Question

Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine, or 1 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 × 104 gallons of water in the pool. (1 gallon = 3.79 L; density of liquids = 1.0 g/mL.) Chang, Raymond. Chemistry (p. 34). McGraw-Hill Higher Education. Kindle Edition.

Answer 1

Answer:

1300 mL

Explanation:

First, we will calculate the grams of water in the pool:

(2.0 x 10⁴ gal)(3.79 L / 1 gal)(1000 mL / 1L)(1.0 g/mL) = 7.58 x 10⁷ g

Now we can relate that value to the desired concentration of chlorine in order to find the amount of chlorine we need:

(1 g chlorine / 10⁶ g water) (7.58 x 10⁷ g water) = 75.8 g chlorine

The chlorine solution is 6.0% chlorine by mass. We will designate x to be the mass of the solution that contains 75.8 g of chlorine:

(0.06)x = 75.8 g

x = 1263.3 g of solution

The density of liquids is 1.0 g/mL, so the volume of solution required, to the correct number of significant figures, is:

(1263.3 g)(1.0 mL/g) = 1300 mL