Expressing the Equilibrium Constant of a Gas in Terms of Pressure
Write the equilibrium expression, KP, in terms of the partial pressures of a gas-phase reaction
According to the ideal gas equation, pressure is directly proportional to concentration, assuming volume and temperature are constant.
Since pressure is directly proportional to concentration, we can write our equilibrium expression for a gas-phase reaction in terms of the partial pressures of each gas. This special equilibrium constant is known as KP.
KP takes the exact same form as KC. To avoid confusion between the two, do not use brackets ([ ]) when expressing partial pressures.
equilibriumThe state of a reaction in which the rates of the forward and reverse reactions are the same.
partial pressureThe pressure that one component of a mixture of gases contributes to the total pressure.
Equilibrium Constants for Gases
Up to this point, we have been discussing equilibrium constants in terms of concentration. For gas-specific reactions, however, we can also express the equilibrium constant in terms of the partial pressures of the gases involved. Take the general gas-phase reaction:
Our equilibrium constant in terms of partial pressures, designated KP, is given as:
Note that this expression is extremely similar to KC, the equilibrium expression written in terms of concentrations. In order to prevent confusion, do not use brackets ([ ]), when writing KP expressions.
KP and the Ideal Gas Law
The reason we are allowed to write a K expression in terms of partial pressures for gases can be found by looking at the ideal gas law. Recall that the ideal gas law is given by:
Re-writing this expression in terms of P, we have:
Note that in order for K to be constant, temperature must be constant as well. Therefore, the term RT is a constant in the above expression. As for n/V (moles per unit volume) this is simply a measure of concentration. Pressure is directly proportional to concentration, so we are justified in our use of KP.
Lastly, there is a very important equation that relates KP and KC. It is given as follows:
In this expression,
is a measure of the change in number of moles of gas in the reaction. For instance, if a reaction produces three moles of gas, and consumes two moles of gas, then
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