A system of physical chemistry - Index of

booksnow2.scholarsportal.info

A system of physical chemistry - Index of

15-^

A SYSTEM OF PHYSICAL CBEMISTR'Y

upon the membrane tending to expand it. This pressure is proportional

to the density of the radiation. It is known that the pressure tt of the

radiation is related to the volume ^ by an expression which is quite

analogous to Boyle's law for gases, viz. -n-cf) = /:.

[Note.—There is a serious difficulty here, as the expression assumes

the temperature of the radiation is constant. If it is isolated its tem-

perature cannot remain constant on expansion or compression.]

If we accept this expression it follows that the maximum work gained

in expanding the radiation from ttj to 7r2, corresponding to the radiation

densities u^ and tio, is -^ log tti/tt^. Further, on the electro-magnetic

theory of light, tt = u/;^, so that the radiation work is A log uju2. The

density terms are proportional to the cube of the refractive indices or to

the I

"5 power of the respective dielectric constants Di and D2. Hence

the radiation work can be written as—

Jk log (DjS/y D.3/2).

We have now to determine the constant /i.

" Let us assume that each

vibrating ion [charged atom] in the undissociated molecule possesses

three degrees of freedom, that is, each ion possesses 3/2 RT of kinetic

energy and a like amount of potential energy, making in all 3RT per

ion, or 6RT for the two ions in the molecule reckoned per gram-molecule—

each gram-molecule when it dissociates requires on the average

an amount of energy 6RT which is drawn from the radiation." Hence—

?/(^ = 6Rr,

and since, TT = i/'t,, it follows that—

7r

= 2RT.

Substituting this in the expression for the work done in the radiation, we obtain—

expanding

A = 2RT log (Dj3/2/d.3/2)

= RT log DjS/Da^

The ionisation equilibrium is defined by the and radiation work terms.'

We obtain therefore—

equality of the osmotic

RT log ^; = RT log ^,

or Ki/Ko = D,3/D./.

That is, on the basis of the assumptions made by Kriiger, we would

as the cube of the dielectric con-

expect the ionisation constant to vary

stant of the system. In order to test this conclusion it is convenient to

put it into another form. It y^ and y^ are the degrees of ionisation at

in the two solvents, then—

the dilutions Vj and V2 respectively

Ki _ yi'^ (I - y,)Y, _ D,-^

K2 (r - •

yi)Vi

y,^

D/


Naturally if the solvent had been the same in both cases, and if the solutions

are dilute, the radiation work term would be zero, and we are left with the osmotic

work terms. The cycle would then reduce to the familiar one employed to deduce

the law of mass action, i.e. Kj would be identical with K._,.

More magazines by this user
Similar magazines