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Graham’s Gas-Rate & Molar-Mass Comparison

Compare ideal gas effusion rates and molar masses using Graham’s inverse-square-root relationship.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

At equal temperature under comparable effusion conditions, gases with molar masses 4 and 16 g/mol have a rate ratio of 2:1.

Rate₁ / rate₂ = √(molar mass₂ / molar mass₁)

Worked example

Enter these known values and leave the other values blank.

Gas-rate comparison mode
Effusion (ideal model)
Gas 1 molar mass
4 g/mol
Gas 2 molar mass
16 g/mol
Gas 1 effusion rate
2 mol/s
Gas 2 effusion rate
1 mol/s

Assumptions and limitations

  • Rates and molar masses are positive. Compare gases at the same temperature and under equivalent pressure and aperture conditions for the ideal effusion model.
  • Effusion through a sufficiently small opening differs from bulk flow and from diffusion through another gas. The diffusion mode retains only a simple relative-rate approximation, not a general diffusion-coefficient model.
  • Both modes use the same inverse-square-root mass relation. Rates are amounts per time, not mass flow rates; using mass per second would change the interpretation.

Common questions

Does the lighter gas have the higher effusion rate?

Under the stated equal-temperature conditions, yes. A fourfold smaller molar mass gives a twofold higher amount effusion rate.

Does this predict diffusion through any material?

No. Diffusion depends on collisions, the surrounding medium and other conditions. The optional mode uses only the elementary relative-rate approximation.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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