Kinetic Theory : Molecular Energy

The kinetic energy of translation of a molecule is ½mG², hence the equation shows that: the product of the pressure and volume of a gas is equal to two-thirds of the kinetic energy of translation of the molecules. The kinetic energy of translation is the energy possessed by the molecules in virtue of their translatory motion in straight lines; only this part of the energy makes any contribution to the pressure. Energy due to rotation of the molecules, or the relative motions of their parts, is without influence on the pressure.

Boyle's law, pv = const, when the temperature is constant, shows that the kinetic energy of translation depends only on the temperature of the gas, not on its volume. This is equivalent to Joule' s law, from which we started.

Now put V = 22.415 litres, then at S.T.P., M = M, the gram-molecule (mol) of the gas, and N = N₀, the number of molecules in a gram-molecule. Avogadro's hypothesis shows that N₀ is the same for all gases; it is called Avogadro's constant. We see that the kinetic energy of translation of the molecules is the same for a mol of any gas at a given temperature. For kinetic energy = ½MG² = 3/2 * pv. But v is the same for a mol of any gas at a given pressure and temperature, and by Boyle's law, pv is also constant at a given temperature. We can now calculate this molecular energy.

At the melting point of ice, V = 22.415 litres = 22.415 x 1000.028 cm³, p = 760 mm. = 76 x 13.595 x 980.6 = 1,013,225 dynes per cm²;

3/2 * pV = 22.415 x 1000.028 x 1013225 x 3/2 = 3.407 x 10¹⁰ ergs.

Thus, the molecular energy of a mol of any gas at 0°, due to the transiatory motion of its molecules, is large enough to raise a weight of about a ton through one foot. The gas constant is

R = pV/T = 3/2 x 3.407 x 10¹⁰/273.09;

R = 8.317 x 10⁷ ergs/C.;

or R = 8.317 x 10⁷/4.184 x 10⁷ = 1.988 g. cal./C.

or in modern units R = 8.314472(15) JK⁻¹mol⁻¹

Protein crystallography
Chemistry guide
Kinetic Theory
-M-
<<<	>>>