James Walker.

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as the ions travel to the opposite electrodes. This idea was intro-
duced by Grotthus, who conceived that the molecules at the two
electrodes, were split up into their positive and negative constituents
under the influence of the electric charges on the electrodes, and that
the intermediate molecules changed partners according to a scheme
like the following, the first action of the electric charges being to
direct all the positive ends of the molecules towards the negative
electrode and the negative ends towards the positive electrode :


This, however, does not get over the difficulty indicated by Clausius,
an account of whose views may be given in the words of Clerk Maxwell.

" Clausius has pointed out that on the old theory of electrolysis,
according to which the electromotive force was supposed to be the
sole agent in tearing asunder the components of the molecules of the
electrolyte, there ought to be no decomposition and no current as
long as the electromotive force is below a certain value, but that
as soon as it has reached this value a vigorous decomposition ought
to commence, accompanied by a strong current. This, however, is
by no means the case, for the current is strictly proportional to the
electromotive force for all values of that force.

" Clausius explains this in the following way : According to the
theory of molecular motion, of which he has himself been the chief


founder, every molecule of the fluid is moving in an exceedingly
irregular manner, being driven first one way and then another by the
impacts of other molecules which are also in a state of agitation.

" This molecular agitation goes on at all times independently of
the action of electromotive force. The diffusion of one fluid through
another is brought about by this molecular agitation, which increases
in velocity as the temperature rises. The agitation being exceedingly
irregular, the encounters of the molecules take place with various
degrees of violence, and it is probable that even at low temperatures
some of the encounters are so violent that one or both of the com-
pound molecules are split up into their constituents. Each of these
constituent molecules then knocks about among the rest till it meets
with another molecule of the opposite kind, and unites with it to
form a new molecule of the compound. In every compound, there-
fore, a certain proportion of the molecules at any instant are broken
up into their constituent atoms. At high temperatures the proportion
becomes so large as to produce the phenomenon of dissociation studied
by M. Ste. Claire Deville.

"Now Clausius supposes that it is on the constituent molecules in
their intervals of freedom that the electromotive force acts, deflecting
them slightly from the paths they would otherwise have followed, and
causing the positive constituents to travel, on the whole, more in the
positive than in the negative direction, and the negative constituents
more in the negative direction than in the positive. The electromotive
force, therefore, does not produce the disruptions and reunions of the
molecules, but. finding these disruptions and reunions already going
on, it influences the motion of the constituents during their intervals
of freedom."

The constituent molecules referred to in the above passage are, of
course, the positive and negative radicals of the dissolved salt, i.e. the
kation and anion of which it is assumed to be composed. At any one
time then we have, on the hypothesis of Clausius, some proportion
of the salt molecules split up into their constituent ions, which,
with their electric charges, move towards the appropriate electrodes.
It must be observed that this state of partial dissociation of the dis-
solved substance is the normal condition of the liquid, and exists
whether there is an electric current passing through the solution or
not. All that the electric forces do is to direct the dissociated charged
products to the electrodes and there discharge them. Nothing has
been said as to the proportion of dissolved substance which is thus
dissociated into ions. For the purpose of accounting for the validity
of Ohm's Law in electrolytic solutions, a very small proportion will
suffice, provided that the small quantity is always regenerated by
the action of the molecules themselves without any interference of
the electrical forces. In proportion as the free ions are removed
from the solution at the electrodes, Clausius supposes them to be


regenerated by the collisions of the undissociated molecules, so that
the process of conduction and electrolysis goes on. If we are to give
the hypothesis definiteness and precision, however, we must take
account of the relative quantities of the electrolyte in the dissociated
and undissociated states. The manner of doing this was first pointed
out by Arrhenius, and it is to his hypothesis of electrolytic dis-
sociation that we must resort if we wish to explain quantitatively
the phenomena exhibited by electrolytic solutions, whether during
electrolysis or in their ordinary state.

