The r.m.s. velocity of a gas at a certain tem | vedclass

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Question

(C) The root mean square (r.m.s.) velocity of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $M$ is the molar mass of the gas.Si

Vedclass · Accepted Answer

$CH_4$

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(C) The root mean square (r.m.s.) velocity of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $M$ is the molar mass of the gas.Since $v_{rms} \propto \frac{1}{\sqrt{M}}$,we can write the ratio for two gases as $\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}$.Given that the r.m.s. velocity of the gas $(v_1)$ is $\sqrt{2}$ times the r.m.s. velocity of oxygen $(v_2)$,we have $\frac{v_1}{v_2} = \sqrt{2}$.The molar mass of oxygen $(O_2)$ is $M_2 = 32 	ext{ g/mol}$.Substituting these values into the ratio: $\sqrt{2} = \sqrt{\frac{32}{M_1}}$.Squaring both sides: $2 = \frac{32}{M_1}$.Solving for $M_1$: $M_1 = \frac{32}{2} = 16 	ext{ g/mol}$.The gas with a molar mass of $16 	ext{ g/mol}$ is methane $(CH_4)$.Therefore,the correct option is $C$.

The r.m.s. velocity of a gas at a certain temperature is $\sqrt{2}$ times that of the oxygen molecules at the same temperature. The gas can be:

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