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If the rms speed of nitrogen molecules is 490 m s^(-1)at 273 K, find the rms speed of hydrogem molecules at the same temperature.

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Answer Text

Solution :
The molecular weight of nitrogen=n is `28 g mol^(-1) and that of hydrogen is `2 g mol^(-1)`. Let `m_(1), m_(2)` be the masses and `v_(1)`,`v_(2)`be the rms speeds of a nitrogen molecule and a hydrogen molecule respectively. Then `m_(1) = 14m_(2)`.Using equation`(24*6)`, <br> `1/2m_(1) v_(1)^(2)=1/2m_(2)v_(2)^(2)` <br> or, `v_(2) = v_(1)sqrt(m_(1)/m_(2))=490m s^(-1)xx sqrt14=1830ms^(-1)`.

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