Solid Fe(OH)_{3} is added to distilled water and allowed to reach equilibrium. At that time, [Fe^{3+}]_{aq}= 4 x 10^{-10} M. Calculate the K_{sp} of Fe(OH)_{3}.

a) 4 x 10^{-10}

b) 4.8 x 10^{-19}

c) 6.9 x 10^{-37}

d) cannot be determined without knowing the [OH^{–}] concentration

**Explanation**

The solubility product, K_{sp}, is given by the product of the equilibrium concentrations of the dissociated ions [A]_{a }+ [B]_{b} in the form K_{sp}= [A]^{a}[B]^{b}. In this case, FeOH_{3} dissociates to [Fe^{3+}]_{aq} and 3[OH^{–}]_{aq}. Even though we are not given the concentration of OH^{–}, we know that it must be three times the concentration of Fe^{3+}, since one Fe(OH)_{3} molecule dissociates into one iron cation and three OH^{–} anions.

Therefore, the solubility product K_{sp }= [Fe^{3+}]^{1}[OH^{–}]^{3 }= [Fe^{3+}]^{1}{3[Fe^{3+}]}^{3}

The math works out to (4 x 10^{-10}) x (27 x 64 x 10^{-30}), and only the correct choice c) is close enough.

a) 4 x 10^{-10}, incorrect, This answer disregards the [OH^{–}] concentration.

b) 4.8 x 10^{-19}, incorrect, This answer disregards the power of 3 on the [OH^{–}] ion.

c) 6.9 x 10^{-37}, correct.

d) cannot be determined without knowing the [OH^{–}] concentration, incorrect, The [OH^{–}] concentration is known by the multiplying the given [Fe^{3+}] concentration by 3.

How did you know the OH concentration from just dissociated Fe3+??

https://nextsteptestprep.com/2014/07/10/mcat-chemistry-question-solubility-product/?inf_contact_key=2ff194ebb4b8e0769e089d7b0d66ac65a27479f3d892164a4c843fc49c2e661d

The question mentions “dissociated FeOH3,” so we can assume that we have solid FeOH3 in solution, and a small amount of it has dissolved. This would produce a saturated solution at equilibrium. In that case, since FeOH3 dissociates into Fe3+ and 3 OH-, the concentration of OH- in solution should be three times that of Fe3+. Since the concentration of Fe3+ is 4 x 10^-10, the concentration of OH- must be 12 x 10^-10 (or 1.2 x 10^-9). Plugging in this value results in the correct answer.

The explanation did explain this math in a way that does seem somewhat unclear, though, so I have updated both the question stem and the explanation to clear up this confusion. Let us know anytime if you have additional questions!