For a gas-phase reaction, which expression correctly relates Kp to Kc when Δn ≠ 0?

• A. Kp = Kc (RT)^Δn
• B. Kp = Kc ÷ (RT)^Δn
• C. Kp = Kc (RT)^(-Δn)
• D. Kp = Kc (RT)^(Δn/2)

Answer: (A)

Relating Kp and Kc for gas-phase reactions hinges on how pressure and concentration of gases connect. For a reaction aA + bB ⇌ cC + dD, the concentration-based expression is Kc = [C]^c [D]^d / ([A]^a [B]^b). The pressure-based expression is Kp = P_C^c P_D^d / (P_A^a P_B^b). Each gas’s partial pressure relates to its concentration by P_i = [i] RT, so substituting into the Kp expression gives Kp = ([C]^c [D]^d / ([A]^a [B]^b)) × (RT)^{c+d - (a+b)}. The exponent c+d - (a+b) is the net change in the number of moles of gas, Δn. Therefore Kp = Kc (RT)^{Δn}. When Δn ≠ 0, Kp and Kc differ by this factor; if Δn = 0, they are equal. The other forms would misplace the dependence on RT, since the correct relation requires the exponent to be Δn, not its negative or half of it.