Question

Magnesium (Mg) is a valuable metal used in alloys, in batteries, and in chemical synthesis. It is obtained mostly from seawater, which contains about 1.3 g of Mg for every kilogram of seawater. Calculate the volume of seawater (in liters) needed to extract 8.0 x 10^4 tons of Mg, which is roughly the annual production in the United States. (rho seawater = 1.03 g/ml).

Answer 1

The first step we have to follow is to convert the given tons to grams:

$8.0\times10^4tons\cdot\frac{1000\operatorname{kg}}{1ton}\cdot\frac{1000g}{1\operatorname{kg}}=8\times10^{10}g$

Use the given ratio of grams of Mg to kg of seawater to find how much of seawater is needed:

$8\times10^{10}gMg\cdot\frac{1kgseawater}{1.3gMg}=6.15\times10^{10}kgseawater$

Use the density of seawater to find how many liters are needed:

$6.15\times10^{10}\operatorname{kg}\cdot\frac{1000g}{1\operatorname{kg}}\cdot\frac{1ml}{1.03g}\cdot\frac{1l}{1000ml}=5.97\times10^{10}l$

5.97x10^10 liters are needed to extract that amount of Mg.