Question

A flask contains Hydrogen and Argon in the ratio 2:1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases (K argon/K hydrogen) is:
(Given: Atomic Weight of Ar = 39.9)

• A. \(\frac{39.9}{2}\)
• B. 1
• C. 39.9
• D. 2

Hint:

The kinetic energy of a gas molecule is proportional to the temperature, and the kinetic energy per molecule of different gases is the same at the same temperature.

Answer 1

The Correct Option is B

Solution:

The kinetic energy per molecule is given by:

\( K = \frac{3}{2} k_B T \)

Thus, the ratio of kinetic energy per molecule of Argon and Hydrogen is:

\( \frac{K_{\text{argon}}}{K_{\text{hydrogen}}} = \frac{\frac{3}{2} k_B T_{\text{argon}}}{\frac{3}{2} k_B T_{\text{hydrogen}}} = \frac{T_{\text{argon}}}{T_{\text{hydrogen}}} \)

Since the temperature is the same for both gases, the ratio is 1. Hence, the correct answer is \( 1 \).