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

Answer

D

Explanation

`B^(-)+H^(+)hArrHB " " K_(b) = ([HB])/([B^(-)][H^(+)]) " "` …(i)
Bronsted base
` B^(-) +H_(2)O hArr HB + OH^(-) " " K_(a)= ([HB][OH^(-)])/([B^(-)] ) " "` …(ii)
Arrhenius base
By equation (i) and (ii)
`(K_(a))/(K_(b)) = ([HB][OH^(-)])/([B^(-)]) xx ([B^(-)][H^(+)])/([HB]) = [H^(+)] [OH^(-)] = K_(w)`
` :. K_(b) = (K_(a))/(K_(w)) = (2.8 xx10^(-17))/(10^(-14)) = 2.8 xx10^(7)`