At what temperature, will the average speed of $C H_{4}$ molecules have the same values as $O_{2}$ at $300 K$ ?

1200 K

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150 K

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600 K

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300 K

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Solution

The correct option is C $150 K$
$u_{a v e r a g e} = \sqrt{\frac{8 R T}{π M}}$
${u_{a v g}}_{C H_{4}} = \sqrt{\frac{8 R T_{1}}{π 16}}$ $∵$ Mass of $C H_{4} = 12 + 4 = 16$
${u_{a v g}}_{O_{2}} = \sqrt{\frac{8 R (300)}{π (32)}}$
${u_{a v g}}_{C H_{4}} = {u_{a v g}}_{O_{2}}$
$\sqrt{\frac{8 R T_{1}}{π 16}} = \sqrt{\frac{8 R (300)}{π (32)}} ⟹ \frac{T_{1}}{16} = \frac{300}{32} ⟹ T_{1} = 150 K$
They have same average velocity when the pemperature of $C H_{4}$ is $150 K .$

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