Calculate the solubility of CaC2O4 (K_sp = 2.3x 10^-9) in a buffer of pH 3.00. For oxalic acid K_a1 = 5.6x 10^-2 and K_a2 = 5.4x 10^-5; oxalate exists as C2O4^2-, HC2O4- and H2C2O4 and the pH is held constant. Give s in units of 10^-4 M to two decimals.

JEE Advanced levelNumerical answerDifficulty 3 of 3ia161

Calculate the solubility of $CaC X_{2} O X_{4}$ ( $K_{s p} = 2.3 \times 1 0^{- 9}$ ) in a buffer of pH $3.00$ . For oxalic acid $K_{a 1} = 5.6 \times 1 0^{- 2}$ and $K_{a 2} = 5.4 \times 1 0^{- 5}$ ; oxalate exists as $C X_{2} O X_{4} X^{2 -}$ , $HC X_{2} O X_{4} X^{-}$ and $H X_{2} C X_{2} O X_{4}$ and the pH is held constant. Give $s$ in units of $1 0^{- 4} M$ to two decimals.

Numerical answer type, answer in x 10^-4 M, tolerance 0.02.

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}) = 0.0504

K_{s p} = s \cdot s α_{2}

, so

s = K_{s p} / α_{2} = 2.14 \times 1 0^{- 4} M

, i.e.

2.14 \times 1 0^{- 4} M