Question

Nitrogen gas is at ${300}^{\circ }\text{C}$ temperature. The temperature (in $\text{K}$) at which the rms speed of a $H_2$ molecules would be equal to the rms speed of a nitrogen molecule is_____. (Molar mass of $N_2$ gas $28\text{g}$);

Answer 1

Room mean square speed is given by

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

Here,
$M=$ Molar mass of gas molecule
$T=$ temperature of the gas molecule
We have given $V_{N_2}=V_{H_2}$
$\therefore \sqrt{\frac{3R{T}_{N_2}}{M_{N_2}}}=\sqrt{\frac{3R{T}_{H_2}}{M_{H_2}}}$
$\Rightarrow \frac{T_{H_2}}{2}=\frac{573}{28}\Rightarrow T_{H_2}\approx 41K$