Compare the effusion rates of two gases with Graham’s law, r₁/r₂ = √(M₂/M₁). Enter each gas as a formula or as its molar mass.
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From the article Graham's Law of Effusion — Why Lighter Gases Escape Faster.
How many times faster does H₂ effuse than O₂ at the same T and P?
M(H₂) = 2 × 1.008 = 2.016 g mol⁻¹; M(O₂) = 2 × 15.999 = 31.998 g mol⁻¹
rate(H₂)/rate(O₂) = √(31.998 ÷ 2.016) = √15.872
√15.872 = 3.984 (check: 3.984² = 15.872)
H₂ effuses about 3.98 times faster than O₂.
Notice that O₂ is roughly 16 times heavier, yet it is only about 4 times slower. The square root always softens the difference — a useful mental check.
An unknown gas effuses at 0.355 times the rate of helium under identical conditions. Find its molar mass.
rate(X)/rate(He) = √(MHe / MX) = 0.355
Square both sides: MHe / MX = 0.355² = 0.126025
MX = MHe ÷ 0.126025 = 4.0026 ÷ 0.126025
MX = 31.8 g mol⁻¹ ≈ 32 g mol⁻¹, so the gas is O₂.
This is the standard "identify the gas" question. Square first, then divide — never the other way round.
Worked in full in Graham's Law of Effusion — Why Lighter Gases Escape Faster.
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