Final answer:
To reach a chlorine concentration of 3.0 ppm in a pool containing 21,200 kg of water, 56.78115 grams of chlorine need to be added.
Step-by-step explanation:
To calculate the mass of chlorine needed to achieve a concentration of 3.0 ppm in a 5,000-gallon pool, we use the equation for concentration:
concentration (ppm) = (mass of solute in mg) / (volume of solution in L). Here, we need to achieve 3.0 ppm of chlorine in a pool containing 21,200 kg (or 21,200,000 g) of water, since 1 gallon equals approximately 3.78541 liters.
Firstly, convert the desired ppm concentration to milligrams:
3.0 ppm = 3.0 mg of Cl per liter of water.
The total volume of the pool in liters is:
5,000 gallons * 3.78541 L/gallon = 18,927.05 L.
Using the concentration equation:
3.0 mg/L * 18,927.05 L = 56,781.15 mg of Cl.
Convert milligrams to grams (since there are 1,000 mg in a gram):
56,781.15 mg = 56.78115 g.
Therefore, 56.78115 grams of chlorine must be added to the pool to achieve the desired concentration of 3.0 ppm.