Partial Pressure and K_p

In a mixture of two or more gases, each component gas contributes to the total pressure of the system. For example, the earth's atmosphere is made up of (by mole percent) 78% nitrogen, 21% oxygen, .9% argon, .03% carbon dioxide, and other trace gases. Each gas contributed to the total pressure of 1 atm in accordance with its percent: for example, 78% of the 1 atm total pressure is .78 atm; argon contributes only .009 atm to the mixture.

The pressure each gas contributes to the total mixture is called its partial pressure; the rule governing them is Dalton's Law of Partial Pressures, which states that the total pressure is the sum of the pressures of the component gases. Furthermore, through a proof using the Ideal Gas Law, we can show that the pressure of each component gas is directly proportional to its mole fraction. The mole fraction (symbol: X) is simply the number of moles of the sample gas over the total number of moles. For example, if a box of normal air contains 5 moles of gas and 3.9 moles of nitrogen, the mole fraction of nitrogen would be X_N2 = 3.9 mol / 5 mol= 0.78. If the total pressure in the box is 1.5 atm, the partial pressure of nitrogen is 0.78 * 1.5 atm = 1.17 atm.

Since partial pressure is directly related to the number of moles present, a gas' partial pressure can be substituted for its concentration in an equilibrium constant. In this case, the subscript "p" is applied to the equilibrium constant, K, indicating the use of partial pressure instead of concentration in moles per liter. Other than the use of partial pressures in place of molarity, there is no difference in the use of K_p from the other equilibrium constants we have already discussed.

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