Kp and Kc for Gas Equilibria

A gas equilibrium can be described two ways: by how many moles per liter of each gas are present (Kc) or by how much pressure each gas exerts (Kp). Both describe the same resting point, since for an ideal gas pressure and concentration are directly proportional through PV = nRT. Rearranged, P = (n/V)RT, so pressure is just concentration times RT. That means swapping concentrations for pressures in the equilibrium expression is not a new idea, just a unit change, but that change carries consequences.

Because each gas term picks up a factor of RT when you convert, and because K is a ratio of products over reactants raised to their coefficients, the RT factors do not cancel unless the total moles of gas on each side are equal. Count up moles of gas product coefficients minus moles of gas reactant coefficients to get delta n. Then Kp = Kc(RT)^{delta n}. For N2 + 3 H2 <→ 2 NH3, delta n = 2 - 4 = -2, so the RT factors survive and Kp differs from Kc. R is 0.08206 L atm/(mol K) when pressure is in atmospheres.

This sits right after writing K expressions and running ICE tables in concentration units. Once a problem gives pressures instead, or asks you to predict how pressure changes shift equilibrium, converting between Kp and Kc lets you use whichever form matches the data. It also sets up Le Chatelier reasoning for pressure and volume changes, where delta n tells you which direction a gas system shifts when the container is compressed.