\(AB\overset {{K_1}} \longleftrightarrow {A^ + } + {B^{ - 1}}\)
\({K_1} = \frac{{[{A^ + }][{B^ - }]}}{{[AB]}}\)
\(AB + {B^ - }\overset {{K_2}} \longleftrightarrow AB_2^ - \)
\({K_2} = \frac{{[AB_2^ - ]}}{{[AB][{B^ - }]}}\)
Dividing \(K_1\) and \(K_2\) we get
\(K = \frac{{{K_1}}}{{{K_2}}} = \frac{{[{A^ + }]{{[{B^ - }]}^2}}}{{[AB_2^ - ]}}\)
\(\therefore \,\frac{{[{A^ + }]}}{{[AB_2^ - ]}} = \frac{K}{{{{[{B^ - }]}^2}}}\)