Two gases, O₂ and CO₂, with molar masses of 32 g/mol and 44 g/mol respectively, are in a closed vessel separated by an impermeable membrane into two equal sub-volumes. If both the temperatures and the densities of each gas are the same, what is the ratio of the O₂ to CO₂ pressures exerted on the membrane?

Question

Quizplus · Accepted Answer

Given that the temperatures and densities of both gases are the same, the ratio of their pressures can be determined using the ideal gas law, $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is temperature. Since the volumes, temperatures, and the gas constant are the same for both gases, the pressure ratio is inversely proportional to the molar mass ratio. Therefore, the pressure ratio of $O_2$ to $CO_2$ is the inverse of their molar mass ratio, which is $44/32 = 1.375$, or approximately 1.4 when rounded.

Two Gases, O2 and CO2, with Molar Masses of 32

Two Gases, O₂ and CO₂, with Molar Masses of 32