Final answer:
A 21-ft by 24-ft by 4-ft swimming pool will contain about 15,080 gallons of water. To achieve a chlorine concentration of 3.0 ppm in a 5,000-gallon pool, approximately 56.78 grams of chlorine must be added.
Step-by-step explanation:
The volume of water that a swimming pool can contain is calculated by multiplying its dimensions together: length × width × height. The volume will be in cubic feet, but to determine the amount of water in gallons, we can use the conversion factor that 1 cubic foot equals approximately 7.48 gallons. Therefore, the volume of a 21-ft by 24-ft by 4-ft swimming pool is:
21 ft × 24 ft × 4 ft = 2,016 cubic feet.
Next, we convert this volume into gallons:
2,016 cubic feet × 7.48 gallons/cubic foot = 15,079.68 gallons.
Rounded to the nearest gallon, the swimming pool would contain 15,080 gallons of water.
As for the chlorine mass needed for a pool, it is crucial to maintain an appropriate concentration for safety and healthy use. For sanitary reasons, the maximum recommended chlorine level in pools is 3.0 ppm (parts per million). To calculate the mass of chlorine needed for a typical 5,000 gallon pool:
You need 3.0 grams of chlorine for every million grams of water since 1 ppm is equivalent to 1 milligram per liter (mg/L), and there are 1,000 grams in a kilogram. First, it's essential to convert 5,000 gallons of water into kilograms (since 1 gallon of water weighs approximately 3.78541 kg). Then, the calculation for the mass of chlorine is as follows:
5,000 gallons × 3.78541 kg/gallon = 18,927.05 kg
×3.0 ppm = 56.78115 grams of chlorine,
So, roughly 56.78 grams of chlorine must be added to reach a concentration of 3.0 ppm in a 5,000-gallon pool.