Which of the following gases will effuse the most rapidly according to Graham's law?

• A. O2
• B. N2
• C. H2
• D. CO2

Answer: (C)

Verified step by step guidance

1. Recall Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, this is expressed as: \[\text{Rate} \propto \frac{1}{\sqrt{M}}\] where \(M\) is the molar mass of the gas.
2. List the molar masses of the given gases: - Oxygen (\(O_2\)): approximately 32 g/mol - Nitrogen (\(N_2\)): approximately 28 g/mol - Hydrogen (\(H_2\)): approximately 2 g/mol - Carbon dioxide (\(CO_2\)): approximately 44 g/mol
3. Apply Graham's law by comparing the rates of effusion relative to each other. Since the rate is inversely proportional to the square root of molar mass, gases with smaller molar masses effuse faster.
4. Calculate or conceptually compare the values of \(\frac{1}{\sqrt{M}}\) for each gas to determine which has the highest rate of effusion. The gas with the smallest molar mass will have the largest value and thus effuse most rapidly.
5. Conclude that hydrogen (\(H_2\)), having the smallest molar mass among the options, will effuse the most rapidly according to Graham's law.