SOLUTIONS AND ELECTROLYTIC DISSOCIATION
§ 1. SOLUTION
Vaporization and fusion are not the only means by which the physical
state of a body may be changed without modifying its chemical
constitution. From the most remote periods solution has also been
known and studied, but only in the last twenty years have we obtained
other than empirical information regarding this phenomenon.
It is natural to employ here also the methods which have allowed us to
penetrate into the knowledge of other transformations. The problem of
solution may be approached by way of thermodynamics and of the
hypotheses of kinetics.
As long ago as 1858, Kirchhoff, by attributing to saline solutions--
that is to say, to mixtures of water and a non-volatile liquid like
sulphuric acid--the properties of internal energy, discovered a
relation between the quantity of heat given out on the addition of a
certain quantity of water to a solution and the variations to which
condensation and temperature subject the vapour-tension of the
solution. He calculated for this purpose the variations of energy
which are produced when passing from one state to another by two
different series of transformations; and, by comparing the two
expressions thus obtained, he established a relation between the
various elements of the phenomenon. But, for a long time afterwards,
the question made little progress, because there seemed to be hardly
any means of introducing into this study the second principle of
thermodynamics.[14] It was the memoir of Gibbs which at last opened
out this rich domain and enabled it to be rationally exploited. As
early as 1886, M. Duhem showed that the theory of the thermodynamic
potential furnished precise information on solutions or liquid
mixtures. He thus discovered over again the famous law on the lowering
of the congelation temperature of solvents which had just been
established by M. Raoult after a long series of now classic
researches.
[Footnote 14: The "second principle" referred to has been thus
enunciated: "In every engine that produces work there is a fall of
temperature, and the maximum output of a perfect engine--_i.e._ the
ratio between the heat consumed in work and the heat supplied--depends
only on the extreme temperatures between which the fluid is
evolved."--Demanet, _Notes de Physique Expérimentale_, Louvain, 1905,
fasc. 2, p. 147. Clausius put it in a negative form, as thus: No
engine can of itself, without the aid of external agency, transfer
heat from a body at low temperature to a body at a high temperature.
Cf. Ganot's _Physics_, 17th English edition, § 508.--ED.]
In the minds of many persons, however, grave doubts persisted.
Solution appeared to be an essentially irreversible phenomenon. It was
therefore, in all strictness, impossible to calculate the entropy of a
solution, and consequently to be certain of the value of the
thermodynamic potential. The objection would be serious even to-day,
and, in calculations, what is called the paradox of Gibbs would be an
obstacle.
We should not hesitate, however, to apply the Phase Law to solutions,
and this law already gives us the key to a certain number of facts. It
puts in evidence, for example, the part played by the eutectic point--
that is to say, the point at which (to keep to the simple case in
which we have to do with two bodies only, the solvent and the solute)
the solution is in equilibrium at once with the two possible solids,
the dissolved body and the solvent solidified. The knowledge of this
point explains the properties of refrigerating mixtures, and it is
also one of the most useful for the theory of alloys. The scruples of
physicists ought to have been removed on the memorable occasion when
Professor Van t'Hoff demonstrated that solution can operate reversibly
by reason of the phenomena of osmosis. But the experiment can only
succeed in very rare cases; and, on the other hand, Professor Van
t'Hoff was naturally led to another very bold conception. He regarded
the molecule of the dissolved body as a gaseous one, and assimilated
solution, not as had hitherto been the rule, to fusion, but to a kind
of vaporization. Naturally his ideas were not immediately accepted by
the scholars most closely identified with the classic tradition. It
may perhaps not be without use to examine here the principles of
Professor Van t'Hoff's theory.
§ 2. OSMOSIS
Osmosis, or diffusion through a septum, is a phenomenon which has been
known for some time. The discovery of it is attributed to the Abbé
Nollet, who is supposed to have observed it in 1748, during some
"researches on liquids in ebullition." A classic experiment by
Dutrochet, effected about 1830, makes this phenomenon clear. Into pure
water is plunged the lower part of a vertical tube containing pure
alcohol, open at the top and closed at the bottom by a membrane, such
as a pig's bladder, without any visible perforation. In a very short
time it will be found, by means of an areometer for instance, that the
water outside contains alcohol, while the alcohol of the tube, pure at
first, is now diluted. Two currents have therefore passed through the
membrane, one of water from the outside to the inside, and one of
alcohol in the converse direction. It is also noted that a difference
in the levels has occurred, and that the liquid in the tube now rises
to a considerable height. It must therefore be admitted that the flow
of the water has been more rapid than that of the alcohol. At the
commencement, the water must have penetrated into the tube much more
rapidly than the alcohol left it. Hence the difference in the levels,
and, consequently, a difference of pressure on the two faces of the
membrane. This difference goes on increasing, reaches a maximum, then
diminishes, and vanishes when the diffusion is complete, final
equilibrium being then attained.
