15.1 Exercise 51

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:

$\text{Mg}^{\text{2}+} \left(a q\right) + \text{Ca}(\text{OH})_{2} \left(a q\right) \rightarrow \text{Mg}(\text{OH})_{2} \left(s\right) + \text{Ca}^{\text{2}+} \left(a q\right)$

$\text{Mg}(\text{OH})_{2} \left(s\right) + \text{2HCl}( a q \left.\right) \rightarrow \text{MgCl}_{2} \left(s\right) + \text{2H}_{2} \text{O} \left(l\right)$

$\text{MgCl}_{2} \left(l\right) \overset{ \text{electrolysis} }{\rightarrow} \text{Mg} \left(s\right) + \text{Cl}_{2} \left(g\right)$

Sea water has a density of 1.026 g/cm³ and contains 1272 parts per million of magnesium as Mg²⁺(aq) by mass. What mass, in kilograms, of Ca(OH)₂ is required to precipitate 99.9% of the magnesium in 1.00 $\times$ 10³ L of sea water?