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Two equilibria AB iff A^(+)+B^(-) and AB...

Two equilibria `AB iff A^(+)+B^(-) and AB+B^(-) iff 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^(-)]`

D

inversely proportional to the square of `[B^(-)]`

Text Solution

Verified by Experts

The correct Answer is:
D
`AB overset(K_1)(hArr) A^(+) +B^(-)`
`therefore K_1 = ([A^(+) ][B^(-) ])/( [AB])`
`AB + B^(-) overset(K_2)(hArr) AB_(2)^(-)`
and `K_(2) = ([AB_(2)^(-) ])/( [AB][B^(-)])`
On dividing Eq. (i) from Eq. (ii),
`([A^(+) ] [B^(-)])/( [AB]) xx ([AB][B^(-) ] )/( [AB_(2)^(-)]) = (K_1)/(K_2)`
or `([A^(+) ][B^(-)]^2)/( [AB_(2)^(-) ])`
where `K. = (K_1)/(K_2) = "constant"`
or `([A^(+)])/( [AB_(2)^(-) ] ) = K. xx (1)/( [B^(-1)]^2)`
or `([A^(+)])/( [AB_(2)^(-)]) prop (1)/([B^(-)]^2)`
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