Question

What is/are the same for O$_2$ and NH$_3$ in a gaseous state
(A) Ratio of specific heats
(B) Average velocity
(C) maximum number of vibrational degree of freedom
(D) None of these.

Answer 1

Hint: We all know that the thermos-physical properties of gases depend upon the mass of gas, atomicity of gas, and degrees of freedom for a gas and the thermo-physical properties are characteristics for the gas to define the gas’s conductivity and thermal diffusivity.

Complete step by step answer:
By looking at the oxygen molecule, we can say that it’s a diatomic molecule and ammonia is a tetra-atomic molecule. The ratio of specific heats that is the ratio of specific heat at constant pressure and the ratio of specific heat at constant volume change as the atomicity of the gases are changed.We know that the formula for the average velocity of gases are,
${V_{avg}} = \sqrt {\dfrac{{8RT}}{{\pi M}}} $
Here ${V_{avg}}$ is the average velocity, R is the universal gas constant, T is the absolute temperature and M is the molecular mass of the gas.Here the molecular mass of oxygen and ammonia are different, and hence the average velocities for both the gases are different. The degrees of freedom of a gas depends on the atomicity. Since the atomicity of oxygen and ammonia molecules is different, the degrees of freedom are also different.
Therefore, all the above three options are wrong, and the correct option is (D).

Note:Apart from the average velocities, the root mean square velocity, translational degree of freedom for both oxygen and ammonia gases is also different. We must also keep in mind that the thermal conductivity and thermal diffusivity of both gases are not the same.