# If the equilibrium constant for A ⇌ B + C is

Question:

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 $\mathrm{A} \rightleftharpoons \mathrm{P}$ is :-

1. $\mathrm{K}_{e q}^{(2)}-\mathrm{K}_{e q}^{(1)}$

2. $\mathrm{K}_{e q}^{(1)} \mathrm{K}_{e q}^{(2)}$

3. $\mathrm{K}_{\text {eq }}^{(1)} / \mathrm{K}_{\text {eq }}^{(2)}$

4. $\mathrm{K}_{\mathrm{eq}}^{(1)}+\mathrm{K}_{\mathrm{cu}}^{(2)}$

Correct Option: , 2

Solution:

$\mathrm{A} \rightleftharpoons \mathrm{B}+\mathrm{C} \quad \mathrm{K}_{e q}^{(1)}=\frac{[\mathrm{B}][\mathrm{C}]}{[\mathrm{A}]}$$\ldots . .(1) \mathrm{B}+\mathrm{C} \rightleftharpoons \mathrm{P} \quad \mathrm{K}_{\text {eq }}^{(2)}=\frac{[\mathrm{P}]}{[\mathrm{B}][\mathrm{C}]}$$\ldots . .(2)$

For

$\mathrm{A} \rightleftharpoons \mathrm{P} \quad \mathrm{K}_{\mathrm{eq}}=\frac{[\mathrm{P}]}{[\mathrm{A}]}$

Multiplying equation (1) & (2)

$\mathrm{K}_{\text {eq }}^{(1)} \times \mathrm{K}_{\text {eq }}^{(2)}=\frac{[\mathrm{P}]}{[\mathrm{A}]}=\mathrm{K}_{\text {eq }}$