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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
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Solution
we know ,
\[V_{avg} = \sqrt{\frac{8RT}{\pi M}}\]
Molar mass of H2 = MH = 2\[\times\]10-3 kg
Molar mass of N2 = MN = 28\[\times\]10-3 kg
Now,
\[< V >_H = \sqrt{\frac{8RT}{\pi M_H}}\]
\[ < V >_N = \sqrt{\frac{8RT}{\pi M_N}}\]
\[\frac{< V >_H}{< V >_N} = \sqrt{\frac{M_N}{M_H}} = \sqrt{\frac{28}{2}} = \sqrt{14} = 3 . 74\]
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