The phenomenon is evidently connected with diffusion. If water is very
carefully poured on to alcohol, the two layers, separate at first,
mingle by degrees till a homogeneous substance is obtained. The
bladder seems not to have prevented this diffusion from taking place,
but it seems to have shown itself more permeable to water than to
alcohol. May it not therefore be supposed that there must exist
dividing walls in which this difference of permeability becomes
greater and greater, which would be permeable to the solvent and
absolutely impermeable to the solute? If this be so, the phenomena of
these _semi-permeable_ walls, as they are termed, can be observed in
particularly simple conditions.
The answer to this question has been furnished by biologists, at which
we cannot be surprised. The phenomena of osmosis are naturally of the
first importance in the action of organisms, and for a long time have
attracted the attention of naturalists. De Vries imagined that the
contractions noticed in the protoplasm of cells placed in saline
solutions were due to a phenomenon of osmosis, and, upon examining
more closely certain peculiarities of cell life, various scholars have
demonstrated that living cells are enclosed in membranes permeable to
certain substances and entirely impermeable to others. It was
interesting to try to reproduce artificially semi-permeable walls
analogous to those thus met with in nature;[15] and Traube and Pfeffer
seem to have succeeded in one particular case. Traube has pointed out
that the very delicate membrane of ferrocyanide of potassium which is
obtained with some difficulty by exposing it to the reaction of
sulphate of copper, is permeable to water, but will not permit the
passage of the majority of salts. Pfeffer, by producing these walls in
the interstices of a porous porcelain, has succeeded in giving them
sufficient rigidity to allow measurements to be made. It must be
allowed that, unfortunately, no physicist or chemist has been as lucky
as these two botanists; and the attempts to reproduce semi-permeable
walls completely answering to the definition, have never given but
mediocre results. If, however, the experimental difficulty has not
been overcome in an entirely satisfactory manner, it at least appears
very probable that such walls may nevertheless exist.[16]
[Footnote 15: See next note.--ED.]
[Footnote 16: M. Stephane Leduc, Professor of Biology of Nantes, has
made many experiments in this connection, and the artificial cells
exhibited by him to the Association française pour l'avancement des
Sciences, at their meeting at Grenoble in 1904 and reproduced in their
"Actes," are particularly noteworthy.--ED.]
Nevertheless, in the case of gases, there exists an excellent example
of a semi-permeable wall, and a partition of platinum brought to a
higher than red heat is, as shown by M. Villard in some ingenious
experiments, completely impermeable to air, and very permeable, on the
contrary, to hydrogen. It can also be experimentally demonstrated that
on taking two recipients separated by such a partition, and both
containing nitrogen mixed with varying proportions of hydrogen, the
last-named gas will pass through the partition in such a way that the
concentration--that is to say, the mass of gas per unit of volume--
will become the same on both sides. Only then will equilibrium be
established; and, at that moment, an excess of pressure will naturally
be produced in that recipient which, at the commencement, contained
the gas with the smallest quantity of hydrogen.
This experiment enables us to anticipate what will happen in a liquid
medium with semi-permeable partitions. Between two recipients, one
containing pure water, the other, say, water with sugar in solution,
separated by one of these partitions, there will be produced merely a
movement of the pure towards the sugared water, and following this, an
increase of pressure on the side of the last. But this increase will
not be without limits. At a certain moment the pressure will cease to
increase and will remain at a fixed value which now has a given
direction. This is the osmotic pressure.
Pfeffer demonstrated that, for the same substance, the osmotic
pressure is proportional to the concentration, and consequently in
inverse ratio to the volume occupied by a similar mass of the solute.
