Which of the following gases will have the slowest rate of effusion at constant temperature?

• A. Cl_2
• B. N_2
• C. O_2
• D. CO_2

Answer: (A)

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. Identify the molar masses of each gas given: - \(\mathrm{N_2}\): approximately 28 g/mol - \(\mathrm{O_2}\): approximately 32 g/mol - \(\mathrm{CO_2}\): approximately 44 g/mol - \(\mathrm{Cl_2}\): approximately 71 g/mol
3. Since the rate of effusion is inversely proportional to the square root of molar mass, the gas with the largest molar mass will have the slowest rate of effusion.
4. Compare the molar masses to determine which is the largest. Among the gases listed, \(\mathrm{Cl_2}\) has the highest molar mass.
5. Conclude that \(\mathrm{Cl_2}\) will have the slowest rate of effusion at constant temperature because its heavier molar mass reduces its effusion rate according to Graham's law.