Question

If the root mean square speed of hydrogen gas at a particular temperature is 1900 m s$^{-1}$, then the root mean square speed of nitrogen gas at the same temperature (rounded off to the nearest integer) is ________.
(Given: Atomic mass of H = 1 g mol$^{-1}$; Atomic mass of N = 14 g mol$^{-1}$)

Hint:

At constant temperature, $v_\text{rms} \propto 1/\sqrt{M}$. Lighter gases move faster than heavier ones.

Answer 1

Correct Answer: 507

Step 1: RMS speed formula.
\[ v_\text{rms} = \sqrt{\frac{3RT}{M}} \] For gases at the same temperature, \[ \frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}} \]
Step 2: Apply for H$_2$ and N$_2$.
\[ \frac{v_{H_2}}{v_{N_2}} = \sqrt{\frac{28}{2}} = \sqrt{14} \Rightarrow v_{N_2} = \frac{1900}{\sqrt{14}} = 508.3 \] Step 3: Conclusion.
RMS speed of N$_2$ = 508 m s$^{-1}$.