Final answer:
To chlorinate a 5,000-gallon pool to a concentration of 3.0 ppm, 0.0636 kg of chlorine needs to be added, which is the mass calculated by multiplying the concentration in ppm by the mass of water in the pool in kilograms.
Step-by-step explanation:
The question focuses on understanding the concept of concentration in a solution and how it relates to the mass of solute that must be added to achieve a certain concentration level. In the case of a swimming pool requiring chlorination, to reach the specified maximum of 3.0 ppm (parts per million) in a 5,000-gallon pool, which is equivalent to 21,200 kg of water, we must calculate the mass of chlorine needed. One part per million (ppm) is the same as one milligram of solute per kilogram of solution. Therefore, to find the mass of chlorine to add to the pool, we multiply the desired concentration (3.0 ppm) by the mass of the water (21,200 kg).
3.0 ppm means we need 3.0 mg of chlorine per kg of water. Thus, the mass of chlorine required is 3.0 mg/kg × 21,200 kg = 63,600 mg, or 63.6 g since there are 1,000 mg in a gram. As a result, to achieve a concentration of 3.0 ppm in the pool, 0.0636 kg of chlorine must be added.