The first and second dissociation constant of an acid `H_(2)A` are `1.0xx10^(-5)` and `5.0xx10^(-10)` respectively. 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^(-)hArrH^(+) + A^(+)`
`K_(2)=([HA^(+)][H^(2-)])/([HA^(-)])` (`2`)
For the reaction
`H_(2)AhArr2H^(+)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)`