A solution contains Fe^3+ and 0.30 M Mg^2+. NaOH is added slowly. Take Fe^3+ as completely removed when its concentration falls to 1.0 x 10^-6 M. With K_sp(Fe(OH)3) = 1.0 x 10^-38, K_sp(Mg(OH)2) = 5.0 x 10^-12 and K_w = 1.0 x 10^-14, find the width of the pH window (in pH units, two decimals) between complete removal of Fe^3+ and the start of precipitation of Mg(OH)2.

JEE Advanced levelNumerical answerDifficulty 3 of 3ia071

A solution contains $Fe X^{3 +}$ and $0.30 M$ $Mg X^{2 +}$ . $NaOH$ is added slowly. Take $Fe X^{3 +}$ as completely removed when its concentration falls to $1.0 \times 1 0^{- 6} M$ . With $K_{s p} (Fe (OH) X_{3}) = 1.0 \times 1 0^{- 38}$ , $K_{s p} (Mg (OH) X_{2}) = 5.0 \times 1 0^{- 12}$ and $K_{w} = 1.0 \times 1 0^{- 14}$ , find the width of the pH window (in pH units, two decimals) between complete removal of $Fe X^{3 +}$ and the start of precipitation of $Mg (OH) X_{2}$ .

Numerical answer type, answer in pH units, tolerance 0.01.

Complete removal of iron:

[OH X^{-}] = (1 0^{- 38} /1 0^{- 6})^{1/3}

, pH = 3.333. Start of

Mg (OH) X_{2}

[OH X^{-}] = 5.0 \times 1 0^{- 12} /0.30

, pH = 8.611. Width = 8.611 - 3.333 = 5.28.