Magnesium metal (a component of alloys used in aircraft and...

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: $\mathrm{Mg}^{2+}(a q)+\mathrm{Ca}(\mathrm{OH})_{2}(a q) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)+\mathrm{Ca}^{2+}(a q)$ $\mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{MgCl}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)$ $\mathrm{MgCl}_{2}(l) \stackrel{\text { electrolysis }}{\longrightarrow} \mathrm{Mg}(s)+\mathrm{Cl}_{2}(g)$ Sea water has a density of 1.026 $\mathrm{g} / \mathrm{cm}^{3}$ and contains 1272 parts per million of magnesium as $\mathrm{Mg}^{2+}(a q)$ by mass. What mass, in kilograms, of $\mathrm{Ca}(\mathrm{OH})_{2}$ is required to precipitate 99.9$\%$ of the magnesium in $1.00 \times 10^{3} \mathrm{L}$ of sea water?

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:
$\mathrm{Mg}^{2+}(a q)+\mathrm{Ca}(\mathrm{OH})_{2}(a q) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)+\mathrm{Ca}^{2+}(a q)$
$\mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{MgCl}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)$
$\mathrm{MgCl}_{2}(l) \stackrel{\text { electrolysis }}{\longrightarrow} \mathrm{Mg}(s)+\mathrm{Cl}_{2}(g)$
Sea water has a density of 1.026 $\mathrm{g} / \mathrm{cm}^{3}$ and contains 1272 parts per million of magnesium as $\mathrm{Mg}^{2+}(a q)$ by mass. What mass, in kilograms, of $\mathrm{Ca}(\mathrm{OH})_{2}$ is required to precipitate 99.9$\%$ of the magnesium in $1.00 \times 10^{3} \mathrm{L}$ of sea water?

Key Concepts

Reaction Stoichiometry

This concept involves using a balanced chemical equation to relate the quantities of reactants and products. It is essential for determining how much of one reactant is needed based on the amount of another, in this case, calculating how much Ca(OH)? is required to precipitate a given amount of Mg²? ions according to the stoichiometry of the precipitation reaction.

Precipitation Reaction

A precipitation reaction occurs when two aqueous solutions react to form an insoluble solid. In this context, Mg²? ions react with Ca(OH)? to form insoluble Mg(OH)?, causing magnesium to be removed from the solution. Understanding this process is crucial for determining the amount of reagent needed to achieve nearly complete precipitation of magnesium.

Parts Per Million (ppm) Concept

Parts per million is a measure of concentration that denotes the mass of a solute per one million units of total mass. In this problem, it is used to express the concentration of magnesium in sea water. Converting ppm to a mass fraction enables the calculation of the total amount of magnesium present in a given volume of water.

Density and Volume Conversion

The density of a solution allows the conversion between volume and mass. Here, knowing the density of sea water is essential for finding the total mass of water in a given volume, which then aids in determining the total mass of magnesium ions present based on their ppm concentration.

Molar Mass and Conversion Factors

Molar mass is used to convert between the mass of a substance and the number of moles, an important step in stoichiometric calculations. In this problem, converting the mass of magnesium and Ca(OH)? to moles (and vice versa) is necessary to relate the measured concentration of magnesium to the required mass of Ca(OH)? through the balanced chemical equation.

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