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Chemical potential and mathematical relation of Kc and Kp

Define chemical potential, equilibrium Constants Kp and Kc. Also derive Kc and Kp mathematically and show the relationship between them

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The chemical potential of the component i in a system is defined as the change in the Gibbs free energy with change in the mole of component i when temperature (T) and pressure (P) and the mole of other components are kept constant.

The condition of equilibrium of a chemical reaction is that the free energy must be minimum

Kc , the equilibrium constant is a function only of temperature. It is a dimensionless quantity, and is the ratio of the molarities of the products and reactants.
For the general reaction : RT ln Kp= -delta G (zero)