Dalton's Law of Partial Pressures

Portrait of John Dalton

John Dalton studied the effect of gases in a mixture. He observed that the Total Pressure of a gas mixture was the sum of the Partial Pressure of each gas.

P total = P1 + P2 + P3 + .......Pn

The Partial Pressure is defined as the pressure of a single gas in the mixture as if that gas alone occupied the container. In other words, Dalton maintained that since there was an enormous amount of space between the gas molecules within the mixture that the gas molecules did not have any influence on the motion of other gas molecules, therefore the pressure of a gas sample would be the same whether it was the only gas in the container or if it were among other gases. This assumption that molecules act independently of one another works fine as long as there is a lot of space between gas molecules in the mixture and the temperature is not too low. Lowering the temperature and/or compressing the gas will upset that assumption. This is really the same assumption made for other Ideal Gas Laws. In fact, this assumption is a postulate of the Kinetic Molecular Theory of Gases. If the assumption breaks down then the gas does not behave as predicted by all the Ideal Gas Laws. The gas "deviates" from Ideal Gas Behavior.

You may receive a short biography of John Dalton here.

There are really two ways of determining the Partial Pressure of a Gas:

  1. Using the Ideal Gas Law Equation
  2. Using the Mole Fraction Relation

Using the Ideal Gas Law Equation

If one has the quantity of each gas either in moles or grams in the mixture, the volume, and the temperature of the gas mixture then one can find the Partial Pressure of each gas:

Here is an example:

If we have 2 moles of H2, 4 moles of O2, and 6 moles of He in a 5 liter vessel at 27 C, determine the Partial Pressure of each gas and the Total Pressure of the mixture.

  1. Convert the temperature to Kelvin: K = 27 + 273 = 300 K
  2. Using the PV = nRT equation determine P for H2:

    P H2 = nRT / V = (2 moles H2) (0.821 liter-atm / mol-K) (300K) / 5 liters = 9.85 atm

  3. Determine the Partial Pressure for the O2:

    P O2 = nRT / V = (4 moles O2) ( 0.0821 liter-atm / mol-K) ( 300K) / 5 liters = 19.7 atm

    P He = nRT / V = ( 6 moles He) ( 0.0821 liter-atm / mol-K) ( 300 K) / 5 liters = 29.55 atm

  4. Determine the Partial Pressure of He:

    Total Pressure = P H2 + P O2 + P He = 9.85 + 19.7 + 29.55 = 59.1 atm

Using the Mole Fraction Relationship

If one knows the moles or grams of each gas and the total pressure, one can determine the Partial pressure of each gas with the following formula:

P1 = X1 ( Ptotal) where X 1 = mole fraction of the gas

Mole Fraction is defined as the moles of the gas divided by the total moles of all the gases in the mixture:

Mole Fraction of Gas 1 = Moles of Gas 1 / Total Moles

Determine the Partial Pressure of each gas in a mixture made up of 6 grams of H2, 32 grams O2, and 56 grams of N2 if the total Barometric Pressure is 750 torr?

Here is the solution:

  1. Determine the moles of H2 present:

    6 grams H2 X 1 mole / 2 grams H2 = 3 moles H2

  2. Determine the moles of O2 present:

    32 grams O2 X 1 mole O2 / 32 grams O2 = 1 mole O2

  3. Determine the moles of N2 present:

    56 grams N2 X 1 mole N2 / 28 grams N2 = 2 moles N2

  4. Determine total moles present:

    Total Moles = 3 moles H2 + 1 mole O2 + 2 moles N2 = 6 moles total

  5. Determine the mole fraction of H2:

    Mole Fraction H2 = moles of H2 / Total Moles = 3 moles H2 / 6 moles total = 0.5

  6. Determine the Partial Pressure of H2:

    P H2 = Mole Fraction of H2 ( Total Pressure) = 0.5 ( 750 torr) = 375 torr

  7. Determine the Mole Fraction of O2:

    Mole Fraction of O2 = moles of O2 / Total Moles = 1 / 6 = 0.167

  8. Determine the Partial Pressure of O2:

    P O2 = Mole Fraction of O2 ( Total Pressure) = 0.167 ( 750 torr) = 125 torr

  9. Determine the Mole Fraction of N2:

    Mole Fraction of N2 = moles of N2 / Total Moles = 2 moles of N2 / 6 = .333

  10. Determine the Partial Pressure of N2:

    P N2 = Mole Fraction of N2 (Total Pressure) = .333(750 torr) = 250 torr

R. H. Logan, Instructor of Chemistry, Dallas County Community College District, North Lake College.

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All contents copyrighted (c) 1996
R.H. Logan, Instructor of Chemistry,DCCCD
All Rights reserved
Revised: 7/10/97

Original Date of Creation: 11/21/96

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