ammonium chloride
will reduce the restraining force of the electrostatic
charges, and Arrhenius shewed that the addition of a
large quantity of this salt increased the diffusion of hydro-
chloric acid, which is chiefly due to the hydrogen, in the
ratio of 1 : 2*24.
In a layer of liquid in our cylinder, at a height x^
let the concentration (i.e. number of gram-molecules per
cubic centimetre) be c, and the osmotic pressure p. At a
height x-\-dx these become c — dc and p — dp respectively.
The volume of the layer cut off by horizontal planes at
these two heights is qdxj where q is the area of cross
13—2
196 SOLUTION AND ELECTBOLTSIS. [CH. XI
section, and it contains cqdx gram-molecules of electro-
lyte. The difference of pressure between the planes
is dp, so that the force acting on the layer is qdp, and the
force on one cram-molecule is - -/- . As we saw above
° c dx
(p. 139), Eohlrausch has calculated the mechanical force
required to move different ions with unit velocity through
dilute solutions. Let us call the velocities produced, when
unit force acts on one gram-equivalent of the two ions,
U and V respectively. The velocities, in our case, will be
U dp t V dp , ,
— -f- and — -^ , so that the amounts passmg across any-
cross section of the cylinder in a time dt are
^Uq^dtaJid^Vq^dt
If £7" is different from V, a difference of potential is set
up, the effect of which, when a steady state is reached, is
to make the ions travel together. If the potential gradient
is dPjdXy the numbers of the two ions which would cross,
under the action of this force alone, are
— Uqc -J- dt and + Vqc -r- dt
Under the action of both the osmotic and the electric
forces the nunibers of gram-equivalents which diffuse in a
given time are equal, so that we get
^=-tr,*(|+cf) = -F,*(|-cf)(S7),
or eliminating dPjdx
,„ WV dp,.
CH. Xl]
THEORIES OF ELECTROLYSIS.
197
From the law of osmotic pressure
p = cRT,
since c is the reciprocal of the volume in which one
gram-molecule is dissolved,
:. dN- - rf — Tr^Tq -j- dt
u+ V ^ doc
Comparing this with the corresponding equation (7),
p. 47, for non-electrolytes
dN^^Dq^dt,
we see that for electrolytes the diffusion constant is
D^
RT.
The following table gives a comparison between the
observed and calculated values of D, the unit of time
being the day.
Substance
D observed
D oaloolated
Hydrochloric acid HCl
Nitric acid HNO3
Potash KOH
Soda NaOH
Sodium chloride NaCl
„ nitrate NaNO
„ formate NaCOOK
„ acetate NaCH COj
Ammonium chloride NH^Cl
Potassium nitrate KNO,
2-30
2-22
1-85
1-40
Ml
1-03
0-95
0-78
1-33
1-30
2-49
2-27
2-10
1.45
M2
106
0-96
0-79
1-44 .
1-38
77. Contact Difference of Potential. We have
already mentioned that the differences of potential
P,-P. = i22'^^log.g (38).
198 SOLUTION AND ELECTROLYSIS. [Cfl. XI
between liquids can be explained by the initial sepa-
ration between the ions. Taking equation (37), which
expresses the relation which must hold between the
potential difference and the osmotic pressure in order that
no cumulative separation of ions should go on, we get
dP^l V-U dp
cUc c V+ Udx*
or, since p = cRT,
dP^RT V^U dp
dx p V+Udx*
which gives on integration
V-U
lofir^
Pi
If we have absolutely pure water in contact with a solu-
tion, pi is zero, and the difference of potential apparently
becomes infinite. But absolutely pure water cannot be
obtained, and, as a matter of &ct, great differences in
the electromotive force are found for small differences in
purity.
In a similar way the potential difference between the
solutions of two different electrolytes or between solutions
of the same electrolyte of different concentrations can be
calculated. This is of great interest, for primary cells
can be constructed with a plate of the same metal for
both electrodes, by placing the electrodes in solutions
of different substances, or even in solutions of the same
substance at different concentrations. The theory de-
scribed above can be applied to deduce the electromotive
force of such cells by slightly modifying the equation.
CH. XI]
THEORIES OF ELECTROLYSIS.
199
The following table ^ gives a comparison between the
observed and calculated values for the potential differ-
ences between solutions of different concentrations.
Electrolyte
Ci
C,
E in volts
(observed)
E in volts
(calculated)
HCI
0-105
00180
0-0710
0-0717
>>
0-1
0-01
0-0926
0-0939
HBr
0-126
0-0132
0-0932
0-0917
KOI
0-125
0-0125
0532
0-0542
NaCl
0125
0-0125
0-0402
0-0408
liCl
01
0-01
00354
0-0336
NH^Cl
0-1
.0-01
0-0546
0-0531
NaBr
0-125
0-0125
0-0417
0-0404
NaO,C4i.
0-125
00125
0-066
0-0604
NaOH
0-235
0-030
0-0178
0-0183
NHOH
0-305
0-032
0-024
0-0188
KOH
0-1
0-01
00348
0-0298
The dissociation theory thus gives a perfectly satis-
factory explanation of the diffusion of electrolytes in
solution, and of the differences in potential at the
junctions of electrolytes.
The difference of potential between metals and elec-
trolytes is explained in a similar manner. Nernst supposes
that each metal in contact with an electrolyte has a
definite solution pressure, analogous to the vapour pressure
of a liquid, in consequence of which ions are detached
from it, and go into solution, carrying their charges with
them, and leaving the metal oppositely electrified. An
^ W. Kemst. ZeiU.fUrphynkaL Chemie, 18S9, iv. p. 161.
200 SOLUTION AND ELECTROLTSIS. [CH. XI
equation similax to (38) can be deduced for this case, and
takes the form
e^RTloge-^ (89),
where p represents the osmotic pressure of the ions of the
metal in the solution, and P the solution pressure of the
metal of the electrode. The electromotive force of a
voltaic cell will be given by
^ = iJ2'(log,g-log,|') (40).
and thus depends on the differences between the solution
pressures of the two electrodes. When a current passes,
the ions of the metal with the smaller solution pressure
are forced out of solution by the others, and deposited at
the electrode.
The electromotive force of the cell
Ag I 01 normal AgNOs I I'O normal KCl with AgCl | Ag
in which silver electrodes are placed, one in silver nitrate,
and the other in silver chloride and potassium chloride,
was calculated by Nemst from this equation to be 0*52
volt, and observed by Ostwald to be 0*51 volt.
78. Diuociation of Water. Eohlrausch's ex-
periments have shewn that the conductivity of pure water
is exceedingly small, so that it can only be dissociated to
a very slight extent. But this is only what we should
expect, for the concentration is so great and the molecules
are so. crowded together that no dissociation can be per-
manent. Nevertheless, there are many indications that
even chemically pure water would, if it , could be pre-
CH. XI] . THEORIES OF ELECTROLYSIS. 201
pared, be slightly dissociated and possess some conducting
power.
Methyl acetate and water react to form methyl alcohol
and acetic acid at a rate proportional to the number of
hydrogen ions or hydroxyl ions present in the solution.
Wijs* used this reaction to measure the dissociation of
water, by preparing an aqueous solution of methyl acetate
carefully freed from acid or other impurity, and titrating
it at intervals with standard alkali to measure the amount
of acetic acid produced. The acid, as it is formed, accele-
rates this action, so that it is necessary to measure the
rate of transformation just at the beginning. The con-
centration of the dissociated ions appeared to be about
10"^ gram equivalents per litre.
If two platinum or palladium electrodes, saturated with
hydrogen, be placed, one in acid and the other in alkali,
.an electromotive force is set up between them, depending
on the concentration of the hydrogen ions in the acid and
of the hydroxyl ions in the alkali. From the laws of
osmotic pressure Ostwald' has developed a theory of this
relation, and from the observed electromotive forces has
calculated that the concentration of the hydroxyl (and
therefore also of the hydrogen) ions in pure water is
0-9 X 10^.
Kohlrausch and Heydweiler* have distilled water in a
vacuum and collected it in a glass vessel, which for ten
years had been kept full of distilled water in order to dis-
1 Zeits. far physikal. Chemie, 1893, 11, p. 492.
a Ibid,, 1893, 11, p. 621.
s Wied. Ann., 1894, 53, p. 209.
202 SOLUTION AND ELECTROLYSIS. [CH. XI
solve out all the soluble constituents of the glass. By this
means they obtained water so pure that its conductivity
was 001 4 X 10-" at 0^ and 01 8 x 10"" at 18^ Now
the temperature coeflScient of conductivity depends on the
influence of temperature on (1) the dissociation, and (2) the
fluidity (p. 193). As the dilution increases and the dis-
sociation becomes more complete, the effect of temperature
on the dissociation gets less, and finally vanishes when
the dilution is infinite, i.e. when the water is pure. The
temperature coefficient then reaches a limit corresponding
to its value for the fluidity alone. The conductivity, when
this limit is reached, is, therefore, the conductivity of pure
water. The limiting value can be estimated from a curve
drawn to shew the variation of temperature coefficient
with increasing dilution. The true conductivity of pure
water was thus estimated as 0*036 x 10""" at 18°. This
gives for the concentration of the dissociated ions a value,
of 8 X 10""^ gram equivalents per litre.
We should expect the dissociation of the water to
become greater as the amount of dissolved substance
increased, and gave room for the ions to separate, and the
fact that insoluble magnesium hydroxide is formed when a
current is passed across the junction between strong and
weak solutions of magnesium chloride, has been adduced
as evidence that part of the current is carried by the
water.
Attempts have, however, been made to explain this
phenomenon by supposing that the hydrolytic dissoci-
ation
MgCl, + 2H,0 = Mg(OH), + 2HC1
J
CH. XI] THEORIES OF ELECTROLYSIS. 203
takes place as well as the. electrolytic dissociation
MgCU = Mg" + CI + CI,
but it is difficult to see, on this hj^othesis, how it is that
Mg(0H)2 only appears at the junction.
It is interesting to observe that liquefied hydrochloric
acid gas, like pure water, is a very bad conductor, while
mixtures of the two conduct freely. Possibly no pure sub-
stance is an electrolyte, and mixture may be an essential
condition for electrolytic conduction, though, if this is so, the
conductivity of fused salts needs some further explanation.
79. Function of the Solvent. In the early de-
velopment of the physical theory of solution no attention
was paid to the part played by the solvent. It was looked
on simply as furnishing a space into which the dissolving
solid could diffuse, and, in the case of electrolytes, as
providing a screen for separating the ions from one
another. The very dififerent power of various solvents,
both in dissolving substances and in enabling them to
conduct electricity when dissolved, directed attention to
the general question of their influence, and measurements
of conductivity of the same salt in water and alcohol were
made by Fitzpatrick*, VoUmer* and others.
The problem of the cause of solubility still remains
unsolved. It is possible that it may depend on similarity
in molecular motion on the part of solvent and substance
dissolved, and this view is supported by the general rule
that bodies are more soluble in liquids whose chemical con-
1 B,A. Report, 1SS6, p. 828, and Phil. Mag,, 1887, 24, p. 878.
2 Wied, Ann., 1894, 52, p. 828.
204
SOLUTION AND ELECTROLYSIS.
[CH. XI
©
®
Fig. 20.
stitution is similar to their own. Thus salts and mineral
acids are usually soluble in water, while organic bodies will
generally more readily dissolve in alcohol or benzene.
Towards the explanation of ionisation power some ad-
vance has been made. If the forces holding
the ions together in a molecule are electrical
in their nature (as is quite possible) it follows,
as J. J. Thomson^ has shewn, that they will be
much weakened by immersing the molecule
in a medium of high specific inductive capacity
like water. The nature of this effect can be
best explained by considering the influence of
a mass of conducting material placed near
two little particles charged with opposite kinds
of (electricity. The efifect of the conductor can be repre-
sented by supposing that electrical images of opposite
sign are formed just inside the conductor. The result is
obviously to reduce the external efifects of the charges
and, therefore, their attraction for each other. The effect
of an insulator of high specific inductive capacity is
similar in kind, though rather less in magnitude. This
may explain the differences observed in the molecular
conductivities of the same salt dissolved in different
solvents, such as water and alcohol for example, for other
conditions being the same, the effect of solvents in
loosening the connexion between two ions, i.e. their
relative ionisation powers, will be proportional to their
specific inductive capacities. Some figures which, as far
as they go, confirm this idea for solutions of calcium
1 PML Mag,, 1898, 86, p. 820.
CH, Xl] THEORIES OF ELECTROLYSIS. 205
chloride in water, methyl alcohol, and ethyl alcohol have
been given by the present writer\
The specific inductive capacities of the three solvents
are, according to Tereschin : water, 83*7 : methyl alcohol,
32'65 : ethyl alcohol, 25*8. If we suppose provisionally
that the resistances ofifered by these solvents to the motion
of the ions are in about the same ratios as their viscosities,
we must divide these numbers by 100, 63 and 120,
respectively. We then get for the theoretical ratio of the
conductivities.
Water 100 Methyl Alcohol 63 Ethyl Alcohol 26.
An investigation by VoUmer shewed that, for many
salts, the ratio of the conductivities in the three solvents
was
Water 100 Methyl Alcohol 73 Ethyl Alcohol 34.
It seems probable, then, that the specific inductive
capacity and the viscosity are important factors in deter-
mining the " relative ionisation power " of solvents.
It is worthy of remark that, as well as reducing the
forces between ions, the conducting body in figure 20 will
attract each ion to itself. The same thing would occur in
a solvent of high specific inductive capacity. When the
forces between two ions have been loosened, a slight
collision with other molecules, or with molecules of the
solvent, will suffice to cause dissociation, the liberated
ions will be annexed by the solvent, and loose compounds
will be formed. The ions, being readily passed on from
one particle of the solvent to another, are able to work
1 Phil, Mag,, 1894, 38, p. 892.
206 SOLUTION AND ELECTROLYSIS. [CH. XI
their way through the liquid under the action of the
external electric forces.
If this theory represents the truth, we have three
things, all of which may produce osmotic pressure effects.
Firstly, the molecular and ionic impacts, secondly, chemical
action between the unaltered molecules and the solvent,
and, thirdly, combination between the ions and the solvent.
In solutions of indifferent substances, and in very dilute
solutions of most electrolytes, the first cause. is probably
the only one of importance, but in other cases all three
may ultimately have to be considered. The fact that,
according to the thermodynamical equation on p. 191, heat
is in most cases developed when a molecule dissolved in
water is resolved into its ions, again suggests that com-
pounds between the ions and the solvent are formed. It
is evident that such combination, provided the ions were
free to move from particle to particle, would not prevent
them from producing their proper osmotic pressure and
electrical effects, and that they would behave, for all the
other purposes of the theory, as free ions should.
80. Hydrate Theory of Ck>lution. The question
of chemical combination with the solvent has given rise
to considerable discussion, and produced an independent
theory of solution.
Before ^the laws of osmotic pressure and the allied
phenomena were known, it was very generally held that
solution was a case of chemical combination^ Chemical
attraction of the solvent for the substance dissolved would
I See Tilden, B,A. Report, 1886, p. 444.
CH. Xl] THEORIES OF ELECTROLYSIS. 207
explain the existence of osmotic pressure, but gives no
reason why it should have the particular value given by
the same amount of substance in the gaseous state. In
the case of dilute solutions of indifferent substances, it has,
therefore, been very generally allowed that the chief cause
of osmotic pressure is molecular impacts, but the influence
of the solvent is recognised in equation (16) on page
69, and becomes sensible as the concentration increases.
It was soon noticed, however, that bodies giving abnormal
values for the osmotic pressure and acting as electrolytes,
are just those for which the evidence of chemical action
is strongest. This suggests the idea that chemical action
is the condition necessary for ionisation, and that the
foimation of complex molecules, from which individual
ions could be more easily removed by collision with other
aggregates, is the meaning of conductivity.
Theories of solution based on these ideas have been
recently framed by H. E. Armstrong^ S. U. Pickering^
and others. Pickering supposes that, when solvent is
frozen out, some of the existing hydrate is decomposed,
and the next lower one formed. From the heats of dilu-
tion of solutions of sulphuric acid of different strengths,
he calculates the work required to do this, and, adding
it to that required to compress the molecules dissolved,
deduces the lowering of fi'eezing-point". The agreement
of his numbers with observation shews that the excess of
freezing-point depression can be calculated from the heat
1 Proc, B,S., 1886, No. 243.
^ For general account see Watts* Diet. Art. Solutions, n.
» B.A. Report, 1890, p. 320.
208 SOLUTION AND ELECTROLYSIS. [CH. XI
of dilution, but does not decide whether that heat of dilu-
tion is due to the combination with additional molecules
of water or (partly at any rate) to the resolution of some
sulphuric acid molecules into their ions.
Pickering's main argument for the existence of hydrates
in solution is based on the sudden changes in curvature,
first noticed by Mendel^eff, which appear in the lines
drawn to represent the variation of some phjrsical property
with the concentration. Pickering has made, for instance,
a long and careful determination of the densities of
sulphuric acid solutions of different strengths, and drawn
a curve to shew his results. Changes of curvature appear
at points corresponding to definite molecular proportions
(e.g. H2SO4 . HjO and H2SO44H2O). These changes can
be more readily seen if a new curve is drawn between the
concentration and the rate of change of density with
concentration (i.e. the tangents at different points of the
first curve). By this process of " differentiation " a series
of straight lines is obtained with breaks at the positions
where, in the first curve, changes of curvature appeared.
Similar figures were drawn for the electric conductivity,
expansion by heat, contraction on formation, heat of dis-
solution, heat capacity, refractive index, magnetic rotation
and freezing-point, and changes of curvature were found
at the same points for all. Ostwald however says* that
the position of the breaks alters with change of tempera-
ture. With weak solutions it is impossible to say whether
the points correspond to definite molecular proportions,
owing to the smallness of the change in percentage
1 Watts* Diet, Art Solutions, i.
CH. Xl] THEORIES OF ELECTROLYSIS. 209
composition which would be caused by the addition of
another water molecule to H3SO4, but the changes are of
precisely the same character as in the case of stronger
solutions, and are, apparently, due to the same cause. The
thermal change, resulting from dilution of a strong solu-
tion. is of the same aign as that obtained by dissolving the
solid in the first instance, and this also indicates that, if
hydrates are present in concentrated, they are also present
in dilute solutions. If we allow this, it follows that one
acid molecule is able to combine with, or at all events, to
influence in some way, an enormous number of water
molecules, and this is confirmed by other facts. For
instance, the volume of substances in solution, as calcu-
lated by subtracting the volume of the water from the
volume of the solution, is in general smaller than its
volume in the solid state, and in some cases even comes
out negative, shewing that the water has been compressed.
This is shewn by the table on page 175. Even clearer
evidence is furnished by the table of thermal capacities
given on page 178. If we call the product of the specific
heat and the molecular weight the molecular heat of the
compound, it is sometimes found that the molecular heat
of the solution is less than that of the water actually
present. Thus the molecular heat of the solution
NaN08 + 25H20 is 461*7, but, if 25HaO more water be
added, the molecular heat is not 461*7 + (25 x 18) = 911*7
but 904 ; again, if SOHjO is added to this, the molecular
heat is not 911*7 + 900 = 1811*7 but 1791, and so on\ It
is very improbable that the salt should so greatly reduce
1 Tilden, B.A. Report, 1886, p. 455.
w. s. 14
210 SOLUTION AND ELECTROLYSIS. [CH. XI
the heat capacity of a few molecules that the average
capacity of the whole is lowered by as much as this, so
that it seems necessary to suppose that the whole, or at
all events a large part, of the added water is affected. It
has also been argued that the diminution of vapour pres-
sure is a proof that no water exists free from the influence
of the salt, for, if it did, the evaporation, though it might
proceed more slowly at first, would eventually reach the
same amount as in the case of pure water.
Several hydrates, before unknown, were indicated by
the presence of these breaks, and subsequently obtained
in the solid form. Thus Pickering isolated H2SO4 . 4H2O,
HBr.SHaO, HBr.4HA HC1.3HA HNO,.HaO and
HNO, . 3HaO. He considers that the crystallization of a
definite hydrate is strong evidence that it exists in solu-
tion, for bodies suddenly formed at the instant of
precipitation come down as amorphous substances — a
common observation in the processes of chemical analysis.
Dilute sulphuric acid, dissolved in acetic acid, produces a
smaller depression of the freezing point than the sum
of those due to the acid and water separately, hence
Pickering argues that no dissociation, but rather chemical
union, resulting in a reduction in the number of molecules,
has occurred.
Since the state of bodies in solution is similar to their
state when gasified, a solid has to be not only liquefied
but also vapourised when being dissolved If allowance be
made for the heat necessary to effect these changes, it is
found that the process of solution, in every case, evolves
heat, which indicates that chemical action has taken place.
CH. Xl] THEORIES OF ELECTROLYSIS. 211
Pickering supposes that the combination of large
numbers of solvent molecules with one molecule of a
body in solution is produced by a sort of induction of
electric charges, just as a number of soft iron rods placed
in a row can be made to cling together by bringing a
magnet near the one at the end. Since the forces are
equal in all directions, the mobility of the dissolved
molecules is secured. Certain definite numbers of solvent
molecules will be capable of more symmetrical arrange-
ment than others, and will form hydrates, but their parts
are freely interchangeable with each other. A dissolved
molecule will be able to pass through a crevasse only
when the number of solvent molecules requisite to keep it
in solution can pass simultaneously, and this may explain
the action of semipermeable membranes. Pickering^ found
that, when a mixture of alcohol and water was placed in a
porous pot, and the whole immersed either in pure water
or pure alcohol, the volume of liquid inside the porous pot
increased, shewing that the phenomenon is due, not to the
impermeability of the pot to either constituent alone, but
to its impermeability to the solution as a whole.
81. Conclusion. We are now able, I think, by
an extension of these ideas, to reconcile Pickering s obser-
vations with the dissociation theory. Since each particle
of the salt extends its influence over a considerable region
round it, the properties of the solution as a whole will
depend on its percentage composition, and may quite
probably undergo some change as the composition passes
^ Ber, DmU Chem, Qes., 1S91, 24, p. 3689.
