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Question

(A) The ideal gas equation is $PV = nRT$. Since $n = \frac{m}{M}$, we have $PV = \frac{m}{M}RT$, which rearranges to $P = \frac{m}{V} 	imes \frac{RT}

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$1:1$

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(A) The ideal gas equation is $PV = nRT$. Since $n = \frac{m}{M}$, we have $PV = \frac{m}{M}RT$, which rearranges to $P = \frac{m}{V} 	imes \frac{RT}{M} = \frac{dRT}{M}$.For equal amounts of the same gas, the molar mass $M$ is constant, so $P \propto d 	imes T$.Therefore, the ratio of pressures is $\frac{P_1}{P_2} = \frac{d_1}{d_2} 	imes \frac{T_1}{T_2}$.Given $\frac{d_1}{d_2} = \frac{1}{2}$ and $\frac{T_1}{T_2} = \frac{2}{1}$.Substituting these values: $\frac{P_1}{P_2} = \frac{1}{2} 	imes \frac{2}{1} = \frac{1}{1}$.Thus, the ratio of their pressures is $1:1$.

Equal amounts of gases are kept in two separate containers. If the densities of the two gases are in $1:2$ ratio and their temperatures are in $2:1$ ratio, calculate the ratio of their respective pressures.

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