Magnesium is commonly extracted from seawater. Assume that there are 1.38 grams of magnesium per kilogram of seawater, and that the density of seawater is 1.029 grams per milliliter. How many cubic meters of seawater are needed to obtain 6.80 teragrams of magnesium.
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First change the density of seawater to kilograms. 1.029 g/ml (1kg/1000g)= .001029 kg/ml. Now change the density of magnesium in water to kilograms 1.38 g/kg (1kg/1000g)= .00138kg magnesium/ kg water. Now multiply the density of seawater by the density of magnesium. .001029 kg of water/ml of water times .00138 kg of magnesium/kg of water. The kg of water cancel out because of the same factor being in the numerator and denominator. This leaves you with .00000142002 kg of magnesium/ml of water. Now just change mililiters to meters. Cubic meters are the milliliter divided by 1 million. .00000142002 kg/ml (1 cubic meter/ 1000000 ml)= 1.42 002 times 10 to the -12 power kg magnesium/ cubic meter water. Divide the 6.8 teragrams of magnesium by the previous number for the density of magnesium in water. The number will be your answer and the units will turn into cubic meters. 6.8/(1.42002 * 10^-12)= 4.79 * 10^12 cubic meters.
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