14—2
212 SOLUTION AND ELECTROLYSIS. [CH. XI
through a value corresponding to simple molecular pro-
portions. This will be independent of the arrangement of
the parts of the salt molecule, since the influence of each
part extends beyond its immediate neighbourhood, and
dissociation into ions can still take place. We can, in
fact, regard a considerable mass of the solution, containing,
perhaps, several molecules and dissociated ions of salt, and
hundreds of molecules of solvent, as chemically one large
molecule, the parts of which are nevertheless to some^
extent physically independent of each other.
The phenomena of supersaturation and the conditions
of equilibrium which hold between solids and solutions in
contact with them (see pp. 18 to 25) indicate that it does
not follow, because a certain hydrate or other compound is
precipitated from a liquid on evaporation or cooling, that
it therefore exists in the same state of molecular aggrega-
tion in the solution. But the adjustment of the chemical
forces, which allows such a hydrate to be formed under
proper conditions, makes it quite likely that, when the
composition of the solution as a whole is the same as
that of the hydrate, the fact should, by reason of the far-
reaching influence of the chemical forces, become apparent
in the physical properties. This at once explains how it
happens that several of the hydrates, indicated by breaks
in the solution diagrams, have actually been separated out
as solids in the crystalline form. In fact, all the evidence
which has been accumulated in favour of the existence of
hydrates in solution, can be accoimted for on this hypo-
thesis, which at the same time allows us fully to accept
the dissociation theory.
APPENDIX.
Freesing points. While this book was passing
through the press, a paper by Nemst and Abegg* ap-
peared, calling attention to the discrepancies which exist
between the values obtained by different observers for the
molecular depression of the freezing point. For instance,
the following numbers have been obtained in the case of
a one per cent, sugar solution in water: Raoult, 2*07;
Arrhenius, 2*02; Pickering, 201; Jones, 2*18; Loomis,
1-81.
Nemst and Abegg point out that the observed sta-
tionary temperature may not always give the true freezing
point, at which liquid and solid can exist together in equili-
brium. A mass of a partly frozen liquid, uninfluenced by
its surroundings, will tend to assume the temperature of
the true freezing point. But a limited volume of liquid,
radiating to an outer enclosure, tends to reach a "con-
vergence " temperature, which depends on the amount of
heat evolved by stirring and on the temperature of the
enclosure; and, unless this convergence temperature
coincides with the freezing pointy or unless the rate of
approach to the freezing point is very great compared
1 ZHU.farphysikal Chemie, 1894, 16. 7, 681.
214 APPENDIX.
with the rate of approach to the convergence temperature,
the thermometer will not shew the true freezing point.
The necessary corrections can be experimentally de-
termined, and Nemst and Abegg obtained good agreement
between the results of experiments performed imder
conditions so diflferent, that the uncorrected numbers for
the molecular depression of the freezing point of a one
per cent, solution of sugar varied from 1*6 to 2*1. Their
mean corrected value is about 1*86 — a number which
agrees exactly with that calculated from the melting
point and heat of fusion of ice (p. 56).
TABLE OF ELECTRO-CHEMICAL PROPERTIES
OF AQUEOUS SOLUTIONS,
COMPILED BY THB
Rev. T. 0. FITZPATRIOK, M.A,
Fellow of Ghbist's College, Gambbidoe,
wnd R&prvnJted^ by permission, from the Report of the
British Association for the Advancement of Science.
The comparison of the numerical results of electrolytic
observations is rendered difficult from the fact that the data are
scattered in various periodicals and expressed by different
observers in units that are not comparable without considerable
labour. The following table has been compiled with the object
of facilitating the comparison.
In the table are included all the observations, as far as they
are known to the compiler, for the metallic salts and mineral
acids; but amongst the solutions of organic substances are not
given all those for which Ostwald has made observations, as it
was thought that they would add unnecessarily to the size of the
table. Observations for a number of additional substances will
be found in Ostwald's papers in the Journal /iir Chemie, vols,
xxxi., xxxii., and xxxiii., and in the Zeitschri/t fii/r physi-
kalische Chemie, vol. i. With this restriction it is hoped that
no important observations have been omitted, and that, in the
reduction of results, expressed in such varied units, the table
is sufficiently free from mistakes for it to be of service. The
data included refer to the strength and specific gravity of
solutions, with the corresponding conductivities, migration con-
stants, and fluidities. The several columns are as follows : —
216 SOLUTION AND ELECTROLYSIS.
I. Percentage composition, i,e. the number of parts by
weight of the salt (as represented by the chemical formula) in
100 parts of the solution.
II. The number of gramme molecules per litre, ue, the
number of grammes of the salt per litre divided by the chemical
equivalent in grammes, as given for each salt.
III. The specific gravities of the solutions: in most cases
the specific gravities of the solutions are not given by the
observers, and the numbers given have been deduced from
Gerlach's tables in the Zeitsclvrift fur cmailytische Chemie, vol.
viiL p. 243, &c,
lY. The temperatures at which the solutions have the
specific gravities given in the previous column for the given
strength of solution.
V. The conductivity, as expressed by the observer. In the
cases in which the observer has expressed his results for specific
molecular conductivity no numbers are given in this column.
VI. The temperature at which the conductivities of the
solutions have been determined.
VII. The temperature coefficient referred to the conductivity
^' i«°' - i (%) •
VIII. The specific molecular conductivity of the solutions
at 18*^ in terms of the conductivity of mercury at 0* ; the specific
molecular conductivity is the conductivity of a column of the
Hquid 1 centimetre long and 1 square centimetre in section,
divided by the number of gramme equivalents per litre.
In some few cases, in which no temperature coefi&cients have
been determined, the results have been given for the temperature
at which the observations were made.
The numbers given in the column are the values for the
specific molecular conductivity x 10*.
TABLE OF ELECTRO-CHEMICAL PEOPEHTIES. 217
IX. This column contains the values for specific molecular
conductivity at 18° in c.g.s. units: they are obtained from
those in the previous column by being multiplied by the value
of the conductivity of mercury at 0** in CG.s. units. This factor
is 1-063 X 10-». '
X. The migration constant for the anion ; for instance, in
the case of copper sulphate (CuSO^), for (SO4).
XI. The temperatures at which the migration constants
have been determined.
XII. The number of gramme molecules per Htre, as defined
for column II., for which the fluidity data are given in the
following columns.
XIII. The fluidity of the solutions of the strength given in
the previous column.
Most of the results given for the fluidity of solutions are
expressed in terms of the fluidity of water at the same tem-
perature: to obtain the absolute values for the solutions they
have been multiplied by the value for the fluidity of water at
the given temperature. The values used for this purpose have
been taken from Sprung's observations for the viscosity of water
given in Poggendorff*8 AnncUen, vol. clix. p. 1.
To obtain the values for fluidity in co.s. units, the numbers
in this column must be multiplied by the factor *1019.
XIV. The temperature at which the solutions have the
fluidity given in the previous column.
XY. The temperature coefficient of fluidity at IS**, that is,
XVI. In the last column are given the references to the
various papers from which the data are taken : against each
reference will be found a number, which appears also against the
first of the data which have been taken - from the paper in
question.
TTBOLYSIS.
I
I I
1 I
I I
I I
I I
l?l I
»0 . O Ov
OS ^ »«
N « M
On
a-i ga-
ll I I
» I 0000
I I
« • • •
Ov« -^ «
I I I I I I I I I II
I I I I M I I III
I I I I I I I I I M
I II M I I I I I I
II I M I I M I I
I I I I M I I III
I I I I I I 11 I I I I I
I I II I I I I I I I I I
00
lO »0 «0 »0 tn «A V) iO U3 «0 «A «Q
C4>0>0 lOMSO W t-tiN o ''l^
I
00 00
OOOOQO
I I I I I I I II I 1 1
to
II I I I I M I ill
~ « "^•00 t^»o
O'So p
M « P0«0 O
NH M -^ 0\0
§§§f8
500. 10 »iN M M3
• • • •
88ss^::
V5
f4 «OOO0 ^n
M W « fC
• • •
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
219
N « *
a2
a
«
Ol
8»P
^
w
•
p«
I
•
i
^H
•k
o
0)
;>
hS
•
^i9
"^
1
s
80S
I
II 1 1 1 1 1
II II I II
II 1 1 1 1 1
II 1 1 I I I
II Mill
II I I I II
I
w OS
I I I I I I I I I I l^f I I I I I I I I I I
I I I I I I SSS8SS I SSSSS SIM
II II II I
SnonSncScSos I cScScScKos on I I I
I II I II I rr«P^?l"?a|fy,p
I I
I ;: I I I I I I I M I I I I i I I I I I I I I I
■H
1 II I
II I I II iSl I lSll.S.1 MM
I I I
I I I
I I I
I I I
I I
I I I
f^ w^ ro ^*0 *^
SS5
fTitfi
N M NO lOiO'^^frsS M -g « «« N c* « N « « M MM^0l*^l loo wS^mO ONONO
« s ^
B S 3358l^2^2^^?2*8?^l 3sl I <S I I I I I I i I
lO OS PO On ''too -^
I I OnnO nOO pO«^5
I 1 rc fO fO w w "^ O
W^ KJ f^ P^ tfi Cfi ff^
II 1 II II II
«A«0 00 00 CO 00 CO 00 00
ON OS VO « -^nO m*>.PO
• • ♦»•••••
O «^ W v>0 Q QOO "^
oQ a
CD 5
o O
-a
•I
1^
M II II II ip II l|if llf- I II II I M
00 00 00 00 00 00 00 00 00 00 00 00 00 00 I CO I I 00 00 00 00 00 00 00 00 00
— ^-
(4Mopopop
I I II II I II I II II II M I -2J?8'8.=»«^
M N t/3(
M e*
I I I I u)iotO
I I II I II
«
I I I I lOMJiOl'OO •^^'O
I I I I M M M t>%M -^M 1^
lO «0 «0 «A I'd vo
ooo o
1 1 \\m
II II II II I II 888??2 = ? I I
OnOOQ «^t« OS
€
„|o pppPr«y5
M f4\Q
• • f • » •
p p r y^r^P ?^!^p
K- M « PO
O P 1^ e*
lOO O O
• • • •
PP »-• « "*OnOO
'^aqo^
5^^
'*>0
O C O <-< -^ *>• •^ "T '^ "^ « PO t^^P5 _
O C O O O O *^ :?*>•« *^'^'*'^«*^ Qt^'^rOQ'^PC
r»»s^rtrr,* «'• • • • • « • 9 r » • • • • •
**5»0*>»fO*>»ON
M po-«>»pOOn
220
SOLXmON AND BLECTBOLTSI&
»5 8 *« too
It,- ■§!
I I I I I I
o I I I I I I
I I I I I I
OS
I 1 I I I I
i ^:o I I 1 1 1 1
i . I I I I I I
s ^
3 s
«
^ COM N«MW f^f^MMM
I 1
I ^mi
>o M N ooo
hS o''*'' poooo
&-i
&
****** fill!
o I I I I i:? I I i I I
..is ^
1^ -e
'i l-i
g-^
8«.:
8 Pt
.r*P
O
1 1 1 1 1 1 1 1 1 1 1 fits 1 1
I I I I I 18888 18888 18
I I I I I I l?8i I l?^5t 1 1
<0«0
I i I
o
e
•^ I I ! I I I'T'^
a
S 1 I I I I I I I I I I I I I I I I
§ I I I I I I I I I I I I itl^l^ls
Q O •-• O O 0\0<85 •O'*© 5>.2> I ^ o
2 I I I I I I I I l|l I I if if
$3 00 00 00 00 00 00 00 00 00 00 00 00 00 I 00 I 00
I
I I I I I I I I I ! I I I I I I I
I I I I I I I I I I I f 9 9 9<f 9<f> Pf 9
I 1 1
I I
I I !
I I i
iS
«« "5 i
p ' p
Qo I oe
I I I
I I I I 18 I I I I I
I I I I I I I I I I I
%
9
.»«
M M
i 11 ? U.9
row) o w) urd m
P P - MM)^© p ^p ^p
M U)
M M tfi\0
O M M i2)M ffj O M M f^ff)
oppo^M oopo>^
PPPi??'p'i?'^f^!^jff^'8>i
N fn«««^ wj
TABLE OF ELBCTRO-CHiailCAL PROPERTIES. 221
1^1
tQ V «B *
Kg-
^ Is
INI 1 1 1 1 1 1
Mil 1 1 1 1 1 1
MM II M M
MM 1 MM
1 II 1 MM 1
MM II 1 II 1
5
is
Id ^
«2!
?«* •!
"i&'i
-^^
|1 |l JSl
do
O <
I OSON «4 M M o o o
CON « « « «
II I I CO w w w w p«
III M M M M f4 e«
III PPPP9P
00000000 OOOOOOQOOOOO
OsudO O
• • • •
O W "^^
II II II
•I
I
1 1 1 ifffi II II II 1 i II II II II
1 1 888 118 II 88888 II II 1 II
llllMsillill^iJ^MMI II
1 1 1 \Hh Ipl ifs'lfy.pl MM II
Ml MM 1 1 11 1 M 1 M 11 1 II
II II II 1 11 1 1 l|l|i|l|ltl 1 1
Hf?85 sSlys? S-llryf^S-S^S'S&SlSNlllKI-S.I* §J
w^ ^^ ^^ V^ ^^ ^^ ^^ ^"^ ^^ hrf ^^J NN 1*4 Vb4 ^14 N^l NN ^4 k^ ki4 P^
risfss*'^'^"
ll*|K|f ll.l'l s<?
(2 s
I
I
II II I II iifii II li i1 i|i| II
00 00 00 00 00 00 00 00 00 00 00 00 i 00 I 00 I 00 I 00 I 00 0000
li I M II II 1! II II I II 11 II 3,^
o o o p
i 1 1 1 1 1
I I I I I I I I I I 99'99:*'9t*9'9999 99
I I I I I I 1 I I I «oMS«o«ot>.M>o v:oo «oro«o *^*n
M M M M
I II II I
w «oo
•*ri
^.00 t^C
N-O «
«
1*3
5 e !f3'i
NK.-^
^
•
i*i
????
1 M frj
O »^ « w;^ O *^ Q to t— w OS
« to
II II II II I I888888S>|'=:^ 88
M M
O O O O O 1^ P01O1O O M vO t^ sO N
OpOOppOpOMN^ iCOO p 00 O "^ o o ^
»^ « erj"^i«
*?i>o pQtp
• • • •
00 »op ffi^f
00 «^^ >0
»0"^ «noo »^"^ »«
Q hq ff) lO M 1C00 *>» M »o W)
8 8 8 8 8 o ^p'^s^fo^^Sovo ^K.pc>o
M M M ci
222
SOLUTION AND ELECTROLYSIS.
•is •
•1-8 a
I
Si
I
g
§
V5
I
I
o
E
E
I
i 1 1 1 1 1 1 1 1 1
1 i 1 i 1 1 Ml
1 1 1 1 1 1 i 1 1
1 1 1 1 I 1 II
oil 1 1 1 II 1 1
1 1 1 1 1 1 1 III
H
O O 0^0\ O O 0\
8v%
I I I I I I
CO
OOO
1 1
1 1 1 1 1 1
pop
o'5'S
M M ft M f4 N
00 00 00
^ M F^
sO O tcM^^ •^ O O
• • •••••• lit
99
I I I I iS, III
99
I I I I I
I I I
1^
' •
ft, -3
til
•"5^00
eS .2 <
ft »o
1 1 1 Iff 1 1 1 1 1 1
1 1
I 8SS
I 3888
I I I I I HE I I ON
'S'* t>» t>» ««o
MM it^l I rF^P
•- ro«>»
Q- II II M I I I I II I I
ri" I M II II I II l|^M
S
a 2 8 o 8 8 8:f8^S;^
«cO
I Soo
to *0 «o fCOO O M M 0^ *o '
«o
M d ^^3^So^9^O^O^Q8«'00 I 00 c<«
*^| M I M 11 llfll II
s •
'3
S 00 00 00 00 00 00 00 00 00 00 00 I 0000
I —
M II M I M II II I
M II II II I M I ?
MJ
I I II II I II II I
II
I I I
IS I
l<iS>l
I p I
I I I
OS
00
rO 00
ia.!>si
IS I SI
isigi
1^ 1^
Mil!
I :?!:?!
O OS
ISiSl
l>»«0
M crj t«» to M mm'
8?? p ? ? ?
5 ?j^ ^
•^ wo _
888?p??88p ^?p*r ? « yx8 p^
M M
00
?S 9
*~ ION tO«0«0
« ^too tow io«o«oMa , __ I I
« "i^r*
TABLE OF ELECTHO-CHEMICAL PROPERTIES. 223
1 i 1 1 1 1 1 i 1 1
1 1 1 i 1 i 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1
Mill 1 1 1 1! II
iHlBl 11 11 1 1 1
!3-l 8.18 5«£-^,S'8.af
llflf ifi I I 1 1!
00 I 00 I 00 00 00 00 00 00 00 00 00
I I 1 1 I I II 1 1 1 II
- I s" I ;? I I I I II yy
Q. O JO 00 fJS
llHls II III ill
• •
•^ • • • •
fOfO"*© o
ff)iAti« M lO
p pSM ^ps pop
M M ii4 M rO
M M WSO
• • • r
I
o 5 3 '63 *
J2 o s c a 3
H
O
I
P
QQ
S!2
99 ^ ^
1 1 M 1 1 1 1
ssss
8SS8 1 8888
OnONW *>• I 0^^3^0?
• • •
« to 1 « uj
• ••••••••
I! I I 11 I I I I I
I I I I I I! I I I I
S
H
OQ
I
I
I
■i
t>«ir) ro W)
*C0>O 2J
M ^ o ^
1 1 1 I i 1 1
o
HI tHSlft
p ' o o o o p o ' ' '
000000 00 QOOOOOOOQOOOQO
I 1 1 1 ilslHI
1 1 1 1 1 1 1 1 I II
I 1 1 1 1 1 1 1 1 1 1
080 **iO **iO «cO >o
M M M M ffiffi
^
§
•"ON , ,
i-i «
MM It
99
I I
•«-C RQO
r* on
00 «
I ^« « 1
N M (S
' PPP I
1 o o o r
I ei n C4 1
o6d6\
I '^si I
t
roiow)
00 M to I
• * • <
€ I
&
1 I
.-Mill
Q $ M ^ Q o^
•^ n M M >- M
«!§.
coc* "N
Z I I! 11
5 ooooQOooao
C ^« W F^ ^ P«
II II I
Mill
Mill
i-i «'
§§
01^
224
SOLUTION AND ELECTROLYSIS.
S.8
1^1
"I '3
1*
J
strA itd ftt^s
^S ^1 is
&* ^M "2?^ .
.'d
g'
a ^t ||.
r-^
1^2 11 |1 1^1 |1
I I ! I 1 I I I I I I I I I I
o8 I 8S8S I 88388 I I I
^ T<J -N W5QO ^ M>0 ^ Q . . ,
00 OsOnOnSo 0^0^900 t^ I
**i
«o
^ p I ? s^y^p I ? ? l^y*P I I I
j d* o I I i I I I I I i I I I I I I
in
•|H- I I I 1 I I l5i5i I^S
^ « • • • • •
§§
Vi §ll?lli;isiEfiii€
r'% S NN M M M M
"**>
?5
m
r 1 1 1 i?i 1 1 1 i§§i I ir
oOOOOOOOOQOQOW 100 I 00 00 I | (00
I I i I i I I I I I I I I I I I
I
|f|l 1 1 1 1 1 1 1 1 1 i 1
888 1 8888 1 8888 1 1
^(0^^ i«^^5^| to««io«o| 1
vO « i-i O^O^O^00 OSOOO «^
f\ 1
p"?*?^! r^^'y^P r?*y>p 1 1
*^ 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
5 'ir.rts
§1 1 1 lal iHlErl \f.
9
I I 1 1 1 1^15 1 ^^s* I i.Ji^'S'
I ili«iHli §?i i§ I s-li
00 fC^<i5*?
o I I 5 I 5888 I
^ ' ' P ' PPPP '
>0 11 ^
I
o* oopoopo o oo
, , , , 000>00*^0007f*CO
O I I I I «OtO«O0StO9\«O»O0S'^A^U3
M w
t>AO «0
. . . . Q « !T^ff\»^ »oO S *^"^»o
08880 ?0*o'm S top S?y38
M M M M re
3"
I
^ Q S ^-00 jj- _
p O O 1^ r^tot^^O t* Osto>00 «0
^ M ^ 0\0 "^ fO
1^ M e«
OOOOOOOOOOpp t>>QO p ^o o o
Q OMOO lOiOtOtOQ tOtOO^C« 10 C4 «OlO0
O 9 M M M t>gy>0 O^O^0 On'^M O *^«i**
O.MMMMC490 Q\>0 ~
?f5'
fCOO »OQ0 o M w M .-I «Q0 0\>0^ «5«j
9 Spy?? »ot^«QO « io»o5oa5 p-i Mvo'>flr
0000^'-""-««««c« CO ec ec «0
00 fO
p^y»opppp:^ppd$^p «^p pr
M « «i "^ "^ »oO O O C^O.00 ONOl
"^00 *^
r^M 1-0 O OS«- 2? 00 ^ <0«OM t^ _
f« -^ to O '^OO C4 O O 9^ p <4 rr>0 *«
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
225
'^IS «•
111
(O
si
RS 2
•M
^A(^
M
lis
1^
« p.
Sri* hi -^'^
1 1 1 1 1 1 1 1
1 1 1 1 1
M III
Mil 1
1 : 1 1
1 III
O O O fQQO « « ^ gSM
QnOvOs O O^O^OOQO ^^
1
00 00 00 00 00 00 00 00 00 00
I I
O p M O U30 O
1 1 11 1 1 1 1 11 1
I I « W M C»
I ssss
I IS-?:
O «O0Q M
OnOnOO *>•
V5
■^ I 11 « vjp ti « 'OO
I I
1 I
o
? II II II I lill
HN
.^ S O' O O ON O>00 O ONOO 00
1^
s s I I I I I I
04
OOO *± .
ovaooo *>•
3;
g
I
!
