JEE Main 2020 — Chemical Equilibrium Question with Solution

We have two reactions:

$A\rightleftharpoons B+C\text{with }{K}_{eq}^{(1)}$

$B+C\rightleftharpoons P\text{with }{K}_{eq}^{(2)}$

We want the equilibrium constant for the overall reaction

$A\rightleftharpoons P.$

How to combine the equilibrium constants

When two reactions are added to yield a net (overall) reaction, the equilibrium constant of the net reaction is the product of the equilibrium constants of the individual reactions. Formally:

$\text{(Reaction 1)}+\text{(Reaction 2)}\Rightarrow \text{(Net Reaction)},$

and

$K_{\text{net}}=K_{\text{(Reaction 1)}}\times K_{\text{(Reaction 2)}}.$

Applying it here

Reaction 1: $A\to B+C$ has $K_{eq}^{(1)}.$

Reaction 2: $B+C\to P$ has $K_{eq}^{(2)}.$

When we add them,

$\underset{\text{Reactant 1}}{\underbrace{A}}⟶\underset{\text{Products of Reaction 1}=\text{Reactants of Reaction 2}}{\underbrace{B+C}}⟶\underset{\text{Product of Reaction 2}}{\underbrace{P}}.$

So the net reaction is $A\to P$, and its equilibrium constant is

$K_{eq}^{\text{(net)}}=K_{eq}^{(1)}\times K_{eq}^{(2)}.$

Thus, the correct answer is:

$\boxed{K_{eq}^{(1)}{K}_{eq}^{(2)}}.$

Hence, the answer (Option D) is correct.