Question

Which of the following gases has maximum rms speed at a given temperature?

• A. Hydrogen
• B. Nitrogen
• C. Oxygen
• D. Carbon dioxide

Answer 1

The correct option is A Hydrogen

We know that, root mean square speed,
$v_{rms}=\sqrt{\frac{3RT}{M}}$
Now, at constant temperature $T$
$v_{rms}\propto \frac{1}{\sqrt{M}}$
As molar mass increases, rms speed decreases. So, gas having lower molar mass will have higher rms speed.
We know, molar mass of hydrogen $=2\text{g}$
Molar mass of nitrogen $=28\text{g}$
Molar mass of oxygen $=32\text{g}$
Molar mass of carbon dioxide $=44\text{g}$
So, we can see that hydrogen has lowest molar mass, therefore it has maximum $v_{rms}$.