Arrhenius supposes substances which give solutions that conduct
electricity freely to be almost entirely split up into their constituent
ions, while substances which yield solutions of feeble conductivity are
supposed by him to be split up only to a very small extent. In fact,
he proposes to measure the degree of dissociation of a substance by the
conductivity of its solutions. On his hypothesis, only those molecules
which are split up into their constituent ions play any part in the
conduction of electricity, the undissociated molecules remaining idle.
It is obvious, therefore, that the conductivity of any given solution
depends on two factors the number of ions in the solution, and the
rate at which these ions move. To simplify matters we will, in what
follows, only consider univalent ions, i.e. those derived from monacid
bases, monobasic acids, and the salts which they form by mutual
neutralisation. Every ion derived from these substances has the same
charge of electricity, i.e. 1 faraday per gram-ion. Since each carrier
of electricity has the same load, the quantity carried can depend only
on the number of carriers and the speed at which they move. Now
the rate at which the ions move may, as we have seen, be determined
from the work of Hittorf and Kohlrausch. It only remains, therefore,
to find the number or proportion of ions in any given solution.

Kohlrausch ascertained experimentally that the molecular conduc-
tivity of a salt increases as the dilution of the solution increases, and
that the rate of increase of conductivity gets smaller and smaller as the
dilution gets greater, until finally the molecular conductivity remains
constant, although the addition of water to the solution is continued.
This may best be figured as follows. Consider a cell of practically
infinite height and of rectangular horizontal section, two parallel sides
of which are of platinum, and are placed at a distance of 1 cm. from
each other. These platinum sides may be used as electrodes. Let
there now be introduced into the cell one cubic centimetre of a
solution containing a gram-molecular weight of common salt (58*5 g.)
dissolved in a litre of water. If the resistance offered to the passage
of the current through the liquid is measured in ohms, the reciprocal
of the number obtained represents the specific conductivity of the
solution (p. 7). If we add the rest of the litre of normal solution,
the conduction between the electrodes will be 1000 times as great as
before, and this represents the conductivity of one gram molecule


dissolved in 1000 cc. of water, i.e. is the molecular conductivity
(p. 251) at the dilution of 1 litre. If now we add water so as to
make up the volume to 2 litres, and again determine the molecular
conductivity, we find that the value for the dilution 2 is greater than
before, although the value of the specific conductivity has diminished.
As we add more water so as to increase the volume in which the
gram-molecular weight of the salt is contained, the molecular con-
ductivity will also increase, finally to reach a limit when the dilution
amounts to about 10,000 litres. The numbers obtained by Kohlrausch
for sodium chloride at 18 are given in the following table :

Dilution = v Mol. Cond. = ^ Dissociation = TO

1 lit. 74-4 (0-678) .

2 80-9 (0737)
10 92-5 0-843
20 95-9 0-874

100 102-8 0-937

500 106-7 0-972

1,000 107-8 0-983

5,000 109-2 0-995





From this table it will be seen that the rate of increase of the
molecular conductivity is much greater when the dilution is small
than when it is great. Doubling the quantity of water when the
dilution is 1 adds more than 6 units to the conductivity; doubling
the quantity when the dilution is 500 only adds 1 unit to the
conductivity. Increasing the dilution tenfold when it is already
10,000 has no further effect, the small variations observed in the
last three values being due to experimental error.

The molecular conductivity, as has been said, depends only on (1)
the number of ions, and (2) the rate at which they move. We have
therefore to determine to which of these causes the increase of mole-
cular conductivity on dilution is due. The rate of the ions depends on
the resistance offered by the liquid to their motion. Now at a dilution
of 10 we have 5 8 '5 g. of salt dissolved in 10,000 g. of water. So
far as viscosity is concerned, this is practically pure water, and further
additions of water should have no appreciable effect in changing
the resistance offered to the passage of the ions. We may suppose
then that the rate at which the ions travel is practically unaltered
after a dilution of about 10 is reached, so that the increase of
conductivity with further dilution is not due to any increase of speed
of the ions, but to an increase in their number. In the imaginary
cell considered above we have always the same amount of salt between
the electrodes, but evidently as we add water we obtain a greater pro-
portion of ions. With increasing dilution the salt then must split up
more and more into ions capable of conveying the electricity, if we
are to account for the increase of molecular conductivity which the


salt exhibits. When all the salt has been split up into its ions the
increase of molecular conductivity with dilution must cease, for further
dilution can neither increase the speed of the ions nor augment their
number. In the case of sodium chloride the salt is entirely ionised
at a dilution of 10,000, and we find that salts in general exhibit this
behaviour. The limiting value of the molecular conductivity corre-
sponding to complete ionisation is called the molecular conductivity
at infinite dilution, and is usually denoted by /*,.

