Question

3. [20pt] For a reaction involving perfect gases, VAA + VRB = VCC + VD (a) (5pt) Define the equilibrium constants (Ky and Kc) in terms of partial pressure and molarity, respectively. RT Δν (b) (5pt) Based on the above definitions, show that K, = K (cºsp)” where Av = vc + vp - (VA + VB). (c) (10pt) Based on the above equation and van't Hoff equation, show that da neko - Aero (The van't Hoff equation can be derived by taking a derivative in the form of (d In Kc/ dT) for the expression, Agº = -RT In Kp.)

Answer 1

3(a) K_p and k_c defined as the ratio between product and reactant concentration in terms of partial pressure and moles respectively.

For a gas phase reaction aA+bB$\rightleftharpoons$cC+dD

K_p= (P_C)^c (P_D)^d / (P_A)^a (P_B)^b

Here K_p relates to the equilibrium constants in terms of molar concentration

K_c = [C]^c[D]^d / [A]^a[B]^b

K_c represents K_p = (RT)^$\Delta$n

Here $\Delta$ n is mol of product gas - mol of reactant gas