1^
I I I I I I ^1 I 1 1
«0 to «0 IT) to 10 QOOOQO I 00
0>00>0 « "^ro
IH M M O O OS
i I
I I I I
I 1 1 I
11 II
I 1 1 1
I I
Itl I
\Q M lOOO
O fpeioo
»o ««0
« lg
81
VO ««0'XOO
o ' o o
s I
00 I QOOOOO I
M I ^> M M I
I I I I I I
nO qo «^»o
"O -(^.sO *>.
O* OnOS
\o 8 M o
On^On
00
1 1 1
1 1 1 1 «o»o«o
M M M
1 1
1 ii8?r
• • •
M M r^
(3 ^ N
H9
« »o
^ « to
9999 9:*?'
1 1 I I IS> I
tOtOsO to to to ^ to to to «o to I
lO •^COtOtOtot>«sOsO -^W '^to
• I I • fi I Q 2 SPSP*C ONOOO M ON^rOO ,
to
88880? O ^O^ m'm loSp p O ^5^0
to w _
OnO^QOO M
M (V)t>>tO M
^ ^
M rototot»>0
tOONW
888
ps
to
t^^C
^qQ t^t«
M
ij 2P'*!
> <*5*>»to
•
999
» M «« to
• • •
\0 M to
»o
8 8 M rr; *>.^ ^'"^p'Jm t»t>»M *m *n.m w ffim
OOOO1-) pw« "^ "^ t>» f'i «^ tcOO M tot
« '*'*« o Ma
-1
H" « W
•8
COM CO
w. s.
15
226
SOLUTION AND ELECTROLYSIS.
1*?
1
■i
,2^
S Pi
p. pi'n? jig is ^St)S ^<S,? 3
M 00 ^ le «
M
5
I
g
5
§
■a
i
I
o
I I
I I I I I I I I
.poop. . .
N « C» «
^S'S;O^I i I
• • • •
I I
It-I I 1 I I?
5 8tv33">S-5|'SjSS 1 S -^'^'S-
t-«i-iOOOOOO ONOvOS I OOQOO «OC4
O O O O O O OnOnOvOnQO I 00 <'-<^ u;m
I
f I I I I I
Mill
I 0^ I ^^^9^0^
«*5« « O
• 9 r m 9 •
M N'
§§888^55^'
w efj
§Q Q >M SS5 "iQ ■*>''*i *>•«
808800 00 8 WJW^O^ "tf 10*008
M « « "^
1 I
1 I
I I
I I
I I
I I
O^
OS On
<>.»0 -^N w iM
&s
9t
OVQO
«4 ^M <00 "^ ^ «
GO 00 ei'^«O0\»oe»
I I
OS OS
00 V*
«OOs
roM too r«aQ (*< «^
m OsO *0 1<« 0\ rri Q
PPPPPPPP
00 00 00 00 QO 00 00 00
00 M
lOT-
(4
IQOI
9 9 o op p p p
O O O i-^ ^* -^vo*^
99
«oO
JO
?8
00 "^t^t^.
4>ftt>>^ )-4 ^3 N4 00
• • • • • . ^ •
99
^'9 9 9 9 9 9 p
TABLE OF ELECTHO-CHEMICAL PROPERTIES.
227
•-•IS p.
ri •
•a
8 P<
^ .
6 .
S ►
I
11
^ •* -: »S ^* «
i
r5
s
I
§
%
i
1 1 1 1 i 1 ! 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1
MINI ^?^S> 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1
11 1 1 1 lIlH 1 11 1 1 1 1 1 1 1 1 II 1 Mil
M M M
11 1! 11 2 s?«p 1 1 1 II 1 11 1 1 i 1 1! MM
11 1111111 1 M 11 1 1 M. 11 11 11 11
Sj lO ^ n 0^ (O •'1^0
1111(5111 <^ III'^ll *^*^ N^ 2 K
IIMRIII *^ 111*^11 *^*^ 1 Op 1 p p 1 11 I
• MM
00 00 t>. to 1 Mi "^ "^ 1 W3 « M 1 M M 1 1 1 1 O Ov O>00
«
(?^€ 1 S,|$ 1 |.&§ 1 ^1 1 1 ^ 1 ^ 1 1 -^ ill-€.
mOm*^ ""^"^NN "'too *>. 00 t^ « M PO i-< ^>o *"*
OOQOOOQOIQOQOOOOOI QOOOOOIOOOOI QO|QO| 100 00000000
iitfr^*N*N|MMMM| mmm|mm| m|m||m MMMM
>0 ri^«o«"* 00>O « M loO O O . . O
* ••• ■•*•• 1 •••■•« II* 1* II* till
■^■00 '^'^I<omO\mI ioiou)e«t>. iMi-^ M 1
M (4 M M M « M
^ 00 0000 00
Mill
tOUdW)«0
C« M M M
I fill;
«j
I M M
• • •
too
11 I II
^
,2. 11 11 1
HN
3 ^ pNO»tO«ot^
SS CO to« M 0\
^ a ^
-■ OnOsOOOO t^
* I I I I I
§
•^ 0000000000
a (14 M M M M
•I —
^ Mill
o o o p too o o o , o p o
.«.r**»** I » r t
00000000 ooooooooo I oooooo
o piotoo o ooooo o
00 00 OSO>00 «<>Q0>O OVX
II II
11 11 1
mnO •^W toON*«»tO\0
• ••••••
MM
Mill
ass's
l-l M to
»o
to O ^ <*5 *>»vO ^OOO «0"^«^i"^«i «O00 «^ OsQif
O M N -^tosSoO M M M ON^^Q «>>Q n tot^O t?iOO>Q Q Q Q Q
OOOOOOOi^i'^'-* O*orl 'Qp>ON>«N>(OMioto to O O O O O
M M M (0<0'^to0 *^*»OS
M pftiOtO
888p
• • • •
S"
900 ^5^J
On ^ On>0 I
<9^
M O *^ ^
to POP
ffi M
ON«^
to OS O OS "^ OsO Qs O •'^M'^Os^ sOO*^«; fCsO sO ^ _
O O N r^toto«»OsO P 00 O O t>*0<00 Os>0 p\toM t>«o *o O O P O
«J^*»**«*^**^ •••••••••^••••* •••^a
MMMMMftMCrj^'^'i^^
poo op
^ • • • •
16—2
SOLUnOIf AND ELECT&OLTSIS,
11^
1^1
I I 1
III
I I I
1 1 1 1 1
1 ffSS'S'
llp?
f''"-5
rf
S. II 1 1 1
1 1 I
U^ II
1 II 1 1 1 II
1 1 a'K'S'S'i 1
iilprn
II=?^_PII
1 1 M 1 1 1 1
liiiiSlI
if«%^ii?
laflli^?
illil'll
i.„„«i,„
i|8»|i|l
S,!.|ipS,2,
mm
umm
1 1 1 I
1 1 1 I
TABLE OF ELECTRO-CHEMICAL PROPERTIES. 229
•'S Pi
^^
a
!•?
l1
•
Tag
itg*
fts 6
|§A |1
ee
«
g
s
S
1 1 1 1 1
1 1 1 1 1 II
MINI
1 1 1 1 1 1 1 1 1
II 1 1! 1
1 1 1 1 1 1 1 1 1
s 1 1 1 1
II 1 1 1 1 II
5 Mil 1
1 1 1 1
III
1 1 1 1 1 1 Is, t
• •
1
1
(4 ^ M M M M
3 '^wjS o*8s«^ 1 1
M M M M M
1
C4 M M ^ M M
III III 1
II III
1 1 Mill
1
00 QO 00 00 00 00
M M M M M M
00 00 00 00 00 00 00 1 1
M M M M F' M »M 1 1
1^
1*
1 1 1 r 1
1 1 M
1 III
1 II II
1 1 II 1
1 1 1
8p??ff
5 JJppp j,« 1
II M II II II M
II M II M M M
I M I II II II M
to
II I II II M II I
&
. I! 1 II II I M I I
e
II II I M I M III
-3
« « M OVW OS^
^ -.,^fi"^*«>>« »«oo ^
rd W3nO vO >0 >£ vO <<0 lOiO'^t^N
Q «yj CO W5 «0 W5 **5 <0 fO W5 fO «*5 '♦i
II II I I II I II I
•2
»0
^ II I I I I II I Ms
op p\f<pO ^••pNpsO w ;«r;if
OOSo 00 00 00 00 00 00 00 00 00 00
M I II I II 2-?2-?
II II I I II lf?f
un
OS9iOOO M «0
8Q M ccvg M tn
. p P P p r r« i«
W5
to
8M m^io^ e» vrj M
Q Q 2 5PS? « ''iO _ NO
. ppppprr<y^pp p^r^
230
SOLUTION AND ELECTROLYSIS.
•i^
3 . •'O
CI
Id
QQ
*-*<0O\
00
.a
H
"a
g I
^ i
H t
o is
«
I
•s
isisi I I
I8S8I I I
I sill I 1
, O «4 «4 , , ,
Pr^op I I I
I I I I I I I
lO
I i I I I la
vi
I
O O 0^0^0^0^
^'
osaoooo 0000
«0 «0 '^ -t^ 1^ >P QO
Q 0>00 txtxO I vO iO
ppoooo ' oo
QOOOQOQOOOQO 10000
^5 Q_ <*i 'T 5J I t^ ^
^ON^rOO MO I PSM
^ M M M
PSM
QQ IT «> •
Si P4
^ .
^
1 1 1 1 1 1 MINI
1 1 1 I 1 1 1 1 1 1 1 1
1 i 1 1 1 1 1 1 1 1 1 1
•
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 II II
9
O
^ ONOS *^<B lO**
*>-.*>. ON «i ON »0
^ f« »IM M
f
N
M W50S«0
^iCOO «oo -*
iO^«.OS«>-00 «*5
N N N e* Q c;
O p O O p p
C4 to (4 OOOOO
M (4 d n o M
o o o o o b
• »•••.
I
1.
1^
000000000000 OOOOQOQOQOQO
M ro00>O00 ro
M fO
W50 •O** »0"^
M M M C4 e«
'^ * 00*
? ^ CO
30 p.
1
1
1
•
1
»o
«
w
^"
^"^^
1
1
Acid.
lecnle
*s.>OQO
NO »-i «
5?
_
insOvO>0 vO
a>
CO <^ w^ r^ f*5
Hydbi
Gramm
1
1
1
1 1
1
•a
1
1
1
1 1
10U)W)U)l/3
•s.
M
N
C«
« «
op p f*5*>»«^
0006 00 0006
°s.ll 1 1 1 1^1 1
III I 1 1 I'll I
000000000000 000000000000
I I I I I
I II i I
«
v^\
Jr
wiP 1*3
• • •
1-4 W
P
10 p li'vjp
• • • • •
00 M "**>
-N « "*
m' 10^00 1^^ *cj8sJ?oo^? 888 oS
ggppp^p pr»»*^p^?^ ppppp
s^i I I I I
00
1 1
OS
S"^ '^ «5vO «0 ^ « .^
O P ^ <4 ^'dO
. - - O »- »OOv
O p »- iM ONON
M M U3P P 0N(4
»- « « "^
99009
TABLE OF ELECTKO-CHEMICAL PROPERTIES.
231
IS
4S^ I"!
I I * •
la ^i
^1 |8"^S
I I I
1 I
I I I
I I
I I I
I I I
I I I I
I I I I
I I I I
I I I I
I I I I
ll I 18
«Qe osM . o ►^ *>
W5 lOM I ^fiOQNO
CO f^ f^ *0 "i *^ f^
I I 1 1 1 1 I i
1 1 1 1 ifl I
• ••• lr«*
QOQOOO QOQOQO
1118 1 oS?
ft'*^
• • •
•"So •
K.-« >s^ QD
Is
i0 t^^
ft P4
Oh .
e
O
•^
S
•i
1 1 1
1
1
2.00 ooo
^ 99999 ^ ' ' ' '
II II
1
ISSSSS 1 1 S 1 1
1 1 1
1
1
M »iM tH >^ M
Mill
1
1
•^ "^ O On«*»
!••••• II* II
Mill
1
M Mill! 1
1 1 |-|
Mill
1
1
MM 11 1 lia
** 1
m 1
O 7? "^OQ "S** 0s»0 00 OSQSOSCNQQ *>»*>.»««^ OSO»<*i<<P t « I »£? -^
IH iS ''i*^ MMMM (^e«NnMe^f)f4f«e«M*4MO I O I O>00
5
H
O
P4
^
i
1
II II II
O >H M ^^ ^^
M N M d M
«5 x<«\0 M CO «
O M COM O\o> 00 Q I
II II II Ml
II II M3|i||lf|^?
• # # • •
mvd«0«OVd«0 00 00 00 00 QO 00 00 00 00 00 00 00 00 00 I 00 I QOOO
»H M IH ^eo'^
• •••••
rcONNO M 0>»«
■^fO tOfO« M
II II II II II II II II I M
II I 11 I II II II I M II <^c^b^« on:, b-bv
II II II II II II II II I
m
f
m MM'
OOvOOsO M
?????? ?
8 8 8 8 §1.
p p p r y^i-p p p p
P M (O|M>0 |OM M M
5??5I^ ii
fO ». ^ ^
M ro $^ *|2 S^S^ i*ai/sQ CO
8 8 8 o o o r ?S^« ioooSoo "
M M M COU)
232
SOLUTION AND ELECTROLYSIS.
•2
V
^
e P4
SI
Ki-I
•
w «
I
I
I
I
3 ^
o
o
?
OvQO
M M 1^ M
ppppp
nOOOOOOOOOO
u H« pM M M M
^
k
•a
§1
« CTJl
M i3
o
OQ
■i
i
oo t«>o>S
« M Q 0\0S
M M M IH i-i
o p o o o
• « • • •
00 00 00 00 00
OS re On (ON
<4 W30 V3 9^
5J§
_ >C W ON
X>*OnO «0«0
Os>0 « 0.«5
M N« M O O
f4 n d M M
O O O O O
'a
•j^ M M M M
00 00 00 00 00
M I0t>.0 «<
00
i^-^OOO
00 ^ « iM «o N, i^
00 «>'0 «o -^ -^ fO
N gvoo^NOo »«
Qo >o »« rr -^ «5 wi
-a
•I
00 00 00 00 00 00 00
M M M M M M M
9999999
00
• •••••• •
m WivO O •^O'ON OS
-00 00 00 00 00
O w M w i« >*
00 00 00 00 00
00 00 00 00 00
oooopoo o
00 00 00 00 00 00 00 00
f
•H « <*i"V
• • • • •
>o »CO0 f^
P P M M M
lOiiOOvO «
r^ rrj »«j .r^
J5
8
fO*^^T>Q OO
• • • • •
*--«-"',^vS-
%i^
»0'
.«
M M f)
W>
O •" «4 eO^iO
PPPPPP
.s
^
99999
2 8%*8,
ppppp
o o o p o
ICO »oQ «o
M »i« f^ e«
«^ • •
u
r>pop9 p :«.
TABLE OF ELECTRO-CHEMICAL PROPERTIES. 233
a »c? tf* cQ
^. •
•8-p
si
lis
8t*
«9
,b •M
11
<M
S*^*:?
1 1 1 1 1 II 1 1
1 .1 1 1 1 II II 1
1 1 1 1 1 11 1 1 1
1 M 1 1! 1 1 III
1 1 1 1 1 1 1 1 1
« N 00
1 ON 1 1^ 1 *^ <^ 1 i
M M M
VTi M «5 O t>. M f)
M t^vs 1 ^ O I ONOO 1
(4 ki, M 1 M M 1 1
Q 1 NO '^ 1 «5 1 O 00 *^ I
el 1 M M 1 M 1 M 1
p 1 8S 1 S I 5 1 888
00 1 0000 1 00 1 00 1 000000
m|mm|m|m|mmm
ysNpp p p pop
9^99<^999 t 999
00 >nOOOO i-iOO -'OO I 000000
M |ooo »oioaN»o*>. . « *^ .
:J" "^nO »*500 00 «0 M 1 00 «o
pPpMMM«fOl ^«0 I
« *cioON« « iC.M ' « «^ '
1 1 f
1 1 I
I 1 1
it 1 1 1
S5
O
1 1 1
I I
NO
M5
g
I
i
o
P4
O fO«^*>»sO00 « O
^ r»«MMMMM
S ^
I S
'W5^^M
iOOnO 'Tf^i
NO mOO 0n«5»-" "^
« « « « « N «
9999999
g 00 00 00 00 00 00 00
pS MMMMMMM
•fl -^ M nnO
P- OnwjponOOnO »C
o«
1^
M WJ'^IOM MQO
M « fO
00 00 00 00 00 00 00
On « »*5 '^ *> *>».'t»
§§1
M M M M
eoco
' M M t>« OMX <*i
>t^fnO0 M -^N
M « N t^-^ds
ON
M MQO iOt>*
ON^f<500 -
r^O ONOOOO
«5
00 **
rfj W « M M
C« f4 (4 f) N
99999
00 00 00 00 00
at
O p O
oq^Q^oo
W5
M (4
00 00 00 00 00
9<
Onm ioQnO
OnO
*>• M
o>>0
M M
o o
00 00
99
00 00
CfJlO
NO Vi
«5 0n
I! I I
I I I I
I I I I
r I I I I
&^ I
^- I I I 1
^ ^ 5
O •^ <^C» P<J>0
o ^^
p
1 1 1 1 1 1
1 1 II
2 (ou^iow)
g « « « M
O* ;;,
W «vO ONM
-<4-IO-^M
• • • •
OnOnO^
sS^
I 11 I
II I I
NO
~ Ov
«
irr
I 00 (0 0>P O vnt^NO ffiO >^ tri
"^WJO "^ONON-^ONWiO "^t^
MMMMMMrO''^'^''^
5*
ONQ ^ fO"^ nO
O O m«i«0nO PP--4MN «5 On m
M mo io»oo ^^n
H< M M wjeo'^
234
SOLUTION AND ELECTROLYSIS.
^
g
It*
3 8
I I I I I I I
°l I I I I I I
I I I I I I
I I I I I i I
O
1 b' °" " " '
I «- 1 I I I I I I
fl
o
11 I I 1 1 1 1 1
i!
w 1
I I I I I I I
c*
O MOO '^Q C^-*
rf;M fCM OOO 10
• ••••••
(#)e4 M M N*
H
O
M
OQ
1 1 1 1 i 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
III 1 1 1 1 II 1
^ llllllilll
^ 1 1 1 1! 1 1! 1 II
^. MM MM!
9
►-I frji>»M>0 M\© MOO ^
«
> ON fCOQ^O ON "^ o
- sO CO
SS
Ai
§
«<*■ t^OsQ «>0 «O0QQQ
pppppppppp
I
>: 00 00 00 00 00 00 00 00 00 00 00
CON©
\P QssO NOOO r« varc
M I I I I I I I
I II I II I I I
II II I I! I I
t
NO
1 1 I I I I I I I
j; I I I I I I I I I
1 I I I I I I I I
el
2 S ="
O
1
M M M I I II
00 00 00 00 00 QO 00 QO OOOO
M II I I I I I!
«M M M I
M II M M I II
I I I! II I I I I
M II I I I
II I I II II I II
i M M 1 1 I! I
O O M rr^sP M lO
JJ»PP^M«
U30 oppoooooo
M f)
• • • *' 5^ J* r
OOnO <4 tC
8 a SP>fi « »^
P O Q M n m
• • • r^ • • •
i I II I 11 I I I!
vb CO 00 rOOOO
O ^ <*5^ w *^ f^ivO OO
88^888 8 SS"^
2*
TABLE OF ELECTROCHEMICAL PROPERTIES.
235
^«?
• a
50 A
M W Qb
M M f( M M I I I
ppppp ' '
I I I I I I I I I I I I I II
SSS8S1 I! I I I I I I M II I! I II
%
liitfi II 1 1 I I I I I I 1 1 I I I M
1«
pr^^^l I I M I I I I I I I I II I 11
PM M W5iO*>»
I I I I I I I I I I I I I I! I I I I II II
i i I I 11 I I I I I I I I I I I I I I I 11
f*i WJ fT5
00 OSU)M p 000
'^^O
I I I I I I I I I I I I I ^ASi^
8
«?fO
«5CCfC«
M I I 11 I I I I I I I I I I I I I II I I I I
QOOOOOOOQOOOOOQO
11 II I 1 1 I
I i
g
p4
M l^api I I
I I ISSS IS I
'COO QO ob
I I ISillvlSl
? I I if pi I p I
; I I I I I I I I I
o
g I I I I I II I I
,g M M ^ ^ >^ -^ " ^ ^
s 7;^ — i^I
® 1 I I I M I I I
fi
'a 00 00 00 00 00 00 00 00 00
p
■^ 1 1 I I 1 I I II
I 11 I I I I 11
I ifl^all, 1 1 I I I I I I imH 8?P
I I I I I 1 I I I
O O M y)0 000
IM W5IOO
5 Si yffv ON 0^00*0 « m
J56?5J5p5ppPf-««j pr«!^
i-i «'
^Evg'g^g^^o^ §88
• •••■••• _-_
PP<
28
IM M *>
*- <^>o O O O *^ M '^
236
SOLUTION AND ELECTROLYSIS.
