The ionization constant of `overset(o+)(NH_(4))` ion in water is `5.6 xx 10^(-10)` at `25^(@)C`. The rate constant the reaction of `overset(o+)NH_(4)` and `overset(ɵ)(OH)` ion to form `NH_(3)` and `H_(2)O` at `25^(@)C` is `3.4 xx 10^(10)L mol^(-1) s^(-1)`. Calculate the rate constant for proton transfer form water to `NH_(3)`.

Explanation

`NH_(3) +H_(2)O overset(K_(f))underset(K_(b))hArrNH_(4)^(o+)+overset(Θ)OH,K_(b)=3.4xx10^(10)`
`NH_(4)^(o+) +H_(2)O hArr NH_(4)OH +H^(o+), K_(a) = 5.6 xx10^(-10)`
`K_(("base"))NH_(3) = (K_(f))/(K_(b)) = (K_(w))/(K_(acid)(NH_(4)^(o+)))`
`(because K_("acid") xx K_("base") = K_(w))`
or `(K_(f))/(3.4xx10^(10)) = (10^(-14))/(5.6 xx10^(-10)) :. K_(f) = 6.07 xx10^(5)`