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What is Graham's Law of Effusion?

Graham's law describes how gases escape through a tiny opening or diffuse through a medium — faster for lighter molecules, slower for heavier ones. The rate of effusion is inversely proportional to the square root of molar mass.

Short answer

Graham's law: rate ∝ 1/√M or (rate₁/rate₂) = √(M₂/M₁). Lighter gases diffuse faster because their molecules move more quickly.

Effusion rate vs molar mass (inverse square root)

x: Molar mass (g/mol) · y: Relative effusion rate

Try it: interactive calculator

Rate ratio (r₁/r₂)

0.25dimensionless

= sqrt(2/32)

Molar mass gas 1 (M₁)32 g/molMolar mass gas 2 (M₂)2 g/mol

Step-by-step worked examples

Hydrogen (M=2 g/mol) and oxygen (M=32 g/mol) effuse from the same container. What is the ratio of their effusion rates?

r_H2 / r_O2 = √(M_O2 / M_H2)
= √(32 / 2)
= √16
= 4
Hydrogen effuses 4 times faster than oxygen.

Gas A (M=40 g/mol) effuses through a pore at 5 mL/s. Gas B (M=10 g/mol) effuses at what rate?

r_A / r_B = √(M_B / M_A)
5 / r_B = √(10 / 40)
5 / r_B = √0.25 = 0.5
r_B = 5 / 0.5 = 10 mL/s

If N₂ (M=28) diffuses at rate 3 units, what is the diffusion rate of CO₂ (M=44)?

r_N2 / r_CO2 = √(M_CO2 / M_N2)
3 / r_CO2 = √(44 / 28)
3 / r_CO2 = √1.571 = 1.254
r_CO2 = 3 / 1.254 ≈ 2.39 units

Flashcards

Quick quiz

Q1.Which statement is correct for Graham's law?

Correct answer: B. Lighter gases (smaller M) have faster average speed → faster effusion.

Q2.H₂ (M=2) vs Cl₂ (M=71). Ratio r_H2 / r_Cl2?

Correct answer: B. √(71/2) = √35.5 ≈ 5.96.

Q3.Graham's law assumes…

Correct answer: B. KE_avg = (3/2)kT is the same for both gases at same T, leading to mass-dependent speeds.

Q4.If gas A effuses 3× faster than gas B, and B has M=36 g/mol, what is M_A?

Correct answer: A. 3 = √(36/M_A) → 9 = 36/M_A → M_A = 4 g/mol.

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Common mistakes

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Thinking faster effusion goes with heavier gas. — Correct: Lighter gas (smaller M) → faster effusion.

✗

Ignoring the square root in the formula. — Correct: It is √(M₂/M₁), not M₂/M₁.

✗

Confusing effusion and diffusion. — Correct: Both follow Graham's law; effusion = through a hole, diffusion = through a medium.

✗

Assuming pressure affects the rate ratio. — Correct: Graham's law ratio depends only on molar mass, not on pressure or volume.

FAQ

What is Graham's law of effusion?

The rate of effusion of a gas is inversely proportional to the square root of its molar mass: r ∝ 1/√M.

What is the difference between effusion and diffusion?

Effusion = through a tiny opening into a vacuum; diffusion = through a medium like air.

Graham's law formula for comparing two gases?

r₁/r₂ = √(M₂/M₁).

Why does temperature not appear in the rate ratio?

Both gases are at the same temperature, so the T terms cancel out in the ratio.