An unknown gas is found to diffuse through a porous membrane 2.92 times more slowly than H2. What is the molecular weight of the gas? (a) 17.0 g/mol (b) 5.84 g/mol (c) 8.52 g/mol

Verified step by step guidance

1. Identify the relevant law for diffusion of gases, which is Graham's Law of Effusion. This law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
2. Set up the equation based on Graham's Law: \( \frac{Rate_{H_2}}{Rate_{unknown}} = \sqrt{\frac{M_{unknown}}{M_{H_2}}} \), where \( M_{unknown} \) is the molar mass of the unknown gas and \( M_{H_2} \) is the molar mass of hydrogen (2 g/mol).
3. Plug in the given rate ratio into the equation: \( \frac{1}{2.92} = \sqrt{\frac{M_{unknown}}{2}} \).
4. Solve for \( M_{unknown} \) by squaring both sides of the equation and then multiplying by 2 to isolate \( M_{unknown} \) on one side.
5. Compare the calculated molar mass of the unknown gas with the given options to find the closest match.

Key Concepts

Graham's Law of Effusion

Graham's Law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases diffuse faster than heavier gases. The relationship can be expressed mathematically as (Rate1/Rate2) = √(Molar Mass2/Molar Mass1), allowing for the comparison of diffusion rates between two gases.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical property in stoichiometry and gas calculations, as it helps determine the amount of substance present in a given volume or mass. For gases, knowing the molar mass allows for the application of gas laws and principles like Graham's Law.

Diffusion

Diffusion is the process by which molecules spread from areas of high concentration to areas of low concentration. In the context of gases, diffusion occurs due to the random motion of gas particles. The rate of diffusion can be influenced by factors such as temperature, pressure, and the molecular weight of the gas, making it essential for understanding gas behavior in various scenarios.