Given the following two reactions:
$A + B \rightleftharpoons C + D$, with equilibrium constant $K_1$
$E + F \r

Question

Given the following two reactions:
$A + B \rightleftharpoons C + D$, with equilibrium constant $K_1$
$E + F \rightleftharpoons G + H$, with equilibrium constant $K_2$
What is the equilibrium constant for the reaction $C + D + E + F \rightleftharpoons A + B + G + H$?

Accepted Answer

Let the given reactions be:
(i) $A + B ightleftharpoons C + D$; Equilibrium constant = $K_1$
(ii) $E + F ightleftharpoons G + H$; Equilibrium constant = $K_2$

Reversing reaction (i), we get:
(iii) $C + D ightleftharpoons A + B$; Equilibrium constant = $1/K_1$ .

Now, add reaction (ii) and reaction (iii):
$(E + F) + (C + D) ightleftharpoons (G + H) + (A + B)$
$C + D + E + F ightleftharpoons A + B + G + H$

The equilibrium constant for a net reaction obtained by adding two reactions is the product of the equilibrium constants of the individual reactions .
Therefore, the equilibrium constant for the new reaction is:
$K = \left(\frac{1}{K_1}ight) 	imes K_2 = \frac{K_2}{K_1}$.

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