Base is added slowly to a solution that is 1.0x10^-3 M in each of Fe^3+ and Al^3+. Take K_sp[Fe(OH)3] = 1.0x10^-38 and K_sp[Al(OH)3] = 3.0x10^-34. Which hydroxide precipitates first and at approximately what pH does it begin?

Fe(OH)3 at pH approx 2.33 (Al(OH)3 only from pH approx 3.83)

both together at pH approx 2.33

JEE Advanced levelSingle correct optionDifficulty 3 of 3qc090

Base is added slowly to a solution that is $1.0 \times 1 0^{- 3} M$ in each of $Fe X^{3 +}$ and $Al X^{3 +}$ . Take $K_{s p} [Fe (OH) X_{3}] = 1.0 \times 1 0^{- 38}$ and $K_{s p} [Al (OH) X_{3}] = 3.0 \times 1 0^{- 34}$ . Which hydroxide precipitates first and at approximately what pH does it begin?

A $Fe (OH) X_{3}$ at pH $\approx 2.33$ ( $Al (OH) X_{3}$ only from pH $\approx 3.83$ )
B $Al (OH) X_{3}$ at pH $\approx 2.33$
C $Fe (OH) X_{3}$ at pH $\approx 3.83$
Dboth together at pH $\approx 2.33$

[OH X^{-}]_{F e} = (1 0^{- 38} /1 0^{- 3})^{1/3} = 2.15 \times 1 0^{- 12}

, so pOH

= 11.67

and pH

= 2.33

[OH X^{-}]_{A l} = (3 \times 1 0^{- 34} /1 0^{- 3})^{1/3} = 6.69 \times 1 0^{- 11}

, so pH

= 3.83

. The smaller

K_{s p}

gives a lower precipitation pH, so iron precipitates first.