Given a graph showing the rates of effusion for four different gases—He, N2, O2, and CO2—which gas has the smallest molar mass?

• A. N2
• B. CO2
• C. O2
• D. He

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. Understand that a gas with a higher rate of effusion will have a smaller molar mass because the rate and molar mass are inversely related through the square root.
3. Look at the graph and identify which gas has the highest rate of effusion among He, N2, O2, and CO2.
4. Since helium (He) is a noble gas with a very low molar mass compared to the diatomic gases N2 and O2 and the triatomic CO2, it is expected to have the highest rate of effusion.
5. Conclude that the gas with the highest rate of effusion on the graph corresponds to the smallest molar mass, which is helium (He) in this case.