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(C) The average kinetic energy per molecule of an ideal gas is given by the formula $\langle KE \rangle = \frac{f}{2} k_B T$,where $f$ is the degrees

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$1:1$

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(C) The average kinetic energy per molecule of an ideal gas is given by the formula $\langle KE \rangle = \frac{f}{2} k_B T$,where $f$ is the degrees of freedom,$k_B$ is the Boltzmann constant,and $T$ is the absolute temperature.Since both hydrogen and nitrogen are diatomic gases at $30^{\circ} C$,they have the same number of degrees of freedom $(f=5)$.Because the gases are in the same vessel,they are in thermal equilibrium,meaning they are at the same temperature $(T_{H_2} = T_{N_2} = T)$.Therefore,the ratio of the average kinetic energies per molecule is $\frac{\langle KE \rangle_{H_2}}{\langle KE \rangle_{N_2}} = \frac{\frac{5}{2} k_B T}{\frac{5}{2} k_B T} = 1:1$.The mass ratio is irrelevant because the average kinetic energy per molecule depends only on the temperature,not on the mass or the number of molecules.

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