The first and second dissociation constant of an acid `H_2A ` are ` 1.0 xx 10 ^(-5) and 5.0 xx 10^(-10) ` respectively . The overall dissociation constant of the acid will be :
` 5.0 xx 10^(-5)`
` 5.0 xx 10 ^(-15)`
` 5.0 xx 10 ^(-15)`
` 0.2 xx 10 ^(5)`

Options

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

Answer

C

Explanation

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