The first and second dissociation constants 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. `0.2xx10^(5)`
B. `5.0xx10^(-5)`
C. `5.0xx10^(15)`
D. `5.0xx10^(-15)`

Answer

D

Explanation

`H_(2)A hArr H^(**) ** HA^(**)`
`therefore K_(1)=1.0xx10^(-5)=([H^(+)][Ha^(-)])/([H_(2)A])`(Given)
`HA^(-) to H^(+) + A^(-)`
`therefore K_(2)=5.0xx10^(-10)=([H^(+)][A^(-)])/([HA^(-)])` (Given)
`K=([H^(+)]^(2)[A^(2-)])/([H_(2)A])=K_(1)xxK_(2)`
`=(1.0xx10^(-5))xx(5xx10^(-10))=5xx10^(-15)`