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(C) The root mean square velocity $(v_{rms})$ of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \frac{1}{\sqrt{

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$\sqrt{3} : \sqrt{2}$

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(C) The root mean square velocity $(v_{rms})$ of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \frac{1}{\sqrt{M}}$ and vapour density $\rho \propto M$,we have $v_{rms} \propto \frac{1}{\sqrt{\rho}}$.Given the ratio of vapour densities $\rho_1 : \rho_2 = 6 : 9$.Therefore,the ratio of their $v_{rms}$ is $\frac{(v_{rms})_1}{(v_{rms})_2} = \sqrt{\frac{\rho_2}{\rho_1}}$.Substituting the values: $\frac{(v_{rms})_1}{(v_{rms})_2} = \sqrt{\frac{9}{6}} = \sqrt{\frac{3}{2}}$.Thus,the ratio is $\sqrt{3} : \sqrt{2}$.

At constant temperature,the vapour density of two gases are in the ratio of $6 : 9$. Compare their $v_{rms}$.

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