A system of physical chemistry - Index of

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A system of physical chemistry - Index of

2 A SYSTEM OF PHYSICAL CHEMISTRY

each complete vibration on the average contains just as much potential

energy as it does kinetic.

To return to the vibrations of the atoms in a gas molecule. In the

case of a diatomic molecule the molecule is said to possess one degree

of freedom in respect to the to-and-fro vibration of one atom with

respect to the other. The molecule also possesses three degrees of

freedom in respect

triatomic molecule

of translation of the molecule as a whole. In a

the atoms ABC probably vibrate in pairs, AB,

BC, CA, each pair functioning like a diatomic molecule, so that the

molecule as a whole has three degrees of freedom in respect of atomic

vibrations. The molecule possesses in addition three degrees of

freedom in respect of translation. Hence, in the case of a triatomic

molecule there are three degrees of freedom in respect of translation

and three in respect of vibration.

It is obvious that no atomic vibration is possible in the case of a

monatomic molecule in a if gas. such an atom is displaced there is no

restoring force ; the atom is not connected to any other as in the case

^m\ - . . - — » - ' —^—J^B^^^Bt

-t

m^.

\- lAitra uvic- >' *

Figure Axis;

"^ ^^^^ also Axis of Spin"

H:^ *^ (Circular Vibration.) ^

\

— >

Fig. 2 —"

(c). Spinning molecule." Two degrees of freedom. Energy, Fig. 2 (^).— Trilinear

kinetic + potential. (Motion not maintained by collisions.)

vibration of an atom

in a solid. Three

degrees of freedom.

Energy, kinetic +

potential.

of diatomic molecules, and any displacement would simply be identical

with Iree translation. Contrast this with the behaviour of monatomic

molecules in solids in which any displacement can only take place

against a restoring force, with the result, as already mentioned, that the

vibration in the case of a solid possesses three degrees of freedom. In

the case of a monatomic gas vibration is impossible, and, so far as we

have gone, we can only ascribe to this kmd of molecule energy of the

translational kind. A difficulty crops up when we come to consider

a monatomic gas molecule in the light of the third possible type of

motion, viz. molecular rotation.

The circular vibration represented by diagram [c), Fig. 2, requires

a little more consideration. The amount of energy represented by a

circular vibration or spin depends upon the square of the rate of spin

and upon the moment of inertia of the spinning particle.^

If a di-

1 If a particle of mass m moving in a circle of radius r round a fixed position

with an angular velocity w (a> being the number of radians swept out by the

particle per second), then the speed of the particle is wr and its kinetic energy

E = 1/2 m . a>-r^. This expression can also be written : E = 1 . 1/2 . or, where 1 = mr'^.

The quantity I is called the moment of inertia of the particle. The dimensions of

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