At a temperature of 27^{circ}C and a pressure | vedclass

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Question

(D) The root mean square velocity is given by the formula $
u_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the absolu

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) The root mean square 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.Since the temperature $T$ is the same for both gases,$
u_{rms} \propto \frac{1}{\sqrt{M}}$.Therefore,the ratio is given by $\frac{(
u_{rms})_{H_2}}{(
u_{rms})_{O_2}} = \sqrt{\frac{M_{O_2}}{M_{H_2}}}$.Given the molar masses $M_{O_2} = 32 \, g/mol$ and $M_{H_2} = 2 \, g/mol$.Substituting these values,we get $\frac{(
u_{rms})_{H_2}}{(
u_{rms})_{O_2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$.

At a temperature of $27^{\circ}C$ and a pressure of $1 \, atm$,the ratio of the root mean square velocities $(\nu_{rms})_{H_2} / (\nu_{rms})_{O_2}$ for hydrogen and oxygen molecules is:

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