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

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.

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.