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

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

Explanation

The gases listed in the table are diatomic and have other degrees of freedom (that is have other modes of motion like vibrational and rotational) possible besides the translational degrees of freedom. To raise the temperature of the gas by a certain amount, heat is to be supplied to increase the average energy of all the modes. Consequently, molar specific heat of diatomic gases is more than that of monatomic gases. It can be shown that if only rotational modes of motion are considered, the molar specific heat of diatomic gases is nearly `5/2` R which is equal to ` 5/2 xx 1.98 = 4.95` which agrees well with all the observations listed in the table except for chlorine. The higher value of molar specific heat of chlorine indicates that besides rotational modes, vibrational modes are also present in chlorine at room temperature.