Question

The Maxwell distribution of speeds of a gas at 300 K is given below. The molar mass (in g mol$^{-1}$) of this gas is ......... (Round off to one decimal place) (R = 8.3 J mol$^{-1}$ K$^{-1}$) 

Hint:

In Maxwell distribution, the most probable speed is related to the temperature and molar mass. Always remember to use the appropriate equation for speed distribution.

Answer 1

Correct Answer: 19.8

Step 1: Understanding Maxwell Distribution.
The Maxwell distribution of speeds is related to the temperature and molar mass of the gas. The formula for the most probable speed \( v_p \) is given by: \[ v_p = \sqrt{\frac{2RT}{M}} \] Where: \( R \) is the gas constant (8.3 J mol$^{-1}$ K$^{-1}$), \( T \) is the temperature in Kelvin (300 K), \( M \) is the molar mass of the gas in kg mol$^{-1}$.

Step 2: Calculation of Molar Mass.
From the given Maxwell distribution graph, we find the most probable speed \( v_p \) is approximately 600 m/s. Substituting this value into the equation, we can solve for the molar mass \( M \). \[ M = \frac{2RT}{v_p^2} \]

Step 3: Conclusion.
The molar mass of the gas is calculated to be 29.2 g mol$^{-1}$, which matches option (A).