Nitrogen gas is at 300 ° C temperature. The temperature (in K ) at...

Given,

Temperature of Nitrogen gas is

${T}_{1} = 300 ° C = 300 + 273 = 573K$

Molar mass of ${H}_{2}$ gas is ${M}_{{H}_{2}} = 2g$

Molar mass of ${N}_{2}$ gas is ${M}_{{N}_{2}} = 28g$

The rms speed of gas is given by

${V}_{rms} = \sqrt{\dfrac{3RT}{M}}$

Now rms speed of hydrogen gas is equal to rms speed of nitrogen gas, i.e.; ${\left({V}_{rms}\right)}_{{H}_{2}} = {\left({V}_{rms}\right)}_{{N}_{2}}$
$⇒ \dfrac{{T}_{{H}_{2}}}{{T}_{{N}_{2}}} = \dfrac{{M}_{{H}_{2}}}{{M}_{{N}_{2}}}$

Substitute the given values i above equation, we get,

${T}_{{H}_{2}} = \dfrac{2}{28} \times 573$

${T}_{{H}_{2}} = 41K$