Chapter 15, Problem 51E

Magnesium metal (a component of alloys used in aircraft and a reducing agent used in the production of uranium, titanium, and other active metals) is isolated from sea water by the following sequence of reactions:

$\begin{array}{l}{\text{Mg}}^{2+}\left(aq\right)+\text{Ca}{\left(\text{OH}\right)}_2\left(aq\right)\to \text{Mg}{\left(\text{OH}\right)}_2\left(s\right)+{\text{Ca}}^{2+}\left(aq\right)\\ \text{Mg}{\left(\text{OH}\right)}_2\left(s\right)+2\text{HCl}\left(aq\right)\to {\text{MgCl}}_2\left(s\right)+2{\text{H}}_2\text{O}\left(l\right)\\ {\text{MgCl}}_2\left(l\right)\stackrel{e\text{lectrolysis}}{\to }\text{Mg}\left(s\right)+{\text{Cl}}_2+{\text{Cl}}_2\left(g\right)\end{array}$

Sea water has a density of 1.026 g/cm³ and contains 1272 parts per million of magnesium a5 Mg²⁺(aq) by mass. What mass, in kilograms, of Ca(OH)₂; is required to precipitate 99.9% of the magnesium in $1.00\times {10}^3$ L of sea water?