Magnesium (mg) is a valuable metal used in alloys, in batteries, and in the manufacture of chemicals. it is obtained mostly from seawater, which contains about 1.3 g of mg for every kilogram of seawater. referring to problem 1.87, 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.

6.0 × 10¹⁰ L

Explanation:

We know that 1 ton = 10⁶ g. 8.0 × 10⁴ tons of Mg are:

8.0 × 10⁴ ton × (10⁶ g/ 1 ton) = 8.0 × 10¹⁰ g

There is about 1.3 g of Mg for every kilogram of seawater. The mass of seawater that contains 8.0 × 10¹⁰ grams of Mg is:

8.0 × 10¹⁰ g Mg × (1 kg seawater/ 1.3 g Mg) = 6.2 × 10¹⁰ kg seawater

The average density of seawater is 1.025 kg/L. The volume corresponding to 6.2 × 10¹⁰ kg is:

6.2 × 10¹⁰ kg × (1 L/ 1.025 kg) = 6.0 × 10¹⁰ L

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