Mixtures of Gases
Ideal Gas Mixtures

Ideal mixtures of gases are comprised of molecules that do not interact.

Their contrubutions simply add together.

Consider a mixture of ideal gases in a volume V aty temperature T. For any ideal gas “X” in the mixture, we have:
 $PV = nRT > P_x = \frac{n_xRT}{V} $
Partial Pressure
 The total pressure of an ideal gas mixture is related to the total number of gas molecules:
 $P_{total} = \frac{n_{total}RT}{V} $
 The total number of moles is the sum of the moles for each componenet gas:
 $ n_{total} = n_a + n_b … $
 Therefore the total pressure is:
 $ P_{total} = \frac{n_aRT}{V} + \frac{n_bRT}{V} + \frac{n_cRT}{V} … $
 Each of these statements of the total pressure due to one gas mixture componenet as if it were alone in the vessel.
 These are called the “partial pressure” pf the component gas, $P_x$
Dalton’s Law of Partial Pressures
 ” The total Pressure of a gas mixture is the sum of the partial pressures of the componenets of the mixture.
 $P_{total} = P_a + P_b + P_c + …$
Mole Fractions
 The “Mole fraction” of gas A is the fraction of moles in a mixture that are of type A:
 $x_a = \frac{moles of a_a}{total moles in a mixture} = \frac{n_a}{n_{total}}$
 As a result we can easily determine partial pressure from mole fractions:
 $P_A = x_aP_{total}$