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

step 1 For this particular scenario, we have equal amounts of gases A and B, and they're found in the s

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

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

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

Key Concepts

Kinetic Molecular Theory

This theory states that, at a given temperature, all gas molecules have the same average kinetic energy regardless of their mass. It establishes that temperature is a measure of the average kinetic energy of the particles, ensuring that, for equal moles of gases at the same temperature, the kinetic energy per molecule is the same.

Ideal Gas Law and Partial Pressures

The ideal gas law (PV = nRT) underlies the behavior of gases in mixtures, where each gas's partial pressure is determined by its number of moles, independent of its molar mass. In a mixture, gases at equal moles contribute equally to the total pressure, meaning that differences in mass do not affect the partial pressure of each component.

Root-Mean-Square Velocity

Root-mean-square velocity is a measure of the average speed of gas molecules that depends inversely on the square root of their molar mass. This concept shows that, at a constant temperature, lighter molecules move faster than heavier ones because they require less energy to achieve higher speeds.

Gas Density in Mixtures

The density of a gas is determined by its molar mass divided by the molar volume. In a mixture, even if the moles of each gas are equal, a gas with a higher molar mass contributes more to the overall density due to its greater mass per molecule, influencing the physical properties of the gas mixture.

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