Question

the graph above shows the distribution of molecular speeds for four different gases at the same temperature. what property of the different gases can be correctly ranked using information from the graph, and why? a the densities of the gases, because as the density of a gas increases, the average speed of its molecules decreases. b the pressures of the gases, because the pressure exerted by a gas depends on the average speed with which its molecules are moving. c the volumes of the gases, because at a fixed temperature the volume of a gas can be calculated using the equation pv = nrt. d the molecular masses of the gases, because the gas molecules have the same average kinetic energy and mass can be calculated using the equation ke_avg = 1/2 mv².

Explanation:

At a given temperature, all gas molecules have the same average kinetic - energy ($KE_{avg}=\frac{1}{2}mv^{2}$). From the graph of molecular speeds, we can observe the distribution of speeds. Heavier molecules (higher molecular mass) will have lower average speeds compared to lighter molecules. The density of a gas is related to its molecular mass, but the direct relationship between density and the graph is not as straightforward as that between molecular mass and the graph. Pressure depends on the number of collisions of molecules with the container walls and is not directly related to the molecular - speed distribution in the way presented in option B. Volume is related to the ideal gas law $PV = nRT$, but the graph does not provide information to rank volumes directly. The molecular mass can be ranked as the gas with lower average speed has a higher molecular mass since $KE_{avg}$ is constant at a fixed temperature.

Answer:

D. The molecular masses of the gases, because the gas molecules have the same average kinetic energy and mass can be calculated using the equation $KE_{avg}=\frac{1}{2}mv^{2}$.