A system of physical chemistry - Index of

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A system of physical chemistry - Index of

BJERRUM'S THEORY 85

translation and rotation, and by applying the quantum theory to the

vibrations of the atoms, using the wave-lengths 2'i/Aand S-Qyu, which

actually occur in the absorption spectrum of ammonia.

It is evident from the foregoing that to account for the observed

values of the molecular heats of gases it is essential to introduce the

quantum theory in some form. Bjerrum's mode of treatment, though

marking a considerable advance, is open to criticism, more particularly

as regards the choice of the number of degrees of freedom.

We shall consider later the views put forward by Kriiger in connection

with the same problem.

One point remains to be emphasised in connection with the molecular

heat, or rather the energy content of gases. Owing to the fact that

the true atomic vibrations inside the molecule correspond to relatively

such vibrations contribute

high frequencies {i.e. short infra-red region)

a relatively small amount to the total energy content for as the fre-

;

quency is high very few molecules will possess even one quantum of

this type of energy. The so-called rotational frequencies (obtained

on applying the quantum theory to rotation) are much more important

as they occur in the longer infra-red region.

The Absorption Spectrum of Water Vapour and of Hydrogen Chloride

Gas in the infra-red region, from the point of view of Molecular

Rotations, treated on the basis of the Quantum Theory.

As already mentioned, Bjerrum has treated the rotational energy of

the di- or tri-atomic gas molecule from the point of view of the quantum

theory. That is, the rotational spectrum should exhibit a number of

lines related to one another by a constant frequency difference ; this, at

any rate, is the simplest possible statement. The spectrum due to such

rotations would be expected to lie in the farther infra-red (beyond io/a),

the principle lines in the shorter infra-red region being due to the vibrations

of the atoms inside the molecule. Bjerrum assumes that the total

rotational energy varies in terms of quanta, and as a further simplification

he assumes that the moment of inertia of the molecule for all axes

through the centre of gravity is the same i.e. we have ; only to deal with

one such moment. The energy of rotation of a particle round an axis

is given by the . expression 1/2 I .

(27rv)'-, where v is the frequency of

rotation and I is the moment of inertia. On the older quantum theory

this ensrgy must be represented by hv, 2hv, etc., or in general by nhv,

where « is a whole number. Hence we have—

1/2 I . = {iTcvf n . hv

or, V — n . hl2-K^ . I.

According to this expression we would expect a difference series in the

frequencies of the band heads in the spectrum of a gas. That is, harmonics

of the fundamental rotational frequency are to be expected in

the spectrum according to the value ascribed to n. From an examination

of the spectrum of water vapour Bjerrum concludes that the frequency

difference in the series of rotational bands is 173 x 10^'^. He

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