Question

Given below are observations on molar specific heats at room temperature of some common gases

Gas	Molar specific heat (Cv) (cal mol–1 K–1)
Hydrogen	4.87
Nitrogen	4.97
Oxygen	5.02
Nitric oxide	4.99
Carbon monoxide	5.01
Chlorine	6.17

The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically, molar specific heat of a monatomic gas is 2.92 cal/mol K. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine ?

Answer 1

The gases listed in the given table are diatomic. Besides the translational degree of freedom, they have other degrees of freedom (modes of motion).
Heat must be supplied to increase the temperature of these gases. This increases the average energy of all the modes of motion. Hence, the molar specific heat of diatomic gases is more than that of monatomic gases.
If only rotational mode of motion is considered, then the molar specific heat of a diatomic
Gas = \(\frac{5}{2}\) R
= \(\frac{5}{2}\) x 1.98 = 4.95 cal mol^-1 K^-1
With the exception of chlorine, all the observations in the given table agree with (\(\frac{5}{2}\) R).
This is because at room temperature, chlorine also has vibrational modes of motion besides rotational and translational modes of motion.