Question

3 mark for review the maxwell - boltzmann distributions of molecular speeds in samples of two different gases at the same temperature are shown above. which gas has the greater molar mass? a gas a b gas b c both gases have the same molar mass. d it cannot be determined unless the pressure of each sample is known.

Explanation:

Step1: Recall Maxwell - Boltzmann distribution principle

At a given temperature, the root - mean - square speed ($v_{rms}=\sqrt{\frac{3RT}{M}}$) of gas molecules is related to molar mass ($M$). The broader the distribution of molecular speeds, the higher the average speed of the molecules.

Step2: Analyze the graph

Gas A has a narrower distribution of molecular speeds compared to gas B. A narrower distribution implies lower average molecular speeds. According to $v_{rms}=\sqrt{\frac{3RT}{M}}$, at a constant temperature $T$, lower average speeds correspond to higher molar masses. Since gas A has lower average speeds (narrower distribution), gas A has a greater molar mass.

Answer:

A. Gas A