Final answer:
To chlorinate a 5,000-gallon pool to 3.0 ppm, you need to add 63.6 g of chlorine, which results from converting the water volume into liters and using the formula ppm = mass of solute (mg)/volume of solution (L).
Step-by-step explanation:
To calculate the amount of chlorine needed to achieve a concentration of 3.0 ppm in a 5,000 gallon pool, we must first convert the volume of water to the same units used for ppm concentration, which is typically mg/L. Given that the pool contains 21,200 kg of water, we know that 1 kg of water is equivalent to 1 L, thus the pool has 21,200 L of water.
To find the mass of chlorine required, we use the formula for parts per million (ppm): ppm = mass of solute (mg) / volume of solution (L). Therefore, for a concentration of 3.0 ppm:
3.0 = mass of chlorine (mg) / 21,200 L
Multiplying both sides by the volume of solution gives us the mass of chlorine needed:
mass of chlorine = 3.0 mg/L * 21,200 L = 63,600 mg, or 63.6 g of chlorine.
This is the amount of chlorine that must be added to the 5,000 gallon pool to achieve the desired concentration of 3.0 ppm.