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equation is to find, as above, K from each measurement, and from the mean of these, recalculate the values of y. This is done in the following table :-

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(K = 1'585 X 10–6]

It will be seen that the experimental numbers are in very satisfactory agreement with the law of mass action.

The application of the law of mass action to dissociation of electrolytes is often known as Ostwald's law of dilution, Ostwald 1 having applied it to his numerous measurements of conductivity. The measurements were all made in a thermostat at 25°, so that the equivalent conductivities are considerably greater than those given by Kohlrausch for 18°. They refer chiefly to organic acids; the law has also been shown by Bredig 2 to apply to many organic bases. The results obtained by these and other observers are given at length in Kohlrausch and Holborn's monograph, to which we must refer; they are, however, considered below (Chap. II.), on account of the important chemical meaning of the dissociation constant. This constant is, in fact, a measure of the “strength" of the acid, as a few examples may serve to show :

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Acetic acid . . . 18 X 1078
Monochloracetic acid. 1550 X 1078

Dichloracetic acid . . 5100'0 X 1078 * Zeitschr. phys. Chem., 3. 170, 241, 369 (1889); Lehrbuch d. Allg. Chemie (1893).

? Zeitschr. phys. Chem., 13. 289 (1894).

The substitution of each chlorine atom increases the strength of the acid considerably. (See Chap. II.)

Mineral acids and the strongest organic acids do not follow Ostwald's law, so that it is not possible to calculate a dissociation constant for them, in the sense given above. (Trichloracetic acid belongs to this class.)

Among bases also it is only the weaker that follow the rule ; . thus for ammonia K = 2'3 X 10-8. But tetra-ethyl-ammonium hydroxide and similar bases, as well as the alkalis, deviate largely from the law of dilution.

Salts in all cases deviate from the rule.

It appears, then, that the law of dissociation in the form given by Ostwald is only applicable to weakly dissociated substances : strong electrolytes—i.e. salts and strong acids and bases, all of which are considerably dissociated even in moderately dilute solution-are subject to disturbing influences.

Many attempts at explaining the behaviour of strong electrolytes were made; but none of them are of value, except that of Jahn. The usual theory of solutions, due chiefly to van't Hoff, is based on the assumption that there is an action between the solvent and the dissolved substance, but none between the parts of the dissolved substance itself; it being supposed that the molecules of dissolved substance are too widely separated for any appreciable forces to exist between them. It is by the mathematical expression of these views that Ostwald's law of dilution is obtained.

Jahn's explanation of the divergence from Ostwald's law by strong electrolytes, is that mutual action between the parts of the dissolved substance is too large to neglect. If this is so, there are two additional terms to be taken into account, one relating to mutual action between the ions (i.e, forces of attraction and repulsion, whilst the ions remain separate in the chemical sense) the other to influence of neutral molecules on ions. The former action is to be expected, for electrical forces exerted by ordinary charged bodies such as can be experimented with, are sensible at great distances, and it is therefore to be presumed that charged ions exert forces on

1 Zeitschr. phys. Chem., 37. 490-503 (1901); 41. 257-301 (1902).

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 (oʻi to o'or normal) dealt with.

This view is not shared by Nernst, 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).
? 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 too high an estimate; i.e. y<i 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 n equivalents (say of cations) in 1 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) Ico.

(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) 100 = leo + lac = 96600 (Uc + UA).

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

A = 96600 (Uc + U)
(v.) The actual conductivity (of 1 cm. cube),

k= An= 96600 ny (Uc + UA) (vi.) On the assumption (which is at least approximately true) that Uc and UA are independent of n,

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

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(100 – 18.00 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 1 c.c. mi equivalents of an ion having mobility U1, N2 of another whose mobility is U,, and so on,

k = 96600(n. Uit n2U, +...) Here ni, na 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

(yn)2 = (1 - YnK where K is constant.

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-yn, that of the undissociated molecules. Writing na, nc, and nca for these three quantities, the equation becomes

NoonA = NAK T. P. C.

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