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Types of Equillibrium

For A g+ B g ...

Question

For $A (g) + B (g) ⇌ C (g) + D (g),$ the equilibrium constant is $K_{1}$ and for $C (g) + D (g) ⇌ A (g) + B (g),$ the equilibrium constant is $K_{2} .$ The correct relation between $K_{1}$ and $K_{2}$ is

K_{1} \times K_{2} = 1

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K_{1} \times (K_{2} - 1) = 0

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K_{1} / K_{2} = 1

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All of these

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Solution

The correct option is A $K_{1} \times K_{2} = 1$
$A (g) + B (g)_{1} C (g) + D (g)$
$K_{1} = \frac{[C] [D]}{[A] [B]}$ -----(1)
$C (g) + D (g)_{2} A (g) + B (g)$
$K_{2} = \frac{[A] [B]}{[C] [D]}$ -----(2)
From (1) and (2), it is concluded that $K_{1} = \frac{1}{K_{2}}$
So, $K_{1} \times K_{2} = 1$

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