Gas Mixtures and Partial Pressures

Learning Goals

Now you will learn how to work problems involving mixtures of gases.

Synopsis

Now we complicate the situation somewhat by considering that the gas sample contains more than one type of gas. The atmosphere is an obvious example for this consideration and the mole percent of some of the gases of atmospheric dry air are given in Table 12.2 on page 559. What is the total pressure of a gas when several different gases are present? For ideal gases, the answer is given by Dalton's law of partial pressures. The partial pressure of a gas in a mixture is the pressure that the gas would exert if it were alone in the same container at the same T and P. Dalton's law then says that the total pressure of all of the gases in the container is the sum of the partial pressures of each gas in the container: Ptotal = P1 + P2 + .... This law only works for ideal gases because it ignores any interaction among the gases that would modify the pressure. Because we are assuming ideal gas behavior, then we can use the ideal gas law for each gas in the mixture.

P_total = n₁RT₁/V₁ + n₂RT₂/V₂ + n₃RT₃/V₃ + ......... Assuming constant T and V, we then hav

P_total = (n₁ + n₂ + n₃ + ..)RT/V = n_totalRT/V ......................eq 7

A very convenient method of expressing gas concentrations and concentrations of solutions as we will see later, is the mole fraction, given the symbol X. The mole fraction of a gas in a mixture is the number of moles of the particular gas divided by the total number of moles of the gas: X₁ = n₁/n_total. We can solve this equation for the total number of moles: n_total = n₁/X₁ and then we can substitute this into equation 7 to give

P_total = n₁RT/(VX₁). But n₁RT/V = P₁ so P_total = P₁/X₁ or

P₁ = X₁*P_total ..................................eq 8

Equation 8 is a very useful equation to allow us to calculate the partial pressure of the gases in the mixture if we know their mole fraction and the total pressure. Then, knowing the partial pressures of each gas, we can use Dalton's law to calculate the total pressure.

Review Question

Work carefully through Example 12.12 to make sure that you understand all of the details.
Now work problem 59 at the end of the chapter, which is the same type of problem as Example 12.12. However, do not look back in the chapter or at your notes, for then you would not be sure that you really understand how to work this problem.
Work problem 53 at the end of the chapter.