Question

In an alkaline solution, the following equilibria exist.
$S^{2-}+S\to S_2^{2-}$equilibrium constant $K_1$
$S_2^{2-}+S\to S_3^{2-}$ equilibrium constant $K_2$
$K_1$ and $K_2$ have the values 12 and 11, respectively.
$S_3^{2-}\to S^{2-}+2S$. What is equilibrium constant for the reaction?

• A. $132$
• B. $7.58\times {10}^{-3}$
• C. $1.09$
• D. $0.198$

Answer 1

The correct option is B $7.58\times {10}^{-3}$

Given,
$S^{2-}+S\to S_2^{2-}:\left(K_1\right)...\left(1\right)$
$S_2^{2-}+S\to S_3^{2-}:\left(K_2\right)...\left(2\right)$

The reaction for which equilibrium constant required is,
$S_3^{2-}\to S^{2-}+2S$

Since the equation is obtained by reversing and adding equation (1) & (2), so the required equilibrium constant will be,
$K_3=\frac{1}{K_1}\times \frac{1}{K_2}=\frac{1}{12}\times \frac{1}{11}=7.58\times {10}^{-3}$