2.2 Pressure, temperature, and rms speed  (Page 6/18)

Vapor pressure, partial pressure, and dalton’s law

The pressure a gas would create if it occupied the total volume available is called the gas’s partial pressure    . If two or more gases are mixed, they will come to thermal equilibrium as a result of collisions between molecules; the process is analogous to heat conduction as described in the chapter on temperature and heat. As we have seen from kinetic theory, when the gases have the same temperature, their molecules have the same average kinetic energy. Thus, each gas obeys the ideal gas law separately and exerts the same pressure on the walls of a container that it would if it were alone. Therefore, in a mixture of gases, the total pressure is the sum of partial pressures of the component gases , assuming ideal gas behavior and no chemical reactions between the components. This law is known as Dalton’s law of partial pressures    , after the English scientist John Dalton (1766–1844) who proposed it. Dalton’s law is consistent with the fact that pressures add according to Pascal’s principle.

In a mixture of ideal gases in thermal equilibrium, the number of molecules of each gas is proportional to its partial pressure. This result follows from applying the ideal gas law to each in the form $p\text{/}n=RT\text{/}V.$ Because the right-hand side is the same for any gas at a given temperature in a container of a given volume, the left-hand side is the same as well.

• Partial pressure is the pressure a gas would create if it existed alone.
• Dalton’s law states that the total pressure is the sum of the partial pressures of all of the gases present.
• For any two gases (labeled 1 and 2) in equilibrium in a container, $\frac{p_1}{n_1}=\frac{p_2}{n_2}.$

An important application of partial pressure is that, in chemistry, it functions as the concentration of a gas in determining the rate of a reaction. Here, we mention only that the partial pressure of oxygen in a person’s lungs is crucial to life and health. Breathing air that has a partial pressure of oxygen below 0.16 atm can impair coordination and judgment, particularly in people not acclimated to a high elevation. Lower partial pressures of ${\text{O}}_2$ have more serious effects; partial pressures below 0.06 atm can be quickly fatal, and permanent damage is likely even if the person is rescued. However, the sensation of needing to breathe, as when holding one’s breath, is caused much more by high concentrations of carbon dioxide in the blood than by low concentrations of oxygen. Thus, if a small room or closet is filled with air having a low concentration of oxygen, perhaps because a leaking cylinder of some compressed gas is stored there, a person will not feel any “choking” sensation and may go into convulsions or lose consciousness without noticing anything wrong. Safety engineers give considerable attention to this danger.