The two equilibrium `AB hArr A^(+) + B^(-) and AB+B^(-)hArrAB_(2)^(-)` are simultaneously maintained in a solutio with equilibrium constant `K_(1) and K_(2)` respectively. The ratio of `[A^(+)] ` to `[AB_(2)^(-)]` in the solution is

Options

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

D

Explanation

`ABhArrA'+B^(-) AB+^(-)hArrAB_(2)^(-)`
`K_(1)=([A^(+)][B^(-)])/([AB]) K_(1)=([AB_(2)^(-)])/([AB][B^(-)])`
`K_(1)//K_(2)= ([A^(+)][B^(-)])/([AB]). ([AB][B^(-)])/([AB_(2)^(-)])=([A^(+)])/([AB_(2)^(-)]).[B^(-)]^(2) rArr ([A^(+)])/([AB_(2)^(-)])=(K_(1))/(K_(2)). (1)/([B^(-)])^(2)`
Therefore, (D) option is correct.