Derive the expression of equilibrium constant, Kc for the reaction: A

1.	Derive the expression of equilibrium constant, Kc for the reaction: A + B ⇌ C + D
Answer» Consider a hypothetical reversible reaction A + B ⇌ C + D. Two reactions, namely, forward and reverse reactions occur simultaneously in a reversible chemical reaction. The rate equations for the forward and reverse reactions are: Rate_forward ∝ [A][B] ∴ Rate_forward = k_f [A] [B] …… (1) ∴ Rate_reverse ∝ [C] [D] ∴ Rate_reverse = k_r [C] [D] …. (2) At equilibrium, the rates of forward and reverse reactions are equal. Thus, Rate_forward = Rate_reverse ∴ k_f [A] [B] = k_r [C] [D] ∴ \(\frac{K_f}{K_r}\) = K_C = \(\frac{[C][D]}{[A][B]}\).............(3) K_c is called the equilibrium constant.

Derive the expression of equilibrium constant, Kc for the reaction: A + B ⇌ C + D

Answer»

Consider a hypothetical reversible reaction A + B ⇌ C + D.

Two reactions, namely, forward and reverse reactions occur simultaneously in a reversible chemical reaction. The rate equations for the forward and reverse reactions are:

Rate_forward ∝ [A][B]

∴ Rate_forward = k_f [A] [B] …… (1)

∴ Rate_reverse ∝ [C] [D]

∴ Rate_reverse = k_r [C] [D] …. (2)

At equilibrium, the rates of forward and reverse reactions are equal. Thus,

Rate_forward = Rate_reverse

∴ k_f [A] [B] = k_r [C] [D]

∴ \(\frac{K_f}{K_r}\) = K_C = \(\frac{[C][D]}{[A][B]}\).............(3)

K_c is called the equilibrium constant.

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