Further Application of the Ideal Gas Law: Dalton's Law, Densities, Mixtures, and Partial Pressure
PV = nRT is an equation, and it can be manipulated just like all other equations. With this in mind, let's see how the ideal gas law can help us calculate gas density.
Density d has the units of mass over volume. The ideal gas law transforms into a form with units in mol per unit volume:
generally has the units of mol per liter. If we multiply both sides of the equation by the molar mass of the gas, μ , we get:
|d = =|
As we can see from this equation, the density d of a gas depends on P , μ , and T . Think about how density will change when the temperature and pressure rise.
Partial Pressure and Mole Fraction
Dalton's law states that the total pressure of a mixture of gases is the sum of the pressures each constituent gas would exert if it were alone. Dalton's law can be expressed mathematically:
|P tot = P A + P B + P C + ...|
Each individual pressure P A , P B , P C , etc. is the pressure exerted by each constituent gas A, B, or C. P A is called the partial pressure of gas A.
Each individual gas obeys the ideal gas law, so we can rearrange PV = nRT to find pressure:
|P A = n a|
Since gases A, B, and C are all in the same mixture, they all have the same temperature and volume. P tot also has the same temperature and volume. When P A is placed over P tot , the variables T , R , and V cancel to give the following result:
The quantity is called the mole fraction of gas A and is abbreviated ρ A .
Dalton's law problems often present two containers of gas, mix them, and ask you to find the partial pressures of each gas. There's usually an easy way and a hard way to do such problems; the trick is finding the easy way. You'll gain this intuition quickest if you jump right in. Try your hand at the problems at the end of this section and in your textbook.