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**