Given two gases, oxygen (O_2) and hydrogen (H_2), which molecule has the higher molar mass, and which would have the higher rate of effusion?

• A. O_2 has the higher molar mass, and H_2 would have the higher rate of effusion.
• B. H_2 has the higher molar mass, and H_2 would have the higher rate of effusion.
• C. O_2 has the higher molar mass, and O_2 would have the higher rate of effusion.
• D. H_2 has the higher molar mass, and O_2 would have the higher rate of effusion.

Answer: (A)

Verified step by step guidance

1. Identify the molar masses of the two gases by summing the atomic masses of their atoms: Oxygen (O_2) consists of two oxygen atoms, each with an atomic mass of approximately 16 g/mol, so its molar mass is calculated as \$2 \times 16 = 32\( g/mol. Hydrogen (H_2) consists of two hydrogen atoms, each with an atomic mass of approximately 1 g/mol, so its molar mass is \)2 \times 1 = 2$ g/mol.
2. Compare the molar masses: Since 32 g/mol (O_2) is greater than 2 g/mol (H_2), oxygen has the higher molar mass.
3. 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. The formula is: \(\text{Rate} \propto \frac{1}{\sqrt{M}}\), where \(M\) is the molar mass.
4. Apply Graham's law to compare the rates of effusion of O_2 and H_2. Since H_2 has a smaller molar mass, its rate of effusion will be higher than that of O_2.
5. Conclude that O_2 has the higher molar mass, and H_2 has the higher rate of effusion based on the molar mass comparison and Graham's law.