#### Learning Objective

- Write the equilibrium expression, K
_{P}, in terms of the partial pressures of a gas-phase reaction

#### Key Points

- 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 K
_{P}. - K
_{P}takes the exact same form as K_{C}. To avoid confusion between the two, do not use brackets ([ ]) when expressing partial pressures.

#### Terms

- 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:

[latex]aA(g)+bB(g)\rightleftharpoons cC(g)+dD(g)[/latex]

Our equilibrium constant in terms of partial pressures, designated K_{P}, is given as:

[latex]K_P=\frac{P^c_CP^d_D}{P^a_AP^b_B}[/latex]

Note that this expression is extremely similar to K_{C}, the equilibrium expression written in terms of concentrations. In order to prevent confusion, do not use brackets ([ ]), when writing K_{P} expressions.

## K_{P} 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:

[latex]PV=nRT[/latex]

Re-writing this expression in terms of P, we have:

[latex]P=\frac{n}{V}RT[/latex]

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 K_{P}.

Lastly, there is a very important equation that relates K_{P} and K_{C}. It is given as follows:

[latex]K_{p} = K_{c}(RT) ^{ \Delta n}[/latex]

In this expression, [latex]\Delta n[/latex] 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 [latex]\Delta n=(3-2)=1[/latex].