Question

A mixture of $1$ mole of nitrogen and $1$ mole of hydrogen is in a container at room temperature. The ratio of root mean square speed of hydrogen and nitrogen molecules is

• A. $\sqrt{14}:1$
• B. $\sqrt{28}:1$
• C. $\sqrt{12}:1$
• D. $\sqrt{15}:1$

Answer 1

The correct option is A $\sqrt{14}:1$

We know that root mean square speed is given by,
$v=\sqrt{\frac{3RT}{M}}$ and is independent of the number of moles.
As temperature is same for both gases, so,
$\frac{v_{H_2}}{v_{N_2}}=\sqrt{\frac{M_{N_2}}{M_{H_2}}}$
$\Rightarrow \frac{v_{H_2}}{v_{N_2}}=\sqrt{\frac{28}{2}}=\sqrt{14}:1$