Since in dilute solutions the addition of more water is assumed
not to affect the speed of the ions, it is obvious that in a cell such as
we considered above, the conductivity of the solution is directly pro-
portional to the amount of ionised substance in it. Now we know
that at infinite dilution all the sodium chloride is ionised. At finite
dilutions, therefore, the degree of dissociation, i.e. the proportion of
the whole which exists in the state of ions, is equal to the quotient of
the molecular conductivity at the dilution considered by the molecular
conductivity at infinite dilution. The degree of dissociation or ionisa-
tion is generally denoted by m, so we have the equation

For example, if we wish to ascertain the degree of ionisation of
sodium chloride at a dilution of 10 litres, i.e. in decinormal solution,
we divide the molecular conductivity, 92*5, by the molecular con-
ductivity at infinite dilution, viz. 109*7, and obtain as quotient 0'843.
In a decinormal solution of sodium chloride then at 18, a little over
eighty per cent of the salt is split up into its constituent ions.

It must be very specially emphasised that the molecular con-
ductivity itself is no measure of the degree of ionisation of a dissolved
substance ; the true measure is the ratio of this conductivity to the
molecular conductivity at infinite dilution. The degree of ionisation
is not proportional to the molecular conductivity unless under certain
conditions which must be carefully specified. For example, the
molecular conductivity of a decinormal solution of sodium chloride
at 50 is 160. This is much greater than the molecular conductivity
at 18, but the increase cannot come from an increase in the number
of ions, as the salt at 18 is already more than four-fifths ionised.
The great increase in the molecular conductivity is due to the
increase in the other factor, namely, the speed of the ions. The
fluid friction of the solution is greatly diminished by the rise in
temperature, and consequently the ions move much faster, thus in a
given time conveying more electricity. At 50 the molecular con-
ductivity at infinite dilution is 197. If we therefore divide 160
by this number we obtain an ionisation approximately equal to 0'81,
which is practically the same value as we got for 18. In general, we
find with salts that rise of temperature, while greatly augmenting the


molecular conductivity, has very little effect on the degree of ionisation,
the increase in the conductivity being almost wholly due to the
increased speed of the ions.

In a similar way the addition of non-conducting substances to salt
solutions lowers the conductivity without appreciably altering the
ionisation as measured by the ratio of the molecular conductivity at
the dilution considered to that at infinite dilution. Thus diethyl-
ammonium chloride dissolved in water and in mixtures of water and
ethyl alcohol gave the following values at 25 for decinormal solutions,
and for infinite dilution :

Percentage of Alcohol . WO

by Volume. **W '* Moo

90-4 1147 0788

10-1 69-2 89-1 0778

307 43-2 57-5 0751

49-2 32-0 45-8 0'699

72-0 25-5 42-0 0'607

90-3 18-1 41-4 0-438

The column headed ^ gives the effect of the alcohol in reducing the
speed of the ions, since at infinite dilution the salt is entirely ionised
in each case, the ionised amount being therefore the same throughout.
In the last column we have the degree of ionisation as measured
by the ratio of the molecular conductivity at 10 litres to fj. M . The
addition of alcohol diminishes both the speed of the ions and the
ionisation, so that the molecular conductivity in decinormal solution
is reduced from both these causes. It will be noticed, however, that
these two effects of the addition of alcohol do not go hand in hand.
The degree of ionisation is scarcely affected by the first substitutions
of alcohol for water (up to 30 per cent), while the speed of the ions,
and consequently the molecular conductivity, is reduced to one-half.
On the other hand, when nearly all the water has been replaced by
alcohol, the effect of further additions is scarcely noticeable on the
speed of the ions, but very marked on the degree of ionisation, and
consequently on the molecular conductivity, in decinormal solution.
On the whole the molecular conductivity in decinormal solution in 90
per cent alcohol is only about a fifth of what it is in pure water : if the
speed of the ions alone had been affected, the reduction would have been
to a value a little more than a third of the value for water ; the balance
of the reduction is due to diminution in the degree of ionisation.

