Question

For the reactions and their equilibrium constants given below,
$CuC{l}_4^{2-}+B{r}^{-}\rightleftharpoons CuC{l}_{3}B{r}^{2-}+C{l}^{-};K_1$
$CuC{l}_{3}B{r}^{2-}+B{r}^{-}\rightleftharpoons CuC{l}_{2}B{r}_2^{2-}+C{l}^{-};K_2$
$CuC{l}_{2}B{r}_2^{2-}+B{r}^{-}\rightleftharpoons CuClB{r}_3^{2-}+C{l}^{-};K_3$
$CuClB{r}_3^{2-}+B{r}^{-}\rightleftharpoons CuB{r}_4^{2-}+C{l}^{-};K_4$
The equilibrium constant, $K$ for the reaction
$CuC{l}_4^{2-}+3B{r}^{-}\rightleftharpoons CuClB{r}_3^{2-}+3C{l}^{-}$, is

• A. $K_1{K}_2{K}_3$
• B. $K_1{K}_2{K}_3{K}_4$
• C. $K_1+K_2+K_3$
• D. $\frac{1}{\left(K_1{K}_2{K}_3\right)}$

Answer 1

Answer: (A)

For the reactions,
$CuC{l}_4^{2-}+B{r}^{-}\rightleftharpoons CuC{l}_{3}B{r}^{2-}+C{l}^{-};K_1\dots (i)$
$CuC{l}_{3}B{r}^{2-}+B{r}^{-}\rightleftharpoons CuC{l}_{2}B{r}^{2-}+C{l}^{-};K_2...(ii)$
$CuC{l}_{2}B{r}_2^{2-}+B{r}^{-}\rightleftharpoons CuClB{r}_3^{2-}+C{l}^{-}{K}_3...(iii)$
$CuClB{r}_3^{2-}+B{r}^{-}\rightleftharpoons CuB{r}_4^{2-}+C{l}^{-};K_4\dots (iv)$
To obtain reaction,
$CuC{l}_4^{2-}+3B{r}^{-}\rightleftharpoons CuClB{r}_3^{2-}+3C{l}^{-}$
Add equations (i), (ii) and (iii)
$\therefore K=K_1\times K_2\times K_3$