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(B) The root mean square (rms) speed of a gas molecule is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas consta

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$v_1$

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(B) The root mean square (rms) speed of a gas molecule is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.From the formula,it is evident that the rms speed of a gas molecule depends only on the temperature $T$ and the molar mass $M$ of the gas.In vessel $A$,the rms speed of $O_2$ is $v_1 = \sqrt{\frac{3RT}{M_{O_2}}}$.In vessel $C$,the temperature is still $T$ and the molar mass of $O_2$ remains $M_{O_2}$. The presence of other gases (like $N_2$) in the mixture does not affect the individual rms speed of $O_2$ molecules because the molecules of different gases in a mixture behave independently in terms of their kinetic energy distribution at a given temperature.Therefore,the rms speed of $O_2$ molecules in vessel $C$ remains the same as in vessel $A$,which is $v_1$.

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