The solubility of a salt of weak acid (AB) at pH 3 is `Y xx 10^(-3) " mol "L^(-1)`. The value of Y is ____. (Given that the value of solubility product of AB `(K_(sp))=2xx10^(-10)` and the value of ionization constant of HB `(K_(a))=1xx10^(-8)`)

Answer

4.47

Explanation

`AB(S) rarr A^(+)(aq) + B^(-)(aq)`........(A)
`B^(-)(aq) + H^(+)(aq) rarr HB(eq)`........(B)
On addition equation (A) and (B)
`AB(s) + H^(+)(aq) rarr A^(+)(eq) + HB(aq)`
`K_(sp)xx1/K_(a) = [A^(+)][HB]/[H^(+)]`
`2xx10^(-10)/1xx10^(-8) = S^(2)/10^(-3) implies S^(2) = 2 xx 10^(-2) xx 10^(-3)`
`implies S^(2) = 2 xx 10^(-5) implies S = 4.47 xx 10^(-3) = y xx 10^(-3) implies y = 4.47`