John Dalton, an English scientist, is most famous for his work in the development of the modern atomic theory. However, Dalton had many other scientific interests. Another incredibly useful observation of Dalton’s, resulted from his study of the properties of air. Dalton found that the total pressure of a mixture of gases is equal to the sum of the pressures that each of the gases would exert if they were alone. This observation is known as Dalton’s Law of Partial Pressures.
If we let Ptotal represent the total pressure of the mixture of gases and P1, P2, P3 and so on represent the partial pressures of each of the individual gases of a mixture, Dalton’s Law will take on the form,
Dalton’s equation can be expanded to use more variables if we assume that each gas behaves as an ideal gas. Remember that the ideal gas law equation is,
If we rearrange this equation to solve for P,
Now we can substitute this equation for each of the partial pressure in Dalton’s Law (P1, P2, P3, etc.) and Dalton’s Law will take the form,
Since each of the individual gases in the mixture will have the same volume, and temperature we can simplify this equation further,