Question

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

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

Answer 1

The correct option is D Carbon dioxide.

By definition, we know that
$v_{rms}=\sqrt{\frac{3P}{\rho }}=\sqrt{\frac{3PV}{M}}$
where $V$ is the molar volume which is a constant.
$\Rightarrow v_{rms}\propto \frac{1}{\sqrt{M}}$
Molar mass of oxygen is $32\text{g/mol}$
Molar mass of nitrogen is $28\text{g/mol}$
Molar mass of hydrogen is $2\text{g/mol}$
and
Molar mass of carbon dioxide is $44\text{g/mol}$
Since carbon dioxide has the highest molar mass, it has the least rms speed at a given temperature.
Hence, option (d) is the correct answer.