8 P«
j» . '
SIS
j^!!^
^
^2
. Pi
^ •
QQ
I I I I I I I I I I
°8SSS I I SSSS
^«sR8 1 I ^^f i
Vi
10
• • •
I
I - M I I I I I 1 I I I
|g
! 1 1 i$ii^i§
I I I I I I
! I I I i 1
i I I I I I
I I I I i I
I I I I I I
I I I I I I
T
O
o ' o
g a -^
» § S^S^I I^IKIft I I I I I I »338«
M H ^ M M
I® |l I I I if 1I ll I i I I I I MM
>2l nOOQOOOQO I I 00 I 00 I 00 I0i0t0i0«0«0 QOOOOOQO
g o^^mmI ImI^nIm Me4r49)C4(« n*M>-i-i
•g
El, ^ n
0\
so
o
si
NO «:*>»os«*5
M M IH M M
p pop p
sssss
N«00
o o
o o\*^
V • • *
1 1 1 1 i
M M I
O
o
I
00 <>^>0 i^atO"^-^
S8
I
•I
>Q O>t^>00 O U3MQO r«
PPPPPP9PP
QOQOOOQOGOOOOOOOQO
ppppppppp
o o p o o o o ^o o
o io»oim«co i>»tO"^ »«M
I I I I I I I lOVSioio
M 1 I I i I M
t^O ON*^
»COQ 5-00 M'^O'-'O ^-^w,
?§||pr§t?' M M I I pl^ff
M M I I I M
SO
Vi
P P'P^r ? P*^^o r o 08880^ "8 2 «'io
r
OnO*00>O M 10
M « Wi
too o p o p o o p
« M fv; •^ OnOs*-^
QNt>>lO
gso>ovON00>o ^
0P00«-<«0 >ON^Ok
M i M I I M
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
237
J«
1^:.^
•8-p
u
ill
CO
^^
41 .
a
. Pi
ft, -3
-I
J»9
' i»«
Pi
I
a
I I I I
INI
I I I I
MM
I I
f
MO ^
mQC 10
I I M
00 00 QC 00
MM
O M "^»0
M M M M I
9 9 9 9
I I ssss
I I ! I I I I
o
SSSS I
"fevfe-
I ^00*08^- I OS I ^Os3n(^ I
i
00
eo
o
525
li
»^
B o
I
§
i«
M M M M M M M
cfj , lo
I M M I M M I Is l^s^si
00000000 OSOSOSOS i
>0 (<« r« M t>*t>>io
«ON O M _
*>• t^ *«• t>M^ 10 10 ^ f) o *■» »o
OS OS OS OS OS OS OS OS OS 900 00 I 00
SO
I M M M M» I M I
1
I
00 00 00 00 00 00 00 QO 00 00 00 00 I 00
l"S
M M M M M M I I
I 1
I I
I I
00
I
I I
I I
I I
I I
1 i
I I
! I M M
I M M I
I M M I
M M M
I M M I
I M I M
000 t^ .
ISO 1/3 u)
cn. 00 OsosOsos
'^to.Q •^•t>»OS0
I lfs9l SV-SS I M I M
pop
I 1 1 I I I I I 1 1
I 000000 I
I ^ )■« M I
00000000 U3totO«0«OiO
M M I I
01 «
*- ■"♦^O P !>»« ^OO "^O
»«O\00 't ^ »^ O O O OS
I I I I I 1 I I I i^r'PfPPP?'?''''' «w«j*
I I I I 1 I I I 1 I b b <<ob b««e4bbbbs bbbb
I M I I b
MM
■5"00 « fC-^OO i««5W •- T**
sO 0.0. f*t
I I M M M I liproi??^? §1?? I I M I
m
I
t-i w
M «'
POpOOOOPPO^w^««^«OOpv5 ^i-«<«4U) 800000'
SO
"kOsOsOOsO «
»■ W^CO
Mil
i«
t>>M 10
*>.i-4 W3W3'^ \0 *>•
55 «CQQ i«fltN,"^Vi«
o 00 « -
• • •
'Tt'^qp o *>.oo
M o O
W5
O _ 000 POsO 5i«f5
O — )^ OOOpi^e*
H4 M w -^00 « «o
- « "^
238
SOLUTION AND ELECTROLYSIS.
r * a-
QQ
8".
•|2
lis
^^P4
« Pi
I I I I I I I I I I I !! 1 I I
I I I I I I I I I I I I I I i
I I
I I
I I I I I I I I I I I I I I
S
I I I I I I I I ! I I I I I
o
°l I I I I I I I I I I I I I
I
tn
I I I I I I I I I I I I I I
I I I I I IffS'S'yi I
I I I I I I
'rrisQ "-* «*5
S-ffI I
g; I I I I I I r « y? I I
o
: I I I I I I I I I 1^1
'V
^ I I I I I I I I I I a I
§5 ^
I I I
1 I I
in:
" I • •
QO I OOOO
%0 , sO t^
M I M («
^K r! _^ h^ ^ ^ ^ ^ tad ^ M^ M^ k^ ^rt
o
^1--
1 MINI f ,2'<2<S RSaiS 2 p I'SS-S-S-S-flS'g'S lisSI§8 I
1
1 1 __
I I I I I I I I I I I I I I I I o I I I I I I I I I i I I I I I I ;
lA ^ tovd«OtOi/3iO 00 00 00 00 00 00 00 00 QO QO
O O OnO\OnOO
• r r » f^ • ••••••••••
(3
4?
^ 00 00 00 QO QO 00 00 QO 00 00 I 00 00 I OO | I
I
^ I ! I I I ! M I I M I I I I ;
°l I I I I I I I I I I I I I I I
I I I M ! I I M M I I I I
I !
1 I ON I OOOOOOOOQC
1 1 1 1 I 1 1
r
qsOnOOnO M
88800^ 8880 o^ 2 N^iop
M N
iilssis ' s^^i ^ I
• • •
«^"^QQ »0
I
tr^ eot>.i^ p^S «*:*:• ''«Q
•^r^i/dO>^ 1-4(4100^(4 i
000*^<^ OOO'^ci'^
§Q liM M POO *>.'^W fO«^« «>•*>.
. 8 ? 8 8 p p p'2 r ?-?^?^?
^K M ^
(
J
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
239
•« Co
!•«*
lis
SI'S
J ^r 5 ^ ^
l-s il-3 ll-s I'M
1 II 1 1 1 1 1 1 1 1. 1 1 1 III
1 1! 1 1 1 11 1 1 1 1 1 1 1 1 1! 11
1 1 1 1 1 1 II 1 II 1 1 1 1 1 1 II 1 1 11 1
MINI 1 1 1 1 1 1 11 1 1 1 II
a>l«loo2>-ll llll.gl<gol>§i8 MM
S|2||^M II lllia^l^ U 11 II
I I I I I
« « « w I
g> - J, u,p
-S I! 11 I
o
MM
ssss
0^ ONQO -t^
W lO
•N « »oO
II II
II I I
g « 2
IKIS-IM^SsSasfl^gySISI Sys-S" ||«SS!3-^f2^ JS'S
00
ON
I S. I -ff II I ?»? 11 I I I I I MM Iffol i^^^r^^S-S- ilsl
00 o
p
igigi Mil I iigii s Ngi lisl
Si £ «o»o«>«oo»o i-<
d M M M M M ill
O p O p O O • • • "
• • • ^ • •
I 00 I 00 I I I QOQO iOiO«OiO I lO «0 lO I iO | 00000000 fl QOOOOOOOOOOO 00000000
I II Mil I I ffslSlK' S I 181 MM S^^^S&& Mil
?« poep:r«M po
0*00000000 O\i-«00Q0
II II II
1 09 1 OD 1
1! II
00 eo-^iO-^OO OSQ ?Q
tOONi^ONWJOO *>•«:!*'
2^ 2 r S! S ^wt
II M II
1 ri?i
*m IH
II II
ioto«otoio«o I I I I
M M M It M M I I 1 I
??r???^ 1111
»0'«^*>.«
crjio
l>.f« M lO
dp V) 10 T^VOON'^ CO O lou:
I I III Q5-fp*>.o«OMa « :fQQQ5 Tf O^ QOsQ Q -^ ii rf;
>»>lpl>loo 8 88 8S? S ^S'-S 88 8^ iP^Svl 88^8
«OM<»i-iOO»Nr<Oi>4^ MMiOMt>*VQ r4 "^1 »o|
"^Os«^Os»n00 r^.M'^ OOOi->Me« "^00 >0
• • •
O t<«00 -OOnOOOO o
IH H4 M c« trixri
• • •
\0 MvO O
rrl?
o p o o o o
• ^ • • • •
lOO WJQ »oiO
•- M « « «5
o •-* ^
o o o
S"
240
SOLUTION AND ELECTROLYSIS.
1
o
^ ^ "^ W :S O
^^3 ^•e.o
I I I I I I I I I I I I I I I
o I I I S'S'S' I I S S I I I I I
-^o *«• woo
H
9t
CO
o
M to
I I lr«^l |r«I I I I I
° I I I I I I I I I I I I I I I
N . O
I I I I M I I I I I IJ IJ
H >-< p-Miii^MIHHltHOOO OS30 I 00 I
55 J
p
3
s
« s
s
a
I
-i-rr
'^rON "-I OQO »0
O O^SOM»Q0 1 *>-
I I I I I I I I Is I I I I I
A 00 00 00 00 00 00 00 00 00 00 00 00 I 00
I I I I I I I M I I I I I I
I III
I 1 1 1
o
I I
I III
I III
I III
lo O O "
-< O
\n o
i
I I I
00 000000
I III
o I I 11 I I I I I I I^St^Sb^ I I I
I I I I I I I I I I 181 So S^^ Ml
M W
M «'
8 8 8 8 8
999 9:* ^ TV
ȣiO OS
o ^ *^
m «5
fOOOO t-i fO M5
M M t^ «^vO 00 ►^ fC »0
§8 ft "^ '^ *^ wjo 00 o "^ CO w;
8 8 8 8 8 p o o'S?^o<tS^^oo 8
■^ M «CsO
^^ N« ^^ »2
00
eft
o
I
I I II
« « « « I
^ ONOOOO .
8^f?S;l
1/5
• • • • I
I I I I I
I I I II
liOtOU^M N« O QO
t>. f^ rO>0 Q »0 O
\n-^r(if* « H« 11
00 ^**
t>.i/5W5
00 M Os»i>0 Q'M « co>- »«
I
1^ M M N« C4 ro»o*>.0 fOO
ppppppppppp
g 00 00 QO 00 00 00 OO CO QO 00 «
I-
& poooopopooo
•^ ^ « ^qo 3::3- •-• 00 0.12
tfi^rxo a^O^ON00 t^Mj-^Wi
? p ^ ^ ^ I I I 1^1
QOOOOOQOOO I I I 1 00 i
« *- «
> Q GOO "?,,,, qe
100 poooopooo
OO f^^^*^
«^ • • • •
M el «
MINI
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
241
•2 « .
11^
1-3
SCO
.«
•si
es •>•
lO
1 1
MM
ssasi
MM
II II
■un
• • • • 1
■4
II II
III 1
MM
ill 1
To , NOO
sO < vP *^
• * •
(4 00 lO N< ^o
iJli
a^^sS
SI 1
1 1 1 II
1
1 1 1
OOOOQOQOOOOO
^ m4 M M liM M
I'S 1 I
c?) to ^ o Sir's «*
1*
•il
m .
S CO
. P4
P4S» •
^^-3 .^
eo :^ O
M
I i I i I I I I I I
OQ
e
^
CO
o
I
I
I
I
5
i/3U3«o«n I O Q Q Q I
^ « o -<*•
" 2 <r^ I ^O*^®
pn e» viO ^ « «oO
I I II II II I I
I II II M II I
t^O POOO « OQO ^>0 O v-jQO
moo *^00 O w^W ONt^f'JQO <J>
sO lO-^o?) 00 00 00 t>.t>.*>.3»o
►- o ON*>.o *^5Q
00 (A <>>t>>t>^<oo
oo>o »o»c ►- O ON*^Pl>
NO MJ-^WJ OOl
00 iflM 4^
issi M I I M 11
•3
I
00000000 00 00 00 00 00 00 00 00
M 00
O O O P ^ O t>."^"^M>0 o
5 -^ c\ 2^ -* «^ o>oo 5 3- Q
I • •
Mill 1
W « N «
O O O OS
ON
- I rr»!«P I
o
I
I
1 11 II I
II I II I
« ON OOO 00 l>>vO «o
tri
100 00 r<«
^QOO
99999 999
0000000000 000000
-a
I
0>i0)^ wdi>. MOO
• •••• •••!
rcOiOO w g W50
I I I I I 00 «>.oo *^«^*
SmM(4 llllliMC)
0000000000 pooox
II I II
Qn
W5(
lift I I II II p'8
t^tn'Ui oo «o
8 8 ppp
M NOO M
*ri
«
*oO P O
O O O *" <^ '
p p p p p '
lO
O I
«
00 a«^*^NO
fisf? If
I
*^ • I- o •-
>o o •^fo
• • • •
O P P P >-• tct^*^
fOO
M
On ^"^N "^
p r r* 7»-p^ ppp
w. s.
16
242
SOLUTION AND ELECTROLYSIS.
S « .-J 5P_s S) t J
•3
S'3
o
?.
r
:«•
X
^
M
A
^
3
_ •
•
1
i
&
-^
P4
1
o
Is
■I I
9
i
o 1 1 1 1
1 1 1 1
1 1
1 1
1 1
^ I I
I I
I I I I I I
M N M M I I
O O
^^8^1 I
r ?!"P I I
I I I I I I
I i I I I I
I I i I I I
I I I I I I
I I I I I I
?> I I I I i I
<3-
^ I I I I I I
H I I I I I I
O .i
I I I
I I I
I I I
fill
«
£ I II
O
iSn,
I
N< N< M W3
« « 55 55
O O O p
• • • •^
V M IH M ■«
pop p
0*00 00
.00 00 00 00
O ^^ ^^ tmt m
g
^
a ^
I -
a p
I 1 1
^ 1 1
1 1
1 1
00 >N >H o (4 '^<*
7f) lO (O t/3 to V3
M (>« M N f4 N
O O O O O
•^ • • • • •
00 00 00 00 00 00
1/3 lA W) to U) V3
M ^ « »N i^ «
r n » m » m
I I I I I I
OB 2 '^'^ « r* -
H a
o 3
I I I I I I ^ I I I I I
g
^ « « « w « «
*3 •::;
u* 00 »op poo 7f
W -^r-^ *>.M fo«o
00 00 o>x^nO to
wi to fo fi fc fo
1 1 1 1 1 1
1 1 1 1 1 1
®
*a QOQOQOOCX
^ I I Ml
I II I
I II I I
x<«iot>«C>
• • • •
OvO
'«-^»0
§8
• ••••••
»i« M It ft
i^»o
rCsO^OONO (<<
. 8?8p5^
^ «
§§
M O P P
pp
PPPPPP
M io
r
p PP r r«
§§§88
J
TABLE OF ELECTEO-CHEMICAL PROPERTIEa
243
8JO
As O
Si"**
^ •
o" ^>
^ QQ
« CO
I I I I I
I I I I I
I I I I I
I I I I I
I I I I I
« , m
I I I I liili I I i I I I
M H> M M IH O O
M iH o o o o o^
I I I I ll I
00 00 00 00 00 00 00
I I I I 1 1 I
I n I I I I
I I I I I 1 1
o 8 8 o p ^o* ' w
I
ON
00
1
I I I I 1 1 I
I I I 1 1 1 1
I I I 1 1 1 1
1 1 I 1 1 1 I
S8SI I I I
Htl I I I
I 1 1 1 1 1 i lf i?ll 1 1 i
I I I I I I I
00
i>5 too *^2i
I M M m O O
^
I I I I I I
N
8 I I I I I
00 lOtC*0*OU3iO
f?5« W « ►^ M
so
b; I I I I I I
oo
^ I I I i 1 1
so
t>>tO
9\OsO^00nO e<
vd 8 8 8 8 o S
ffi
8mMt>>CINOOOi-4r4Q • "-"N ^0\0*OP
O O P M *OvO00 «0 0\ O P O O S f?j
m
O
6
eS
si
§ I
1
1 1 I 1 1 1
Mill!
M M O O O Ov
1 1 1 1 1 1
II 1 1 I I
»0V5Wi»0»0«O
« « « « N «
• •••■•
O •^ i-iOO io«
O O O OsCnOn
I I I I I I
I I I I I I
. 8?85?
^QO V510
O O "^ W W5M
V •CO
Njfgao
o
C4
rH
e<
1 1
1
1 1
1
1 1
1
1 1
1
09
o
1 1
1
2 a?
I 1
i
il
il
g 1
M M
OnCsOnOO
1 1
1
1 1 1
1
1 1
1
1 1 1
1
lO tc U^ to t/3 to
« « « W « «
*3 -
o< p « p>M i^t^
9v^ON00 00 00
I II II I
I I I I I I
t^tO
oscsosoo>o w
O •- «5*>»»0 H.
Q p O Q tr t2>
. 9999?
t^io>-4 (^ to
o o p p « r*
16—2
244
SOLUTION AND ELECTROLYSIS.
I v.
o
So'?
o
?1 §fe
It'?
o
%3r
o
CH ea
I I I I I I
I I I I I I I
I I I I I I
i I I I I i
o| I I I I I
I I 1 1 I I
1 1 I i I 1 1
I I I I I 1 1
1 1 1 1 1 1
I i 1 1 i I
1 1 I I I I
I I I I I I
t 1 1 1 1 1 1
8 __^___
5 I I I I I I
O
§ 1 1 1 1 1 1
'il^O OQOOO Q
« M 6 Q O>00
I I I I I I
I I I I I I
" c* « « « « f*
f^ W^ P^ f^ f^ CO
s I 1 1 1 1 1 I
• o
B 53
; I i I I I I I
"In
i
S or
g S Tf -"T "^ **i f^i M 1
i I
Pi ^
^ 1 1 1 1 1 1
O' I I I I I I
. s
gil 1 1 1 1 1 1
f I I I I 1 I
: i i I I I I
a a I " ' 1 1
M S (T) O -»> ^O >H pQ
& a
M § I I I I I I
B S
i I I I I I I <^o I I I I I i
I I I I I I I
i
« M « M
& QO ""WO WOO *^
w ••••••
1/3 10 *0 V3 U) O
« « N « N W
1
o« r r-<» f f p
M M IM O O O
O 0) «
p. W M l-i l-l « ^
g I I I i I I I
as
I I I I M
s
3 'V'«*^o oso^o^
" O O O ONOvON
°l 1 1 1 1 I
I I I I I I !
I I I I I I
I I I I I I
I I I I I I
I I i I I I I
I I I I I I
I I I I 1 I
rO^O>00>0 r«
ii (t; t>« U3 »!
OsONONQOvO M
fONO>000 (4
NO Vd
ON*-" 940 rn
p p P P r t^
O p O -^ « 'TOO
OvQO m
S S 3•C^ON00
p p O O M «C
0*^-1
S S5 if 9fi '^ '^
P P P P r r-
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
245
QQ
s « ►
t^
Is
^^A
all
Oh o
s,
I •
01
Ost^QO CVN ON<^ **i<« ^
' ' ' ' • • ' ' ' ' 'oooooooooo'
• •••••••••
I I I I OOQOQOOO I I I 00 00 QO 00 00 00 00 00 00 00 I
I I I lEs^^l I l^l'^iH^*^*^*^!
MS
m
>& r«00
I I I J r :•!«? I 1 I r y^i^^r^f* r?* r l
« •^O'O "^00 ^oono «
•^ M iH N f« re (Vd
1 I I I I I I I I I I I I I I I I 1 I I I I
I I I I I I I I I I 1 I llsl^l l?l ll
o
n
■^ p O Q •-• t-i«.«0« ^ 0\ f'i *>• 0\ •-•
5 wjN »H po "T "^ ^'i ^ '-' OO ■^N
a 2
»o
»- « to W5 PO «5 <n f*5 f*5 to « « N
S
P
I
I
i
rot^OiOO Q ?lvO O I- w5i/5»*5"^
•^O Cs^ N r<SfO« O00»« fO O
M M « tfi rri ro rfi tfi rri ti n m m
I I I I I I if if I I I
QOQOOOQOOOQOOOOOOOOOQOQOOO
I I I II II II I I II
I I I I I I I! I I I I ::
Mi
I I I I I I I I I I M§
*4 f4<
N» N'
§Q Q *-* (^vO
988800 0*0* •-•
. <» . }S90 . O 5
M I W^IO I 100
I O I ONO I P0«^
(<| MM M
I 00 1 00 «o I c)lO
I I 1 1 1 1 I I
I 00 I QOOO I 0000
I M I M M I M M
1 1 I 1 1 I I I
I M I »* M I M M
ifilflll
!" P P P 9
M CO too
I I
1 1
I'l
I I
I I
I I
00 W w^mOO
i/i «5 f<5 *^ <*5
4>.iOfr5 M O
(4 M M n M
iOtO« Q ON
N N « « M
MM!
00 00 00 00 00
9*
pNCfiNO 0^00
* • • • •
M P0>O
I I ^]f?^
»o
Mill
O 00 t^ f*5
H
H
^
I I I
I I I
I I I
oM II
QC
M
BS,! 1 1
-^
^ 9
11
100 «5
M M M
C
1*^
«>CS MS
CQ 1
« N N
M M M
^ g
f
p< i
1 1 1
•*j
e
•3
0000 00
M M M
>
•s
I I I
1 1 1
I I I
M N
^ONt>»M} Q^VO
00
O O ^ N ^>0 O '^•Nt^'^iow PC «
M « •^■^«5«O»-00 "^ "^
1^ M « **5'^>0
ONOO M)
• • •
246
SOLUTION AND ELECTROLYSIS.
Q O *» *^ <0
5 « ► '^•f* • «- ..
i^
8-=; S,
^^4§ |-«l? jgiS5
^50
. Pi
CO *^
I * •
-Si
00
If 1 11 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 Mill
088 1 IS I88S8 II II 1 1 1 1 II Mill
1^1 lilflHl III M M 11 Mill
00 o\ 10
>?? 1 1 P 1 T^Y'O 1 1 1 i 1 1 1 1 1 i 1 1 1 1 1
° 1! 1 1 1 1 1 M 1 II II 1 II II 1 1 II II
1 II II 1 ill 1 1 III 1 II II 1 Mill
• •
c« ^ 0*00 «o >o I «» ^ u^oo 1 M >5 >e 9<e ^0 m 00 ^o «cqo
f<5w:NNN«Ni* 1 00 ON«>. 1 *^ cv ovw « ao t^ «n « « n*
f^§8«»-f il^Si^ s^StHa ^BH
fO 00 0\ 00 *^ON« Wi
M 1 11 1 p 1 1 II p 1 1 II II 1 1 ^ffff
Q 00 00 00 00 00 00 00 100 00 00 00 100 OOOOOOOOOOQO 0000000000
1 II 1 M 1 II II 1 II ^m 1 II II
►- i-i w po
O
o
OQ
§'l
OQ
QO ON"*
M N «
pop
sss
• • •
1^ e* ^
I I I
I I I
2 ;ts>8 s?
