For which gas is the rms velocity maximum? | vedclass

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(A) According to the kinetic molecular theory of gases,the root mean square $(rms)$ velocity is given by the formula:$u_{rms} = \sqrt{\frac{3RT}{M}}$w

Vedclass · Accepted Answer

$H_2$

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(A) According to the kinetic molecular theory of gases,the root mean square $(rms)$ velocity is given by the formula:$u_{rms} = \sqrt{\frac{3RT}{M}}$where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.At a given temperature,$u_{rms} \propto \frac{1}{\sqrt{M}}$.This implies that the $rms$ velocity is inversely proportional to the square root of the molar mass of the gas.Comparing the molar masses: $M(H_2) = 2 \ g/mol$,$M(He) = 4 \ g/mol$,$M(N_2) = 28 \ g/mol$,and $M(O_2) = 32 \ g/mol$.Since $H_2$ has the lowest molar mass,it will have the maximum $rms$ velocity.

For which gas is the $rms$ velocity maximum?

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