A system of physical chemistry - Index of

A system of physical chemistry - Index of

142

A SYSTEM OF PHYSICAL CHEMISTRY

solvent acting as a positive catalyst is to increase the radiation density

of the type absorbable by the reactant, whereby a greater number

of the molecules of the reactant attain the critical value for their in-

ternal energy per second, with the result that the reaction-velocity is

increased.

Planck's expression for the radiation density factor in the following form :—

may be written

u, = constant x ^i^^^^-^^

where h is Planck's constant, k the gas constant per molecule, and T

the absolute temperature. For the short infra-red region the above

expression reduces to the following one,^ which is identical with the

expression of Wien :—

Ui, = constant e ' ''/*t_

This expression may be regarded as holding for a gaseous system.

, simplify the treatment still further we shall assume that the reaction

considered is unimolecular, and that a single frequency is absorbed by

the substance in the process of activation. For this case the rate of

reaction can be written in the following way, in which a denotes as

usual the initial concentration of the substance and x is the amount

transformed after a time / ; dx\dt is proportional to {a - x)ii^, or

dxjdt = constant {a - x)e-'"'l^''

On integrating this expression we obtain—

. . •

To

-

log = constant . e ~ '"'/*^

, . . (2)

f a - ^

X

At constant temperature this expression becomes identical with the

. . I a

ordinary mass action expression. Further - log = kobs, where

^obs is the experimentally determined velocity constant. Hence—

^obs = constant x ,?-''W*t _ •

(3)

The " constant " which occurs here is practically independent of tem-

perature, especially for a gaseous system. We can find the effect of

temperature upon the observed velocity constant by simply differentiating

the above expression with respect to T. The resulting expression

is—

d log ^obs/dT = /ly/AT' . . . .

(4)

But k, the gas constant per molecule, can be written as R/N where R

is the gas constant per gram-molecule and N is the number of molecules

in one gram-molecule. Hence—

d log /^obsKT = N/iv/RT' .

1

Cj. W. C. M. Lewis, Bril. Assoc. Report, p. 394, 1915.

. .

(i)

(5)

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