The solubility of a salt of weak acid (A...

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)`)

Text Solution

Verified by Experts

The correct Answer is:

4.47

`AB (s) hArr A^(+) (aq) + B^(-) (aq) ` ...(i)
`B^(-)(aq)+ H^(+) (aq) hArrHB (aq) ` ...(ii)
Adding eqns (i) and (ii), we get
`{:(,AB(s),+,H^(+)(aq),hArr,A^(+)(aq),+,HB(aq)),("Initial conc",x,,10^(-3),,0,,0),("Final conc.",x-S,,10^(-3),,S,,S),(,,,,,,,):}` (S = solubility when pH = 3)
From eqn. (i), `K_(sp)=[A^(+)][B^(-)]`
From eqn. (ii), `K_(a)=([HB])/([B^(-)][H^(+)])`
`:. (K_(sp))/(K_(a))=([A^(+)][HB])/([H^(+)])`
`(2xx10^(-10))/(10^(-8))=(SxxS)/(10^(-3))`
or `S^(2) = 2 xx10^(-5) = 20 xx 10^(-6) or S = 4.47 xx 10^(-3)`
Hence , y = 4.47.

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