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Two equilibrium, $A B (a q) ⇌ A^{+} (a q) + B^{-} (a q)$ and $A B (a q) + B^{-} (a q) ⇌ A B_{2}^{-} (a q)$ 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 :

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directly proportional to the concentration of $B^{-} (a q)$

inversely proportional to the concentration of $B^{-} (a q)$

directly proportional to the square of the concentration of $B - (aq)$

inversely proportional to the square of the concentration of $B^{-} (a q)$

answer is D.

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Detailed Solution

Here, we have

$K_{1} = \frac{[A^{+}] [B^{-}]}{[A B]}$

$K_{2} = \frac{[A B_{2}^{-}]}{[A B] [B^{-}]}$

$\frac{K_{1}}{K_{2}} = \frac{[A^{+}]}{[A B_{2}^{-}]} \times {[B^{-}]}^{2}$

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