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Graham's Law

r_mean ∝ √T/M; Graham's law: r₁/r₂ = √(M₂/M₁)
Quick Reference
Formula / Notationr_mean ∝ √T/M; Graham's law: r₁/r₂ = √(M₂/M₁)
Also Known AsGraham's law of diffusion/effusion, effusion rate law, gaseous diffusion law

What is Graham's Law?

Graham's law of effusion states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass. Lighter gases diffuse faster than heavier gases. This principle is used in separating isotopes and in kinetic theory of gases.

Formula & Notation

r_mean ∝ √T/M; Graham's law: r₁/r₂ = √(M₂/M₁)

Other Names / Synonyms: Graham's law of diffusion/effusion, effusion rate law, gaseous diffusion law

Properties & Characteristics

Graham's law of effusion states that the rate of effusion (passage of a gas through a small hole into a vacuum) is inversely proportional to the square root of the gas's molar mass: r ∝ 1/√M. For two gases: r₁/r₂ = √(M₂/M₁). This follows from the kinetic molecular theory: mean kinetic energy is equal for all ideal gases at the same temperature (½mv² = 3/2 kT), so lighter gases have higher mean speeds and effuse faster.

Uses & Applications

Graham's law is used to separate isotopes (gaseous diffusion of UF₆ for uranium enrichment, r(²³⁵UF₆)/r(²³⁸UF₆) = √(352/349) = 1.0043), to measure molar masses of gases by comparing effusion rates, and to explain the faster diffusion of lighter gases in atmospheric chemistry.

Safety Information

Gaseous diffusion enrichment plants (uranium isotope separation) handle UF₆, which is corrosive and reacts violently with moisture to form HF and UO₂F₂. Strict containment, radiation monitoring, and chemical safety systems are required.

Always consult the SDS/MSDS before handling any chemical. This information is for educational purposes only.

Key Facts

Term Graham's Law
Formula r_mean ∝ √T/M; Graham's law: r₁/r₂ = √(M₂/M₁)
Synonyms Graham's law of diffusion/effusion, effusion rate law, gaseous diffusion law

Frequently Asked Questions

Graham's law of effusion states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass. Lighter gases diffuse faster than heavier gases. This principle is used in separating isotopes and in kinetic theory of gases.

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