Question

Magnesium is used in lightweight alloys for airplane bodies and other structures. The metal is obtained from seawater in a process that includes precipitation, neutralization, evaporation, and electrolysis. How many kilograms of magnesium can be obtained from 1.00 km³ of seawater if the initial Mg²⁺ concentration is 0.13% by mass (dof seawater = 1.04 g/mL)?

Short answer

The mass of magnesium is 1.35x10⁹ kg.

Step-by-step solution

Determination of volume of sea water.

Let us take 100 g sea water, the mass of Mg⁺² will be 0.13 g

The volume of sea water containing 0.13 g Mg⁺² is,

$$\begin{gathered} \mathbf{Volume}\mathbf{=}\frac{\mathbf{mass}\mathbf{}\mathbf{of}\mathbf{}\mathbf{sea}\mathbf{}\mathbf{water}}{\mathbf{density}\mathbf{}\mathbf{of}\mathbf{}\mathbf{sea}\mathbf{}\mathbf{water}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{100}\mathbf{g}}{\mathbf{1}\mathbf{.}\mathbf{04}\mathbf{g}\mathbf{/}\mathbf{mL}} \end{gathered}$$

The given volume for is 1 km³. Conversion of given volume into mL is,

$\mathbf{1}{\mathbf{km}}^{\mathbf{3}}\mathbf{\times }\left(\frac{{10}^{3}m}{1\mathrm{km}}\right)\mathbf{\times }\left(\frac{{10}^2{\mathrm{cm}}^3}{1m}\right)\mathbf{\times }\left(\frac{1\mathrm{ml}}{1{\mathrm{cm}}^3}\right)\mathbf{=}{\mathbf{10}}^{\mathbf{15}}\mathbf{mL}$

Determination of mass of magnesium

The mass of magnesium that can be obtained from 10¹⁵mL of sea water is,

$$\begin{gathered} \mathbf{Mass}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{Mg}}^{\mathbf{+}\mathbf{2}}\mathbf{=}{\mathbf{10}}^{\mathbf{15}}\mathbf{mL}\mathbf{\times }\frac{\mathbf{0}\mathbf{.}\mathbf{13}{\mathbf{gMg}}^{\mathbf{2}\mathbf{+}}}{\mathbf{96}\mathbf{.}\mathbf{15}\mathbf{mL}\mathbf{}\mathbf{sea}\mathbf{}\mathbf{water}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{35}\mathbf{\times }{\mathbf{10}}^{\mathbf{12}}\mathbf{g} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{35}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{kg} \end{gathered}$$

Thus, the mass of magnesium is 1.35x10⁹ kg.