He gave figures from which it was easy, as Professor Van t'Hoff found,
to draw the conclusion that, in a constant volume, the osmotic
pressure is proportional to the absolute temperature. De Vries,
moreover, by his remarks on living cells, extended the results which
Pfeffer had applied to one case only--that is, to the one that he had
been able to examine experimentally.
Such are the essential facts of osmosis. We may seek to interpret them
and to thoroughly examine the mechanism of the phenomenon; but it must
be acknowledged that as regards this point, physicists are not
entirely in accord. In the opinion of Professor Nernst, the
permeability of semi-permeable membranes is simply due to differences
of solubility in one of the substances of the membrane itself. Other
physicists think it attributable, either to the difference in the
dimensions of the molecules, of which some might pass through the
pores of the membrane and others be stopped by their relative size, or
to these molecules' greater or less mobility. For others, again, it is
the capillary phenomena which here act a preponderating part.
This last idea is already an old one: Jager, More, and Professor
Traube have all endeavoured to show that the direction and speed of
osmosis are determined by differences in the surface-tensions; and
recent experiments, especially those of Batelli, seem to prove that
osmosis establishes itself in the way which best equalizes the
surface-tensions of the liquids on both sides of the partition.
Solutions possessing the same surface-tension, though not in molecular
equilibrium, would thus be always in osmotic equilibrium. We must not
conceal from ourselves that this result would be in contradiction with
the kinetic theory.
§ 3. APPLICATION TO THE THEORY OF SOLUTION
If there really exist partitions permeable to one body and impermeable
to another, it may be imagined that the homogeneous mixture of these
two bodies might be effected in the converse way. It can be easily
conceived, in fact, that by the aid of osmotic pressure it would be
possible, for example, to dilute or concentrate a solution by driving
through the partition in one direction or another a certain quantity
of the solvent by means of a pressure kept equal to the osmotic
pressure. This is the important fact which Professor Van t' Hoff
perceived. The existence of such a wall in all possible cases
evidently remains only a very legitimate hypothesis,--a fact which
ought not to be concealed.
Relying solely on this postulate, Professor Van t' Hoff easily
established, by the most correct method, certain properties of the
solutions of gases in a volatile liquid, or of non-volatile bodies in
a volatile liquid. To state precisely the other relations, we must
admit, in addition, the experimental laws discovered by Pfeffer. But
without any hypothesis it becomes possible to demonstrate the laws of
Raoult on the lowering of the vapour-tension and of the freezing point
of solutions, and also the ratio which connects the heat of fusion
with this decrease.
These considerable results can evidently be invoked as _a posteriori_
proofs of the exactitude of the experimental laws of osmosis. They are
not, however, the only ones that Professor Van t' Hoff has obtained by
the same method. This illustrious scholar was thus able to find anew
Guldberg and Waage's law on chemical equilibrium at a constant
temperature, and to show how the position of the equilibrium changes
when the temperature happens to change.
If now we state, in conformity with the laws of Pfeffer, that the
product of the osmotic pressure by the volume of the solution is equal
to the absolute temperature multiplied by a coefficient, and then look
for the numerical figure of this latter in a solution of sugar, for
instance, we find that this value is the same as that of the analogous
coefficient of the characteristic equation of a perfect gas. There is
in this a coincidence which has also been utilized in the preceding
thermodynamic calculations. It may be purely fortuitous, but we can
hardly refrain from finding in it a physical meaning.
Professor Van t'Hoff has considered this coincidence a demonstration
that there exists a strong analogy between a body in solution and a
gas; as a matter of fact, it may seem that, in a solution, the
distance between the molecules becomes comparable to the molecular
distances met with in gases, and that the molecule acquires the same
degree of liberty and the same simplicity in both phenomena. In that
case it seems probable that solutions will be subject to laws
independent of the chemical nature of the dissolved molecule and
comparable to the laws governing gases, while if we adopt the kinetic
image for the gas, we shall be led to represent to ourselves in a
similar way the phenomena which manifest themselves in a solution.
Osmotic pressure will then appear to be due to the shock of the
dissolved molecules against the membrane. It will come from one side
of this partition to superpose itself on the hydrostatic pressure,
which latter must have the same value on both sides.
The analogy with a perfect gas naturally becomes much greater as the
solution becomes more diluted. It then imitates gas in some other
properties; the internal work of the variation of volume is nil, and
the specific heat is only a function of the temperature. A solution
which is diluted by a reversible method is cooled like a gas which
expands adiabatically.[17]
[Footnote 17: That is, without receiving or emitting any heat.--ED.]
