The first and second dissociation constants of an acid `H_(2)A` are `1xx10^(-5) and 5xx10^(-10)` respectively. Calculate the value of overall dissociation constant.

Explanation

`H_(2)(A)(aq)+H_(2)O(l) hArr H_(3)O^(+)(aq)+HA^(-)(aq),K_(1)=1xx10^(-5)` . . . (1)
`HA^(-)(aq)+H_(2)O(l) hArr H_(3)O^(+)(aq)+A^(2-)(aq),K_(2)=5xx10^(-10)` . . (2)
The overal dissociation reaction is the sum of the reaction (1) and (2). `H_(2)A(aq)+2H_(20O(l) hArr 2H_(3)O^(+)(aq)+A^(2-)(aq)` thus, the overall dissociation constant,
`K=K_(1)xxK_(2)=(1xxx10^(-5))xx(5xx10^(-10))=5xx10^(-15)`.