Given k_p for the reaction 1 2 C(g) 1 2 A(g)+ 1 2 B(g) at a fixed temperature is 0.25 ~atm ⁻² . Find the K_p for the reaction A(g)+B(g) C(g) at the same temperature.

Step-by-step solution

For the reaction, 1 2 C(g) 1 2 A(g)+ 1 2 B(g) Given, K_p=0.25 ~atm ⁻² We know that, K_C= [ Product ]^b [ Reactant ]^a , where a and b are stiochiometric coefficients. Also, K_p=K_C(R T)^ n_g where, n_g=b-a For above reaction, K_ C₁ = [A]^ 0.5 [B]^ 0.5 [C]^ 0.5 n_g=1-0.5=0.5 So, K_ p₁ =K_ C₁ (R T)^ 0.5 ...(i) Similarly for reaction, A(g)+B(g) C(g) , at same temperature aligned K_ C₂ & = [C] [A][B] n_g & =1-2=-1 K_ p₂ & =K_ C₂ (R T)⁻¹...(ii) aligned Now, divide K_ p₁ and K_ p₂ , we get, K_ p₁ K_ p₂ = K_ C₁ [R T]^ 0.5