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Why is K(a2) lt lt K(a1) for H2SO4 in wa...

Why is `K_(a_2) lt lt K_(a_1)` for `H_2SO_4` in water ?

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`H_2SO_4` is a dibasic acid, it ionises in two stages and hence has two dissociation constants as given below :
(i) `H_2SO_4(aq) + H_2O (l) to H_3O^(+)(aq) + HSO_4^(-) (aq) , K_(a_1) gt 10`
(ii) `HSO_4^(-) (aq ) + H_2O (l) to H_3O^(+) (aq) + SO_4^(2-) (aq) , K_(a_2)= 1.2 xx 10^(-2)`
`K_(a_2) ` is less than `K_(a_1)` i.e., tendency to move towards the products is much less in (ii) than (i) . This is because the negatively charged `HSO_4^(-)` ion has much less tendency to donate a proton to `H_2O` as compared to neutral `H_2SO_4`.
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