Partial Pressures

Author: John Hutchinson

We referred briefly above to the pressure of mixtures of gases, noting in our measurements leading to Boyle's Law that the total pressure of the mixture depends only on the number of moles of gas, regardless of the types and amounts of gases in the mixture. The Ideal Gas Law reveals that the pressure exerted by a mole of molecules does not depend on what those molecules are, and our earlier observation about gas mixtures is consistent with that conclusion.

We now examine the actual process of mixing two gases together and measuring the total pressure. Consider a container of fixed volume 25.0L. We inject into that container 0.78 moles of N₂ gas at 298K. From the Ideal Gas Law, we can easily calculate the measured pressure of the nitrogen gas to be 0.763 atm. We now take an identical container of fixed volume 25.0L, and we inject into that container 0.22 moles of O₂ gas at 298K. The measured pressure of the oxygen gas is 0.215 atm. As a third measurement, we inject 0.22 moles of O₂ gas at 298K into the first container which already has 0.78 moles of N₂. (Note that the mixture of gases we have prepared is very similar to that of air.) The measured pressure in this container is now found to be 0.975 atm.

We note now that the total pressure of the mixture of N₂ and O₂ in the container is equal to the sum of the pressures of the N₂ and O₂ samples taken separately. We now define the partial pressure of each gas in the mixture to be the pressure of each gas as if it were the only gas present. Our measurements tell us that the partial pressure of N₂, P_N2, is 0.763 atm, and the partial pressure of O₂, P_O2, is 0.215 atm.

With this definition, we can now summarize our observation by saying that the total pressure of the mixture of oxygen and nitrogen is equal to the sum of the partial pressures of the two gases. This is a general result: Dalton's Law of Partial Pressures.

Dalton's Law of Partial Pressures

The total pressure of a mixture of gases is the sum of the partial pressures of the component gases in the mixture.