It must, however, be acknowledged that, in other points, the analogy
is much less perfect. The opinion which sees in solution a phenomenon
resembling fusion, and which has left an indelible trace in everyday
language (we shall always say: to melt sugar in water) is certainly
not without foundation. Certain of the reasons which might be invoked
to uphold this opinion are too evident to be repeated here, though
others more recondite might be quoted. The fact that the internal
energy generally becomes independent of the concentration when the
dilution reaches even a moderately high value is rather in favour of
the hypothesis of fusion.
We must not forget, however, the continuity of the liquid and gaseous
states; and we may consider it in an absolute way a question devoid of
sense to ask whether in a solution the solute is in the liquid or the
gaseous state. It is in the fluid state, and perhaps in conditions
opposed to those of a body in the state of a perfect gas. It is known,
of course, that in this case the manometrical pressure must be
regarded as very great in relation to the internal pressure which, in
the characteristic equation, is added to the other. May it not seem
possible that in the solution it is, on the contrary, the internal
pressure which is dominant, the manometric pressure becoming of no
account? The coincidence of the formulas would thus be verified, for
all the characteristic equations are symmetrical with regard to these
two pressures. From this point of view the osmotic pressure would be
considered as the result of an attraction between the solvent and the
solute; and it would represent the difference between the internal
pressures of the solution and of the pure solvent. These hypotheses
are highly interesting, and very suggestive; but from the way in which
the facts have been set forth, it will appear, no doubt, that there is
no obligation to admit them in order to believe in the legitimacy of
the application of thermodynamics to the phenomena of solution.
§ 4. ELECTROLYTIC DISSOCIATION
From the outset Professor Van t' Hoff was brought to acknowledge that
a great number of solutions formed very notable exceptions which were
very irregular in appearance. The analogy with gases did not seem to
be maintained, for the osmotic pressure had a very different value
from that indicated by the theory. Everything, however, came right if
one multiplied by a factor, determined according to each case, but
greater than unity, the constant of the characteristic formula.
Similar divergences were manifested in the delays observed in
congelation, and disappeared when subjected to an analogous
correction.
Thus the freezing-point of a normal solution, containing a molecule
gramme (that is, the number of grammes equal to the figure
representing the molecular mass) of alcohol or sugar in water, falls
1.85° C. If the laws of solution were identically the same for a
solution of sea-salt, the same depression should be noticed in a
saline solution also containing 1 molecule per litre. In fact, the
fall reaches 3.26°, and the solution behaves as if it contained, not
1, but 1.75 normal molecules per litre. The consideration of the
osmotic pressures would lead to similar observations, but we know that
the experiment would be more difficult and less precise.
We may wonder whether anything really analogous to this can be met with
in the case of a gas, and we are thus led to consider the phenomena of
dissociation.[18] If we heat a body which, in a gaseous state, is
capable of dissociation--hydriodic acid, for example--at a given
temperature, an equilibrium is established between three gaseous bodies,
the acid, the iodine, and the hydrogen. The total mass will follow with
fair closeness Mariotte's law, but the characteristic constant will no
longer be the same as in the case of a non-dissociated gas. We here no
longer have to do with a single molecule, since each molecule is in part
dissociated.
[Footnote 18: Dissociation must be distinguished from decomposition,
which is what occurs when the whole of a particle (compound, molecule,
atom, etc.) breaks up into its component parts. In dissociation the
breaking up is only partial, and the resultant consists of a mixture
of decomposed and undecomposed parts. See Ganot's Physics, 17th
English edition, § 395, for examples.--ED.]
The comparison of the two cases leads to the employment of a new image
for representing the phenomenon which has been produced throughout the
saline solution. We have introduced a single molecule of salt, and
everything occurs as if there were 1.75 molecules. May it not really
be said that the number is 1.75, because the sea-salt is partly
dissociated, and a molecule has become transformed into 0.75 molecule
of sodium, 0.75 of chlorium, and 0.25 of salt?
This is a way of speaking which seems, at first sight, strangely
contradicted by experiment. Professor Van t' Hoff, like other
chemists, would certainly have rejected--in fact, he did so at first--
such a conception, if, about the same time, an illustrious Swedish
scholar, M. Arrhenius, had not been brought to the same idea by
another road, and, had not by stating it precisely and modifying it,
presented it in an acceptable form.
