Which of the following gases has maximum value of root mean square velocity $(v_{r m s})$ at same temperature $C O_{2}, H_{2}, N H_{3} ?$

C O_{2}

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H_{2}

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N H_{3}

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All have same velocity

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Solution

The correct option is B $H_{2}$
$v_{r m s} = \sqrt{\frac{3 R T}{M}}$

given, $T =$ constant

$∴ v_{r m s} \propto \sqrt{\frac{1}{\sqrt{M}}}$

Means, higher be the value of molecular mass, lower be the $v_{r m s}$ and vice-versa.

We have $M_{C O_{2}} = 44, M_{H_{2}} = 2, M_{N H_{3}} = 17$

Hence, $v_{r m s}$ of $H_{2}$ will be maximum.

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