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

Exactly equal amounts (in moles) of gas A and gas B are combined in a 1-L container at room temperature. Gas B has a molar mass that is twice that of gas A. Which statement is true for the mixture of gases and why? a. The molecules of gas B have greater kinetic energy than those of gas A. b. Gas B has a greater partial pressure than gas A. c. The molecules of gas 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 A.

Exactly equal amounts (in moles) of gas A and gas B are combined in a 1-L container at room temperature. Gas B has a molar mass that is twice that of gas A. Which statement is true for the mixture of gases and why?
a. The molecules of gas B have greater kinetic energy than those of gas A.
b. Gas B has a greater partial pressure than gas A.
c. The molecules of gas 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 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.

Transcript

00:01 Hi there.

00:03 We note that the average kinetic energy, so kinetic energy we say ke, is dependent on the temperature alone, whereas the average velocity of the gas molecule is directly proportional to the temperature, but inversely proportional to the molar mass.

00:33 So this means that gases under the same temperature but have different molar mass, the one that has greater molar mass travels slower than the one with lower molar mass.

00:54 So we say at same temperature, so this implies that at same temp, greater molar mass means lower average velocity.

01:10 Where we say that the gas moves slower if it has greater molar mass.

01:17 Another is that the partial pressure is directly proportional to the amount in terms of most.

01:29 So the more the higher the most is, the greater is the pressure that the gas can exert.

01:37 And then finally, we can also speak something about the density.

01:41 So the average density of a gas mixture is dependent on the mass.

01:55 So the greater the mass of the substances, the greater will be the, will its contribution to the average velocity.

02:04 So let us take a look at gas a and gas b.

02:15 Now it is defined that gas a and b have equal most.

02:27 So you can imagine in a container we are putting in gas a and gas b with the same amount.

02:36 And then that container is set at the same volume, where i mean the same temperature, and the same, as well as the container is fixed so that gas a and gas b occupy the same volume...

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