Question

If the rms speed of the molecules of a diatomic gas at a temperature of 322K is 2000 m/s, then the gas is

• A. hydrogen
• B. nitrogen
• C. oxygen
• D. chlorine

Hint:

For identifying gases based on rms speed, use the formula \( v_{rms} = \sqrt{\frac{3kT}{M}} \), where the lighter gases like hydrogen will have higher rms speeds.

Answer 1

The Correct Option is A

The rms speed \( v_{rms} \) is related to the temperature \( T \) and molar mass \( M \) of the gas by the formula \( v_{rms} = \sqrt{\frac{3kT}{M}} \). Substituting the given values, we find that hydrogen, with its low molar mass, matches the given rms speed.