Question

The Greater Vancouver Regional District (GVRD) chlorinates the water supply of the region at the rate of 1 ppm, that is, 1 kilogram of chlorine per million kilograms of water. The chlorine is introduced in the form of sodium hypochlorite, which is 47.62% chlorine. The population of the GVRD is 1.8 million persons. If each person uses 750 L of water per day, how many kilograms of sodium hypochlorite must be added to the water supply each week to produce the required chlorine level of 1 ppm?

Answer 1

Answer:

2835 kilograms of sodium hypochlorite must be added to the water supply each week to produce the required chlorine level of 1 ppm.

Explanation:

Volume of water used by 1 person =  750 L

Volume of water used by 1.8 million persons : V

$V=1.8\times 10^6\times 750 L=1.35\times 10^{9} L$

Density of water,d = 1 kg/L

Mass of water used by 1.8 million persons =  m

$m=d\times V=1 kg/L\times 1.35\times 10^{9} L=1.35\times 10^{9} kg$

1 kilogram of chlorine per million kilograms of water. (Given)

Concentration of chlorine in water = 1 kg/ 1000,000 kg of water

In 1000,000 kg of water = 1 kg of chlorine

Then $1.35\times 10^{9} kg$ of water have x mass of chlorine:

$\frac{x}{1.35\times 10^{9} \text{kg of water}}=\frac{1 kg}{1000,000 \text{kg of water}}$

$x=\frac{1}{1000,000}\times 1.35\times 10^{9} kg=1.35\times 10^3 kg$

Mass of chlorine in water of mass $1.35\times 10^{9} kg=1.35\times 10^{3} kg$  

Percentage of chlorine in hypochlorite = 47.62%

$47.62\%=\frac{1.35\times 10^{3} kg}{\text{Total mass of sodium hypochlorite}}\times 100$

Total mass of sodium  hypochlorite = $2834.94 kg\approx 2835 kg$

2835 kilograms of sodium hypochlorite must be added to the water supply each week to produce the required chlorine level of 1 ppm.