Dalton's Law and Graham's Law Calculator: Partial Pressures, Mole Fractions, Effusion Rates and Gas over Water

Partial pressures, effusion and gas collected over water.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose Dalton, Graham or gas over water.

For a mixture enter the moles of each gas and the total pressure. For Graham enter two molar masses. For gas over water enter the temperature, volume and atmospheric pressure.

The calculator gives the mole fractions and partial pressures, the rate ratio, or the dry gas pressure and moles.

Formulas used

  • P_i = x_iP_{total}
  • \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}
  • P_{gas} = P_{atm} - P_{H_2O}
  • n = \frac{PV}{RT}

Worked example

With the default numbers in the calculator above:

  1. Total moles: 4.00 mol
  2. Mole fraction of each gas: 0.5 for gas 1; 0.25 for gas 2; 0.25 for gas 3
  3. Partial pressure of each gas (the mole fraction times the total pressure): 50.6625 kPa for gas 1; 25.3313 kPa for gas 2; 25.3313 kPa for gas 3
  4. Check: the partial pressures add up to the total: 101.33 kPa

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? Rates of effusion (Graham).

  1. Ratio of the rates of effusion of gas 1 to gas 2: 3.98397 (gas 1 effuses faster)
  2. Ratio of the times to effuse the same amount: 0.251006
  3. Ratio of the average speeds (the same square root law): 3.98397

Common questions

What is Dalton's law?

The total pressure of a gas mixture is the sum of the partial pressures. Each partial pressure is the mole fraction times the total.

What is Graham's law?

The rate at which a gas effuses is inversely proportional to the square root of its molar mass, so light gases escape faster.

Why subtract the vapour pressure of water?

A gas collected over water is mixed with water vapour, which takes part of the total pressure.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any first-year chemistry text (gas laws).

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