Question 17.14: Finding the Concentrations of Ions Left in Solution after Se...
Finding the Concentrations of Ions Left in Solution after Selective Precipitation
You add potassium hydroxide to the solution in Example 17.13. When the [OH^-] reaches 1.9 × 10^{-6} \ M (as you just calculated), magnesium hydroxide begins to precipitate out of solution. As you continue to add KOH, the magnesium hydroxide continues to precipitate. At some point, the [OH^-] becomes high enough to begin to precipitate the calcium ions as well. What is the concentration of Mg^{2+} when Ca^{2+} begins to precipitate?
First, calculate the OH^- concentration at which Ca^{2+} begins to precipitate by writing the expression for Q for calcium hydroxide and substituting the concentration of Ca^{2+} from Example 17.13.
\mathcal{Q}= [Ca^{2+}][OH^-]^2
= (0.011)[OH^-]^2
Set the expression for Q equal to the value of K_{sp} for calcium hydroxide and solve for . Ca(OH)_2 precipitates above this concentration.
When \mathcal{Q}=K_{sp}
(0.011)[OH^-]^2 = K_sp = 4.68 × 10^{-6}
[OH^-]^2=\frac{4.68 \times 10^{-6}}{0.011}
[OH^-] = 2.\underline{0} 6 \times 10^{-2} M
Find the concentration of Mg^{2+} when OH^- reaches the concentration you just calculated by writing the expression for Q for magnesium hydroxide and substituting the concentration of OH^- that you just calculated. Then set the expression for Q equal to the value of K_{sp} for magnesium hydroxide and solve for [Mg^{2+}]. This is the concentration of Mg^{2+} that remains when Ca(OH)_2 begins to precipitate.
\mathcal{Q}= [Mg^{2+}][OH^-]^2= [Mg^{2+}](2.\underline{0} 6 \times 10^{-2})^2
When \mathcal{Q}=K_{sp}
[Mg^{2+}](2.\underline{0} 6 \times 10^{-2})^2=K_{sp}=2.06 \times 10^{-13}
[Mg^{2+}]=\frac{2.06 \times 10^{-13}}{(2.\underline{0} 6 \times 10^{-2})^2}
[Mg^{2+}]= 4.9 \times 10^{-10} M
As you can see from the results, the selective precipitation worked very well. The concentration of Mg^{2+} dropped from 0.059 M to 4.9 \times 10^{-10} M before any calcium began to precipitate, which means that 99.99% of the magnesium separated out of the solution