Question

A vessel contains hydrogen and nitrogen gases in the ratio 2:3 by mass. If the temperature of the mixture of the gases is 30°C, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is:

• A. \( 3:7 \)
• B. \( 2:3 \)
• C. \( 1:1 \)
• D. \( 1:14 \) \bigskip

Hint:

According to the kinetic theory of gases, the average kinetic energy per molecule of an ideal gas depends only on the temperature and is given by: \[ KE_{\text{avg}} = \frac{3}{2} k_B T \] Since the temperature is the same for both hydrogen and nitrogen gases, their average kinetic energies per molecule are equal, leading to the ratio \( 1:1 \).

Answer 1

The Correct Option is C

The average kinetic energy per molecule of a gas is given by: \[ E = \frac{3}{2} k_B T \] Where \( k_B \) is the Boltzmann constant and \( T \) is the temperature in Kelvin. Since the temperature is the same for both gases, the average kinetic energy per molecule depends only on the type of gas. The ratio of the average kinetic energies per molecule of hydrogen and nitrogen is: \[ \frac{E_{\text{H}_2}}{E_{\text{N}_2}} = \frac{\frac{3}{2} k_B T}{\frac{3}{2} k_B T} = 1 \] Thus, the ratio of the average kinetic energies per molecule of hydrogen and nitrogen is \( 1:1 \).