A brief examination will easily show that all the substances which are
exceptions to the laws of Van t'Hoff are precisely those which are
capable of conducting electricity when undergoing decomposition--that
is to say, are electrolytes. The coincidence is absolute, and cannot
be simply due to chance.
Now, the phenomena of electrolysis have, for a long time, forced upon
us an almost necessary image. The saline molecule is always
decomposed, as we know, in the primary phenomenon of electrolysis into
two elements which Faraday termed ions. Secondary reactions, no doubt,
often come to complicate the question, but these are chemical
reactions belonging to the general order of things, and have nothing
to do with the electric action working on the solution. The simple
phenomenon is always the same--decomposition into two ions, followed
by the appearance of one of these ions at the positive and of the
other at the negative electrode. But as the very slightest expenditure
of energy is sufficient to produce the commencement of electrolysis,
it is necessary to suppose that these two ions are not united by any
force. Thus the two ions are, in a way, dissociated. Clausius, who was
the first to represent the phenomena by this symbol, supposed, in
order not to shock the feelings of chemists too much, that this
dissociation only affected an infinitesimal fraction of the total
number of the molecules of the salt, and thereby escaped all check.
This concession was unfortunate, and the hypothesis thus lost the
greater part of its usefulness. M. Arrhenius was bolder, and frankly
recognized that dissociation occurs at once in the case of a great
number of molecules, and tends to increase more and more as the
solution becomes more dilute. It follows the comparison with a gas
which, while partially dissociated in an enclosed space, becomes
wholly so in an infinite one.
M. Arrhenius was led to adopt this hypothesis by the examination of
experimental results relating to the conductivity of electrolytes. In
order to interpret certain facts, it has to be recognized that a part
only of the molecules in a saline solution can be considered as
conductors of electricity, and that by adding water the number of
molecular conductors is increased. This increase, too, though rapid at
first, soon becomes slower, and approaches a certain limit which an
infinite dilution would enable it to attain. If the conducting
molecules are the dissociated molecules, then the dissociation (so
long as it is a question of strong acids and salts) tends to become
complete in the case of an unlimited dilution.
The opposition of a large number of chemists and physicists to the
ideas of M. Arrhenius was at first very fierce. It must be noted with
regret that, in France particularly, recourse was had to an arm which
scholars often wield rather clumsily. They joked about these free ions
in solution, and they asked to see this chlorine and this sodium which
swam about the water in a state of liberty. But in science, as
elsewhere, irony is not argument, and it soon had to be acknowledged
that the hypothesis of M. Arrhenius showed itself singularly fertile
and had to be regarded, at all events, as a very expressive image, if
not, indeed, entirely in conformity with reality.
It would certainly be contrary to all experience, and even to common
sense itself, to suppose that in dissolved chloride of sodium there is
really free sodium, if we suppose these atoms of sodium to be
absolutely identical with ordinary atoms. But there is a great
difference. In the one case the atoms are electrified, and carry a
relatively considerable positive charge, inseparable from their state
as ions, while in the other they are in the neutral state. We may
suppose that the presence of this charge brings about modifications as
extensive as one pleases in the chemical properties of the atom. Thus
the hypothesis will be removed from all discussion of a chemical
order, since it will have been made plastic enough beforehand to adapt
itself to all the known facts; and if we object that sodium cannot
subsist in water because it instantaneously decomposes the latter, the
answer is simply that the sodium ion does not decompose water as does
ordinary sodium.
Still, other objections might be raised which could not be so easily
refuted. One, to which chemists not unreasonably attached great
importance, was this:--If a certain quantity of chloride of sodium is
dissociated into chlorine and sodium, it should be possible, by
diffusion, for example, which brings out plainly the phenomena of
dissociation in gases, to extract from the solution a part either of
the chlorine or of the sodium, while the corresponding part of the
other compound would remain. This result would be in flagrant
contradiction with the fact that, everywhere and always, a solution of
salt contains strictly the same proportions of its component elements.
M. Arrhenius answers to this that the electrical forces in ordinary
conditions prevent separation by diffusion or by any other process.
