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Kp is the equilibrium constant using partial pressure. Normally if all the compounds in a chemical reaction are in the gas phase then you don't need to change the partial pressure of a gas into concentration unless you are asked to find Kc. If a reaction has aqueous and gas compounds then you will have to convert the gases to concentration in order to have the units uniform when finding Kc.
It really depends on the information given to you in the problem. If you are given the concentrations of the gases and Kc, then use concentrations. If you are given partial pressures and K (p is usually implied in the textbook), then use partial pressures. The homework problems use both cases. This is generally what you do for homogeneous gas reactions; however, if you are given a heterogeneous reaction with aqueous solutions and gases, then you have to convert the partial pressures of the gas (if you are given partial pressures) to concentration because aqueous solutions don't have partial pressures.
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