A system of physical chemistry - Index of

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A system of physical chemistry - Index of

A/AS:S A CTION EQ UILIBRIUM IN SOL UTIONS 1 5 1

statistical mechanics, i.e. 3RT per "active" gram-ion. The high

dielectric constant, according to Kriiger, also sets a number of the

charged atoms in the undissociated molecules of the solute into vibra-

" " ^

tion again with the amount of energy per active gram-atom required

by statistical mechanics. The higher the radiation density of a medium,

that is, the higher its dielectric constant, the greater will be the number

of molecules of solute activated in this sense, and hence the greater the

degree of ionisation of the solute. This is suggested as the basis, in

terms of radiation, of the relation known as the Nernst-Thomson rule.

We now pass to the consideration of the mass action equilibrium

resulting from such ionisation. Kriiger carries out a thermodynamic

work process in which allowance is made for the difference in radiation

density arising from the fact that two different solvents or media are

employed.

Let us consider two media, dielectric constants Dj and D;,, the media

being capable of mixing in all proportions. We might imagine a

cylinder containing one solvent placed above the other with a mixture

layer between the two. In each solvent let us suppose that there is

one gram-molecule of a binary electrolyte dissolved, the ionisation con-

stant of the electrolyte being K^ in solvent I. and K2 in solvent II. ;

Ki > K2. The following cyclic process is then carried out. In medium

I. one mole of the undissociated electrolyte ionises. The ions are

brought by the aid of semi-permeable membranes into solvent II. where

they unite, the undissociated molecule being returned to solvent I. The

osmotic work of transferring the material is as follows : let Cu, Cj, Cj

be the equilibrium concentrations of the undissociated molecules and

the ions respectively of the solute in solvent I. ; C'o, C'l, C'2 are the cor-

responding quantities in solvent II. The osmotic work of the cycle is

then given by— ^,

A = log Rt( §i;

+ log

§2^

-

log

[;;3

- RT log

|.

In this process a certain amount of radiation is absorbed when

ionisation occurs in solvent I., and the same amount is given out when

the ions unite in solvent 11.'^ We have to deal therefore with a transport

of radiation at the same time as we deal with a transport of material.

The radiation is transported from a region of higher radiation density

(solvent I.) to a region of smaller radiation density (solvent II.). The

work of transporting the radiation may be calculated in the following

manner :—

Let us consider a certain amount of radiation, i.e. the amount required

to "activate " one gram-molecule of the electrolyte, and let us

suppose that this radiation is enclosed in a membrane impermeable to

radiation. The radiation exerts a pressure —" the pressure of light

"—

^In the present case the "critical increment " of the undissociates molecule is

very small (cf. Chap. VI., section dealing with Thermal Reactions).

2

Kruger assumes here that the heat of the reaction is the same in both solvents.

This, in general,

will not be the case.

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