A system of physical chemistry - Index of


A system of physical chemistry - Index of


(Physical equilibrium in gaseous systems) —Molecular heats of gases — Bjerrum's

theory — Kriiger's theory.

bjerrum's theory.

In I. Chapter we have already had occasion to discuss briefly the

problem of the molecular heats of gases. It has been pointed out

that the observed values cannot be accounted for on the basis of the

equipartition principle, especially the fact that the molecular heat varies

with the temperature. In view of the considerable advance which has

been made possible in the analogous case of solids by the application

of the it quantum theory, is of interest to see how far the same considerations

can be applied in tie present case. This problem was

first taken up by Bjerrum {Zeitsch. Ekktrochem., 17, 731 (1911); ibid.^ 18,

1 01 (191 2)).

In Chapter I. we have given a table showing the number of possible

degrees of freedom, as estimated by Bjerrum, which are possessed by

mono- , di-, tri-, and tetra-atomic gas molecules in respect of translation,

rotation, and vibration. In the case of monatomic gases, which appear

to possess translational energy only, the equipartition principle of

classical statistical mechanics gives a satisfactory explanation of the

observed values, e.g. the case of argon already discussed. So long

as we restrict ourselves to translational movement the equipartition

principle necessarily holds good, whether the molecule be monatomic

or polyatomic ; the distribution of energy in terms of the quantum

i.e. move-

theory only enters when we deal with vibrations or rotations,

ment with respect to a centre of gravity.

As already pointed out, the result obtained in the case of argon

leads us to regard a monzXomxc gas as possessing no energy other than

that of translation. This is somewhat unexpected, and we shall return

to it later in connection with Kruger's theory. For the present, however,

we are discussing Bjerrum's treatment.

As regards rotation of the molecule as a whole Bjerrum shows that

the potential energy of rotation is negligible compared with the kinetic

energy. (The case is quite different of course for the vibrations of the

atoms inside the molecules.) In regard to vibration of one atom with

respect to the other in a diatomic gas molecule, according to the

quantum hypothesis the sum of the kinetic and potential energies, instead

of being RT, is a fraction ^ of this quantity. That is the total

vibrational energy is

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