The student is particularly recommended to a close study of the
above examples, in order that he may become familiar with the two
factors on which the molecular conductivity depends, as beginners
almost invariably neglect to take account of the change in speed of
the ions under different conditions, and thus from the values of the
molecular conductivity draw utterly erroneous conclusions regarding
the degree of ionisation. Degree of ionisation is never proportional
to molecular conductivity unless the speed of the ions is the same in


the two solutions compared. If two dilute solutions contain the same
salt dissolved in the same solvent at the same temperature, then the
degree of ionisation of the substance in the two solutions is pro-
portional to the molecular conductivity, for the maximum molecular
conductivity is the same in both cases. But if in the solutions compared
the dissolved substance is different, if the solvent is different, or if
the temperature is different, then the molecular conductivity is no
longer a measure of the degree of ionisation, for the maximum
molecular conductivity will no longer be the same.

If we investigate the influence of dilution on the molecular con-
ductivity of dilute solutions, we find that the weak acids and bases
which form the group of half -electrolytes obey a law which was
deduced by Ostwald from theoretical considerations, as will be shown
in a subsequent chapter. Since other conditions are the same, and
increase in dilution does not affect the speed of the ions, the change
in the molecular conductivity observed is due entirely to change in
the degree of ionisation. If we represent the degree of ionisation
by m and the dilution by v, the following relation holds good :

= constant.

(1 -m)v

The constant is usually denoted by k, and is called the dissociation
constant. In the subjoined tables are given the values obtained at
25 for acetic acid and ammonia respectively.


Moo =387

v n 100m lOOfc

8 4-63 1-193 0-00180

16 6-50 1-673 0-00179

32 9-2 2-380 0-00182

64 12-9 3-33 0-00179

128 18'1 4-68 0-00179

256 25-4 6-56 O'OOISO

612 35-3 9-14 0*00180

1024 49-0 12-66 0'00177

Mean . . 0*00180

v M 100m lOOfc

8 3-4 1-35 0-0023

16 4-8 1-88 0-0023

32 67 2-65 0-0023

64 9'5 3-76 0-0023

128 13-5 5-33 0-0023

256 19-0 7-54 0'0024

Mean . 0'0023


In the third column of the tables is given the percentage ionisa-
tion, i.e. the degree of ionisation multiplied by 100; and in the
fourth column is one hundred times the value of the dissociation
constant derived from the above formula. This centuple constant is
often used instead of the smaller number on account of its leading for
all substances to more convenient figures. The values of the constant
at particular dilutions vary as a rule only 1 or 2 per cent from
the mean, and this variation is due to errors of observation, which are
greatly magnified in the calculation of the constant.

In the first place, it is evident from the tables that acetic acid
and ammonia in equivalent solutions are about equally ionised, the
former into hydrion, H', and acetanion, CH S COO', the latter into
ammonion, NH* 4 , and hydroxidion, OH'. If we compare these tables
with that given on p. 261 for a good electrolyte, it will be seen that
dilution has a far greater influence on the molecular conductivity in
the former case than the latter. For sodium chloride an increase of
the dilution from 1 to 100,000 only increases the molecular con-
ductivity by about half its value ; while an increase in the dilution
from 8 to 1024 increases the molecular conductivity of acetic acid
more than tenfold. Although the molecular conductivity thus
increases much more rapidly with the dilution than is the case for
good electrolytes, yet the increase is not nearly proportional to the
increase in the dilution. When the degree of ionisation is small the
molecular conductivity is roughly proportional to the square root of the
dilution, as may be seen from a consideration of the general formula

