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Graham Law Of Diffusion Calculator

Work out graham law of diffusion instantly with clear inputs, formula shown and shareable results.

About Graham Law Of Diffusion Calculator

Graham's law makes diffusion rate inversely proportional to the square root of molar mass, so rate1/rate2 = sqrt(M2/M1). Hydrogen at 2.016 g/mol diffuses 3.98 times faster than oxygen at 32. The square root is why the effect is milder than the mass difference suggests, and why uranium enrichment by gaseous diffusion needs thousands of stages.

Formulas

Graham's law

rate1 / rate2 = sqrt(M2 / M1)

Effusion time

t1 / t2 = sqrt(M1 / M2)

Worked example

With the default values below, Graham Law Of Diffusion Calculator returns Rate Ratio (First Gas To Second) of 3.9841. Change any input above and every figure here is recalculated in your browser.

Inputs used

Molar mass of the first gasminimum 0 g/mol
2.016 g/mol
Molar mass of the second gasminimum 0 g/mol
32 g/mol

Results

Rate Ratio (First Gas To Second)
3.9841
Time Ratio For Equal Amounts
0.2510
Molar Mass Ratio
15.8730
Which Diffuses Faster
The first gas diffuses faster

Step by step

  1. 1Values used
  2. 2Graham's law
  3. 3Effusion time
  4. 4Rate Ratio (First Gas To Second)= 3.9841
  5. 5Time Ratio For Equal Amounts= 0.2510
  6. 6Molar Mass Ratio= 15.8730
  7. 7Which Diffuses Faster= The first gas diffuses faster

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does mass affect diffusion at all?

Because at the same temperature all molecules share the same average kinetic energy, so heavier ones must move more slowly.

Is this how isotopes are separated?

It was, for uranium hexafluoride. The mass difference gives a rate ratio of only 1.0043, so thousands of cascade stages were required.

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