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The equilibrium constant is written as Kc when you use the concentrations of the reactants and products in the formula, in mol/L. The equilibrium constant is written as Kp when you use the partial pressures instead of the concentrations for the equation. You cannot mix concentrations and partial pressures in the formula. You would usually use Kp when all the reactants and products are in the gas phase and the units are for gases. You can use PV=nRT if needed to convert the partial pressure of a gas to concentration (n/V) and vice versa.
Kc is the equilibrium constant that uses concentration and you typically use this expression when you deal with aqueous solutions or are given molarities. Kp is the equilibrium constant that uses partial pressure and you use it when one or more of your reactants or products is in the gas phase.
Kc is used when the concentrations are given in the question, and Kp is used when the partial pressures are given in the question. For Kp, the given amounts typically have a unit in pressure (i.e. bar) which helps distinguish between the two.
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