Chemistry - Ideal Gas Question with Solution | TestHub

$\mathrm{\mu }=\sqrt{\frac{3\mathrm{R}\mathrm{T}}{\mathrm{M}}}$
$\mathrm{\mu }\propto \sqrt{\frac{\mathrm{T}}{\mathrm{M}}}$
So${\mathrm{\mu }}_{{\mathrm{H}}_2}/{\mathrm{\mu }}_{{\mathrm{N}}_2}=\sqrt{\left[\right({\mathrm{T}}_{{\mathrm{H}}_2}/{\mathrm{M}}_{{\mathrm{H}}_2})\times ({\mathrm{M}}_{{\mathrm{N}}_2}/{\mathrm{T}}_{{\mathrm{N}}_2}\left)\right]}$
$\sqrt{7}=\sqrt{({\mathrm{T}}_{{\mathrm{H}}_2}\times 28/{\mathrm{T}}_{{\mathrm{N}}_2}\times 2)}$
$=\sqrt{{\mathrm{T}}_{{\mathrm{H}}_{2\mathrm{}}}\times 14/{\mathrm{T}}_{{\mathrm{N}}_2}}$
On squaring both sides and solving we get
${\mathrm{T}}_{{\mathrm{N}}_2}=2{\mathrm{T}}_{{\mathrm{H}}_2}$
so${\mathrm{T}}_{{\mathrm{N}}_2}>{\mathrm{T}}_{{\mathrm{H}}_2}$