Question

Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine or \(1 \mathrm{~g}\) of chlorine per million \(\mathrm{g}\) 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 \(2 \times 10^{4}\) gallons of water in the pool. (1 gallon \(=3.79 \mathrm{~L}\); density of liquids \(=1.0 \mathrm{~g} / \mathrm{mL} .)\)

Short answer

By carrying out the aforementioned calculations, the required volume of the chlorine solution will be obtained.

Step-by-step solution

Convert volume of water to grams

Convert the volume of the water in the swimming pool from gallons to liters, and then from liters to grams. Use the given conversions: \(1 \)gallon \(=3.79 \) L and the density of liquid \( = 1.0 \mathrm{~g} / \mathrm{mL} \). So the weight of water in the pool is \(2 \times 10^{4}\) gallons \( \times 3.79 \mathrm{~L/gal} \times 1000 \mathrm{~g/L} \).

Calculate mass of chlorine needed

Calculate the mass of chlorine needed by considering the concentration requirement of 1ppm (1g of chlorine per million g of water). Therefore, the weight of chlorine needed = \( \frac{1}{10^6} \times \) weight of water in pool.

Find the volume of chlorine solution needed

The solution contains 6.0 percent chlorine by mass. This means that 100g of solution contains 6g of chlorine. Therefore, the volume of chlorine solution needed = \( \frac{\text{Mass of chlorine needed}}{0.06}*1 \mathrm{mL/g} \)

Key concepts

Stoichiometry

Stoichiometry is the aspect of chemistry that concerns the calculation of the quantities of reactants and products involved in chemical reactions. It is based on the conservation of mass where the total mass of reactants equals the total mass of products. In our case, stoichiometry helps us understand the relationship between the mass of chlorine required to achieve the desired concentration in the swimming pool and the mass of the chlorine solution to be added.

When we talk about a 1 ppm concentration, we are saying that for every million parts (by mass) of water, there should be one part (by mass) of chlorine. Stoichiometry enables us to translate this information into a concrete amount of substance, taking into account the mass percentages of the solution and the actual volume of the pool.

Concentration Calculations

Concentration is a measure of how much of a given substance is contained within a certain volume or mass of a solution. It can be expressed in many different ways, such as mass per volume, molarity, or percent concentration. For example, a 6.0 percent chlorine solution indicates that there are 6.0 grams of chlorine in every 100 grams of the solution.

To ensure safety and effectiveness, the accurate calculation of the concentration of chlorine in pool water is essential. By using the concept of ppm, we base our calculations on the mass of the substance, which allows us to use stoichiometry to determine the actual amount of chlorine solution needed.

Unit Conversion

Unit conversion is essential in stoichiometry and concentration calculations because it allows us to translate different measurements into a common unit for easy computation. In the given problem, we have to convert gallons to liters and then to grams, using the provided conversion factors and the assumption of density.

Understanding unit conversion enables us to navigate between the imperial system (gallons) and the metric system (liters and grams). The conversion of the given volume of pool water from gallons to grams is a critical step because it aligns the units with the desired ppm concentration units, facilitating the subsequent stoichiometry process.

Percent Concentration

Percent concentration is a way of expressing the ratio of solute to solution mass, and it plays a crucial role in determining the volume of a solution needed for a particular purpose. It is commonly used in the preparation of chemical solutions where accuracy is paramount.

In our exercise, the percent concentration helps us to understand that in a 6.0 percent chlorine solution, every hundred grams of the solution contain 6 grams of pure chlorine. Knowing this, we can calculate the volume of the chlorine solution that must be added to the pool to reach the target concentration of 1 ppm. It is the fundamental link between the desired concentration in the pool and the concentration of the chlorine solution available to the homeowner.