Rank the following gases in order of decreasing rate of effusion: H2, O2, CO2, N2.

• A. CO2 > O2 > N2 > H2
• B. O2 > CO2 > N2 > H2
• C. N2 > H2 > CO2 > O2
• D. H2 > N2 > O2 > CO2

Answer: (D)

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 each gas: - \(\mathrm{H_2}\) (hydrogen gas): approximately 2 g/mol - \(\mathrm{N_2}\) (nitrogen gas): approximately 28 g/mol - \(\mathrm{O_2}\) (oxygen gas): approximately 32 g/mol - \(\mathrm{CO_2}\) (carbon dioxide): approximately 44 g/mol
3. Apply Graham's law by comparing the rates of effusion using the inverse square root of their molar masses. The gas with the smallest molar mass will have the highest rate of effusion, and the gas with the largest molar mass will have the lowest rate.
4. Rank the gases from highest to lowest rate of effusion based on their molar masses: \[\mathrm{H_2} > \mathrm{N_2} > \mathrm{O_2} > \mathrm{CO_2}\]
5. Confirm that this ranking matches the expected order of decreasing rate of effusion, which is consistent with the principle that lighter gases effuse faster than heavier gases.