1. The rms speed of a gas molecule is

$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

where:

• $T$ = absolute temperature,
• $M$ = molar mass.

2. We are given that nitrogen gas ($\mathrm{N_2}$) is at $300^\circ \mathrm{C}$. Convert to Kelvin:

$T_{N_2}=300+273=573\,\text{K}$

3. Let the required temperature of hydrogen gas ($\mathrm{H_2}$) be $T_H$. For equal rms speeds:

$\sqrt{\frac{3RT_H}{M_{H_2}}}=\sqrt{\frac{3RT_{N_2}}{M_{N_2}}}$

Squaring both sides:

$\frac{T_H}{M_{H_2}}=\frac{T_{N_2}}{M_{N_2}}$

So,

$T_H=T_{N_2}\cdot \frac{M_{H_2}}{M_{N_2}}$

4. Substitute values:

• $M_{H_2}=2\,\text{g mol}^{-1}$
• $M_{N_2}=28\,\text{g mol}^{-1}$
• $T_{N_2}=573\,\text{K}$

$T_H=573\times \frac{2}{28}=573\times \frac{1}{14}$

$T_H=40.93\,\text{K}$

5. Therefore, the required temperature is approximately

$\boxed{41\,\text{K}}$