B o «< ec»*a« -y
C ^ O 3^c — O
s I
9 I « « — «^(>o
^ e N •- o ovo\
J p p p p p
■^ QOQOQOQOOO
S
'a
I I I 1 i I l^PPPPPP PPPPPP , , , , ,
M »i4 »« »i« I
I I I I II 18
I I 1 1 1
ooo8ooooooi-> «oOnO O O i-> m S^w>
QQ ton I
O p o
• • •
««
^
SI
*^o poo
00 *^« *^^fO»*
« 5p
• • • •
^*>"00
(4 Q^O ^ t^M w>o.rooo>0
"^tkoB *nt^m 00 »^^®
too O (>4-^M pooop
- N-l « ■*
TABLE OF ELECTBO-CHESaCAL PBOPEBTIES. 247
§11
^?
1 * 1 1 1 1
II MM
II MM
II Mil
II II II
i
ON »0 ^ .
'«0 0000 A^^
55 I I I I
OOOO 00000000
" «n too ON^
1
'2?;?
i
» ^ • • t^ _• • • • • i • •
.^^
S^
02
Q
O
OQ
»o
p
O
I
1 1 \fff\ 11 II II II II 1 II 11 ill
1 1 ISS8 18 IS8S8I II II II II Ml
MllEll^it^HlIM Ml
1 iffllPl r««P| MM II II III
MM M
1 II 1 II 1 1 II 1 1 II II II II II ill
II II II 1 11 M ll|l 111 Mil ill
M ««0«<0CVM « O « N fOO 'OO !fJ O ^*^'^00 "^M <
^'I^JMi'Svl^Si
ON«5 . >0
(0
M t^-^
O 0\0s
43
I
I
II II II I lllll lilllf II I I Ml
• m • • •
OOOOQOQOQOOOOOOOOOOOQOQOQO I OOCO 100 00000000 000000
I
II II I II II II II II I II
"too «s*>
M «
i 1 1
^1
tr>w>u)«0
I i I I i I I I I I i I :?«^:?:?«^i? i ;?:?:? i i i
M 00 *nuv^
ro . M '«• O\00
^1 sfis
00 »«•
11 II II II II I illHil ii?? I M
r % m % % % r r ^
w>0
M «\Q ifjr^OO
QQQMgvg^ to GO eot/;
PPPPPPPPPPPP^c* w)p Mp pMMy) 999
M M «
M Q MO
M « fOPO
M «"-
M « SO
§
88880 PC'S wjRSStNi^*^
?1
M (n>0 l>*(4
• • •
HI CO
248
SOLUTION AND ELECTROLYSIS.
■i
s
l|S
o
"IS
-3 g:3
••» rs '^
It."
^*pS Pi
•S •
CO
E3 • •
•
. &«
P IN*
OQ ^
o
O
.J?
H
•I
i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
o o o o o
1 1 1 1 ;.| 1 io^o^:^! 1 1 1 1 1
1« "Vo *-• »^
1 1 1 IrtI g'S^^ MINI
1 1 1 1 p 1 1 ? !f«P 1 1 1 1 1 1
° 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 lllfl 1 1
8 8 o 8 S^^'Ss^w^oo* t>»^ 1 o «o^«^
M P4 M M
^toSj'^foS 5)00 -^^ ^O 1 tri 1 t>^QO
CvO\OsOsOsONONOOOOOO *>.*>. 1 vO 1 "T fO w
1 1 1 1 1 1 1 1 ifl 1 1 I iffl
Q 00 00 00 00 00 00 00 00 00 00 00 00 1 00 1000000
1 1 1 1 1 1 1 1 1 1 1 MM
° 1 M M M 1 1 1 M 1 M ll 1
1 M 1 M 1 1 M M M if 1
I M I
I M I
Mil
S I II I
v>
o
OQ
MM
0;
OQ
*i« N4 o o
I I I I SS
I I I I
Mi
10 1^00
? I I I I (g-s
.^ I I I I I I
o
OQ
-?.l I I I gll I I I I I I
OQ
I
I
o o o
o o o
OS
O 00000000
f^ IM M M »■
>>
» II I I
I II I
I! II
HN
!3 P M 1^ ;;n
a g M »^ «
OS>0
o o
g © OOOOOOk
g I
I I 1 1 ^1 I I 11 1 1
§ OOOOQOQOOOX
^ M •-< M *« M p4
till III
I I II I I
I i II I I
8 ? p p p'p^S'r T\
top p
8m rr;iOM PC»0»0«0 I 00 I I
M lO
o p o
V
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
249
'i
r
III I I I I I I I I I I I I I I I
SSI8 ISS8SI II I! I I I I
«
^
I «
•i
g
3 1^
it
M 1 1 1 1 1 1 1 1 iifii
I I I 88SSS I S I 888S
if I E I §^<&& 111 I I I I I I
I I I s?
I 00 t^ I *^ I *>• W5 ■* «^
00 ^
vi
^!^|p| PITVpl II I I I 11 I
« PO "^
I I I I I I I 1 I I I I I I I I I I
I i 1 1 1 ill 1 1 li 1 1 1 1 1 1
&
O
03
a
!> I I lf?J?y>plplf?5JS!
M (4 M
I! I I I I I I I I I I I I I
1 1 1 1 1! II I nil I I
Os p^ N vO « >0 I O •coo O 2 *ot;^ w^ P 2 B K « "* Q>^ >0 »- t>» ►- Ov « on F fO »0 «
i#5 M ff5ioi>»« "^ O O *^
O^OO *^*^»OiC I -^fON "-> I
I I I I I I
I I l?l II ipifl
I I I I I I
00 00 00 00 00 00
00 00 00 00
«4 M M M N M
I I 1 1 I 1 1 11 1 1 I
»^ o
(«00
o
M
bQ
2 o o o o o ON ONoe *^>3 lo I »o '^ fc
^ M M M M M
<S I I I I 11 I I if I I I l|
I
00 00 00 00 00 00 00 00 00 00 00 1000000
I I II I 1 1 1 1 1 1 1 I I I
I I I I I toV»o«o»owi»0 I I I I I I
1 I I I I 1 I I 1 I I 1 r^^^
r4 ^ to O 00 t^O
I 1 1 1 l^SSls-'^S- I II I I 1
r m • • • * •
I 1 1 1 1 1 1 1 1 1 1 1
M (4 NO
ON
O P M w>0 O "
rONOOOvC M
SSSpS"
w «
l-l «'
. pp83?p?' p\«^
t« nO ON«Ot^« »OM m;>c po*>
o op M a 'i- to o\o 'i'pN ooopp^
« W>U)10
lO"
oob "^ <^
9 O 8 O op « wi^*'»QO
250
SOLUTION AND ELECTROLYSIS.
Oi
15 }^.
Oft. P. {g^g I?
•I
T
I
GQ
O
M
%
&
o
OQ
a
bQ
-B
I
I
a
-i
I
pp
o8S
«CQO
ol I
1 1
s
o to
99
qOOOO
I I
_ «o»o
4>0
I
99
00
Rl II I
I III
I III
I III
I III
I III
I 1 II I I I I I I II I I
I I I I I I 11 I I II I I
I I I I I I I I I I I I I I
i I II I I I I I I I I I I
I I I I I I I I I I I I I I
i MM I M II II I!
I I I II
Mill
I I I I I
Mill
Mill
II I I I
00
Is^li^ %^^ ^tftrh^b^b^^z^^
00
II II I 111^ II I M I II I II I I I I
8 II I M II II II II I II I I I! II I I
00 0000000000 00000000 00 00 00 00 00 00 00 00 00 00 00 00 00 OO QO OO 00 K
?f>'^r>9 MM
ooopoooooopopooooo
00 '^ a^o »co«OQ-i»5«ON*- "^ ovo "*
to
I I totoio i I I I u) u) u) u) w> «o «o to «o u) ua ic w) w) «o I I I
I I
XN.IOOMO
M5 1^ M « N « PO W5 W5 fO fO fO "^ "^ Mi
KJd Tf P
*>»ONON00 ON M trj t>.OV»^ Vit^OsQ « « p0W5"*w>O «• 9fiUit*
M M «5 N
TABLE OF ELJECTRO-CHEMICAL PROPERTIES. 251
■Si
fli
«-5
►•^ Pi
§§•3
s: Pt
r
s^ -
"^ j*»
®*?
1 1 1 1 1 1 I 1 1 1 1 1 I I 1 1
I I I I *^ I »0»C»0»Oto 1 1 i I 1
^ «_
I I I 1^1 B-^oSJ I I I I I
g
•a
00
O
OQ
d
I
J
O
O
I
•I
I I I I pl'??«yp Mill
11 1 II II II 1 1! =:i
•9.
I I I I I I I I 11 I I § I i-i
II 1 1
1 1 1 1
1 1 II
I I 1 1
»o I »o»o
u) I >0 X)
«
vO t^t^
I I I I I I
I I I I I I
I I I I I I
I I
I I
11 i I I I
I! I I I I
M M M l« PH O O ON'»>^0*OU) 1
$1
illl"!
1?
« 1-4 »iN
i\
ill tl
iS'
O O^O^00 08 t^
PH
1 1 1 1 1 1 1 1 l|l 1 1
1 1
vO 00
•M
r
1 1 i 1 11
00 00 00 00 00 00 00 00 00 00 00 00 1
«l
1-2 ["S 1
[■s
00 00 00 00 00 00
M «H ^t p^ ^ m
I I I I I I! I I I I I I I I i I I I M I I I I I I I
I I I I I I I I I I oo 00 Voo ^tfioo wicio W I I I I I I I
>«f4S fit
a w
IP.-
80^
9
o
OQ
. *«
"I —
'^ « 00 *>•
woo
II Mill II I8f8?5sl^§2-2'l II MM
f^wi
•SOO 'f>0 »«
8 8 8 o ^p*^ J* M ^.y>S^o Jn'Sxp 8 8 8 8 8 8
QO «
8 ? ?8 5 y§ ?l3$^g^ ^5?;r^ '
M N fOior«»0^f*:
I \0 *■ M
f
252
SOLUTION AND ELECTROLYSIS.
I •
9 ^
5 «=^
lis
•§1
1^
s
CO «e^
O *g3 O
?
"2 o
•I s
V
i I
04
£9
OQ
g
P
i
»
o
9
•«A
u
3
1
P4
I I I I
" w «>» « «
o o COO
O
o
o«
o«
1 I
I I
I I I
I I I
I I
I I I
I I
I I
2>« 00-*^pO^©2J -S^>e.^
Os>0 u><C O \0 00 vO O O Q
■^fO »o«^w « - c^oooo
pp p p p p p p ''
0000 000000000000 000000
MOO
fop\p pop
« 5* -^oo *^« b «
1 1 1
00 00 000000000000
I I I
■^■^ lO tC «0 Ov «OsO
f$ §1 Iff? i 1 1
'f r* fo Nb OMo
»o *><o ytyO t^vTi Q Q -
On ciO\«t^«wi OOO
O O O *oO »* '^ OOO
1^ f<J»o
?<§s ^SS'gS^S' 88 p
• • • » r m 9 m m • r
PH «cO «iO
OQ
OD
&
O
OQ
MM
1 M 1
1 M 1
MM
MM
•i
1
9>qo>o f4
00 do ^^t^"
MM-
§
1
N *» N
O o '
• •
00 00 00 00
^4 BH ■• M
1
MM
MM
Mil
00 X>>QO
?88
OQ *>*Ov^
0"^*^
o o p o
• • • •
S5
O
OQ
-a
;2:
CO I
g
o
§
■a
i
1
1
1 1
U^UJIOW)
«
«
<^ f^
^O
»i.<*5
O
O
?£
■N
w>
«
m:
•
•
top
I I I
I I I
I I I
00 00 00
I I I
! I I
I I I
88o
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
253
P?
■n
'«
«
• /« Pi
MM
N M (« N
• • » .
o
GQ
O
O
<S
1
I
I I I
i I I
•^ 06 o
00 *^*^
I i I
00 00 00
1 1 1
1 1 1
1 1 1
99
S-28
99P
t: " «o ^ ^ .
*s . ^ 5 Pi
iJ'S 9:^'3
f4 n
Mil
C« N (« M
^0 *^*^
•
p
« to _
i-i « «00
. • . •
o
OQ
I I I
B :g" I M
^ 00*>-vO
^ i I I
I I I
I I i
100
8
8
Q »0
o
pa
e<
1
M M 1
1
1 M M
1
M M 1
. OQ
I M M
9 td 1
^1 '
1 M M
OQ S 1
II M
ll
Mill
■4»
e< ei e< M c«
•a M WOOOO "^O
f^ "J "3 "5 "• "•
I I! II I
II M II
P^OS^QOvO N
M w ^00 t>.^
»o »»P*
3
I M II I
II I II I
I II II I
^ II II I I
g I M II I
CO
» I I II I I
NQQ '^M "^^
O^ 0^ On 9^00 00
II I I M
II I I II
U) U) *0 to *0 W)
W W « « N «
^W 0<C «vO
9O0QOX00 t^
II II I I
I II I II
^ON900>O M
9999?
P •^ (4 U)
(ho « !f fi^oo
O O O ^ (^ ^
254
SOLUTION AND ELECTBOLTSia
MIS*
11"d
is
1!-:^
|«.^
^
|<?
%
1
1
1
•
o
o
1
t^
1
CO
. ,«
1
fid o
v'tQQ
00 t^vS^'xS
ffi ff^ tfi rfi rfi rfi
g s
n »r3
OQ S
1
1
1
1
1 1
^§
H 1
1
1
1
1
1 J
J
O « « N « N W
I 1 1 1 1 1
I I I 1 1 I
I I I I I I
^1 1 1 1 1 1
1 1 1 1 1 1 1
i^
g J
h!^ I I I I 1 I
g I
§1 I i I I I I
OQ o
■a
• •••••
rfi rfi rfi tfi tfi rfi "
« « « « w «
a »0 eo '^ M 00 «
00 00 00 00 t^t^
41
o
04
•>4
m
1 1
1
1 1
1
1 i
1
? 1 1
1
Ml
"^^
__,^__
?'"
1
oc
«
.w
1
1
Q^
O (^
r «
^■5
9? ^
«
*^
>m
o
w
e\
M
•^^
0$ M
^rfiO
tn tfi pft '^ 4"* PQ
i^
I oooo
t>.>0
UTitTi
N4
ONf>.iO^
. ^ «
■"
M
^t
M
p^
M
§1
^1
1 1
1
1
1
1
i
1
1
1 1
1 1
1
1
1
1
1
1
1
1 1
-g
g
, ,
«
W3tf3tOiCtO<0«OU}W)*OU)
'i
N «
ei
«
«
w
«
N
N
W «
•a-
rOQt^riOOO O *- « «oOv
00 00 *^ *>.0 to lo •^ crj N ft
1-1
«
1
1 1 1
1
1
1 1 1
•
1
I 1 '
1
1 1 1
1
1 1 1
[c Acid
olecule
9*
ONOCOC
& 1
I
1 1 1
1
i
1 :
1
M « « «
°i n 1 1 1
1 1 1 1 1 I
1 1 1 1 1 1 1 1 1 1 1
I 1 1
IN I I I
I 1 1 1 I I
1 1 1 I i 1 1 I 1 1 1
I 1 1 1
ON ON 900 "O M
SSSSpS"
p o o o >^ <^
jjsOvO^OOvO «
(I Pm rritr^xnt^
9
O^Q0 U3
O -H «'>
•^ ^ • • •
8??P
O O M (4 in
Q Q V **
8888
8g8o?«2;?s.' • 8 8 83
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
255
1^1
&
G4
«
v.,
si'
o^4
« • to
1^1
I 1 I I I i I I I
I I I I i I
I I I I I I I I I I i I I
I I I I I I I I I
I I I I I I I I I
I I I I I I
I I I I I I
I I I I I I I I I v?^^^
1 1 1 1 1 M I ilii^
1 1 1 1 1 1 1 i I
1 1 11 1 1 1 1 1
1 1 1 1 1 1 1 1 1
CO «rj fn «^ « N N « «
I I I I M I I I
I I I I I I I I I
• • • j>_ • • • » •
O W5^ W5 « M O O ON
H
■<
a
eg
M
§
OQ
o
OQ
1
I
1 1 1 I I I
1 1 1 1 1 I
I i 1 1 1 1
_
(4 M ^ O O On
I I i I I I
I I I I I I
,^ « N « « N N
o8
•I -
'^ "^ ^ O O OnOn
NO
o
00
m
i I
o p
H E
P4 S
a
I I I I ! I I I I
rfi
I I I M [ I I I I I I I
i I I I I I I I I I I I I
>0 "^ ON to N M CN t»00 QO >H >d "^
00 QCC fO»0«rsON'3-«Q mTo-!
iM ^ M M. O 0^■^^0 wj ^ W5 N «
I I I I I I I I I I I i I
I I I I I I I I I I I I i
p. r.
^
00 00 P -^ 0*00 *^ O '^ M fO O W
00 OnON»OOs>- fOf«(^'^t>.>i» ^".-^
I I I I I I I 1 1
1 1 I I I I
I I 1 1 1 1 1 1 I ^^^^
I I I I I I I I I
1 1 1 1 I I
W ■!>• «SnO
I I I I I I I I i 88oS
8 "^ '^Nb W IC
0x^(^10
t>.iO
rOv^OOv© «
CO «o
^ rr5t>»iO
5P*^^ONO*Q0 ^O _^_
O Q i^ M iO>^ «^t>»^00
lO
. *^»o
« «o _
ooo foso «
30O fOSO Willi
O O r « !<■ ' ' ' '
• • •
mi?^
-* « 5"0»
8888
8
« to
O<00 «^ -^ f QO «0 _
M 5pf>1000N«-" -^O
OOO'^fOtON^t^
256
SOLUTION AND ELECTROLYSIS.
• • I • •
?
o
^
o
P4
O
I
I
1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 MM
o 1 1 i 1 1 1 1 1 1 i 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ifl 1 1 1 1 1 1 Mil
1 i 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1. 1 1 1 1 1 1 1 Mil
*-4
o\ 1 1 1 1 1 1 1 1 1 1 II 1 1 1 1 II 1 1 1 1 II III
II II 1 1 1 1 m|| l^l^il^^Ul lllsl i M 1
• • •• ••• • •
i:ig|fifff|!i'8iSiiSii.ilSi^i'g i^^i's
^s3;^iil!fi€i;i^iii.ili€Si?i>? ^i«:r
1 1 1 1 1 1 1 1 ifl 1 1 1 1 1 fipi|i||if 1 1 1 1
qOOQOOOOOOOOOQOOOQOQO IQOQO IQO 1 100 100 IQOOO 100 100 00 GO 00 00
1 1 1 1 1 1 11 1 1 1 1 1 1 1 II 1 1 1 1 1 1 1 1 1 1 '%s<s ^
o| 1 1 1 1 1 1 1 1 1 1 I^TIK'I |:?|S>|2>| IS'IS' 1????
1 1 1 1 1 1 1 1 1 1 1 Ip 81 lll|l = l Ig-I? §^838
•iN M « cOrOWMO O
OvXvO e«
O m t^ ^
•^ • • •
tC>-
V>M
MJM
999
iS-iisii^^iSiaNsi? ?ll^
fO >o «
"^
• • • •
J
TABLE OF BLECTRO-CHEMICAL PBOPERTIES.
257
I
a
eo
o
1 1 i^
sdcS I I
100 00
1
I
I
?58nc8 I I
00
1 1 I
1 1 I
I I
I 1
1 1
11^ fit I--
O
I
o
1 1 1 1 1 1 1 1 1 1 1 i i 1 1 1 1 1 1 1 Mil
i 1 1 1 1 II II 1 1 1 II 1 II 1 II Mil
1 11 1 11 i II 11 II II M 1 11 11 II
Illlllllllli^luiliSlu)' llll
I Hll|S§f|il»liiSi25i5i& HSi
I
I
I^SIiHsf ff sll^^S I i 1 1 1 5 1 J H1^3
??
o
1 1 1 1 1 1 1 I ill 1 1 i Igll'll llll
III
p
00 00 00 00 00 00 00 00 00 00 00 00 I 00 I 00 I 00 I 00 00000000
^ i M II II II II 11 II II I i I S^t^
I I I I I I I I I I I s»l :?! yiyjS" W]?v
0\ O ^ Ov OS
t—N- ON
M II M I M II ^ I p 1^ 1^1? |p^^
wj
8 8 8^5?
mQQ
M'
ils8|5 5^^?r?y*'^.l
N to
^ M «0
►- N fn
Q Q Q Q ^ spipo *•* f<ia^f 00 I 51 00 I ^ ONt:»N«
OOOOOOOi-< <^udu>0 N OS <0 i >P «oO OstO
OQOOOOOOOO>-iM toto lop O 00 O ro*oO
f^ M5»C fO
11 « ITS
w. s.
17
258
SOLUTION AND ELECTROLYSIS.
N S> 05
"3
sir
^
I I I I I
oSSSI I
ill 1 1
^ H?
»- « -^
<?' o I I I I I
6
id 1 1 1 IS
a # -
9t
S ooooS *^ I
O N< M M M I
S r pop ,
M « W5
_ • • • • I
O OVONONON I
r
s^ • • •
1 1 1 1
1 1 1 1
1 1 1 1
^ 00 »<«o O
I I I I
"^ OOQOOOQO
Mil
Mil
^ar-
^
M « MJ
W>
-noo
00 00 *^
1 1 1
00 00 00
lis
• • •
PPP^
>0 «OvO
O 1^. w
&
5
00
^
?
*
I I I I
MM
MM
:: II II
O
I I I
I I mi
« i
! M I
QOQOQOOO
S
1 *.
(^ »ii* « "*
Ml!
Mil
»J
f
r • • • •
I II I
gj*-
IIS'
I I 11
TABLE OP ELECTRO-CHEMICAL PROPERTIES,
259
.is .J
h
'9 Pt
•I
1
e2
St
^^;2;-s1
M
o
41
I I I I
I I I I
I I I I
a
» i I I I
V • • • •
s
p
NO
ii
I M I i I,
2 II II II
I
•a
e< M N «
«%5
!
