Question

A sample containing 4 moles of $H_2$ gas and 2 moles of He gas have most probable velocity of 50 m/sec find the average translation at kinetic energy per mole of the given mixture (in kilojoules)?

Answer 1

Given : $n_{H_2}=4$ $n_{He}=2$ $V_{mp}=50$ $m/s$

Molecular mass of the mixture $M=\frac{n_{H_2}\times M_{H_2}+n_{He}\times M_{He}}{n_{H_2}+n_{He}}$

$\therefore$ $M=\frac{4\times 2+2\times 4}{4+2}=\frac{8}{3}$

Most probable velocity $V_{mp}=\sqrt{\frac{2RT}{M}}$

$\therefore$ $50=\sqrt{\frac{2RT}{\frac{8}{3}}}$ $⟹RT=\frac{10000}{3}$ J

Average translation kinetic energy $K.E=\frac{3}{2}RT=\frac{3}{2}\times \frac{10000}{3}=5000$ J