Question

The two equilibria, $AB\left(aq\right)\leftrightharpoons A^{+}\left(aq\right)+B^{-}\left(aq\right)$ and
$AB\left(aq\right)+B^{-}\left(aq\right)\leftrightharpoons A{B}_2^{-}\left(aq\right)$ are simultaneously maintained in a solution with equilibrium constants, $K_1$ and $K_2$ respectively. The ratio of concentration of $A^{+}$ to $A{B}_2^{-}$ in the solution is:

• A. Directly proportional to the concentration of $B^{-}$ (aq.)
• B. Inversely proportional to the concentration of $B^{-}$ (aq.)
• C. Directly proportional to the square of the concentration of $B^{-}$ (aq.)
• D. Inversely proportional to the square of the concentration of $B^{-}$ (aq)

Answer 1

The correct option is D Inversely proportional to the square of the concentration of $B^{-}$ (aq)

Given,
$AB\leftrightharpoons A^{+}+B^{-}$
$AB+B^{-}\leftrightharpoons A{B}_2^{-}{K}_1=\frac{\left[A^{+}\right]\left[B^{-}\right]}{\left[AB\right]};K_2=\frac{\left[A{B}_2^{-}\right]}{\left[AB\right]\left[B^{-}\right]}\frac{K_1}{K_2}=\frac{\left[A^{+}\right]\left[B^{-}\right]}{\left[AB\right]}.\frac{\left[AB\right]\left[B^{-}\right]}{\left[A{B}_2^{-}\right]}\frac{K_1}{K_2}=\frac{\left[A^{+}\right]}{\left[A{B}_2^{-}\right]}.[B^{-}{]}^2\Rightarrow \frac{\left[A^{+}\right]}{\left[A{B}_2^{-}\right]}=\frac{K_1}{K_2}.\frac{1}{[B^{-}{]}^2}$