I I I I
I I I I
v>
S»»l
o '
00 00
M>
r?\
I I I I III I I u \.
M I II I I M I I I
II I II I II I I I I
i II II M 11 I II I
00
¥?
s
: 11 II II
n I II II
n n II I
H 11 I I I
u' I 11 I I I I I M I I
^ P^ I I I I I I I I I I I I
9 »*«
■^1
? a
i I Ml I I I I I I I I I
II
"« I I I I I I. I. I I I I I
g I I I I I! I
11 I I I I I I I
*^ 10W)*0«OW)W)«OtOW)U3IOW)
^ "mOO ^COO u»u)M (4 00 N (0-K»
00 000000000000 OOQO 00 <^<^
1 1. 1 1 i I i 1 1 1 I I
I [ II 1 1 II 1 1 I I
I I I :i I I I
"2 iOlo«OU3tOU3«0
S (4Me*C««4MM
•a
w^ •^ •_ • • • •_
St **« o ^
M OO «• t>^OQ^M^
W5
NO
iir
p\<>Q0NO n «c.
)t«>10M W Mi
8 Q Q HI <0>Q N «0
I I I I I I I
I I I I I I i
9>O>00nO
M ro^*0
P99?p
• • •
58 ^w>
• • • •
Iflf^fifi III
17—2
260
SOLUTION AND ELECTROLYSIS.
it
" !
o
en
.d ^ •
It
n
'§«»
I 1 I I I I I I I I I I I I I I I
P I I I I I I I ^^^^ I I I I I I
•^1
p^ OT W
I 1 1 1 1 I ill
II I II I III
iS
3
i 1 II 1 1 1 1'§'^ 1 1 1 1 1 1 1 1 1 1 1 1 III
M M M M
. , I II I I I I 2 i?y>p I I I I I I ? I I I I I
I I I
00
g ° I I I I I I I I I I I I I I I I I M I I I I I I III
g . . O
g 1 J II I I I I I I I I I I I I I ,$1 I I I I I I 1 1 1
^^ ^«« MM ^^MMMMMMMMMS^
»N w m ft. »r*
IK
I 1 1
1 is>
I il
iS' II I
o
o
» I 1 1
® IM
o
1^
s I i I I I I I I I I I I I i I I I
I i 1 1 1 1 III
&
g
QQ
W IM Q«*
1 ^58
5 »i« M »•
• 111
a
I I I I 1.1 I I I I I I ill I I ^1 I I I I I I I Is" Sill
•g OetMMftNMviMMMM MMMMMM •^Ne«M M N N M m m
► S
fOM M M M O t'^COM MM f«MMMOO 9\ OOO
►
•g ^
o I I I I I I I I ^S>^ I I I i I I
1 1 1 1 1 1 i I i*!! 1 1 1 1 1 1
1 1 1 1 1 1 II I
1 1 1 1 i I ill
I i
i II
NO
pppp?p?«y» gSpo^:- P^JSpS" 888 g
8$
5^
M <*
oo
TABLE OF ELECTBO-CHEMICAL PKOPERTIES.
261
e<
ea
1
1
1
e» e» «
« »«o
I I I
I i I
I I i
I I I
MOM
ppop
In
O
©4
*S^
4*a
• a
II
5'^ A
II
" !l
g-^A
I I I I I I
I I I I I I
I I I I I I I I I I I I I I I I I I I I I I I
I i I I I I I i I ^^^T^ I I I I I I I I I I
I I I I I I I I I I I I I I I ?l ^ I I I I I I I I I I
M N« M
g 1 1 I I I I
«
10 m^i^m^^tmmmi
>^ I I I I I 1 I I I r ? yp I I I I I I I I I I
t
13 I I I I I I
8 I I i I I i
n
»
o
I
§ I 1 1 I I I I I 1 1 I 1 1 1 1 1 I 1 1 I 1 1 1
i" I I I I I i I I I I I I I I I I I I I I I I I
^ f>S« M M M a^
^1
I I I I I I
a S I I I I I I I I I I I I I
CQO M
I I I I I I
•♦a
M M M M M M
"3
0**^00 '^OO p^o
"^ 8 J?.S'<8 sis
i I I I I I I I I I I I Ml I I i I I I I I
I I I I I I I I I I I
*3 •* fO'i'OOvO O
0S'<^0t^«O-^M M M ^
I I I
I I I I I I
I I I I I I I I I :??f i I I I I I I I I I i
I I I
fp'tO
1 1 1 1 i I 1 1 1 1 1 1 1 1 1 isfi 1 1 1 1 1 1 1 1 1 1
000
m
.o.»fl
>M
?p
?
l£l0
M
Pr
•
10
g^O^ONg0D"O « «> S *^ Is S S^ nO
8 8 § 8 p 9 ^p 7) cTy) I pppPPp^Spp
8 o p 0% r 8 8 8 p o c
MVO
M «
00^ ff:%p Mvo
262
SOLUTION AND ELECTROLYSIS.
••J
i1
i
?
*
1^
to
it
I I I I I I I I III
o| I I II I II III
I I I I I I I I III
^ I I I I I I I I III
Tg I I I I I I I I III
M
o
o
o
•6?
•I"
I
I*
I I I i I I I I ill
I I 11 I 11 II
I I I I I I I I I
I I i I I I I I I
i I I I I I I I I I
o I I I 11 I I I I
eE4 I I 11 II I I I
I I I
I I
;^i I
. 1 I
1 I 1
I I IB
iJS w »« •
« -3 ^-
,11, |s ^§^sj:5a»2^:?SsS53.8^
I'll So OSOSOVONOVOSONOVOOOOOOOO *^
1 1 1 1 1 1 1 1 1 1 1 1 '^ I 1 1 1 1 1 1 II 1 1 1 1 1
. 00 00 00 00 00 00 00 00 t>>t>i4^t>i
1 I 1 I I I I U3W30 w
00 00 00000000 QOOO 00 QOOO 0000
I 1 1 1 i 1 1 I I 1 1 1 1
'S^ll^*
M el f« M) I «
• • • ^ •
00 QO QOOO I 00
1 1 II 1 1
o I 1 1??:??:?^ I I I I
II I I I I II I I I I l?lS I I =1
iHlfl
ll^pSff I I I I
I I I I I III I M I ig^l
fl it
►- fO»«0
• ••••• %^ • ^ •
M Wit'oQO'O
«o
PN d'
■^ rC*O*A0
k-SS
gH??|fft|ll^l?5llJ
** o\ . «
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
263
1^1 l-sa
•f
?
N
lis
^^ !*4 O
1^1
5 1
■o.s .
si's
I 1 1 I I i I I 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 I
I [ I 1 1 1 I I I I 1 1
1 1 1 1 1 1 1 1 1 1 i I
1 1 1 1
1 1 1 1
Mil
4
^ I I I I
n
I I 11 I
§5 III!
5 f's « <* «
I II I I I II II II g» I iHl^^ls^ I I I I I I §* I I M
r
1 1 1 1 1 1
1 M <>« M M 1
IS-8Sv%l
• f
^ 1 1
1 M M lO 1
1 • • • • 1
§ M
1 II 1 1
S-H
ll^ll?
e«
iis<§^(j? s'8>s3;sSv g ^ i i §>2 1 S's i s 2 tsa^^H
1 I I I I I I! I I I I I I l^p^l^llf^ I I I I I I 11 I I I i
^lll
• ••••• ••••••
«o ro O GO w) M eo b 00 t>*0 «0
O O O CSOSOV 0000 «^*^*>»«^
"a I I 0000 I 0000 I 0000 v>waw)>ov>io
i
■a
1^ OD <9y>c>
I I I I I I I I I I I I
= Si is?i ij:i I 1 1 1 1 1 1
1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 If I ill if 1 1 1 1 1 1 1 1
1 1 r I
kON^OOvO «« V) t!3 ^ 9^0V9<00^0 «*
-^ t^ W rOfO'^wj
S««
r
IflfP^ s^iiaii^sii Ilif?
M f4
m M
«
88
264
SOLUTION AND ELECTKOLTSIS.
I i I I ! i I I
SI
<S^A
o
CI
I I I I I I I I I I I I
5^A ;:g
I I I I I I I I
°l I I I I I I I
I I I I I I I I
°l I I I I I I I
I I I I I I I I
! I I I I I I I I I I I
I I I I I I I I I I I I
ON
^
g I I I I I I I I I I I I
^ I I I I I I I I I I I I
I I I I I I I I
I I I I I I I I
%
I I I I I I I I "§ I I I i I I I 1 I I I I ^ I I I I I I I I
•^ I I I I I I I I
CN.t<i{0 t^i'd'^*^!^ B ^ >0 vO sO O 'T « G *^ **i OV «0 -•
a
II
O
I I I I I I I I I
o « — :
fO *0 'O W5 r^ tf^ tt^ tfi
I -I
1
llllllll ISlllllllllill SlillllMII
I 1 1 I I I 1 1
OO^POO MOD uTosOn
<fj« « w "^
of I I I 1 I I I
I 1 1 1 1 1 1 1 I I I I
1:^
I I I I I I I I I I I I
a
llllllll
llllllll
1 1 1 1 1 i 1 1
I I I I I I M I I I I
I II I I I i I
p p PPP r 5«y>
O O *^ c<t>b M w)
?^
g" »TJ *r* ■■* ^
??Hii
p O ►* w *
« lO
TABLE OF ELECTBO-CHEHICAL PBOPERTIES.
265
I
1
1
1
I
1
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2^
5f
1
1
1
1
1
1
1
1
«« d M M
m^ • • •
I I I I
«
I 1 1 I i 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 I 1 1 1 1
1 1 1 I 1 1 I 1 1 I
I I I I I I I I 17
1 1 1 1 1 1 1 1 1 1
0\m iO ro rCOQ vO 00 «*<* i^
' V3 OS O Qfi >0 00
9 f*5 W « « M 1^
Ost^^'i'O
S I I I I i I I I I I
I I I i I I I I I I
w>OO00 t-iO »400
ss
1 1 1 1 1 1 1 1 1 1
c i
1^^
^rfg-H
2 >»^
o*
Ti*^"^
n
iS
S ^ .
lO
04
i» »«^rs
OI
^
!«.?
^
iH
M
1
1
1
t 1
8 _
CBTATE.
C!1.C00E.
1
. 1
fOOO ON« M5«
M M M M
1
i 1 1 1 i
1
_
! «
Mil
"1
M e« (4 N M
I
5m • • • • ^ • ^^
1 1 1 1 II
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
w
^ I i 1 1 1 1
00
^ ''I'll
^1 1 1 1 1 1 1
1^ =
5 qT oooooo *^*^t^
II i I i i I I
g
g I I I i I I I
02
•*» «• M M C4 M e«
I
•a ^
g, ooovo •*«• o
JT 00 *^«N.t>»t>»tN.
I I I I I I
1 1 I I
1 1 1 1 I I I I I I
I 1 1 II I
I I I 1 1 I
O >^ ^« V)
• • • •
8:
OS^OOvO N
r
1 1 1 1
•S,"*
t^»«
O (1 >o
P P P M w^vS
00*0 e« ^OOO
ppp^^yi
266
SOLUTION AND ELECTROLYSIS.
o
0«
S ft* ■»
o
I I I I I I
I I I I I I I I I I I I
I I i I i I
"I I I I I I
I I I I I I I I S'S'S'S
««
1 1 I I 1 1
1 1 1 1 1 1
1 1 1 1 1 1 ifllS
1 1 i i 1 1
M
o
o
e
G
!
1
•*<
" i 1 1 1 1 1
i
g
1 III
' II 1 1 1 1
1
1
1 II 1 1 1
III II
O « « « « M M
I -
* M Nri O ¥• O OV
a
M
O
s
I
4
O
o
I
I
9
I
M I II I I I r r !".
II I I I I 1 II I I I
II I I I I II I II I
MOe« O MOO M0>0 os«^*oo
00 MS-^fOW M M
II 1 1 I II I II 1 1
I 1 1 1 1 1 1 I I I 1 1
« « »C00 O^ MS ^ tN. H 00 o ^
• •■•••••••••
00 fiOvO ^eO« w »-i
fTi
o
&
I
•; I i I I I i
O
o
I II I II
I II I I!
5- OO O 6
I
a
I
i
I I I II I
II II 11
«/) 1#3 «/) 1/} tC If)
«4 C4 M M M «
• • • • • •
o o ovd^ooo
°l I I! I I
I I I 1 1 1 1 I I j?!?y
I II 1 1 1
I I 1 1 1 1
M M CO
1111111118 3$
I I I 1 1 1
O\0vO00n0 (4
^^ *>•»*»
Q Q Q ■« rOt^udM M lo
NO
1^900 >0 (*
f
8 8 8S?
3?
p p p r r«y^
88858^= 5^ i3s
wa
o 0«0 1— ^^
TABLE OF ELECTRO-CHEMICAL PROPEBTIE&
267
If?
1^2^
-1
« «
II
III
°s
S^i^ :3
I I i I I I
I I I I I I
I I I I I i I I I I i I
I M «l M N I
I I I I I I
I I I I I I
I I I I I I I I I I I I
I i I I I I I I I I I I
Z
%
eS
o
o
o
I ^-
K -I
^ 1
O
o
OQ
I
1.
I r?y>. I
I I 1 I I I
I I I I I I
00 00 00 t*»t^*«»
1 1 1 1 1 1
1 1 1 1 1 1
10 10 u) w) wa 10
N e« M M N M
^«0 »0»OOS"^
• •••••
booo "^M g\
1 1 1 1 1 I
s
O
o
I I I I I I
I I I I I I
I
I I I I I I
I I i I I I
M M M M e* C4
1 -
• •••••
\^ ^ sO O^ v>
I I I I I I
s> I I I I I I I I I I I I
a
I I I I I I I I I I I I
I I I I I I si I M I I I I I I I I I
B
I
&
Q
O
m <*i W « « t.^ M tN
I I 1 1 1 1 I I I 1 1 1 1
»
f 1 1 1 I I I i 1 1 I i I
* I I I I I 1 1 I 1 1 I I
I
w
I I 1 1 i 1 1 I I I I I
1 1 1 1 1 1
1 1 1 1 1 1
I I I I 1 1 1 1 1 I i I
NO
r
OS9O0VO M
• • • ^ • ^^
?
I NO
Q Q Q ? ^{^''^^S!
8?8 p?^rr y>
H
p O O M «o
^ • • • •
OOvO M w> ^
• • ^ • • •
« v>
flfS^^iiii
??p^Pr
268
soLunoir and electboltsis.
§1
o* d^:a
^3 ^^^
l^i
o
1 1 1 1 1 I I I I 1 1
1 1 1 1 1 1 1 1 1 1 1 I
I I I I 1 1
o| I I I I I I I I I I
»o
I I I I I I I iS'S'S'S
I i I I i I
00
8^
»
O
o
§1
o "
M o
I
1
I M I I I I i I I I I I I i I I I llsl^l I I I I I I
1 1 1 1 1 1 1 1 1 1 1
°l I I I I I I I I 1 1
i I 1 1 1 1 I 1 1 1 1
I I I I I I I I f?y>^
w :
I 1 1 1 1 1 1 1 1 1 1 1 1
eo
r I 1 I I I I
O
I I I I I I
I I I I I I I I I I I I g I I 1 I I I i
vO M OS*^«o«nM M M I- J3 « OOO 'TPQW « »^ 5 ^ O O OOsOkO*
I i 1 1 I I I I 1 1 i
I 1 1 1 I 1 1 1 1 1 I
^ W} >0 wa >0 «0 «0 >0 U) U3 V) to
P« rCOOO "^M «5^M M to
sOOO M iomOOO ^<«)M ^
CO w « M M
1^
I i I I I I I I I I M bI I I I I I i
1 I I I I I I I I I I I
il
<s § i I I I 1 1
•a
O* "^ '^** ^0>i0 M txQO Q OS
M O '^rt^'P P tOiCOO MOOO «0
00 eOOS**«OW5« "H M
^ « «« W « « W
I-
•^ * * • • • •
o| I I I I I I I I I I
I I I I I I I I I I I
I I I I I I I I I ^^^
I I I I I I I I I
I I i I 1 1
I I I M I
M fOt^wlOM N lO
8 O O •^ fO>P ^ I')
O^O^O«0^O e« lO
Q M ffJ^lOM « »o
8 8 8'8o^2;fya 8 8 88??'
r
o p p >•* <CnS ' ' *
O O p P M (CO
• • • "^ • • •
'*0Q *fi
^^^pp'7$rr>!^prr
p s ??^?a
TABLE 07 ELBCTBO-CHEMICAL PBOPERTIES.
269
^
n
»< s
>< s
^ ^
•< §
•3 '^•'i<
ISS
•
2-2 •
0'
N'S^K'S
1^-^
»
isJs
»
•aS"-3
1^^.
5^«.g
0^^
^
S'^A
^
!«.?
g
t
o
o
I i
I I
s
1 1 1 i 1 1
1 N M M M 1
1 ^'^ 1
• ' . • •
MINI
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
e« N et M e< M
73
>
"^O "^w P^«
• • • • • •
I I I I I i
I I I I I I
I I I I I I
p I I I I i I
S
i 1 1 1 1 1 1
° 1 1 1 1 1 1
^ £^\S vO O >0 10
n J — r
; I 1 1 1 i 1 1
q o
»^ I I I I I I I
.4» U)«OW)*OW)«0
d N N M e< M (4
I
Ell •.••••
. «
I ^
M «
1 1 1 1 1 1 1 1 1 1 1 1
I I I I 1 1 1 1 ^s*;?^
I I I I I I 1 1 f sU
8 I I I I 11 |.lf«!».
o
I I I I I I I in I I
I I I I I i I I I I I I
•• «
>oo
•a o»oo Q*^ «"0 MOO »o^5r»^
I I I I I I I I I I I I
S I I I I I I I I I I I I
•i
•I -
I I I I I I
I I I I I I
I I I I I I I I I ^?»
«o
1 1 1 1 1 1
1 1 1 1 1 1
111111111888
r
ONO'OO^O f«
?
??5?
r
^O«0vO «<
M «50»»OM
8$8S?
• * • • •
?8^
Pi888pS^Sirv
O O 00 M <^
M « 10
« ws
Q Q 51 s 5ps5 «^t>»»oo o^os
popOOOMdiOMN^rf)
M « ""^
270
SOLUTION AND ELECTROLYSIS.
^'^ CI
is
m
o
to
It
o
I I I I I I
I I I I I I
I I I I I i
I I I I I I
I I I I I I
1 1 1 1 I I
«*5
^ I I I I I I
O o| I I I I I
o
I I I I I I
I M N M e^ I
^^ M OS
t
tN I • . . • I
§111111
o
eg| ii'iii
« ^»^ cS>o «*ao
O 0000 t>«t^t^t^
1 1 1 1 1 1
1 1 1 1 1 1
I I I I M I
i 1 1 1 1 1 1
o
ill 1 1 1 1 1 1
III III
I I I I I I
„- I I I I I I
H
S I I I i I I
w
g I I I I I I
llllll mImIIII gl^llllll glllllll
§ s
11 II II « I I I I I I I
llllll
•31
§111111
It
OVONOOOOO
d" 8
o| I I I I I
et M M M e< M
IT
llllll
e< M M M M M
•g tcQppt^:t>p
s*
>S^^^^ lO
lO
llllll
lowaioiowdM)
N M f« f« M n
s OOO O vo'^-O
•^ • • • • • •
1 ?^ 2^2-2
I
llllll
llllll
llllll
llllll
llllll
r
OVPJOOO M
999??
rOvOOOO M
<7^OSO«0DnO C«
99999?
Olio
PP
Hl?^^
im
?r
TABLE OF ELECTBCKiHEMICAL PBOPEBTIES.
271
1 1 1
iou)waio
« M M «
«0«r;«>.t>»
O O O^
MM
ee
N «0
M M Vi
• • • "
M
MM
1 1 M
^
M M
1
MM
1
MM
«0 US *0 U3 lO to
f« C« M f* e« M
^r • • • • •
."Sow
•
M
<
N
1
1
M
1 1
1
1
1 1
1 I
I
I
1 1
1 1
«*i -
M
00
«
1 1
i
1 1
1 1
O ^
8 1
1 1
n
w' 1
1
1 1
•
1
o
1
^
fl*
p M MOQO
^
M
M
M M
»
1 '
1
1 1
1 1
flO
1
1
1
1
1 1
1 1
3
iAtC>0«0>OiO
6 !1
«
M M
« «
I I I
io«o»o
C4 M d
§ O OMOOO OVON
pJ5 • • • "^ • »
i:
I I M M
ball's
a«.i
0« «
1 M M I
i C4 M N M I
^I|
5.1
«
. I M f« lO I
§ ^
O I I I I I I
S^ I I I I I i
o
I M M I
§ I
^ • M M M
M e« (1 f* M M
M « M^ ON*^
— . »•••••
•s.
^
M M M
i •M
I M I M M
I I M M M
M I M M I
^ M M M I I
W I M M M I
t M M M M
^*>»0\M *»0O Q.*^
a ;
2 :3 —
• I III II II
I •
I I I I I I II I
a
I
• •••*«••
Sfi V^ '^ "* «*5 <*i <^.
I M M M I
Miir?
M I M I
M M I I
I i I I I M I
>0 c< io
UdM «« lO
p ^M<«y>
rOSOOOO t*
M ro-r^tOM
OSO^QOv© «
M rot^w)M
????«'
M «* lOM M ^
M « "^
« »oO
M M lO
o o o
n%
M M fQt^tOCo
M ei ^tQB v>
M (« ^« *^1
8 O'M eo*^ ,
. 99999:^
«^iOp Q
272
SOLUTION AND ELECTROLYSIS.
