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You can use either, but sometimes they state explicitly to find Kc (concentration) or Kp (pressure) or they give the equilibrium constant in those two forms. If they give Kc, you have to use concentration and if they give Kp you have to use pressure.
If the gas is in a reaction with other aqueous solutions whose equilibrium concentrations are given as concentrations, you may need to convert the partial pressure of your gas to a concentration using the ideal gas equation. In a reaction, you want to use all pressures or all concentrations, not a mixture.
It depends upon if the question initially gives you a Kc value, for which you would have to use concentration measurements, or if the problem gives a Kp value, for which you would use partial pressure measurements.
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