Why is `K_(a_(2)) ltlt K_(a_(1))` for `H_(2) SO_(4)` in water ?

Explanation

`H_2SO_4` ionises in two steps and hence has two dissociation constants, i.e., `H_2SO_4` acts as a dibasic acid.
(a). `H_2SO_4+H_2OtoHSO_4^(ɵ)+H_3O^(o+)` `K_(a_1)`
(b). `HSO_4^(ɵ)+H_2OtoSO_4^(2-)+H_2O^(o+)` `K_(a_2)`
`K_(a_1)ltK_(a_1)` because the negatively charged `HSO_4^(ɵ)` ion has much less tendency to donate a proton as compared to netural `H_2SO_4`.