For a gas-phase reaction, which expression correctly relates the equilibrium constants Kp and Kc given the change in moles of gas Δn?

• A. Kp = Kc (RT)^Δn
• B. Kp = Kc ÷ (RT)^Δn
• C. Kp = Kc (RT)^Δn
• D. Kp = Kc (RT)^(-Δn)

Answer: (C)

When you relate Kp to Kc for a gas-phase reaction, the key idea is that partial pressures and concentrations are connected through P_i = c_i RT for ideal gases. The equilibrium expression for Kp uses partial pressures, while Kc uses concentrations. Writing them out and substituting P_i = c_i RT gives Kp = ∏ (c_i RT)^{ν_i} = (RT)^{Δn} ∏ c_i^{ν_i}, where Δn is the change in moles of gas, defined as (moles of gas on the product side minus moles on the reactant side). That leads to the relationship Kp = Kc (RT)^{Δn}.

Interpretation: if Δn is positive, Kp exceeds Kc by a factor of (RT)^{Δn}; if Δn is negative, Kp is smaller by that factor. The correct expression is exactly Kp = Kc (RT)^{Δn}.