Question

Find the ratio of the mean speed of hydrogen molecules to the mean speed of nitrogen molecules in a sample containing a mixture of the two gases.

Use R = 8.314 JK^-1 mol^-1

Answer 1

we know ,

\[V_{avg}  = \sqrt{\frac{8RT}{\pi M}}\]

Molar mass of H₂ = M_H = 2\[\times\]10^-3 kg

Molar mass of N₂ = M_N = 28\[\times\]10^-3 kg
Now,

\[< V >_H  = \sqrt{\frac{8RT}{\pi M_H}}\] 

\[ < V >_N  = \sqrt{\frac{8RT}{\pi M_N}}\] 

\[\frac{< V >_H}{< V >_N} = \sqrt{\frac{M_N}{M_H}} = \sqrt{\frac{28}{2}} = \sqrt{14} = 3 . 74\]