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?

Short answer

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

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 \( 750 \, \text{L/person/day} \times 1,800,000 \, \text{persons} \times 7 \, \text{days/week} \).

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 \( \text{Total water consumption from Step 1} \, \text{kg} / 1,000,000 \, \text{kg of water for each kg of chlorine}\).

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.

Key concepts

Water Treatment

Water treatment is essential for ensuring that the water we consume and use daily is safe and free from harmful contaminants. Chlorination is a common method used in water treatment processes. By adding chlorine or chlorine compounds like sodium hypochlorite, we can disinfect water. This process eliminates bacteria, viruses, and other pathogens that can cause diseases.

In places like the Greater Vancouver Regional District, maintaining a specific chlorine concentration, such as 1 ppm (part per million), is crucial for public health. The careful calculation of chlorine levels ensures that the water is safe to drink while avoiding excessive amounts that could lead to unpleasant tastes or potential health issues.

• Chlorination is effective and widely used due to its ability to kill microorganisms quickly.
• It is a cost-effective method that can be easily managed and monitored.
• Maintains water safety in a continuous supply system.

Sodium Hypochlorite

Sodium hypochlorite is a chlorine compound used extensively in water treatment. It is preferred due to its ability to disinfect water efficiently while being easy to handle compared to gaseous chlorine. Sodium hypochlorite, commonly found in household bleach, comprises 47.62% chlorine by weight. In the context of water chlorination, it is essential to calculate the exact amount of sodium hypochlorite needed to achieve the desired chlorine concentration.

For instance, if you need to achieve 1 ppm chlorine concentration in the water supply, you have to account for the portion of sodium hypochlorite that is chlorine. This is why the calculation involves multiplying the desired chlorine amount by the inverse of its percentage in sodium hypochlorite.

• 47.62% composition indicates nearly half of its weight contributes to available chlorine content.
• Preferred for its stability and lower handling risks compared to chlorine gas.
• Easily integrates into water treatment systems without special equipment.

Chemical Calculations

Chemical calculations play a vital role in determining the proper quantities of chemicals like sodium hypochlorite needed for effective water treatment. The calculations ensure that the water supply maintains the required levels of disinfectant, keeping it safe for consumption.

When performing chemical calculations, it is important to consider the relationship between the concentration and volume of the water. The calculation involves determining the total water volume used by the population, translating this into a mass (since water has a density of approximately 1 kg/L), and then calculating the required mass of chlorine.

Finally, we use the percentage composition of chlorine in sodium hypochlorite to find the actual amount needed.

• Understand the concept of ppm: Parts per million is a concentration metric indicating mg/L.
• Convert volumes to mass: Useful when dealing with aqueous solutions.
• Use percentage by weight: Knowing the percentage allows precise quantification of the effective chemical component.