Final answer:
To obtain a chlorine concentration of 3.0 ppm in a 5,000 gallon pool with 21,200 kg of water, one must add 63.6 grams of chlorine.
Step-by-step explanation:
To find the mass of chlorine needed to achieve a concentration of 3.0 ppm in a 5,000 gallon pool, we need to convert the volume of water to kilograms and the desired parts per million concentration to a mass of chlorine. We are told the pool contains 21,200 kg of water. Since 1 ppm is equivalent to 1 milligram of a substance per kilogram of water, 3.0 ppm would require 3.0 milligrams of chlorine per kilogram of water.
To calculate the total mass of chlorine needed, multiply the concentration (3.0 mg/kg) by the mass of the water in the pool (21,200 kg):
Mass of chlorine = 3.0 mg/kg x 21,200 kg = 63,600 mg
To convert milligrams to grams, remember that 1 gram is equal to 1,000 milligrams:
Mass of chlorine = 63,600 mg / 1,000 = 63.6 grams
Therefore, to achieve a chlorine concentration of 3.0 ppm in a 5,000 gallon pool, you must add 63.6 grams of chlorine.