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Mole Concept

If a chemical...

Question

If a chemical equation can be written as the sum of two equations whose equilibrium constants are $K_{1}$ and $K_{2}$ , then the new equilibrium constant of the new equation is given by $K_{n} =$ $K_{1} \times K_{2}$ .
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Solution

If a chemical equation can be written as the sum of two equations whose equilibrium constants are $K_{1}$ and $K_{2}$ , then the new equilibrium constant of the new equation is given by

$K_{n} = K_{1} \times K_{2}$ .
Consider the following chemical equations.
$A ⇌ B$ ; $K_{c} = K_{1}$ ......(1)
$C ⇌ D$ ; $K_{c} = K_{2}$ .....(2)
$A + C ⇌ B + D$ ; $K_{c} = K_{n}$ ....(3)
When equations (1) and (2) are added, the equation (3) is obtained.
The equilibrium constant expressions are as given below.
$K_{1} = \frac{[B]}{[A]}$
$K_{2} = \frac{[D]}{[C]}$
$K_{n} = \frac{[B] [D]}{[A] [C]} = (\frac{[B]}{[A]}) \times (\frac{[D]}{[C]}) = K_{1} \times K_{2}$ .

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