J "S ^ ^-.s "*
j2l I'S
s V ^ so o ^
IIS |2^ I'sa |1
»
o
o
5
I
O
I
>
■a
I I
o| I I
1 1 1
$ III
1 1 1
1 1 I
I I
I I
I I
I I
I I
I i
11 II I II
II 1 1 1 1 1
II Mill
II I I I I I
II I I I II
II Mill
Q> MM MM MmmMM
'3
N O Ovn)
I I I I I S^&T^ I I I I I
I I l?l I I I I I I I I I
0<«««etNM MMMM
sssss
• • • ^ • T^ • • » W
OO « r-^ wjM 0*0 »o^^ O^O
f*SW«MM C^r^MlO 00 'T « M M
M«fO MMMMM
o II I I I I I I I I I I I I
I I I I I I I I I I I I I I
Prr'y*. Pr«y» 99999
M
M
O
O
I
8111^1111 III
•*
k
J2 P^
I
1
H
O
99I
Vi
"S OOQOOO
g M M M
1
9s
I I I
I I
wj lo
I I I I III
I I I I I II
I I I I III
Ml! Ill
I I II III
SlJ^ ?■??<?
I'ta'S I I II
I I I I Ills
OOOOQOOO Q O O
M M rO b« M
I II I I I 1 1
I I I I Mil
O "^ M
wa
fl.1 II lii I UfH
1 1
1 1 1 I
TABLE OF ELECTRO-CHEMICAL PBOPERTIES.
273
1,^
g
.Si? »•
•
i
o
o
i
1
v^
M
«
MM
1 1
1 1 1
1 1
1
1
1 1 1
MM
II II
1
1 1
1 1 1
MM
II
1 1 1
1 1
1
1 1
i 1 1
1 M 1
1 1
1 1 1
1 1
1
1 1
1 1 1
1 1 1
1 1
1 1 1
1 1
1
1 1
1 1 1
MM
1 1
1 1 1
1 1
1
1 1
1 1 i
•
1
f^ M M M
Isl
M
i
1
Mil
1
1 1
1
1 1 1
1 1
1
1
1 1 1
1! II
1
1 1
1
1 1 1
1 1
1
1 1
Ip 1
•a
1
S
I?
•II
o
II II II I Ml
II II II I III
II II I II III
w
«
.. I II II II III
u II II M I III
o
8 II II M I III
«C.
^ I 1:1
I I II M II I II II
& S —
lllllll IMP
.4* «inMc<n«i«« NtftaMN*
5 «>«o^>o»^^ « "^Oqp
S
II II II II S'S'S'SK' II II II
lllllll MM
II I I M II
i 11 i II
iiri
isHss
M II II I MM
. 888p 8??p
«
00 vQ
88o?S'^
M eo<^
w. a
to N
18
t
274
SOLUTION AND ELECTROLYSIS.
o
2O .
|Sa i^
3
:<
■rf.:f
1^;
S f 3
iSp, ^-9
S
:;
I 1 1 I I I i III
°ll I I I I I III
I
I I II II ill
I
1 1 1 1 1 1 III
I 1 1 I II II II 1 1
I I I 1 1 I 1 1 I I 1 1
1 I
%
1 1 I 1 1 1 1 1 1 1
^4
II
2-8 .
I 1 i
I I 11
■: 1 1 1 1 1 1 1 1
8 °l I I I I II I I I I 8 11111111 Mil 81111
9; lllllll MM ooiiiiiiii MM .o|Mi
l|-s ItOg inJ,
O rCNMNriMM et^MMOOMM m4)m
9 g -g g 3
I lllllll MM glllllllll MM ijllli
^ I s B ^
I lllllll Mil It iiiiiiii iiiiliiiii
I ' s s
H H pq
lllllll II I I
I 11 I II I I II I
^00 ^oW)
M^O\OVOOOO wj
O O O 1^ fQt>«io M M 10
10 00 10
^ w 100 ^ *^ < .-_
O O O M M O OB t-i
IIIIIIII 11 1 1
II I! I I I I II I I
« "3- S\ ON aoo o M
O O O <^ (>nt>»iOi-i
1 1 II
1 1 1 1
r
8
V) 00 «0
P P 9 r 5* :^ P P 5 ?«
Ma
TABLB OF ELECTBO-CHEMICAL PROPERTIES.
275
|0A
O
^1
41
5Sp.
o
C9
^a
^ X
£^
s*^
• O o
S >
s'-s,
•
-Sl^
i?..!
«o
A:3
I 1 1 1 III
I I II Ml
I I I I Mi
I II I III
I I II III
II II ill
€^1^
II 1 1
1 1 II
1 1 II
Mi
f« C« C« M
M M »4 »^
Mdt<<40 OS * ^ ^
I I I I I II I
II M M II
I II II I I I
. II II I 11 I
?
^ II I I II I I
I I I I I! I I!
I I I II I I I I
I 11 I II I
t
I I! II I I
I I! I II I
- II I I I M
§1111111
01
a O
I I I I I I I
O ^M 10
fOWJWiW « « •^ M
» ®
"I II 11 II 1 1
^1
if I i 1 1 1 II I
o
v3 Me«Me«(ie«Ne<
3 -
i
1 1 1 II 1 1 1
g ^ N A N. M
§1
iO«^
^S,
I
I II M II
S g I I II I I I
a I
.»a
&
1 1 1 1 1 i I
?
I I II
I II I
I II I
= 1111
H
o
o
I II I
II 1 1
01
il
SI
II I II I
1 1
Jb io«OWdW)
O M M M M
I II I
MM I I I I
I I I I I II I
II I II I I
II II
O O *^ fQo.io*N
????
O O *^ eO«
10
OsOOOnO
§i§8
Wf?9 9ff?
¥>
•^ • • • •
¥>
Vi
^5
PPP9
18—2
276
SOLUTION AND ELEOTBOLYSIS.
O <
II
$
^-^
M
in
II
N ** «o
rars
4> o
I 1 1 I I I
ol I i I I I
I 1 1 1 1 I
^
^ I I I 1 1 I
n
o
o
is
1
■a
i
°l 1 1 1 1 I
1 1 i 1 1 1
CO (4 «< Cl M M
I I I I I I
I I I I I I
M M N N 9t N
I I I 1 1
Mill
I I I I I
«.| I I I I
STTTTT
O
a 1 1 I I I I
^4^
S ^ 0\«0 0\OVO
^ P
I'll"
I i I I I
.«a M N N (4 C<l
S
•a P4
~ • • • • •
I I I I I I I I I I I I I I I
I I I I I I I I I I I I I i I
I M I I I I I I i I I I I I
^ I I I I I I I I I I I I I I I
? I I I I I I I I I I M I I I
I I I I I I I I I I I I I
I
I
I
t^ «o nt p^ 51 '^ O Q - 500
- tMJO -^^OO O '-''-' ►^ *-• Q
MMMMMMNNCi
^
Os)-«0'^^«^«tcQ4>'i-i I I v>| n
>«^Or4NNf«Mf^i-iMl lOvlOO
M 00
I I I I I I I I ifl I I I l|lf
':S QOOOQOqOQOQOOOQOOOQOOOOOQO I I OO | 06
u
" I I I I I I I I I I I I I I I I II
° 1 1 1 1 1 1
I I I I I I
1 1 1 1 I
I I I I I
i I 1 1 I I I I i I \^^\ I SI?
I I I I I I I II I 18? I I S'l
)sO
- - w »^ Jo**
00 VO « «£J
T 'OQ «»»«0
l^^gsONON
1 r r » r
00 M *£i
M «'
(5 Ni mna
ij S 8 8 ? 8 8 p ?^- ^§^«l,
1AM POO «0 — ^
'^ M (0«Om poo «0 ^
" " M POWJNI POO(
TABLE OF ELECTBO-CHEMICAL PROPERTIES.
277
I
•§1
i*^
lis
^ CO
Itllllltll i'llllll
ill 1 1 1 1 1 I- 1 1 1 1 1 1 1 1 1 1 1
t
m
■bo. w) rn O 00 vO « OsQ Q Q OnOnOn
^15 I I i I I I I I I I 111 IviH o s Ha'lal'?^ I I I I I I I
999
0\9\Q OnOSOS4>« o
I i I I I I I I I I I I I I I I I
COOOQO W)V>«OV>*^«OV>W)V>v> 00 00 00 00 00 00 00
00 M MVO <»p\fOM>p ^ U)
N
I
--»2J|^ I I I I I I I
pA 00 00 00 00 00 00 00 u)«OW)W)V)iAW)
J:
g.
00
• ••••••
***00 *^Q 7fO*0 *•* too t«« O »«:
mOQ '^V^vO W)0^ m m m m m m O
X^'TQ.^WOO ««««•«««
MMMMMMM IIIIIIm
WS
?s
Sffsltl III I ll§
♦o»oo
9s9«00>O M w)
O M «^<^iOM « 10
Q O O Q M («>Q N W)
pooppoor'r'i^
ntO
■" o ■»o O "^ «'
^ « « "^■00
»o
M N fO^WaO
f
ON94PVO M «0
^^<2*
00 tN.w)^«>0 e* <»
f^ 10 <» u) ^ t^kiO
. • T^
"♦•CO^
M N
M « -^
•-I M ro
^oSnOOO *- Ov 0'-' ^o^ «▼
o«o «*>25 00 *>i . oopop*-'**
M r^r^O ^O O
278
SOLUTION AND ELECTROLYSIS.
H u <E a^«
lis
55 A g-^S
f1
i1 •
•Si's
r
I
O
CQ
I
i 1 1 1 1 1 1 1 1 1 1 1 1 1
o| 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
i 1 1 1 1 i 1 1 1 1 1 1 1
°l 1 1 1 1 1 1 1 1 1 1 1 1 1
1 lll 1 II 1 1 III
MM M HMMMMMMM
*^0 M Nl 1«M ON'*
1 I 1 I *--0 W *^M 9\*N.OV
1 1 1 1 1 1 *^A'»*^tN.W>3 U>«5
II II 1 1 1 1 II 1 1 i 1
1 ^IS* 1 !? 1 00 00 00 00 00 00 00 00
INrtlMI M^«MN^N^MN^M
' Son ' « ' ^'€^«'«^§S*
M Nl M M M M ^ICOOO
M M
V|Mm|m| M^tf^MpHMMM
Ipplpl l??855lp'
Mill
I I I I I
I I I I I
I i I I I
8
5"
p
11
Mill
I I I I I
II I M
Mill
I I II I
I I I II
Mill
I I I
*o
00
M «^ W5« ~
0\ ^ON*^
M ^fr* I I
100 *»^
5>l
Mae«
^
I 11 I M I M II I.?
M I! I III i II g
M N4
PP
!
Mr4Me««4NMc4e«| I
0000
II II II I I II I II
I I II II M I I I II
H
•Q
^1
o o
00 QC
II'
« «
I I
I I
m2^^? S»^2^J?S>y8^ 888 83 3^2 S*8 I ^ ?
M w «
"ii
— M « V
flUi^Hi 11 HIM
TABLE OF ELECTRO-CHEMICAL PROPERTIES.
279
-€
85
I
•8 .
<5^0.
w
00
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
H
o
. m
ll
n
? I I I I I I I I I
I I I I I I I I I
fOf^^^ M M Q O>O0
I I I I I I I I I
wi
<8
I I I I I I I
! I I I I I I
I I I I I I I
I I I I I I I
e- I I I I I I I
o
B^ I I I I I I I
* "*NO O •• « 0^ •-•
M B e« f« (4 N M
W W « « M
ll
I I I I I I I I
I I I I I I I I I "^1 I I I I I I I
I I i I I I
I I I I I I
I I I I i I
A I I I I t I
g I I I I I I
^ I I I I I i
fi M M C<l N N N
a ^
« I I I I I I
I I I I i I
I
SZ5 _
5 M5^«^
.p «
I
a 5
Mjt-*'
1 1 1
I
t
C4NNMNC4MNM
00 o>oo «oo t9 5* tp-*
M« M M M M O 900 'C^
I-
« « M « « M M
^ N N (4 e« M N
I :
S QOQOOO
•2 "-I ^ "^
I —
N N M «< f« M
I I I I I I I I I
I I I i I I I
I I I I I I
I I I
11 I I I I I I I
I I I I I I I
I I I I I I
I I
$88S^S^
»o
888-^
o o o p
►^ ?*"
i§
280
SOLUTION AND ELECTROLTSIS.
|S6 ;5
-* .mi
50 P.
O
I i 1 1 1 1 1 1 1 1 1 1 1 1 1 I i 1 1 1 1 1 1 1 i
I I I I I
° I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 I I
I I I I I
I I I I I
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I 1 1 1 1 1 1 I
>: o I I I I I I I I I I I I I I I I I I I I I I I I I
CO _
U 1 1 1 1 1 1 1 1 1 1 1 1 1 i I 1 1 1 1 1 1 1 1 1 1
to
»o
J
p;ryo
* 2a?^8^^SN&^?oS«*^«
O lOCdM w Ni
1 1 1 1 1 1 1 1 1 I
f 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
o 00 00 QO 00 00 00 QO 00 00 00 00 QO 00 00 00 iOV>«OiOU)W)«C«OV)V>
^ I I I I I
tfi
7 I I I I I
n
1"^
I I I I I
a
:a
Mill
I I I I I
N vt «« et M
*o
ol I I I I I I I I I I'S'SI I I I i I I I I I I I
Mill
■S'g.
II I M I I I I II |K I I I I I II I I I I I
I II I I
iilssis
• • • •
O O P O •" «o
wj
.«©
O\9O0vO M V)
?0 O O qO m M u)
• ■••••••
8880
ri
M W>
8888^S^S-<^S.S< > 88
« w>
w>0 eosp « w>
o o p « « '^^O
• ft ^ • • ft •
O M «« W>
TABLE OF ELECTRO-CHEMICAL PROPERTIES. 281
iii
in
2-2 •
J:a
«.-p
eS
II
S-S •
ijSa
I I 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 I
I I I 1 1
Mill
i I I I I 11 I I I
II I I I I! I I I
I II II I I I I
I I I I I I I I I
I I II
I I I I
I I M I ^ I I I I I II I I! ^ I I I I I I I I I
I I I I I
I I I I I
*
>4
; I I I I! I I I II
I I I I I I I I 11
^ I I I I I I I I I
^
1 1 1 1 1 1 1 1 1
. o or
«n2« i^^HSi^s'JS^ i^^lf$^S42«
I M I I g il I I I I I II I I I
» g
11 1 1 1 i 1 1 1 1 1 1 1 1 II
%» 1 1 1 1 1 1 1 1 I
1 1 i I 1 1 1 1 1
1 1 1 1 1
i^
t^ M II
*3 W^ MS^
I « I I i I
8
^ I I I I
C« M f« «« ft
• • • • •
S 9« N M c<
1
• • • T^
S*
W^J^ft
I 1 1 1 I
1 1 1 I II 1 1 1 1
I I 1 1 1 1 1 1 1
1 1 1 1
1 1 1 II
1 1 I 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 I
eftvQ « MS
O 9 •-« N w)
O
Q Q Q M WJ>b W WS
.WS
• • •
"l^ssss.'
• • •
• ^ • 9 m m *
ppp?
O O •^ «^*^
O M c4 m
O O p O
• • • •
282
SOLUTION AND ELECTBOLTSIS.
1
MM
o|
1 M 1
1
MM
1
1 M 1
°l
MM
1
I M 1
1
1
1 1 1
1
Mil
o s*;? ffi??
• • • • •
N M M
IP
o
I^A 5
M I M M I I
M I M I M I
M I M M M
t I I I I I M M
00
7 M M M i M
W
I I I M M M I
«r SP« 5P*i!5«'»QO woo
I r
I M M I M M
M I M M M
1 -
•S3 IC^ON^M « « P^O*
2* •
•II
lis
9
M M I M I M
M M M I I M
M M M I I M
M M M I I I I
TTTTTTTTTT
g M I M M M I
O MM
I ___
^ M M M I I I I
I M M M M I
w) «o V) u} w) wa w) «o «c «c
s
o I I I M
M I M M M
I M M M M I
I M I I
M M I I M I
M M M I M I
r
ONO«0>O «4 w)
p??8?^SS'
ONOOOvO M w»
^ « Vim I
• • • •
f 5^H5I I
wa
?^|Sfii I
TABLE OF ELECTBO-CHEiaCAL FBOPEBTIES.
283
e
ft) ^ •
50 ft
°s
1 1 I I I 1 1 I I
ft
I I I I I I I I I I
e«
1 I i I I I I I I i
I I I i I I I I I
I I I I I I I i I
I I I I I I I I I I
I I I I i I i I I I
I I I I I I I I 1 I
I I I I I I I I I I
^ I I I I I I I I I
^ I I I I I I I I 1
i I I I I I i I I I
o,
at
a « I 1 i i t I M I
I I I I I I I I I
•»5
I-
WQdp vowa^iOOQO M
r I I I I I 1 I I I I
- I I I I I I I I I I
*i
? I I I I I I I i I I
. o
-r ^«of4 « <^N !J>0 5«>
I
a
I I I I I I I I I I
^1 I I I I I I I I I I
'ai
♦*»
i-i 0000 M «»ro«0 9ve« MO
^ 1 1 I 1 1 1 1 1 1 1
o
i^ I I I I f I I I I I
^ 1 1 1 1 1 I i I 1 1
- «•
1 1 1 1 1 i 1 1 1 I
1 1 1 1 1 1 1 1 i I
vOvOO C^^M 100 NOO
• •■•••••••
^OvOQO «i
M <»>e Q«o \o QO «4 00 '^
moos5 —
1 1 1 1 1 1 i I I
I I I I I I 1 1 I I
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
I 1 1 1 I I I 1 1 1
vO
8880 ^^ 2 «? p 8 8 8 9 ^p 2 «*y5 P S 8 8 ^ ^p 2 «?•«
M MW>
OOVO M M lA
O O O P M «• '^Os o p 6 O O •-■ f<^«»
rS\^o>oo v)o I I I
O 00 M «*>0 * *
INDEX.
{TJie numbers refer to ths pagei,)
A.
Abbot and Notes, solnbility and di880oiation...l87
Abxoo, freezing points of solutions... 72, 213
Absorption of gases by liquids... 10
„ coefficient... 13
Accumulators ... 113
Acetic acid, conductivity of solutions of... 140, 142
„ vapour pressure of solutions in... 82
Adds, affinity of... 162
„ conductivity of... 149
Additive properties of salt solutions... 174
Adie, osmotic pressure... 39
Affinity, chemical... 152, 162, 164, 182, 189
Alcohols, vapour pressure of mixtures with water... 98
Alcoholic solutions.. .142, 203, 205
AuBZEJEFF, mutual solubility of liquids... 16
Alloys, melting points of... 73
Alternating currents, use of... 145
AuAOAT, deviation of air from the gaseous laws... 70
Amalgams, freezing points of... 73
„ vapour pressures of... 93
Ammonia, conductivity of solutions of... 150
„ solubility of.. .14
Applications of Electrolysis... 131
Abxstbono, theory of solution... 207
286 INDEX.
Abbhenixts, oondaotivity and ohemioal affinity... 162
„ „ osmotio pres8iiie...l66
diffosion of eleotrolytes...l95
dissociation theory of electrolysis... 155, 171, 184, 187
freezing points... 213
heats of iomsation...l92
isohydric eolations... 186
temperatore of maxiTnuTn condaetivity...l94
vapour pressures of solutions... 74
Avogadro's law, application to solutions... 88, 40
B.
BsoKMAim, freezing points... 61, 67
„ vapour pressures and boiling points... 90, 93
Bbcquebbl, preparation of chemical compounds by electrolysis... 131
Bbbtz, resistance of electrolytes... 144
Bbbthblot and Junoflbibch, solubility in mixed liquids... 81
Bbbzbliitb and Hisihobb, electrolysis of salt solutions... 105
„ theory of chemical action... 127
Bichromate group, ionic velocity of the,... 142
Blaodbn, freezing points of solutions... 54
Boiling points of solutions... 85, 90
BouTT, resistance of electrolytes... 144
Boyle's law for solutions... 27, 36, 40
Bbbdio, influence of concentration in osmotic pressure... 69
BuNSBN, absorption coefficients... 18
c.
CSadmium iodide, electrolysis of alcoholic solutions of... 132, 135
Calcium oxalate, decomposition of... 163
,, sulphate, solubility of... 21
Gaujemdab, platinum thermometer... 62
Capacity of solvent, specific inductive... 156, 204
„ electrostatic... 146
Cablislb and Nicholson, decomposition of water... 104
Cell sap, motion of, and osmotic pressure... 37
Cells, concentration... 198
„ voltaic. .103, 113, 114, 122, 198
Chemical affinity... 152, 162, 178, 182, 184, 187
„ decomposition by electrolysis... 104, 127
INDEX. 287
Ghemioal eqailibrimii...l52, 180, 186, 187, 189
„ interchanges in solutions... 106, 151, 173
„ theory of solution... 12, 22, 206, 210, 211
Glausius, theory of electrolysis... 151
Cobalt salts in solation...l75
Coefficient of ionisation...l57, 166, 168, 181, 187, 204
Oolligatiye properties... 42
Colloids... 58
Concentration, its influence on conductivity... 154, 157
„ „ „ freezing points... 67
„ „ „ vapour pressures... 92
„ cells...l98
Conductivity of electrolytes... 135, 143
„ „ and chemical affinity... 162
„ )) ») osmotic pressure... 165
Connection between electrical and other properties of solutions... 162
Contact difference of potential... 116, 121, 160, 197
Copper, deposition from solution... 131
„ ion, velocity of the... 142
„ sulphate, electrolysis of... 132, 134
CoppBT, freezing points of solutions... 54
CBxnoKSHANS, cleotrolysis of salt solutions... 104
Cryohydrates...72
Crystalloids... 53
CzAPSXx, theory of primary cell... 125
D.
Dalton, solutions of liquids in gases... 9
Daniell, electrolysis of sodium sulphate... 128
„ primary cell... 115, 125
Davt, electrochemical researches... 104, 105, 107
Definition of the term ** Solution "...6, 7
Densities of salt solutions... 174
Db Vbibs, isotonic solutions... 37
Dialysis... 53
Dielectric constant of solvent... 156, 204
*< Differentiation '* curves... 208
Diffusion... 32, 45, 179, 194
„ constants... 47, 50, 53, 197
„ experiments on... 49
288 INDEX.
Diffasion of electrolytes... 179, 194
„ throngh liquids... 45
Dissociation theoiy of electrolysis... 154, 155, 171, 180, 187, 211
DistiUation of mixed liquids... 99
DoNDEBs and Hambxtbgeb, variation of osmotic pressure with tempera-
ture... 36
Double decomposition in solutions... 106, 151, 173, 184, 187, 189
Double layer of electricity... 119, 161
E.
