http://www.ck12.org Chapter 14. The Behavior of Gases
given sample of air, it exerts 78% of the pressure. If the overall atmospheric pressure is 1.00 atm, then the pressure
of just the nitrogen in the air is 0.78 atm. The pressure of the oxygen in the air is 0.21 atm.
Thepartial pressureof a gas is the contribution that gas makes to the total pressure when the gas is part of a
mixture. The partial pressure of a gas is indicated by a P with a subscript that is the symbol or formula of that
gas. The partial pressure of nitrogen is represented by PN 2 .Dalton’s law of partial pressuresstates that the total
pressure of a mixture of gases is equal to the sum of all of the partial pressures of the component gases. Dalton’s
law can be expressed with the following equation:
PTotal= P 1 + P 2 + P 3 ...The figure below (Figure14.13) shows two gases that are in separate, equal-sized containers at the same temperature
and pressure. Each exerts a different pressure, P 1 and P 2 , reflective of the number of particles in the container. On
the right, the two gases are combined into the same container, with no volume change. The total pressure of the gas
mixture is equal to the sum of the individual pressures. If P 1 = 300 mmHg and P 2 = 500 mmHg, then PTotal= 800
mmHg.
FIGURE 14.13
Dalton’s law says that the total pressure
of a gas mixture is equal to the sum of
the partial pressures contributed by each
component of the mixture.Mole Fraction
One way to express relative amounts of substances in a mixture is with the mole fraction.Mole fraction (X)is the
ratio of moles of one substance in a mixture to the total number of moles of all substances. For a mixture of two
substances, A and B, the mole fractions of each would be written as follows:
XA=
mol A
mol A+mol Band XB=27.2 B
mol A+mol BIf a mixture consists of 0.50 mol A and 1.00 mol B, then the mole fraction of A would be XA= 0.5/1.5 = 0.33.
Similarly, the mole fraction of B would be XB= 1.0/1.5 = 0.67.
Mole fraction is a useful quantity for analyzing gas mixtures in conjunction with Dalton’s law of partial pressures.
Consider the following situation: A 20.0 liter vessel contains 1.0 mol of hydrogen gas at a pressure of 600 mmHg.