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Chapter 1: Problem 81

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?

Short Answer

Expert verified
To workout the amount of sodium hypochlorite that needs to be added to the water supply per week in order to achieve a chlorine level of 1 ppm, follow the above steps in order: Work out the total amount of water consumed per week (from Step 1), then determine the amount of chlorine needed based on this consumption (Step 2), and finally calculate the amount of sodium hypochlorite required to produce this quantity of chlorine (Step 3).

Step by step solution

01

Calculate the total amount of water consumed in a week

First, we calculate the total amount of water consumed by the population in a week. This is done by multiplying the water consumption per day per person (750 L) by the number of persons (1.8 million) and by the number of days in a week (7). So, the calculation is \( 750 \, \text{L/person/day} \times 1,800,000 \, \text{persons} \times 7 \, \text{days/week} \).
02

Determine the amount of chlorine needed

We need to find out how much chlorine is needed for the water consumption. As 1 kilogram of chlorine is introduced per million kilograms of water, we can calculate this by dividing the weekly water consumption in kilogram (since 1 liter is approximately equal to 1 kilogram) by one million and taking this amount as the amount in kilograms of chlorine. Therefore, the calculation is \( \text{Total water consumption from Step 1} \, \text{kg} / 1,000,000 \, \text{kg of water for each kg of chlorine}\).
03

Calculate the amount of sodium hypochlorite required

Lastly, calculate how much sodium hypochlorite is needed to get the amount of chlorine from Step 2. We know that sodium hypochlorite is 47.62% chlorine, so we divide the chlorine needed (from Step 2) by 47.62%. Thus, the calculation is \( \text{Chlorine needed from Step 2} \, / \, 0.4762 \, \text{ (representing the 47.62% in decimal form) } \). This gives the answer in kilograms of sodium hypochlorite.

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