Question

Chlorine is used to disinfect swimming pools. the accepted concentration for this purpose is 1.00 ppm chlorine, or 1.00 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 9.00 percent chlorine by mass and there are 2.29 × 104 gallons (gal) of water in the pool (1 gal = 3.79 l; density of liquids = 1.00 g/ml). enter your answer in scientific notation.

Answer 1

The accepted concentration of chlorine is 1.00 ppm that is 1 gram of chlorine per million of water.

The volume of water is $2.29\times 10^{4} gal$.

Since, 1 gal= 3785.41 mL

Thus, $2.29\times 10^{4} gal=2.29\times 10^{4}\times 3785.41 mL=8.66\times 10^{7}mL$

Density of water is 1 g/mL thus, mass of water will be $8.66\times 10^{7}g$.

Since, 1 grams of chlorine →$10^{6}$ grams of water.

1 g of water →$10^{-6}$ g of chlorine and,

$8.66\times 10^{7}g$ of water →86.6 g of chlorine

Since, the solution is 9% chlorine by mass, the volume of solution will be:

$V=\frac{100}{9}\times 86.6 mL=9.62\times 10^{2} mL$

Thus, volume of chlorine solution is 9.62\times 10^{2} mL.