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Kp and Kc are equilibrium constants expressed in different units. Kc uses molar concentrations of gases, while Kp uses partial pressures. They are not necessarily equal because partial pressure and molar concentration are separate values. However, they are related through the ideal gas equation and temperature, allowing conversion between the two constants.

For a gaseous reaction, the equilibrium expression using partial pressures is written as Kp, where each reactant and product partial pressure is raised to its stoichiometric coefficient. For example, in the reaction A + B ⇌ C + D, Kp equals the partial pressure of C times the partial pressure of D, divided by the partial pressure of A times the partial pressure of B.

The relationship between Kp and Kc is expressed as: Kp = Kc(RT)^Δn, where R is the gas constant, T is temperature in Kelvin, and Δn is the difference between the sum of product coefficients and the sum of reactant coefficients. This equation is derived by substituting the ideal gas law into the equilibrium expression.

Δn represents the change in the number of moles of gas during the reaction. It is calculated as the sum of stoichiometric coefficients of gaseous products minus the sum of stoichiometric coefficients of gaseous reactants. This value determines how temperature and pressure changes affect the relationship between Kp and Kc.

The ideal gas equation (PV = nRT) relates pressure to molar concentration. By rearranging it to express pressure in terms of molarity, partial pressures in the Kp expression can be substituted with concentration equivalents. This substitution, combined with the definition of Kc, yields the mathematical relationship between the two equilibrium constants.

Kp is used for gas-phase reactions because it directly relates to the partial pressures of gases, which are experimentally measurable quantities. While Kc uses concentrations, Kp is often more convenient for gaseous systems where pressure data is readily available. Both are valid; the choice depends on the available experimental data and the specific application.

Δn equals zero when the total number of moles of gaseous products equals the total number of moles of gaseous reactants. In this case, (RT)^Δn equals one, so Kp equals Kc regardless of temperature. This simplifies calculations for reactions where the number of gas molecules remains constant.