Two equilibria, AB A^ + + B^ - and AB + B^ - AB_2^ - are simultan… - Vidyadip

MCQ

Two equilibria, $AB \rightleftharpoons {A^ + } + {B^ - }$ and $AB + {B^ - } \rightleftharpoons AB_2^ - $ are simultaneously maintained in a solution with equilibrium constants, $K_1$ and $K_2$ respectively. The ratio of $[A^+]$ to $[AB_2^-]$ in the solution is

A
directly proportional to $[B^-]$
B
inversely proportional to $[B^-]$
C
directly proportional to the square of $[B^-]$
✓
inversely proportional to the square of $[B^-]$

✓

Answer

Correct option: D.

inversely proportional to the square of $[B^-]$

d
Given,

$AB\overset {{K_1}} \longleftrightarrow {A^ + } + {B^{ - 1}}$

${K_1} = \frac{{[{A^ + }][{B^ - }]}}{{[AB]}}$

$AB + {B^ - }\overset {{K_2}} \longleftrightarrow AB_2^ - $

${K_2} = \frac{{[AB_2^ - ]}}{{[AB][{B^ - }]}}$

Dividing $K_1$ and $K_2$ we get

$K = \frac{{{K_1}}}{{{K_2}}} = \frac{{[{A^ + }]{{[{B^ - }]}^2}}}{{[AB_2^ - ]}}$

$\therefore \,\frac{{[{A^ + }]}}{{[AB_2^ - ]}} = \frac{K}{{{{[{B^ - }]}^2}}}$

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