Question

The recommended concentration of chlorine in a swimming pool to keep it disinfected is 1x10⁻⁴ % by mass chlorine. Calculate the volume of a 6% by mass chlorine solution (in mL) that should be added to disinfect a pool containing 1.0x10⁴ gallons of water. (Assume the density of the water in the pool and the aqueous 6% by mass chlorine solution are approximately 1.0 g/mL each.)

Answer 1

To disinfect the swimming pool with the recommended concentration of chlorine, approximately 63.083 mL of a 6% by mass chlorine solution is required.

Step-by-step explanation:

The student wants to calculate the volume of a 6% by mass chlorine solution required to disinfect a swimming pool. To do so, we need to establish how much chlorine is needed in total and then find out the volume of the solution that will provide this quantity. The total mass of chlorine required can be calculated by using the recommended concentration (1x10⁻⁴ % by mass) and the volume of the water in the pool given in gallons (which can be converted to grams or milliliters, as the density of water is taken to be approximately 1.0 g/mL). Once we have the mass of chlorine needed, we can use the concentration of the chlorine solution (6% by mass) to find the volume of the solution.

First, we need to convert the volume of the pool from gallons to liters, and since 1 gallon is approximately 3.785 liters, the pool contains:

1.0x10⁴ gallons × 3.785 L/gallon = 3.785x10⁴ liters

Assuming the density of water is 1.0 g/mL, this is also the mass of the water in grams. The mass of chlorine needed for disinfection is:

(3.785x10⁴ L) × (1,000 mL/L) × (1.0 g/mL) × (1x10⁻⁴ %) = 3.785 g of chlorine

To find the volume of the 6% chlorine solution, we use the mass of chlorine needed and the percent by mass of the solution:

(3.785 g of chlorine) / (0.06 g chlorine/g solution) = 63.083 mL

Therefore, the student needs to add approximately 63.083 mL of a 6% by mass chlorine solution to disinfect the pool.