You are working on a project to recycle nickel and cadmium from old nickel-cadmium batteries. The batteries are dissolved in aqueous nitric acid, producing a solution containing primarily Ni²⁺, Cd²⁺, and Fe³⁺ cations and associated anions. The iron comes from the casing. One idea is to concentrate the solution by evaporation using solar energy, and then add sodium hydroxide to neutralize the acid and cause precipitation of Ni(OH)₂, Cd(OH)₂, and Fe(OH)₃. For simplicity, assume the concentration of each of the cations is 0.100 M before the sodium hydroxide is added. The pH increases as the sodium hydroxide is added. Your task is to identify the compound that will precipitate first, and determine the pH at that point. You report that the ________ hydroxide will precipitate first, and that the pH at that point will be ________ $$\begin{array} { c c } \text { Cmpd } & \boldsymbol { K } _ { \text {sp } } \ \mathrm { Ni } ( \mathrm { OH } ) _ { 2 } & 2.8 \times 10 ^ { - 16 } \ \mathrm { Cd } ( \mathrm { OH } ) _ { 2 } & 1.2 \times 10 ^ { - 14 } \ \mathrm { Fe } ( \mathrm { OH } ) _ { 3 } & 6.3 \times 10 ^ { - 38 } \end{array}$$

Question

Quizplus · Accepted Answer

Fe(OH)₃ has the smallest Ksp value, indicating it will precipitate first. The pH at which Fe(OH)₃ begins to precipitate can be calculated using the Ksp expression: [Fe³⁺][OH⁻]³ = 6.3 × 10⁻³⁸. Solving for [OH⁻] when [Fe³⁺] = 0.1 M gives [OH⁻] = 1.78 × 10⁻¹² M, corresponding to a pH of approximately 1.9.

You Are Working on a Project to Recycle Nickel and Cadmium