Chemistry calculator

Graham's Law Calculator

Calculate gas diffusion or effusion rate, time, and molar mass using Graham's law, with automatic time-unit conversion.

Compare two gases

Solve Graham's law

Free tool
relative rate

This value will be calculated.

relative rate

The diffusion or effusion rate of the second gas.

g/mol

The molar mass of the first gas.

g/mol

The molar mass of the second gas.

Try an example:

Calculator guide

How this calculator works

Graham's Law Calculator determines the relationship between gas diffusion or effusion rates and molar masses. It helps chemistry students, researchers, and laboratory professionals calculate gas movement rates using Graham's Law.

Formula explanation

Graham's law compares gas diffusion rates based on molar masses.

Formula

Graham's Law: Rate₁/Rate₂ = √(M₂/M₁)

Worked example

Example: Lighter gases diffuse faster than heavier gases under similar conditions.

Assumptions

  • Gases behave approximately as ideal gases.
  • Temperature and pressure conditions remain comparable.
  • Molar mass values are accurate.

Examples

  • Example: Compare the diffusion rates of two gases with different molar masses.
  • Example: Scientists use Graham's Law to estimate unknown molar masses from measured gas movement rates.

Common mistakes

  • Using incorrect molar masses.
  • Reversing diffusion rate ratios.
  • Ignoring gas conditions.

Variables

  • Diffusion or effusion rate of gas one
  • Diffusion or effusion rate of gas two
  • Molar mass of gas one
  • Molar mass of gas two
  • Time required for gas movement

Limitations

  • Accuracy decreases when gases significantly deviate from ideal behavior.
  • Results depend on comparable temperature and pressure conditions.

Scientific references

  • OpenStax Chemistry: Gas Diffusion and Effusion
  • NIST Chemistry Reference Data
  • Scientific gas measurement guidelines

Content review

Reviewed by: ScienceCalcHub Chemistry Review Team | Last reviewed: 2026-08-30

Applications

  • Gas diffusion analysis
  • Chemistry education
  • Laboratory gas experiments
  • Molar mass calculations

Frequently asked questions

How is Graham's Law calculated?

Graham's Law is calculated by comparing gas diffusion rates with the square root relationship of their molar masses.

What does Graham's Law describe?

Graham's Law describes how lighter gases diffuse or effuse faster than heavier gases under similar conditions.

What variables are used in Graham's Law?

Graham's Law uses gas rates, molar masses, and sometimes time measurements to calculate unknown values.

Accuracy and transparency

Created and maintained by our editorial team

This chemistry calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

Gas-rate guide

What is Graham's law?

Graham's law compares the diffusion or effusion rates of two gases through their molar masses. Under the same conditions, lighter gas particles move faster than heavier gas particles.

The rate is inversely proportional to the square root of molar mass. This means a gas does not become twice as fast merely because its molar mass is half as large; the relationship follows a square root.

Core equation

Graham's law formula

r₁/r₂ = √(M₂/M₁)
  • r₁ is the diffusion or effusion rate of gas 1.
  • r₂ is the diffusion or effusion rate of gas 2.
  • M₁ is the molar mass of gas 1.
  • M₂ is the molar mass of gas 2.

Molar masses must use the same unit, normally grams per mole. The two rates must also represent the same process and use compatible rate units.

Time relationship

Graham's law using time

t₁/t₂ = √(M₁/M₂)

Time is inversely proportional to rate. For equal quantities of gas effusing, or gases covering the same diffusion distance, the slower gas requires more time. The calculator can mix seconds, minutes, and hours.

Solve any variable

Rearranged Graham's law equations

  • Gas 1 rate: r₁ = r₂ × √(M₂/M₁)
  • Gas 2 rate: r₂ = r₁ × √(M₁/M₂)
  • Gas 1 molar mass from rates: M₁ = M₂ × (r₂/r₁)²
  • Gas 2 molar mass from rates: M₂ = M₁ × (r₁/r₂)²
  • Gas 1 time: t₁ = t₂ × √(M₁/M₂)
  • Gas 2 time: t₂ = t₁ × √(M₂/M₁)

Worked example

Compare hydrogen and oxygen effusion

Compare hydrogen gas, H₂, with a molar mass of approximately 2.016 g/mol to oxygen gas, O₂, with a molar mass of approximately 32.00 g/mol.

  1. Write the equation: rH₂/rO₂ = √(MO₂/MH₂).
  2. Substitute the molar masses: rH₂/rO₂ = √(32.00/2.016).
  3. Evaluate the square root: rH₂/rO₂ ≈ 3.98.
  4. Hydrogen effuses approximately 3.98 times as fast as oxygen under the same conditions.

Gas movement

Diffusion versus effusion

Diffusion is the spreading and mixing of gas particles through available space. Effusion is the escape of gas particles through a very small opening into a vacuum or lower-pressure region.

Graham's law is commonly applied to both processes, although controlled effusion experiments usually match its assumptions more closely.

Required conditions

When Graham's law applies

  • Compare gases at the same temperature.
  • Use comparable pressure and experimental conditions.
  • Compare the same diffusion distance or the same effused quantity when using time.
  • Use positive rates, times, and molar masses.
  • Treat the gases as approximately ideal.

Calculation limits

Important limitations and mistakes

  • Do not reverse the molar-mass ratio: rate and molar mass have an inverse relationship.
  • Apply the square root instead of using the mass ratio directly.
  • Keep rate units compatible when entering two measured rates.
  • Use time mode only for equivalent distances or effused quantities.
  • Expect deviations for strongly interacting gases or non-ideal conditions.

Related tools

Use the Dalton's Law Calculator to calculate partial pressures in a gas mixture.

Use the Avogadro's Law Calculator to relate gas volume to the amount of gas at constant temperature and pressure.

Use the Ideal Gas Law Calculator when pressure, volume, amount, and temperature are involved.

Questions and answers

Calculator FAQ

How is Graham's Law calculated?

Graham's Law is calculated by comparing gas diffusion rates with the square root relationship of their molar masses.

What does Graham's Law describe?

Graham's Law describes how lighter gases diffuse or effuse faster than heavier gases under similar conditions.

What variables are used in Graham's Law?

Graham's Law uses gas rates, molar masses, and sometimes time measurements to calculate unknown values.