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It just depends on what unit the the products and reactants are given in. If it's in molar concentration, then the equilibrium constant is denoted as Kc. If it's given in partial pressures, then it's denoted as Kp. They both mean the same thing, but it's just to differentiate between both.
It also depends on the states of the molecules. For instance, if given gases and their partial pressure, Kp will be used. For aqueous substances and concentration, Kc will be used. However, you can convert between partial pressure and concentration for a gas by using the ideal gas law and deriving that P=conc(RT) or conc=P/RT.
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