Question

For the reaction $2P\stackrel{K_1}{\underset{K_2}{\rightleftharpoons }}Q\stackrel{K_3}{\underset{K_4}{\rightleftharpoons }}R+S$; $K_1,K_2,K_3$ and $K_4$ are $4\times {10}^3,2\times {10}^4,16\times {10}^2$ and $40$ respectively. The overall equilibrium constant is:

Answer 1

$K=\frac{K_1}{K_2}=\frac{\left[Q\right]}{[P{]}^2}$

$K^{\prime }=\frac{K_3}{K_4}=\frac{\left[R\right]\left[S\right]}{\left[Q\right]}$

$K"=\frac{\left[R\right]\left[S\right]}{[P{]}^2}=\frac{\left[P\right]\left[S\right]}{\left[Q\right]}\frac{\left[Q\right]}{[P{]}^2}=K^{\prime }\times K=\frac{K_3}{K_4}\times \frac{K_1}{K_2}=\frac{16\times {10}^2\times 4\times {10}^3}{40\times 2\times {10}^4}=8$.

Hence, the overall equilibrium is $8$