(1 -m)v

For small degrees of ionisation, 1 - m is not greatly different from 1,
so that the formula becomes

m 2 = kv, or m =

If in the general formula we put m = 0'5, i.e. if we assume that
the electrolyte is half ionised, we obtain a conception of the physical
dimensions of the constant k. The expression becomes

0-5 2
(1 -0'5)v~ '

whence r- = k, or -c = k, if c = -

In words, the dissociation constant k is numerically equal to half the
concentration at which the substance is half dissociated, the concen-
tration being expressed in gram molecules per litre. Thus for acetic
acid we have & = 0*000018, whence c = 0-000036, i.e. acetic acid is
half ionised when the concentration of its aqueous solution is
0-000036 normal.


It is obvious that if in such a solution, which contains only about
2 parts of acetic acid per million, the acid is only half ionised, the
direct determination of the molecular conductivity for solutions in
which the acid is wholly ionised is an impossibility. Yet the
value of the molecular conductivity must be known in order that
the degree of ionisation may be calculated. It has therefore to be
determined indirectly by means of Kohlrausch's Law. Although weak
acids and weak bases are but half-electrolytes, their salts are good
electrolytes, and as much dissociated in solution as the corresponding
salts of strong acids and bases. Thus for sodium acetate at 25
have the following numbers :











For ammonium chloride, Kohlrausch found at 18 numbers much the
same as those for sodium chloride, p. 261, viz.













It is an easy matter, then, to find numbers for the molecular con-
ductivity at infinite dilution in the case of salts of weak acids or
bases. Now, according to Kohlrausch's Law, there is a constant
difference between the maximum molecular conductivities of all acids
and their sodium salts a difference due to the difference in speed
of hydrion and sod ion. But strong acids like hydrochloric acid
are at equivalent dilutions quite as much ionised as their sodium
salts, so that their maximum molecular conductivities may be deter-
mined experimentally. For these acids we can thus get directly
the difference between their maximum molecular conductivity and
that of their sodium salts. This difference, amounting at 25 to about
296 in the customary units, when added to the maximum molecular
conductivity of the sodium salt of an acid, which can always be
directly determined, gives the molecular conductivity of the acid itself
at infinite dilution, and this enables us to give the degree of ionisation
of the acid at any other dilution.


The following table gives the conductivity values for some of the
principal ions at 25 :

Rations. Anions.

IT 347

K' 73-8

Na* 50-5

Ag' 62-5

OH' 196

NO' 71-0

C1O 8 ' 65-0

01' 75-2

These numbers are proportional to the speeds of the ions, and the
maximum molecular conductivity of the salt, acid, or base may be
obtained by adding together the numbers for the corresponding kation
and anion. Thus the maximum molecular conductivity of sodium
chloride at 25 is 50'5 + 75'2 = 125'7. It should be noted that not-
withstanding their importance, the values for H' and OH' are less
accurately known than those for the other ions.

It is a curious fact, of which no adequate explanation has as yet
been given, that good electrolytes do not obey Ostwald's dilution law,
which holds so accurately for the half-electrolytes. Certain empirical
relations have, however, been found connecting the degree of ionisa-
tion and the dilution, and these have a form similar to that of
Ostwald's dilution formula, although they have not the theoretical
foundation possessed by the latter.

One of these relations is known as van 't Hoff S dilution
formula. We may write Ostwald's dilution formula in the form

= constant,


where - is the concentration of the ionised portion of the electrolyte,


and - - the concentration of the unionised part. If C^ and C u repre-
sent these concentrations, we have the simple expression

77- = constant.

Van 't Hoff proposed the expression

m 1 ' 5 m 3

7- = constant, or = constant,

which may be written in the form


= TTz = constant.


or -77 = constant.


Here again we have a simple relation between the concentration of
the ionised and non-ionised portions, and the constancy of the ex-

Online LibraryJames WalkerIntroduction to physical chemistry → online text (page 27 of 43)