Question

the two gas samples represented in the graph above are at the same temperature. which of the following statements about the gases is correct? a the molecules of gas z have a higher average kinetic energy than the molecules of gas x. b there are fewer molecules in the sample of gas z than in the sample of gas x. c gas z has a smaller molar mass than gas x. d gas z has a greater molar mass than gas x.

Explanation:

Step1: Recall kinetic - theory of gases

The average kinetic energy of gas molecules is given by $KE_{avg}=\frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the temperature. Since both gases are at the same temperature, their average kinetic energies are equal. So, option A is incorrect.

Step2: Analyze the relationship between molar mass and molecular speed

The root - mean - square speed of gas molecules is $v_{rms}=\sqrt{\frac{3RT}{M}}$, where $R$ is the ideal gas constant, $T$ is the temperature, and $M$ is the molar mass. At the same temperature, gases with lower molar masses have higher average speeds.

Step3: Observe the graph

From the graph, gas Z has a higher average speed than gas X. According to the formula $v_{rms}=\sqrt{\frac{3RT}{M}}$, if $T$ is constant, a higher speed corresponds to a lower molar mass. So gas Z has a smaller molar mass than gas X.

Answer:

C. Gas Z has a smaller molar mass than gas X