Exactly equal amounts (in moles) of gas A and gas B are combined in a 1 L container at room tem

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Exactly equal amounts (in moles) of gas A and gas B are...

Exactly equal amounts (in moles) of gas $\mathrm{A}$ and gas $\mathrm{B}$ are combined in a $1 \mathrm{~L}$ container at room temperature. Gas $\mathrm{B}$ has a molar mass that is twice that of gas $\mathrm{A}$. Which statement is true for the mixture of gases and why? a. The molecules of gas $\mathrm{B}$ have greater kinetic energy than those of gas $\mathrm{A}$. b. Gas $\mathrm{B}$ has a greater partial pressure than gas $\mathrm{A}$. c. The molecules of gas $\mathrm{B}$ have a greater average velocity than those of gas A. d. Gas B makes a greater contribution to the average density of the mixture than gas $\mathrm{A}$.

Exactly equal amounts (in moles) of gas $\mathrm{A}$ and gas $\mathrm{B}$ are combined in a $1 \mathrm{~L}$ container at room temperature. Gas $\mathrm{B}$ has a molar mass that is twice that of gas $\mathrm{A}$. Which statement is true for the mixture of gases and why?
a. The molecules of gas $\mathrm{B}$ have greater kinetic energy than those of gas $\mathrm{A}$.
b. Gas $\mathrm{B}$ has a greater partial pressure than gas $\mathrm{A}$.
c. The molecules of gas $\mathrm{B}$ have a greater average velocity than those of gas A.
d. Gas B makes a greater contribution to the average density of the mixture than gas $\mathrm{A}$.

Key Concepts

Kinetic Energy of Gas Molecules

At a given temperature, all ideal gas molecules have the same average kinetic energy regardless of their mass. This is a fundamental result of the kinetic molecular theory, where the kinetic energy is proportional to the absolute temperature. Therefore, even if two gases have different molar masses, their molecules will have the same average kinetic energy when they are at the same temperature.

Partial Pressures in Gas Mixtures

The pressure exerted by each gas in a mixture, known as its partial pressure, depends on the number of moles of that gas and the temperature, according to the ideal gas law (PV = nRT). Since the gases contribute independently to the total pressure, if equal moles of gases are mixed at the same temperature and volume, they will exert equal partial pressures, regardless of their individual molar masses.

Molecular Velocity and Molar Mass

Although the average kinetic energy of gas molecules is the same at a given temperature, their average speeds differ depending on the mass of the molecules. According to the relation derived from kinetic molecular theory, lighter molecules move faster than heavier molecules. This relationship is generally expressed as the root-mean-square speed being inversely proportional to the square root of the molar mass.

Density of Gas Mixtures

The density of a gas is determined by its mass per unit volume. In the context of a gas mixture, even if the number of moles of each gas is equal, a gas with a higher molar mass will contribute more mass and thus a higher density than a lighter gas. This key relationship explains why, in a mixture of equal moles, the gas with the higher molar mass will have a greater impact on the overall density of the mixture.

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