Question

Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is \(1 \mathrm{ppm}\) chlorine, or \(1 \mathrm{~g}\) of chlorine per million grams of water. Calculate the volume of a chlorine solution (in milliliters) a homeowner should add to her swimming pool if the solution contains 6.0 percent chlorine by mass and there are \(2.0 \times 10^{4}\) gallons (gal) of water in the pool (1 gal \(=3.79 \mathrm{~L} ;\) density of liquids \(=1.0 \mathrm{~g} / \mathrm{mL}\) ).

Short answer

The homeowner should add 1263.3 mL of chlorine solution to the pool.

Step-by-step solution

Convert Gallons to Grams of Water

First, convert the water volume in the pool from gallons to liters and then to grams. Given:* Water volume = \(2.0 \times 10^{4}\) gallons* 1 gallon \(= 3.79\) L* Density of water \(= 1.0\, \text{g/mL}\)Conversion:The volume in liters is \(2.0 \times 10^4 \text{ gal} \times 3.79 \text{ L/gal} = 7.58 \times 10^4 \text{ L}\).Since 1 L = 1000 mL and density is 1.0 g/mL, the mass of water is:\[7.58 \times 10^4 \text{ L} \times 1000 \text{ mL/L} \times 1 \text{ g/mL} = 7.58 \times 10^7 \text{ g}\].

Calculate Required Mass of Chlorine

Next, calculate the mass of chlorine required to achieve 1 ppm concentration.1 ppm is equivalent to 1 g chlorine per 1,000,000 g of water. Therefore, the chlorine needed for 7.58 million grams of water is:\[ \frac{1 \text{ g}}{1,000,000 \text{ g}} \times 7.58 \times 10^7 \text{ g} = 75.8 \text{ g chlorine} \]

Determine Mass of Chlorine Solution Needed

The chlorine solution contains 6.0 percent chlorine by mass. To find out how much solution is needed to provide 75.8 g of chlorine, use the percentage formula:\[ \text{mass of solution needed} = \frac{75.8 \text{ g chlorine}}{0.06} = 1263.3 \text{ g of solution} \]

Convert Grams of Solution to Milliliters

Convert the mass of the solution to volume in milliliters, using the density of liquids:Since the density is 1.0 g/mL, the volume in milliliters is the same as the mass in grams:\[ 1263.3 \text{ g of solution} = 1263.3 \text{ mL of solution} \]

Key concepts

Disinfection

Disinfection is a crucial process that ensures harmful microorganisms are eliminated from the water, making it safe for humans to use. Chlorine is often used for this purpose in swimming pools because it is an effective disinfectant. It works by killing bacteria, viruses, and other pathogens.
Why is chlorine so effective?
- It breaks down the cell walls of harmful microbes.
- It reacts with the proteins in the microorganisms, deactivating them.
- It remains in the water, providing continuous disinfection.
Maintaining the correct concentration of chlorine in a pool is essential. If the concentration is too low, pathogens may survive. Too high, and it could cause irritation to swimmers' eyes and skin. Therefore, careful calculations, such as the one made in the exercise, ensure the pool remains safe and enjoyable for all.

Swimming Pool Chemistry

Swimming pool chemistry might sound complex, but it's simply about balancing different chemical levels in the pool water to ensure it is safe and pleasant for swimmers. One of the key components is chlorine, used primarily for disinfection. When added to water, chlorine undergoes chemical reactions to form compounds like hypochlorous acid, which is effective in keeping the water free from germs.
Another important aspect of pool chemistry is maintaining a balanced pH, which ensures chlorine works effectively without being too harsh on swimmers. The ideal pH range is between 7.2 and 7.8. Other chemical considerations include the management of cyanuric acid levels, which helps stabilize chlorine, and calcium hardness, which affects the water’s clarity and prevents damage to pool surfaces.
Overall, swimming pool chemistry is all about monitoring and adjusting these chemical elements for a clean, safe, and comfortable swimming environment.

Solution Calculations

Solution calculations involve determining how much of a particular solution is needed to achieve a desired concentration of solute, in this case, chlorine. This process starts by understanding the concept of concentration, often expressed as parts per million (ppm) in the context of pool chemistry.
For instance, a concentration of 1 ppm means there is 1 gram of solute per million grams of solvent. The exercise demonstrated calculating mass concentration by converting gallons to grams to figure out the mass of water and then determining the required chlorine mass for 1 ppm.
The next step used the percentage concentration provided (6% chlorine in the solution) to find out the total mass of solution needed. This involved dividing the chlorine mass by the concentration ratio, providing the necessary amount of the liquid solution.
These calculations are important in real-world applications to ensure that precise chemical dosages are maintained, achieving the necessary disinfection while avoiding overuse of chemicals.

Mass and Volume Conversion

Mass and volume conversion are critical when dealing with solution preparation and chemical calculations. In the context of pool chemistry, these conversions help in determining the correct amounts of chemicals needed based on different units of measurement.
Key Conversion Steps:
- Convert gallons to liters using the conversion factor (1 gal = 3.79 L), then liters to milliliters because density calculations typically make use of milliliters.
- Convert the volume of water (in mL) to mass (in grams) using the density of water, which is typically 1 g/mL. This step is straightforward as the density of water simplifies the conversion.
- Calculate how many grams of a solution are required to achieve a given concentration of the active substance (such as chlorine).
- Lastly, translate the mass of the solution back into volume, considering that the solution's density is also 1 g/mL, making mass and volume numerically equivalent.
Understanding these conversion principles ensures accurate measurements, which is crucial for maintaining a safe and balanced swimming environment.