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

To solve this problem, we need to determine the ratio of average kinetic energy per molecule for hydrogen and argon gases. Let's break down the problem step-by-step.

1. Average kinetic energy per molecule of a gas is given by the formula: K = \frac{3}{2} k T, where k is the Boltzmann constant and T is the temperature in Kelvin.
2. The kinetic energy formula indicates that it only depends on the temperature of the gas and not on its nature or atomic weight.
3. Both gases are in the same flask, hence at the same temperature T = 30^\circ C = 303 \text{ K}.
4. This implies that the average kinetic energy per molecule for both gases will be the same because they are at the same temperature.
5. Thus, the ratio of the average kinetic energy per molecule of Argon to Hydrogen is: \frac{K_{\text{Argon}}}{K_{\text{Hydrogen}}} = \frac{\frac{3}{2}kT}{\frac{3}{2}kT} = 1.

Therefore, irrespective of the mass or atomic weight, the ratio of average kinetic energy per molecule of the two gases is 1. This is consistent with the given correct answer.