Professor Nernst goes further, and has shown that the concentration
currents which are produced when two electrodes of the same substance
are plunged into two unequally concentrated solutions may be
interpreted by the hypothesis that, in these particular conditions,
the diffusion does bring about a separation of the ions. Thus the
argument is turned round, and the proof supposed to be given of the
incorrectness of the theory becomes a further reason in its favour.
It is possible, no doubt, to adduce a few other experiments which are
not very favourable to M. Arrhenius's point of view, but they are
isolated cases; and, on the whole, his theory has enabled many
isolated facts, till then scattered, to be co-ordinated, and has
allowed very varied phenomena to be linked together. It has also
suggested--and, moreover, still daily suggests--researches of the
highest order.
In the first place, the theory of Arrhenius explains electrolysis very
simply. The ions which, so to speak, wander about haphazard, and are
uniformly distributed throughout the liquid, steer a regular course as
soon as we dip in the trough containing the electrolyte the two
electrodes connected with the poles of the dynamo or generator of
electricity. Then the charged positive ions travel in the direction of
the electromotive force and the negative ions in the opposite
direction. On reaching the electrodes they yield up to them the
charges they carry, and thus pass from the state of ion into that of
ordinary atom. Moreover, for the solution to remain in equilibrium,
the vanished ions must be immediately replaced by others, and thus the
state of ionisation of the electrolyte remains constant and its
conductivity persists.
All the peculiarities of electrolysis are capable of interpretation:
the phenomena of the transport of ions, the fine experiments of M.
Bouty, those of Professor Kohlrausch and of Professor Ostwald on
various points in electrolytic conduction, all support the theory. The
verifications of it can even be quantitative, and we can foresee
numerical relations between conductivity and other phenomena. The
measurement of the conductivity permits the number of molecules
dissociated in a given solution to be calculated, and the number is
thus found to be precisely the same as that arrived at if it is wished
to remove the disagreement between reality and the anticipations which
result from the theory of Professor Van t' Hoff. The laws of
cryoscopy, of tonometry, and of osmosis thus again become strict, and
no exception to them remains.
If the dissociation of salts is a reality and is complete in a dilute
solution, any of the properties of a saline solution whatever should
be represented numerically as the sum of three values, of which one
concerns the positive ion, a second the negative ion, and the third
the solvent. The properties of the solutions would then be what are
called additive properties. Numerous verifications may be attempted by
very different roads. They generally succeed very well; and whether we
measure the electric conductivity, the density, the specific heats,
the index of refraction, the power of rotatory polarization, the
colour, or the absorption spectrum, the additive property will
everywhere be found in the solution.
The hypothesis, so contested at the outset by the chemists, is,
moreover, assuring its triumph by important conquests in the domain of
chemistry itself. It permits us to give a vivid explanation of
chemical reaction, and for the old motto of the chemists, "Corpora non
agunt, nisi soluta," it substitutes a modern one, "It is especially
the ions which react." Thus, for example, all salts of iron, which
contain iron in the state of ions, give similar reactions; but salts
such as ferrocyanide of potassium, in which iron does not play the
part of an ion, never give the characteristic reactions of iron.
Professor Ostwald and his pupils have drawn from the hypothesis of
Arrhenius manifold consequences which have been the cause of
considerable progress in physical chemistry. Professor Ostwald has
shown, in particular, how this hypothesis permits the quantitative
calculation of the conditions of equilibrium of electrolytes and
solutions, and especially of the phenomena of neutralization. If a
dissolved salt is partly dissociated into ions, this solution must be
limited by an equilibrium between the non-dissociated molecule and the
two ions resulting from the dissociation; and, assimilating the
phenomenon to the case of gases, we may take for its study the laws of
Gibbs and of Guldberg and Waage. The results are generally very
satisfactory, and new researches daily furnish new checks.
Professor Nernst, who before gave, as has been said, a remarkable
interpretation of the diffusion of electrolytes, has, in the direction
pointed out by M. Arrhenius, developed a theory of the entire
phenomena of electrolysis, which, in particular, furnishes a striking
explanation of the mechanism of the production of electromotive force
in galvanic batteries.
