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

Gas	Molar specific heat (Cv) (cal mo1–1 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?

The gases given in the given table are diatomic. Besides the translational degree of freedom, they have other degrees of freedom. Heat must be supplied to increase the temperature of these gases. This increases the average energy of all the degrees of freedom. 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 is equal to (5/2)R (where, R = Ideal gas law constant = 1.98 cal mol^-1 K^-1)

So, molar specific heat = (5/2) × 1.98 = 4.95 cal mol^-1 K^-1

With the exception of chlorine, all the observations in the given table agree with this value of molar specific heat. This is because of the fact that at room temperature, chlorine also has vibrational modes of motion besides rotational and translational modes of motion.

NOTE: Molecular degrees of freedom refer to the number of ways a molecule in the gas phase may move, rotate, or vibrate in space.

The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.