The densities of 2 gases are in the ratio 1:2 | vedclass

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Question

(A) From the ideal gas equation,density $d = \frac{PM_w}{RT}$,where $P$ is pressure,$M_w$ is molar mass,$R$ is the gas constant,and $T$ is temperature

Vedclass · Accepted Answer

$1:1$

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(A) From the ideal gas equation,density $d = \frac{PM_w}{RT}$,where $P$ is pressure,$M_w$ is molar mass,$R$ is the gas constant,and $T$ is temperature.Assuming the gases have the same molar mass $(M_w)$,the relationship is $d \propto \frac{P}{T}$ or $P \propto d 	imes T$.Given the ratio of densities $\frac{d_1}{d_2} = \frac{1}{2}$ and the ratio of temperatures $\frac{T_1}{T_2} = \frac{2}{1}$.The ratio of pressures is $\frac{P_1}{P_2} = \frac{d_1}{d_2} 	imes \frac{T_1}{T_2}$.Substituting the values: $\frac{P_1}{P_2} = \frac{1}{2} 	imes \frac{2}{1} = \frac{1}{1}$.Thus,the ratio of their pressures is $1:1$.

The densities of $2$ gases are in the ratio $1:2$ and their temperatures are in the ratio $2:1$. What is the ratio of their respective pressures?

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