A system of physical chemistry - Index of

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A system of physical chemistry - Index of

2 8 A SYSTEM OF PHYSICAL CHEMISTRY

IS . But it has just been shown that Ar = fnu^/r. Hence the po-

tential energy, viz. is equal to (i/2);«?A But the term (i/2)w«^ is

the average kinetic energy of the particle.

Hence in a complete circular

vibration f/ic kinetic energy is just equalin magnitude to the potential energy .

W'e return now to the question of the diatomic molecule.

The linear vibration executed by one atom with respect to the other

involves one degree of freedom, i.e. the line of junction of the two atoms.

On the equipartition principle the kinetic energy involved per mole is

^RT. Since there is likewise an equal amount of potential energy, the

total energy due to vibration is iRT. Adding the amount due to the

(kinetic) energy of translation of the diatomic molecule as a whole, viz.

|RT, we obtain fRT as the total energy due to translation and vibration.

That is, the rise in this energy per i° is fR = 5'o cal. per mole

per degree, taking R = 2 cals. If now we take rotation of the molecule

as a whole into account we again have two degrees of freedom, to which

one must assign RT units of kinetic energy. The total energy of a

diatomic molecule, provided the law of equipartition is true, axxdi provided

ALL the degrees offreedom are effective, should be I^RT, and the

molecular heat therefore IR = 7

'o

approx.

Experiment shows, however, very different values. For hydrogen

at 0° C. the molecular heat Cy = 4*9 to 5*2 cal. per degree, and at

2000° C, Cv = 6'5 cal. {cf Nernst, Zeitsch. Elektrochem., 17, 272, 191 1).

For nitrogen at 0° d, = 4*84, and at 2000° d, = 67. For chlorine

at 0° C-,' = 5 "85, at 1200° Cy = 7*0. For oxygen at 0° d = 4'9) ^'^

2000° Cy = 6"7. These values are only approximately correct. It is

evident, however, that not only is there lack of agreement in the numerical

values between those observed and those calculated at lower tem-

peratures, but the fact that the molecular heat (f diatomic gases varies

considerably with the temperature is quite unaccounted for by the theory of

equipartition unless, indeed, the number of degrees of freedom is a

function of the temperature ; which is difficult to believe.

In the case of triatomic gas molecules the degrees of freedom in

respect of translation are three, the [kinetic] energy corresponding bemg

|RT. As regards vibration, there are possibly three vibrating pairs

each with one degree of freedom, corresponding to the quantity

3 X :^RT of kinetic energy. To this has to be added an equivalent

amount of potential energy, making 3RT as the total energy term in

respect of vibration. Hence translation and vibration apparently entail

fRT units of energy, and the increase in this for 1° rise in temperature

is fR = 9'o cal. per mole per degree. Logically we should likewise

add a terra for rotation of the molecule as a whole, which we have seen

amounts to #RT. The observed molecular heat Cy for CO2 at 18° is

709, and this becomes 10-47 ^'^ 2210° (Pier, I.e.). For water vapour

Cy at 50° C. = 5'96 (Nernst and Levy), and at 2327° C, C„ = 9'68

(Pier). Again the discordance between theory and experiment is very

apparent since theory predicts a constant molecular heat of either 9 or

12 cals. per mole per degree.

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