If the equilibrium constant for $\mathrm{A} \rightleftharpoons \mathrm{B}+\mathrm{C}$ is $\mathrm{K}_{(\mathrm{eq})}^{(1)}$ and that of $\mathrm{B}+\mathrm{C} \rightleftharpoons \mathrm{P}$ is $\mathrm{K}_{(\mathrm{eq})}^{(2)}$, the equilibrium constant for $A \rightleftharpoons P$ is:

(A) $\mathrm{K}_{(\mathrm{eq})}^{(1)} \mathrm{K}_{(\mathrm{eq})}^{(2)}$

(B) $\mathrm{K}_{(\mathrm{eq})}^{(1)} / \mathrm{K}_{(\mathrm{eq})}^{(1)}$

(C) $\mathrm{K}_{(\mathrm{eq})}^{(1)}+\mathrm{K}_{(\mathrm{eq})}^{(2)}$

(D) $\mathrm{K}_{(\mathrm{eq})}^{(2)}-\mathrm{K}_{(\mathrm{eq})}^{(1)}$

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Equilibrium

If the equilibrium constant for

A ⇌ B + C

K_{(eq)}^{(1)}

and that of

B + C ⇌ P

K_{(eq)}^{(2)}

, the equilibrium constant for

A ⇌ P

is:

Answer: (A)

Adding two equilibria multiplies their equilibrium constants. Since

A ⇌ B + C

has constant

K_{eq}^{(1)}

and

B + C ⇌ P

has constant

K_{eq}^{(2)}

, their sum

A ⇌ P

has equilibrium constant

K_{eq}^{(1)} K_{eq}^{(2)}

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Single correct option