Which of the following gases has the lowest rate of diffusion under the same condition? [H = 1.00; He = 4. 00; O = 16.0; CI = 35.5]

Analyze the question: We need the gas that diffuses slowest under the same conditions of temperature and pressure.

Concept: Graham's Law of Diffusion

The rate of diffusion of a gas is inversely proportional to the square root of its molar mass (or density):

Rate ∝ 1/√M

So the heavier the gas, the slower it diffuses, and the lighter the gas, the faster it diffuses.

Solution: Calculate the molar mass of each gas

• Cl₂ = 2 × 35.5 = 71.0 g/mol
• H₂ = 2 × 1.00 = 2.00 g/mol
• He = 4.00 g/mol
• O₂ = 2 × 16.0 = 32.0 g/mol

Compare the relative rates (∝ 1/√M):

• H₂: 1/√2 ≈ 0.707
• He: 1/√4 = 0.500
• O₂: 1/√32 ≈ 0.177
• Cl₂: 1/√71 ≈ 0.119

Cl₂ has the smallest value, so it diffuses the slowest.

Answer: A. Cl₂

Tip: In "lowest rate of diffusion" questions, just find the gas with the highest molar mass. Remember that diatomic gases like Cl₂, O₂ and H₂ must have their atomic masses doubled, since students often forget this. Heavy gas means slow diffusion, and light gas means fast diffusion.