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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).

User Jonas Granvik
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1 Answer

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9 votes

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


8.0*10^4tons\cdot\frac{1000\operatorname{kg}}{1ton}\cdot\frac{1000g}{1\operatorname{kg}}=8*10^(10)g

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


8*10^(10)gMg\cdot(1kgseawater)/(1.3gMg)=6.15*10^(10)kgseawater

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


6.15*10^(10)\operatorname{kg}\cdot\frac{1000g}{1\operatorname{kg}}\cdot(1ml)/(1.03g)\cdot(1l)/(1000ml)=5.97*10^(10)l

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

User Sahil Dahiya
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