Rate of Effusion Calculator (Grahams Law)
Calculate the relative rates of gas effusion or determine unknown molar mass from effusion rates using Graham law of effusion.
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First gas (-symbol or molar mass)
Second gas (symbol or molar mass)
Effusion rate of known gas
Observed rate of unknown gas
What is Grahams law of effusion?
Grahams law states: Rate₁/Rate₂ = √(M₂/M₁). Gas effusion rate is inversely proportional to the square root of molar mass. Lighter gases effuse faster. Helium (4 g/mol) effuses √(44/4) = √11 ≈ 3.3× faster than CO₂ (44 g/mol).
How do you calculate rate ratio?
r₁/r₂ = √(M₂/M₁) = √(molar mass of slower gas / molar mass of faster gas). Rearranged: M₂ = M₁ × (r₁/r₂)². If He effuses 4× faster than X: M_X = 4 × (4/1)² = 64 g/mol (likely O₂).
What is the difference between effusion and diffusion?
Effusion: gas escapes through tiny holes. Diffusion: gases mix through random motion. Both follow the same kinetic principle: rate ∝ 1/√M. Graham measured effusion through porous plugs; diffusion rates are measured by mixing time.
Why do lighter gases move faster?
At same temperature, all gases have same average kinetic energy (½mv²). So lighter mass means higher velocity. v_avg ∝ √(T/M). Lower molar mass means higher average molecular speed, explaining faster effusion and diffusion.