The first and second dissociation constant of an acid `H_(2)A` are `1.0xx10^(-5)` and `5.0xx10^(-10)` repectively. The overall dissociation constant of the acid will be

Options

A. `5.0xx10^(-5)`
B. `5.0xx10^(15)`
C. `5.0xx10^(-15)`
D. `0.2xx10^(5)`

Answer

C

Explanation

`H_(2)AhArrHA^(-)+H^(+)`
`K_(1) = ([HA^(-)][H^(+)])/([H_(2)A])` ……(1)
`HA^(-)hArr H^(+)+A^(2-)`
`K_(2) = ([H^(+)][A^(2-)])/([HA^(-)])` ……(2)
For the reaction, `H_(2)A hArr 2H^(+)+A^(2-)`
`K = ([HA^(-)][H^(+)])/([H_(2)A])xx([H^(+)][A^(2-)])/([HA^(-)])`
`= ([H^(+)]^(2-)[A^(2-)])/([H_(2)A])= K_(1)xxK_(2)`
`1xx10^(-5)xx5xx10^(-10)`
`=5xx10^(-15)`