Graham's Law Calculator

Calculate effusion and diffusion rates of gases using Graham's law: rate1/rate2 = sqrt(M2/M1). Find relative rates or identify unknown gas molar mass from effusion time ratio.

💨 Gas Laws📐 r₁/r₂ = √(M₂/M₁)🧪 Chemistry

Molar Mass of Gas 1 (g/mol)

Molar Mass of Gas 2 (g/mol)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Graham's Law Calculator	See formula	r₁/r₂ = √(M₂/M₁)	ratio

Step-by-Step Examples

Example 1

H₂ vs O₂

Compare effusion rates of H₂ (M=2.016) and O₂ (M=32.00).

r(H₂)/r(O₂) = √(32.00/2.016) = √15.87
ratio = 3.98

✓ H₂ effuses 3.98× faster than O₂

Example 2

Unknown Gas

Unknown gas effuses 0.500 times as fast as N₂ (M=28.02). Find M.

r_X/r_N₂ = 0.500 = √(28.02/M_X)
0.25 = 28.02/M_X
M_X = 28.02/0.25 = 112.1 g/mol

✓ Unknown gas M = 112.1 g/mol (likely Cd)

Example 3

He vs CO₂

He (4.003) vs CO₂ (44.01).

ratio = √(44.01/4.003) = √10.99 = 3.31

✓ He effuses 3.31× faster

Real-World Applications

☢️

Uranium Enrichment

U-235 and U-238 hexafluoride gases differ slightly in effusion rate, used for isotope separation.

🧪

Gas Identification

Effusion time ratio identifies unknown gases without complex spectroscopy.

🌍

Atmospheric Gas Loss

Lighter gases (H₂, He) escape Earth atmosphere faster than heavier N₂, O₂.

🔬

Mass Spectrometry

Molecular beam effusion provides monoenergetic gas samples for experiments.

Common Mistakes to Avoid

⚠️

Rate and time are inversely related

If gas 1 effuses 4x faster, it takes 1/4 the time. r₁/r₂ = t₂/t₁ (inverted for time).

⚠️

Use molar mass not atomic mass

Use molecular molar mass: O₂ = 32.00 g/mol, not 16. H₂ = 2.016 g/mol, not 1.008.

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Graham's law is for effusion through small holes

Diffusion in bulk gas is also proportional to 1/√M but involves additional factors like collision frequency.

Frequently Asked Questions

What is effusion? ▾

Effusion is the process by which gas molecules pass through a tiny hole into a vacuum. Rate depends only on molecular speed = √(3RT/M).

What is the difference between effusion and diffusion? ▾

Effusion: gas through a pinhole into vacuum. Diffusion: gas spreading through another gas. Both follow Graham's law approximately.

How was Graham's Law used for uranium enrichment? ▾

U-235F₆ (M=349) and U-238F₆ (M=352) effuse at rates differing by only 0.43%. Required thousands of separation stages.

What is molecular speed related to temperature? ▾

v_rms = √(3RT/M). Heavier molecules move slower at same temperature. This explains why lighter gases effuse faster.

Can Graham's law identify unknowns? ▾

Yes. Measure effusion time of unknown vs known gas. t₁/t₂ = √(M₁/M₂). Solve for unknown M.

Related Chemistry Calculators

Formula Explorer connections

Interpretation: This relationship connects pressure, volume, temperature, amount or phase composition for gases and volatile mixtures. Assumption: Use absolute temperature and compatible pressure-volume units. Ideal behavior weakens at high pressure, low temperature, strong intermolecular attraction or near phase change.

Graham's Law Effusion Calculator →Henry's Law Calculator →Ideal Gas Law Calculator →Chemistry Formula Explorer →