When does kc = kp?

The relationship between Kc and Kp, two equilibrium constants, is a fundamental concept in physical chemistry. Kc is the equilibrium constant in terms of concentrations, while Kp is the equilibrium constant in terms of partial pressures. The question at hand is: when does Kc equal Kp?

To answer this question, we first need to understand the relationship between Kc and Kp. This relationship is given by the equation:

Kp = Kc(RT)^(Δn)

where:
- Kp is the equilibrium constant in terms of partial pressures,
- Kc is the equilibrium constant in terms of concentrations,
- R is the ideal gas constant,
- T is the temperature in Kelvin,
- Δn is the change in moles of gas in the reaction (calculated as moles of gaseous products minus moles of gaseous reactants).

From this equation, it is clear that Kc equals Kp when Δn equals zero, i.e., when the number of moles of gaseous products is equal to the number of moles of gaseous reactants. This is because any number (except zero) raised to the power of zero equals one, making Kp = Kc(1), or simply Kp = Kc.

In conclusion, Kc equals Kp for reactions where there is no change in the number of moles of gas, i.e., the number of moles of gaseous reactants equals the number of moles of gaseous products. This is a key concept in the study of chemical equilibrium, particularly in the context of gas-phase reactions.