Which of the following gases will diffuse most rapidly? [H = 1.00, C = 12.0, O = 16.0, S = 32.0, Cl = 35.5]

Analyze the question: We need the gas that diffuses fastest. This depends on molar mass, according to Graham's Law.

Concept: Graham's Law of Diffusion

Rate of diffusion is inversely proportional to the square root of the molar mass (or density):

Rate ∝ 1/√M

So the lighter the gas, the faster it diffuses.

Solution: Calculate the molar mass of each gas

• A. Cl₂ = 2 × 35.5 = 71.0 g/mol
• B. SO₂ = 32 + (2 × 16) = 64.0 g/mol
• C. CH₄ = 12 + (4 × 1) = 16.0 g/mol
• D. C₂H₆ = (2 × 12) + (6 × 1) = 30.0 g/mol

CH₄ has the smallest molar mass (16.0 g/mol), so it diffuses most rapidly.

Comparison (relative to CH₄):

• Rate(CH₄)/Rate(C₂H₆) = √(30/16) ≈ 1.37, so CH₄ is about 1.37 times faster than C₂H₆.
• Compared to Cl₂, it is √(71/16) ≈ 2.1 times faster.

CH₄**.

Exam tip: For "which gas diffuses fastest or slowest" questions, you don't need to do any square roots. Just calculate the molar masses and compare them. Lightest = fastest, heaviest = slowest. A handy memory phrase: "Light gases are Lively."