A cetrain ion `B^(-)` has an Arrhenius constant for basic character (eq. constnat `2.8xx10^(-7)`). The equilibrium constant for Lowry-Bronsed basic character is:

Options

A. `2.8xx10^(-7)`
B. `3.57xx10^(-8)`
C. `3.57xx10^(8)`
D. `2.8xx10^(7)`

Answer

D

Explanation

`B^(-)underset("Bronsted base")(+H^(+))hArr HB, K_(b)=2.8xx10^(-7)`
`= ([HB])/([B^(-)][H^(+)])` …..(i)
`B^(-)underset("Arrhenius base")(+H_(2)O)hArr HB+OH^(-)`,
`K_(a)= ([HB][OH^(-)])/([B^(-)])` ….(ii)
By eqs. (i) and (ii),
`(K_(a))/(K_(b))= ([HB][OH^(-)])/([B^(-)])xx([B^(-)][H^(+)])/([HB])`
`= [H^(+)][OH^(-)]= K_(w)` .....(iii)
`:. K_(b)= (K_(a))/(K_(w)) = (2.8xx10^(-7))/(10^(-14))=2.8xx10^(7)`