Question 17.13: Finding the Minimum Required Reagent Concentration for Selec...
Finding the Minimum Required Reagent Concentration for Selective Precipitation
The magnesium and calcium ions present in seawater ([Mg^{2+}] = 0.059 M and [Ca^{2+}] = 0.011 M) can be separated by selective precipitation with KOH. What minimum [OH^-] triggers the precipitation of the Mg^{2+} ion?
The precipitation commences when the value of Q for the precipitating compound just equals the value of K_{sp}. Set the expression for Q for magnesium hydroxide equal to the value of K_{sp}, and solve for [OH^-]. This is the concentration above which Mg(OH)_2 precipitates.
\mathcal{Q}= [Mg^{2+}][OH^-]^2
= (0.059)[OH^-]
When \mathcal{Q} = K_{sp},
(0.059)[OH^-]^2 = K_{sp} = 2.06 \times 10^{-13}
[OH^-]^2=\frac{2.06 \times 10^{-13}}{0.059}
[OH^-] = 1.9 \times 10^{-6} \ M