Extending the analogy, already so happily invoked, between the
phenomena met with in solutions and those produced in gases, Professor
Nernst supposes that metals tend, as it were, to vaporize when in
presence of a liquid. A piece of zinc introduced, for example, into
pure water gives birth to a few metallic ions. These ions become
positively charged, while the metal naturally takes an equal charge,
but of contrary sign. Thus the solution and the metal are both
electrified; but this sort of vaporization is hindered by
electrostatic attraction, and as the charges borne by the ions are
considerable, an equilibrium will be established, although the number
of ions which enter the solution will be very small.
If the liquid, instead of being a solvent like pure water, contains an
electrolyte, it already contains metallic ions, the osmotic pressure
of which will be opposite to that of the solution. Three cases may
then present themselves--either there will be equilibrium, or the
electrostatic attraction will oppose itself to the pressure of
solution and the metal will be negatively charged, or, finally, the
attraction will act in the same direction as the pressure, and the
metal will become positively and the solution negatively charged.
Developing this idea, Professor Nernst calculates, by means of the
action of the osmotic pressures, the variations of energy brought into
play and the value of the differences of potential by the contact of
the electrodes and electrolytes. He deduces this from the
electromotive force of a single battery cell which becomes thus
connected with the values of the osmotic pressures, or, if you will,
thanks to the relation discovered by Van t' Hoff, with the
concentrations. Some particularly interesting electrical phenomena
thus become connected with an already very important group, and a new
bridge is built which unites two regions long considered foreign to
each other.
The recent discoveries on the phenomena produced in gases when
rendered conductors of electricity almost force upon us, as we shall
see, the idea that there exist in these gases electrified centres
moving through the field, and this idea gives still greater
probability to the analogous theory explaining the mechanism of the
conductivity of liquids. It will also be useful, in order to avoid
confusion, to restate with precision this notion of electrolytic ions,
and to ascertain their magnitude, charge, and velocity.
The two classic laws of Faraday will supply us with important
information. The first indicates that the quantity of electricity
passing through the liquid is proportional to the quantity of matter
deposited on the electrodes. This leads us at once to the
consideration that, in any given solution, all the ions possess
individual charges equal in absolute value.
The second law may be stated in these terms: an atom-gramme of metal
carries with it into electrolysis a quantity of electricity
proportionate to its valency.[19]
[Footnote 19: The valency or atomicity of an element may be defined as
the power it possesses of entering into compounds in a certain fixed
proportion. As hydrogen is generally taken as the standard, in
practice the valency of an atom is the number of hydrogen atoms it
will combine with or replace. Thus chlorine and the rest of the
halogens, the atoms of which combine with one atom of hydrogen, are
called univalent, oxygen a bivalent element, and so on.--ED.]
Numerous experiments have made known the total mass of hydrogen
capable of carrying one coulomb, and it will therefore be possible to
estimate the charge of an ion of hydrogen if the number of atoms of
hydrogen in a given mass be known. This last figure is already
furnished by considerations derived from the kinetic theory, and
agrees with the one which can be deduced from the study of various
phenomena. The result is that an ion of hydrogen having a mass of 1.3
x 10^{-20} grammes bears a charge of 1.3 X 10^{-20} electromagnetic
units; and the second law will immediately enable the charge of any
other ion to be similarly estimated.
The measurements of conductivity, joined to certain considerations
relating to the differences of concentration which appear round the
electrode in electrolysis, allow the speed of the ions to be
calculated. Thus, in a liquid containing 1/10th of a hydrogen-ion per
litre, the absolute speed of an ion would be 3/10ths of a millimetre
per second in a field where the fall of potential would be 1 volt per
centimetre. Sir Oliver Lodge, who has made direct experiments to
measure this speed, has obtained a figure very approximate to this.
This value is very small compared to that which we shall meet with in
gases.
Another consequence of the laws of Faraday, to which, as early as 1881,
Helmholtz drew attention, may be considered as the starting-point of
certain new doctrines we shall come across later.
Helmholtz says: "If we accept the hypothesis that simple bodies are
composed of atoms, we are obliged to admit that, in the same way,
electricity, whether positive or negative, is composed of elementary
parts which behave like atoms of electricity."
The second law seems, in fact, analogous to the law of multiple
proportions in chemistry, and it shows us that the quantities of
electricity carried vary from the simple to the double or treble,
according as it is a question of a uni-, bi-, or trivalent metal; and
as the chemical law leads up to the conception of the material atom,
so does the electrolytic law suggest the idea of an electric atom.