each other even when at more than molecular distance apart, i.e. when outside the range of ordinary molecular forces. The second action, that of neutral molecules on ions, has been observed in many cases; as, for instance, when the addition of a neutral salt modifies the properties of an acid unrelated to it.

In the first of the two papers by Jahn quoted above, the mutual action of ions is introduced into the equations, and the results of calculation compared with the data obtained by freezing-point measurements. But as the modified theory of solutions affects the freezing-point formula also, Jahn in his second paper gives a complete theoretical discussion, in which all the usual laws of solutions are recalculated on the widened basis. He then applies his results to the data for KCl and NaCl. In doing so, however, it must be noted, he confines himself to the action of neutral molecules on ions, expressing the view that interaction of ions is not important over the range of concentration (o'r to o'or normal) dealt with.

This view is not shared by Nernst,1 who has also discussed the extended theory of solutions. Nernst's view, which seems to be the better founded, is that interaction of ions, and action of neutral molecules on ions, are of the same order of magnitude; interaction of neutral molecules being much less considerable. This being so, the two former actions should both be retained in the equations. Goebel 2 has worked out the data for KCl and NaCl on this assumption.

It appears from both Jahn's and Goebel's papers that the extended theory of solutions is capable of adequately representing the facts. The degree of dissociation is a function of the concentration of the electrolyte, though the formula. expressing the relationship is not so simple as that of Ostwald; and consequently a "dissociation constant" can be calculated, though with a somewhat modified meaning, for strong electrolytes. The formula of Ostwald may be taken as practically correct up to a concentration of one hundredth normal or thereabouts; the formulæ of the new theory up to decinormal concentration; stronger solutions than that have not hitherto been 1 Zeitschr. phys. Chem., 38. 487-500 (1901). 2 Zeitschr. phys. Chem., 42. 59-67 (1902).

systematically considered. Unfortunately, the matter is not yet so far settled that it is possible to say with certainty whether Arrhenius' method of calculating the degree of dissociation is reliable or not. Jahn considers that the conductivity yields

A

A∞

too high an estimate; i.e. y< in strong solutions. But this view cannot be regarded as satisfactorily proved.

We may here conveniently summarize the various theoretical relations that have been found to hold with regard to the conductivity of electrolytes.

(i.) A gram-equivalent of ions carries a charge of 96600 coulombs. If there are 7 equivalents (say of cations) in I c.c. the quantity of (positive) electricity in 1 c.c.

96600 n.

(ii.) If these cations are subjected to unit potential gradient they move with velocity Uc (mobility). The current produced by one equivalent of ions moving with this velocity is therefore 96600 Uc. This is called the ionic conductivity (for complete dissociation) •

=

(iii.) The conductivity of one equivalent of salt when completely dissociated is the sum of the conductivities of its ions. This is called the equivalent conductivity (for complete dissociation) A∞ = x + lax = 96600 (Uc + U1).

(iv.) If the dissociation is incomplete, and amounts to y, the equivalent conductivity is

A = 96600 y(Uc + U1)

(v.) The actual conductivity (of 1 cm. cube),

k = An = 96600 ny (Uc + U1)

(vi.) On the assumption (which is at least approximately true) that U and U, are independent of 7,

A

A

y=

(vii.) According to the law of mass action (simplest theory) for binary electrolytes,

For electrolytes yielding more than two ions, corresponding, but more complicated, relations hold. [For further discussion of the light thrown by conductivity measurements on dissociation, and on chemical constitution, vide infra, Chap. II.]

$ 9.

CONDUCTIVITY OF MIXTURES

In a solution containing more than one electrolyte, the conductivity is that due to all the ions together. Stated formally, we may say, if there are in I c.c. n equivalents of an ion having mobility U1, 7 of another whose mobility is U, and so on,

« = 966oonUi+nU+
96600(m, U1+ n2U2 + . . .)

Here 1, 2 are, of course, to be taken as referring to the actual ions in solution without regard to any undissociated compounds from which they may have arisen.

So far the rule is quite simple and obvious. Complications come in, however, in determining the amount of ions present. In general, if two solutions are mixed, the mixture does not contain the same quantity of ions as the separate parts held between them.

The dissociation in mixtures of electrolytes, like other cases of chemical equilibrium, is regulated by the law of mass action. This must now be considered in a more general form than was required in § 8, where the ionisation of a single salt was dealt with.

It was there stated that for a binary electrolyte

where K is constant.

(yn)2 = (1-x)nK

It will be more convenient to write this equation in a slightly different form. yn is the concentration of either the anion or the cation: (1-y)ŋ, that of the undissociated molecules. Writing NA, nc, and CA for these three quantities, the equation becomes

Now, when more than one electrolyte is present in solution, ne and are not necessarily equal. E.g. if the cation and anion considered are hydrogen and the acetyl group, then, in a solution of acetic acid to which some sodium acetate has been added, there will clearly be more acetyl than hydrogen. Nevertheless, it is found that the same relation holds, the value of K being unaltered; so that the formula expressing the law of mass action comes to have a widened meaning.

For a numerical example we will suppose a quarter normal solution of acetic acid, to which sodium acetate is added sufficient to make it normal with respect to that salt. In the original acid we have—

The dissociation of the acid is therefore a little less than 1 per From this we may calculate the quantity of ions:

cent.

1 4000

H = |CH3000 – 0.0085 X = 2 1 X 10" equivalents per

cubic centimetre.

1

20

We

Sodium acetate is a strongly dissociated substance. shall not be far out if in n. solution we take it as completely dissociated. If this is so, the amount of acetyl ions in I c.c. is 20000 50 X 10 equivalents.

It appears, then, that the sodium acetate solution would contain about 24 times as much free acetyl as the acetic acid alone. In a mixed solution (though the exact mathematical treatment is difficult) we may take it that there are 24 or 25 times as many acetyl ions as in the pure acid. But we have the relation

Ин хуснзсоо = Куснасоон

As most of the acid remains undissociated in any case, we

may treat the right side of the equation as being the same in the two problems: i.e. take cнзCоон, the concentration of the undissociated acid as being practically identical with 7, the weighed amount of acid per cubic centimetre. Practically, then, the equation becomes

nнNCHзC00 = constant

But addition of sodium acetate has made the amount of acetyl ions some 25 times as great as without it; it must, therefore, have made the amount of hydrogen ions about 25 times as small as before.

Remembering, then, that the strength of an acid means merely the amount of hydrogen ions it contains, we arrive at the important conclusion that, weak as the acetic acid is alone, it becomes about 25 times weaker by addition of the stated amount of sodium acetate. The rule is general that a weak acid is greatly weakened by addition of its own neutral salts.

This instance may serve to show the complexity of the conditions occurring in mixed solutions. The case of two electrolytes with a common ion and that of double decomposition 2 have been partly worked out, on the basis of the ordinary formula for the law of mass action. To solve these problems strictly it would be necessary to make use of the extended theory of solutions (of Jahn and Nernst).

$ 10. NON-AQUEOUS SOLUTIONS

It was at one time thought that only aqueous solutions conduct electricity. This is not the case; some other liquids, notably the liquefied gases, ammonia, sulphur dioxide, and hydrocyanic acid, dissolve salts, and make excellently conducting solutions, frequently of higher conductivity than aqueous. Very little is at present known with regard to these solutions, but enough to show that their properties are in general more complicated than those of solutions in water. We have seen

1 Arrhenius, Zeitschr. phys. Chem., 5. 7.

2 Arrhenius, loc. cit., 2. 293. See also van't Hoff, Theoretical and Physical Chemistry, vol. i.