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

Options

A. `5.0 xx 10^(-5)`
B. `5.0 xx 10^(15)`
C. `5.0 xx 10^(-15)`
D. `0.0 xx 10^(-5)`

Answer

C

Explanation

`H_(2)A hArr HA^(-) + H^(+) " " K_(1) = ([HA^(-)][H^(+)])/([H_(2)A])` ...(i)
`HA^(-) rarr H^(-) + A^(2-) " " K_(2) = ([H^(+)][A^(2-)])/([HA^(-)])` ...(ii)
For the reaction
`H_(2)A hArr 2H^(+) + A^(2-)`
`K = ([H^(+)]^(2) [A^(2-)])/([H_(2)A]) = K_(1) xx K_(2)`
`= 1 xx 10^(-5) xx 5 xx 10^(-10) = 5 xx 10^(-15)`.