This graph shows the distribution of molecular velocities...

This graph shows the distribution of molecular velocities for two different molecules $(A$ and $B)$ at the same temperature. Which molecule has the higher molar mass? Which molecule has the higher rate of effusion?

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Key Concepts

Maxwell-Boltzmann Distribution

This concept describes the statistical distribution of speeds for molecules in a gas at a given temperature. It shows that at a fixed temperature, lighter molecules on average move faster, while heavier molecules have a distribution shifted toward lower speeds. The peak of the distribution corresponds to the most probable speed of the molecules.

Molar Mass

Molar mass is the mass of a given substance (usually in grams per mole) and plays a key role in determining molecular speed at a fixed temperature. According to kinetic theory, for a gas at a set temperature, molecules with a higher molar mass will, on average, move more slowly than those with a lower molar mass.

Graham’s Law of Effusion

Graham’s Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means that, at a constant temperature, lighter gases effuse faster than heavier ones. The law helps link the molecular speed distribution (from the Maxwell-Boltzmann distribution) with the rate at which gas molecules escape through small openings.

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