A vessel contains 1 , mole of O_2 gas (molar | vedclass

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(C) The ideal gas equation is given by $PV = nRT$.Since the vessels are identical,the volume $V$ is the same for both gases.For the first vessel conta

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$2P$

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(C) The ideal gas equation is given by $PV = nRT$.Since the vessels are identical,the volume $V$ is the same for both gases.For the first vessel containing $O_2$ gas: $P_1 V = n_1 R T_1$,where $n_1 = 1 \, mole$,$T_1 = T$,and $P_1 = P$.So,$PV = (1)RT \Rightarrow PV = RT$.For the second vessel containing $He$ gas: $P_2 V = n_2 R T_2$,where $n_2 = 1 \, mole$,$T_2 = 2T$,and $P_2$ is the unknown pressure.So,$P_2 V = (1)R(2T) \Rightarrow P_2 V = 2RT$.Dividing the two equations: $\frac{P_2 V}{PV} = \frac{2RT}{RT}$.This simplifies to $\frac{P_2}{P} = 2$,which gives $P_2 = 2P$.

$A$ vessel contains $1 \, mole$ of $O_2$ gas (molar mass $32$) at a temperature $T$. The pressure of the gas is $P$. An identical vessel containing one mole of $He$ gas (molar mass $4$) at a temperature $2T$ has a pressure of:

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