Two equilibrium `ABhArrA^(o+)+B^(Θ)` and `AB+B^(Θ)hArrAB_(2)^(Θ)` are simultaneously maintained in a solution with equilibrium constants `K_(1)` and `k_(2)`, respectively. Ratio of `[A^(o+)]` to `[AB_(2)^(Θ)]` 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.