Which gas law states that at the same temperature and pressure, the rates of diffusion or effusion of gases are inversely proportional to the square root of their molar masses?

• A. Amonton's Law
• B. Mariotte's Law
• C. Graham's Law
• D. Charles' Law

Answer: (C)

The concept being tested is how the speed of gas molecules at a given temperature depends on their mass, which directly affects diffusion and effusion rates. Lighter molecules move faster on average than heavier ones, so at the same temperature and pressure, the rate at which gases diffuse or effuse is controlled by how heavy the molecules are.

Graham's Law captures this: the rates of diffusion or effusion for two gases are inversely proportional to the square root of their molar masses. In formula terms, rate1/rate2 = sqrt(M2/M1), so each gas’s rate is proportional to 1/√M. This means a light gas will diffuse or effuse much faster than a heavier one.

For example, helium (low molar mass) will diffuse and effuse far faster than xenon (high molar mass); the ratio of their rates would be about sqrt(131/4) ≈ 5.7, meaning helium moves roughly six times as fast. Other gas laws deal with pressure, volume, and temperature relationships rather than diffusion or effusion rates, so they don’t describe this behavior.