Electrical double layer... 119, 161
„ endosmose. . . 159
„ properties of solutions... 103, 127, 143, 1C2
Electrolysis, practical applications... 131
„ theories of... 170
Electrolytes, conduction by... 113
„ conductivity of... 143
„ diffusion of... 179, 194
„ freezing points of... 67
„ osmotic pressures of... 38
„ vapour pressures of... 92
Electrometers, Lippmann*s...ll8
Electromotive force of contact... 116, 121, 197
„ „ polarisation... 112, 144, 146
,, „ primary cells... 122, 198
Electroplating <9to....l31
Endosmose, electrical... 159
Enobl and ]^akd, influence of temperature on solubility... 23
Equilibrium of saturated solutions... 19, 21
„ at the melting point... 29
„ chemical... 152, 180, 184, 187, 189
£tabd and Enobl, influence of temperature on solubility... 23
Evaporation, analogy with solution... 25
Eykman, freezing points... 60, 67
F.
Fabaday, electrochemical researches... 105 to 117
„ laws of electrolysis... 108
FiGK, theory of diflusion...47, 50
INDEX. 289
Films, resistanee of liquid... 158
Fitzgerald, iom8ation...l56
„ oflmotio pressure... 42
„ and Tboutoh, Ohm's law for electrolytes... 151
FiTzPATBiCK, electro-chemical properties of solutions... 184, Appendix
„ measurement of resistance of electrolytes... 147
„ ftinction of the solvent... 208
Fluidity, ionic. .198, 202
Forces acting on the ions... 188, 156, 205
Freezing points of solutions... 4, 54, 168, 218
„ „ „ connection with conductivities... 165, 171
M „ „ „ ,, osmotic pressures... 55
,) » M „ „ vapour pressures... 84
,1 „ „ experiments on... 54, 61, 168, 213
Friction coefficients, ionic... 188
Fused salts, electrolysis of... 105
G.
Qab constant... 41
Gaseous laws, application to solutions... 85, 40
Gases, discharge through... 105
„ solutions in... 8
„ solutions in liquids... 10, 94
„ „ „ salt solutions... 15
Gautzinb, solutions of liquids in gases... 9
Gay Lussao's law, application to solutions... 86, 40
Gladstomb, properties of salt solutions... 177
Graduation of thermometers... 4
Gbaham, experiments on diffusion... 49, 52, 58
Gram-molecule, definition of... 88
Gbotthus, theory of electrolysis... 106
Grovb, gas battery... 114
„ primary cell... 115
GuLDBBBO and Waaob, chemical equilibrium... 152, 189
GuTHBiB, cryohydrates...72
H.
Hahbitbobb and Domdbbs, influence of temperature on osmotic pressure...
86
Heat capacity of solutions... 177, 209
„ effects of chemical action... 162, 189, 192
W. S. 19
290 INDEX.
Heat, effects of, solation and dilation... 3, 12, 28, 209
„ of ioniBation...l90, 206
Helmholtz, Yon, contact difference of potential... 118, 160
„ „ electrical endosmo8e...l60
„ ,, theoiy of primary cell.. .125
Henby, law of solution of gases ..13
Hess, law of tliermo-neatralit7...189
Heyoock and Neville, melting points of alloys... 73
Heydweilbb and Eohlbausch, conductivity of pore water... 201
HisiNOBB and Bebzelius, electrolysis of salt solutions... 105
HiTTOBF, conductivity and chemical activity... 162
„ „ of mixed solutions... 130
„ migration of the ions... 133, 134
„ nature of the ions... 128
HoBSFOBD, resistance of electrolytes... 144
Hydrate theoiy of solution... 12, 22, 206, 210, 211
Hydrochloric acid, solutions of... 10, 14, 96, 102
Hydrogen ion, velocity of the... 140, 142
Hydroly tic dissociation . . . 202
I.
Indicators, theoiy of... 176
Induction, self, with alternating currents... 146
Inductive capacity, specific, of solvent... 156, 204
Ionisation...l56, 166, 170, 181, 190, 204
„ power of solvents... 156, 204
Ionic fluidity... 193, 202
Ions, combination with solvent... 156, 205
concentration of... 180, 185, 187
electrical charges on.. .111, 136, 178, 195, 204
freedom of... 106, 138, 151, 155, 171, 178
friction coefficients of... 138
function of, in chemical change... 153, 162, 184, 187
heats of, formation of... 190, 206
migration of... 132, 179
nature of... 108, 127
velocities of... 135, 138, 140, 154, 173, 196
Isohydric solutions... 186
Isotonic solutions... 37
„ coefficients... 38
I
INDEX. 291
J.
Jahn, contact difference of potential... 117
.„ theory of primary cell... 125
Jones, freezing points of eolations... 69, 168, 218
JuMOFLBiscH and Bebthblot, solubility in mixed liquids... 81
K.
Kelvin, Lord, theory of primary cell... 128
EoHLBAUBCH, coefficient of iomsation...l57
conductiyity of electrolytes... 185, 145, 148
of pure water... 129, 149, 201
velocities of the ions... 135, 178
EoNOWALOFF, vapour pressures of mixed liquids... 97
L.
Lamb, electrical endoBmose...l61
LiPPKANN, contact difference of potential... 117
Liquid films, resistance of... 158
Liquids, solutions of, in gases... 9
„ „ of, in liquids... 16, 97
„ „ of gases in... 10, 94
„ „ solids in... 17
LivEiNo, chemical equilibrium of solution... 25
Lodge, velocities of the ions... 140
LoEB and Nebnst, migration of the ions... 184
Looms, freezing points of solutions... 168, 218
M.
Magnesium hydroxide, formation of... 202
Mass action, law of.. .152, 180, 184
Maiimnm conductivity, temperature of... 198
Membranes, diffusion through... 58
„ semipermeable... 84, 179
MsNDEiisEFF, pTopcrties of solutions... 208
Mercury-dropping electrode. . . 120
Methyl acetate, decomposition of... 168
Migration of the ions.. .182, 179
„ constants... 185
292 INDEX.
Mixed liquids... 16, 97
,, ,, solubility in... 81
,, solutions, dissociation of... 184, 187
Mixtures, electrolysis of... 130
solubility of... 29, 187
Molecular conductivity... 186, 149, 181
„ interchanges in solution... 106, 151, 162, 178
„ volumes... 174, 209
N.
Nebnbt, contact difference of potential... 121, 197
dissociation theory... 171, 186, 194
diffusion through liquids... 46, 194
solubility of mixtures... 80, 186
„ in mixed liquids... 81
and Abegg, freezing points... 218
and Loss, migration of the ions... 134
Neutralisation of acids and bases... 168, 175, 189, 192
Neyille and Hsycock, melting points of alloys... 78
Nicholson and Gablisle, decomposition of water... 104
NicoL, volume changes... 175
Notes, influence of concentration on osmotic pressure... 69
,, and ABBbT, solubility and dissociation... 187
o.
Ohm's law for electrolytes... 148, 151
Osmotic pressure... 82, 84, 89, 206
and conductivity... 165
freezing point... 55, 67
thermodynamics. . .43
vapour pressure... 74
OsTWAiiD, affinities of acids... 168, 164
contact difference of potential... 120
dissociation theory... 155, 171, 180
on Pickering's curves... 208
osmotic pressure ... 69
,, solution of zinc in acids... 115
„ vapour pressures... 80, 90
„ volume changes in neutralisation... 175
a n ft
»» f» f»
»» f» »»
WA
})
ti
»»
INDEX. 293
p.
Pbllat, contact difference of potential... 120
Pbltibb, contact difference of potential... 117
Pebein, magnetic rotation in salt solutions... 177
Pfbfveb, osmotic pressure... 34, 86, 89
PiCKEBiNo, freezing points of solutions... 71, 207, 213
„ theory of solution... 207, 210, 211
Planck, theory of diffusion... 46, 194
PiiANTfc, accumulator... 114
Polarisation.. 112, 144, 146
„ in primary cells... 114
Polymerisation of dissolved molecules... 68
Potash, electrolysis of... 105, 129
Potassium chloride and nitrate, solubility curves... 2
„ isolation by electrolysis... 105
Potential, contact difference of.. w 116, 121, 160, 197
Practical applications of electrolysis... 181
Pressure, influence on solubility... 10, 13, 20
„ osmotic. .82, 34, 89, 206
,, „ and conductivity... 165
,, „ „ freezing point... 55, 67
,, „ „ thermodynamics... 43
„ ,, „ vapour pressure... 74
Primary cells... 114, 122, 198
Q.
Quincke, electrical endosmose...l60
R.
Bahsat, vapour pressures of amalgams... 93
Baoult, electromotive force of polarisation... 113
„ freezing points of solutions... 55, 57, 63, 172, 213
„ vapour pressures of solutions... 77, 88
Bayleigh, Lord, and Mrs H. Sidowick, Faraday's law... 110
Bbinold and B^okbb, resistance of liquid films... 15$
Befraction coefficients of salt solutions... 177
Beonault, solutions of liquids in gases... 9
Besistance of electrolytes... 143
„ „ liquid films... 158
294 INDEX.
Besistance, specific... 148
BoBCOE, distillation of solutions of hydrochloric add... 102
Rotatory power of salt solationB...177
BOcKBB and Beinold, resistance of liquid films... 158
B^DOLF, freezing points of solutions... 54
„ solubility of mixtures... 30
8.
Sack, temperature of maximum conductivity... 194
Salt solutions, properties of... 174
Saturation.. .1, 18, 24, 187
ScHETFEB, experiments on diffusion... 51
Secondary actions in electrolysis... 128
„ cells.. .118
Self-induction with alternating currents... 146
Semipermeable membranes... 84, 179
Setschenoff, solubility of gases in solutions... 15
Shaw, on electrolysis... 110, 182
SiDowiCK, Mrs H., and Lord Bayleigh, Faraday's Law... 110
Sims, solubility of anmionia, <&c....l4
Sodium, isolation of... 105
chloride, solubility curve... 2
sulphate, solubility... 19, 23
Solids, solutions in... 6, 78
„ „ „ liquids... 17
Solubility, conditions necessary for... 17, 208
connection with dissociation... 187
curves... 2, 17, 23
„ in gases.. .8
„ „ liquids of gases... 10
„ „ „ liquids... 16
„ „ „ solids... 17, 187
„ table of... 31
Solvent, conductivity of... 129, 149, 200
function of ..18, 182, 156, 200, 203, 204
Solution pressure... 21, 25, 34, 121, 199
SoBET, diffusion... 49
Specific inductive capacity of solvent... 156, 204
Spectra of salt solutions... 177
Stefan, theory of diffusion... 51
»»
»» If »»
f> *» >f
fl If f)
INDEX. 295
Sugar solution... 84, 40, 213
Sulphur dioxide, solubility of... 14
Sulphuric aoid, electrolysis of... 130
Super8aturation...l8, 24
Surface tension of solutions... 25, 118, 177
T.
Takmann, isotonic solutions... 88
„ melting points of alloys... 73
„ osmotic pressures... 39
„ vapour pressures... 91
Telephone used as galvanometer... 146
Temperature, its influence on conductivity... 148, 176, 193, 202
diffusion... 58
osmotic pressure... 36, 45
solubiHty...l, 10, 16, 20, 25
of maximum conductivity... 193
Tebbschin, specific inductive capacities of solvents... 205
Thermal capacities of solutions... 177, 209
„ effects of chemical action... 162, 189, 192
„ „ ioni8ation...l90, 206
„ „ solution and dilution... 8, 12, 28, 209
Thermodynamics of solutions... 25, 43, 55, 74, 191
„ voltaic cells... 122
Thomben, thermochemical researches... 122, 162, 190
Thomson, J. J., discharge through gases... 105
„ function of the solvent... 204
Thorium sulphate, solubility... 23
TniDBN, theories of solution... 206, 209
Tbouton and FirzoEBALD, Ohm's law for electrolytes... 151
V.
Van deb Waals, formula for gases... 69
Van 't Hoff, application of thermodynamics to solutions... 48
„ diffusion... 49
„ freezing points... 59
„ gaseous laws appUed to solutions... 85
Vapour pressures of solutions... 4, 74, 210
„ „ „ connection with boiling points... 85
296 INDEX.
I
Vapour pressures of solutions connection with freezing points... 84 '
>f it H 11
,f osmotic pressures... 75
Velocities of the ions... 135, 138, 140, 154, 173, 196
Viscosity and conductivity... 154
„ of salt solutions... 177
VoioTLANDEB, diffusion... 48, 52
VoLLMEB, conductivity of alcohol solutions... 203, 205
Volta's pile.. .103, 116
Voltaic cell... 103, 113, 114, 122, 198
Volumes, molecular... 174, 209
W.
Waage and Guldbbbo, chemical equilibrium... 152, 189
Walkeb, heat of fusion... 29
„ and OsTWALD, vapour pressures... 90
Water, conductivity of.. .129, 149, 200
„ decomposition of... 104, 112, 129
„ dissociation of... 200
„ heat of formation of... 190
Wbbeb, experiments on diffusion... 48, 49
Wbetham, velocities of the ions... 141
„ ionisation powers of solvents... 205
Wiedemann, electrical endosmose...l60
„ resistance of electrolytes... 144
WiLLiAHSON, molecular interchanges...l53
WoiiLASTON, "galvanism "...105
z.
Zinc, its solution in acids... 115
CAMBBineB: PBIITTBD BT J. AND C. P. CLAY, AT THB UVrVEBSITT PBBB8.
Cambrtlige iBatural S^timtt £Rmauli^
BIOLOGICAL SERIES.
Gbneral Editob, a. E. Shipley, M.A.,
Fellow and Tutor of Christ's College.
Now Ready,
EleiiMiitaiy Fatoontology— Iny«rtelinkte H. Woods, B.A., F.G.3. 6«.
Elements of Botany F. Dabwin, M.A., F.B.S. 6«.
Practical Physiology of Plants F. Dabwim, & £. H. Aoton, M.A. 6«.
Practical MorUd Anatomy H. D. Bollbston, M.D., F.B.C.P.
<&A.A.Eanthaok,M.D.,M.B.C.P. 6«.
Zoogeography F. £. Bbddabd, M.A, F.B.S. 6«.
In Prepa/rcUion,
FoBsU Plants A. C. Seward, MA., F.G.S.
Text-book of Physical Anthropology ... A. Macaustbb, M.D., F.B.S.
The Vertebrate Skeleton S. H. Beynolds, M.A.
PHYSICAL SERIES.
General Editor, R. T. Glazebrooe, M.A. F.R.S.,
Fellow of Trinity College, Cambridge, Assistant Director of the
Cavendish Laboratory.
Now Ready.
Heat and Light B. T. Glazbbbook, MA., F.B.S. 5«.
„ „ in two separate parts „ „ each Zi.
Mechanics and Hydrostatics
Part I. Dynamics
„ II. Statics
„ IIL Hydrostatics
„ [In Preparation
In Preparation,
Electricity and Magnetiam B. T. Glazebbook, M.A., F.B.S.
SOlntlon and Electrotysis W. C. D. Whetham, M.A.
Now Ready.
Elements of Petrology A. Habkeb, M.A., F.G.S. Is, Qd,
Other volumes cure in preparation and vrUl be announced shortly.
5/5/95
Press Opinions,
BIOLOGICAL SERIES.
Elementary Palaeontology— Invertebrate. By Henry
Woods, B.A., F.G.S. With Illustrations. Crown 8vo. 6«.
Nature. As an introdnction to the study of palaaontology Mr Woods's
book is worthy of high praise.
Saturday Review, The book is clearly and concisely ez]^es8ed; it
conveys much information in a oomparatiyely small compass and cannot
fail to be most useful to the student. Not only will it give him dear ideas
upon the subject, but with it as a guide he will find his way more easily
about the larger works or special memoirs on Palaaontology, to the saving of
his time and the increase of his knowledge.
Academy. It will be distinctly useful to any student entering on the
study of geology.
Science and Art Journal, Geological students will find this admirable
work on Invertebrate PaUaontology easy reading, and thoroughly up-to-date.. . .
We consider the book a most valuable addition to our scientific literature,
and recommend it to all who desire to acquire a sound introduction to a
knowledge of the past life-forms of our planet.
Practical Physiology of Plants. By F. Darwin, M.A.,
F.R.S., Fellow of Christ's College, Cambridge, and Reader in
Botany in the University, and E. H. Acton, M.A., late
Fellow and Lecturer of St John's College, Cambridge. With
Illustrations. Crown 8vo. 65.
Natu/re, A volume of this kind was very much needed, and it is a
matter for congratulation that the work has fallen into the most competent
hands. There was notiiing of the kind in English before, and the book will
be of the greatest service to both teachers and students The thoroughly
practical character of Messrs Darwin and Acton's book seems to us a great
merit ; every word in it is of direct use to the experimental worker and to
him alone.
British Medical Journal, This book will prove a valuable one for the
student of practical botany. The insti^ctions for the study 'of these and
similar facts in the botanical laboratonr are set out with great clearness, and
the figures illustrating apparatus used and tracings obtained are extremely
good, and will greatly help the investigator who avails himself of the
guidance of this work.
Glasgow Herald, Mr F. Darwin is well known as an authority on
Botany, and the work before us will certainly prove a safe and satisfactory
guide to the student in the botanical laboratory.... The directions for work
are all clearly given, and for teachers possessing a laboratory a better
students' guide to practical work in botany could not be found.
Natural Science, The text throughout is exceedingly clear, and the
index full and carefully compiled.
Press Opinions,
BIOLOGICAL SERIES.
Practical Morbid Anatomy. By H. D. Rolleston, M.D.,
F.R.C.P., Fellow of St John's College, Cambridge, Assistant
Physician and Lecturer on Pathology, St George's Hospital,
London, and A. A. Kanthack, M.D., M.R.C.P., Lecturer
on Pathology, St Bartholomew's Hospital, London. Crown
8vo/ 65.
British Medical Journal. The editor of the ** Cambridge Natural Science
Manuals " has been fortunate not only in the selection of the above-named
subject but also in securing as authors Drs Bolleston and Kanthack
This manual can in every sense be most highly recommended, and it should
supply what lias hitherto been a real want.
The Medical Chronicle, "This handbook is an attempt to supply a
practical guide to the post-mortem room," say the authors in their intro-
duction, and any competent reader will acknowledge that they have succeeded
in their attempt. They have not only supplied the student with a large
amount of reliable information, but have done it in a clear and very
readable form.
PHYSICAL SERIES.
Heat and Light. An Elementary Text-book, Theoretical and
Practical, for Colleges and Schools. By B,. T. Glazbbrook,
M.A., F.R.S., Assistant Director of the Cavendish Labora-
tory, Fellow of Trinity College, Cambridge. Crown 8vo.
58, The two parts are also published separately.
Heat. Ss, Light. 3«.
Nature, Teachers who require a book on Light, suitable for the
Glass-room and Laboratory, would do well to adopt Mr Glazebrook*8 work.
Science and Art, For the practical courses on Heat and Light now
forming such a prominent feature in the curriculum of so many of our
schools and colleges, these books are admirably suited.
Edtuiational Review, Mr Glazebrook's great practical experience has
enabled him to treat the experimental aspect of the subject with unusual
power, and it is in this that the great value of the book, as compared with
most of the ordinary manuals, consists.
Saturday Review, It is difficult to admire sufficiently the ingenuity and
simplicity of many of the experiments without losing sight of the skill and
judgment with which they are arranged.
Journal of Education, We have no hesitation in recommending this
book to the notice of teachers.
School Guardian, It is no undue praise to say that they are worthy both
of their author and of the house by which they are issued.
Teachers' Aid, Text-books of which it would be almost impossible to
speak too highly.
Press Opinions.
PHYSICAL SERIES.
Mechanics and Hydrostatics. An Elementary Text-book,
Theoretical and Practical, for Colleges and Schools. By
R. T. Glazebrook, M.A., F.R.S., Fellow of Trinity College,
Cambridge, Assistant Director of the Cavendish Laboratory.
Part I. Dynamics, is. Part. II. Statics, as.
Part III. Hydrostatics. [In Preparation.
Educational Beview. In detail it is thoroughly Bonnd and scientific.
The work is the work of a teacher and a thinker, who has avoided no
difficalty that the student ought to face, and has, at the same time, given
him all the assistanoe that he has a right to expect. We hope, in the
interests both of experimental and mathematical science, that the sdieme of
teaching therein described will be widely followed.
Scotsman, While expounding well the theory of the subject, the book is
essentially a practical one for use in large classes in sdiools and colleges.
It is simply and clearly written and has a large number of examples, experi-
ments, and illustrative diagrams; and will be welcome to those who have to
instruct beginners in the study of Physics.
Educational Times. We are bound to say that the book is full of good
matter, clearly expressed, set out in excellent form and good print.
Educational News. We recommend the book to the attention of all
students and teachers of this branch of physical science.
Journal of Education. A very good book, which combines the theoretical
and practical treatment of Mechanics very happily.
Machinery. It is quite clear that a great deal of care has been taken in
the arrangement of tiiis volume, which will be found of great value to
students generally whose initial difficulties have been carefully considered
and in many cases entirely overcome.
Knowledge, We cordially commend Mr Glazebrook's volumes to the
notice of t^u^ers.
Educational Times. The absurdities which infest books on MechanicB,
even the very best, in their language involving the term " force " are
absolutely avoided.
Glasgow Herald. The student will also find excellent instructions for
the working of experiments in the laboratory.
Technical World. The apparatus used is simple and effective and well
adapted for classwork.
aonl^ott: C. J. CLAY and SONS,
CAMBRIDGE UNIVERSITY PRESS WAREHOUSE,
AVE MARIA LANE.
AND
H. K. LEWIS, 136, GOWER STREET, W.C.
Medical Publisher and Bookseller.
_
NOV 9 nm
tiW^ «♦■-.*.■*
NOV 7 1396
. • 'T?-*
■.•■oO''j37
■Ml
H
S'lTSIL-STUDY
-'AN 2
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11