A system of physical chemistry - Index of

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A system of physical chemistry - Index of

I40

A SYS2EM OF FHy:SlCAL CHEMISTRY

the average internal energy of the molecule. This critical limit is

known as the critical energy of the molecule. The term E denotes

the difference between the critical energy and the average or mean internal

energy reckoned per gram-molecule. E may therefore be called

the critical increment E ; denotes the amount of energy which has to

be added to make an average [gram] -molecule react. It is at this point

that the radiation hypothesis of chemical reactivity enters, the assumption

being that the quantity E is contributed by the absorption of infrared

radiation of a given frequency which the substance is capable of

absorbing. It is assumed that this energy is communicated in terms of

quanta, the same assumption as is made by Einstem in obtaining his

expression for the photochemical equivalent.

It will be observed that the Marcelin-Rice equation is identical in

form with the empirical equation of Arrhenius, already discussed in

Vol. I., which is known to be in good agreement with experiment. A

considerable advance has been made, however, in that the empirical

term A which occurs in Arrhenius' equation is now replaced by the

term E to which a definite physical significance can be attached. In

the case of polymolecular reactions the active molecular state actually

exists, as is shown by the experiments of Baly and F. O. Rice {Trans.

the rate of observed chemical reaction

;

Chem. Soc, 101, 1475, 191 2)

depends then upon the frequency of collision between activated molecules.

In the case of unimolecular change molecules in the active state do

not exist, for it is assumed that when a molecule becomes active it immediately

decomposes and becomes transformed into resultant. If the

reaction be reversible it follows, on the statistical basis of the expression,

that the activated resultant has exactly the same critical energy as the

activated reactant. This does not mean that the E term is the same

for both reactant and resultant, E being the difference between the critical

and mean internal energies.^

Having indicated in a general way the role which radiation plays in

regard to the activation of a molecule, it is now necessary to show how

an expression analogous to that of Marcelin and J. Rice may be obtained

on the basis of Planck's radiation theory.

In order that any of Planck's relations may be it applied is essential

that temperature radiation alone be considered, and further, that the

radiation and the matter composing the system be in temperature

equilibrium. On Planck's view, the interchange between matter and

radiation is effected through the medium of oscillators, situated on the

molecules of the substances composing the system. In the case of

thermal reactions occurring at constant temperature in a thermostat

(which defines the temperature of the system both with regard to the

^ Granted that the critical increment is due to radiation, and further assuming

that a single quantum is capable of accounting for the E of a single molecule, it

can be easily shown from a knowledge of the magnitude of the temperature coefficient

of a reaction, that the effective radiation must belong to the short infra-red

region, i.e. of the order i to 3/u, in the case of reactions which occur with sensible

velocity at ordinary temperatures.

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