At the same temperature, which of the following gases will have the fastest rate of effusion?

• A. N2
• B. CO2
• C. O2
• D. H2

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. Identify the molar masses of the gases involved: \(\mathrm{N_2}\), \(\mathrm{CO_2}\), \(\mathrm{O_2}\), and \(\mathrm{H_2}\). For example, \(\mathrm{N_2}\) has a molar mass of approximately 28 g/mol, \(\mathrm{CO_2}\) about 44 g/mol, \(\mathrm{O_2}\) about 32 g/mol, and \(\mathrm{H_2}\) about 2 g/mol.
3. Compare the molar masses to determine which gas has the smallest molar mass, since the gas with the smallest molar mass will effuse the fastest according to Graham's law.
4. Use the inverse square root relationship to understand that a smaller molar mass results in a higher rate of effusion. Therefore, \(\mathrm{H_2}\), having the smallest molar mass, will have the fastest rate of effusion.
5. Conclude that among the given gases, \(\mathrm{H_2}\) effuses the fastest at the same temperature because its molar mass is significantly lower than that of \(\mathrm{N_2}\), \(\mathrm{CO_2}\), and \(\mathrm{O_2}\).