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(D) From the ideal gas equation,$PV = nRT$,where $n$ is the number of moles.Since $V$,$R$,and $T$ are constant for both vessels,we have $P \propto n$.

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Both $(B)$ and $(C)$

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(D) From the ideal gas equation,$PV = nRT$,where $n$ is the number of moles.Since $V$,$R$,and $T$ are constant for both vessels,we have $P \propto n$.Given the ratio of pressures is $\frac{P_1}{P_2} = \frac{1}{2}$,it follows that the ratio of the number of moles (and thus the number of molecules) is $\frac{n_1}{n_2} = \frac{1}{2}$.Also,the root mean square velocity is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $T$ and $M$ are the same for both vessels,the ratio of $v_{rms}$ is $1 : 1$.Therefore,both statements $(B)$ and $(C)$ are correct.

Two vessels of the same volume contain the same gas at the same temperature. If the pressure in the vessels is in the ratio of $1 : 2$,then

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