The equilibrium constants $K_c$ and $K_p$ are fundamental concepts in the study of chemical reactions, each representing the position of equilibrium for a given reaction. However, they differ in their formulations: $K_c$ is expressed in terms of concentrations, while $K_p$ is expressed in terms of partial pressures.

The equilibrium constant $K_c$ is applicable to reactions occurring in solution. It is calculated by taking the product of the molar concentrations of the products, each raised to the power of its respective stoichiometric coefficient, and dividing this by the product of the molar concentrations of the reactants, also raised to the power of their respective stoichiometric coefficients. Importantly, only gases and aqueous solutions are included in the equilibrium expression for $K_c$.

In contrast, $K_p$ is used for reactions that involve gaseous reactants and products. Similar to $K_c$, it is calculated by taking the product of the partial pressures of the products, each raised to the power of its stoichiometric coefficient, divided by the product of the partial pressures of the reactants. The partial pressure of a gas is defined as the pressure that the gas would exert if it occupied the entire volume alone.

A key relationship exists between $K_p$ and $K_c$, expressed by the equation:

In this equation, $R$ represents the ideal gas constant, $T$ is the temperature measured in Kelvin, and $\Delta n$ is the change in the number of moles of gas during the reaction.

In summary, while both $K_c$ and $K_p$ serve the essential role of indicating the position of equilibrium for a chemical reaction, they are utilized in different scenarios and calculated using different parameters. Specifically, $K_c$ is employed for reactions in solution and is based on concentrations, whereas $K_p$ is designated for reactions involving gases and is based on partial pressures.