A sparingly soluble salt MA (K_sp = 2.0 x 10^-10) is the salt of a weak acid HA with K_a = 1.8 x 10^-5. Its solubility in a buffer of pH 4.00 is (neglect hydrolysis of M+)

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A sparingly soluble salt $MA$ ( $K_{s p} = 2.0 \times 1 0^{- 10}$ ) is the salt of a weak acid $HA$ with $K_{a} = 1.8 \times 1 0^{- 5}$ . Its solubility in a buffer of pH 4.00 is (neglect hydrolysis of $M X^{+}$ )

Total A = S =

[A X^{-}] + [HA] = [A X^{-}] (1 + [H X^{+}] / K_{a})

and

[M X^{+}] = S

. So

K_{s p} = S \cdot S / (1 + [H X^{+}] / K_{a})

, i.e.

S = K_{s p} (1 + [H X^{+}] / K_{a})

. Here

1 + 1 0^{- 4} / (1.8 \times 1 0^{- 5}) = 6.556

, so

S = 3.6 \times 1 0^{- 5} M