Find the solubility of CaC2O4 in a buffer of fixed pH 2.00. K_sp(CaC2O4) = 2.3 x 10^-9; for oxalic acid K_a1 = 5.6 x 10^-2, K_a2 = 5.4 x 10^-5. Total dissolved oxalate (all species) equals [Ca^2+].

JEE Advanced levelSingle correct optionDifficulty 3 of 3ia087

Find the solubility of $CaC X_{2} O X_{4}$ in a buffer of fixed pH 2.00. $K_{s p} (CaC X_{2} O X_{4}) = 2.3 \times 1 0^{- 9}$ ; for oxalic acid $K_{a 1} = 5.6 \times 1 0^{- 2}$ , $K_{a 2} = 5.4 \times 1 0^{- 5}$ . Total dissolved oxalate (all species) equals $[Ca X^{2 +}]$ .

Fraction as

C X_{2} O X_{4} X^{2 -}

α_{2} = K_{a 1} K_{a 2} / ([H X^{+}]^{2} + K_{a 1} [H X^{+}] + K_{a 1} K_{a 2}) = 0.0046

(using only

K_{a 2}

gives 0.0054).

K_{s p} = s \cdot s α_{2}

, so

s = K_{s p} / α_{2} = 7.1 \times 1 0^{- 4} M