Problem 96 - Chemistry and Chemical Reactivity

Question

The fluoridation of city water supplies has been practiced in the United States for several decades. It is done by continuously adding sodium fluoride to water as it comes from a reservoir. Assume you live in a medium-sized city of 150,000 people and that \(660 \mathrm{L}(170 \mathrm{gal})\) of water is consumed per person per day. What mass of sodium fluoride (in kilograms) must be added to the water supply each year (365 days) to have the required fluoride concentration of 1 ppm (part per million)-that is, 1 kilogram of fluoride per 1 million kilograms of water? (Sodium fluoride is \(45.0 \%\) fluoride, and water has a density of \(1.00 \mathrm{g} / \mathrm{cm}^{3} .\) )

Step-by-Step Solution

Answer

80,300 kilograms of sodium fluoride is needed annually.

Step 1: Calculate Total Water Consumption

First, determine the total amount of water consumed by 150,000 people in one year. Each person consumes 660 L per day.\[ \text{Total Water Consumption per Day} = 150,000 \times 660 \, \text{L/day} = 99,000,000 \, \text{L/day} \]Since there are 365 days in a year:\[ \text{Total Water Consumption per Year} = 99,000,000 \, \text{L/day} \times 365 \, \text{days} = 36,135,000,000 \, \text{L/year} \]

Step 2: Convert Water Volume to Mass

We need to calculate the mass of this volume of water. Given that the density of water is 1.00 g/cm³, we can convert liters to kilograms because 1 liter of water equals 1 kg.\[ \text{Mass of Water} = 36,135,000,000 \, \text{kg} \]

Step 3: Determine Mass of Fluoride Needed

We need to find out how much fluoride is required for a concentration of 1 ppm. For 1 ppm:\[ \text{1 ppm} = \frac{1 \, \text{kg of fluoride}}{1,000,000 \, \text{kg of water}} \]Calculate the fluoride needed:\[ \text{Fluoride Needed} = \frac{36,135,000,000 \, \text{kg of water}}{1,000,000} \times 1 \, \text{kg of fluoride} = 36,135 \, \text{kg of fluoride} \]

Step 4: Calculate Mass of Sodium Fluoride Required

Since sodium fluoride (NaF) is only 45.0% fluoride, we need more sodium fluoride to obtain the necessary amount of fluoride. The mass of sodium fluoride required is calculated as follows:\[ \text{Sodium Fluoride Required} = \frac{36,135 \, \text{kg of fluoride}}{0.45} = 80,300 \, \text{kg of sodium fluoride} \]

Step 5: Conclusion

Therefore, 80,300 kilograms of sodium fluoride must be added to the water supply each year to achieve a fluoride concentration of 1 ppm.

Key Concepts

sodium fluoride

Sodium fluoride is a chemical compound that plays a crucial role in the fluoridation of drinking water. It is often represented by its chemical formula, NaF. This compound is chosen for water treatment because it effectively provides fluoride ions that help in reducing dental caries or tooth decay.
In its pure form, sodium fluoride is a colorless solid, and it's highly soluble in water. The importance of using sodium fluoride in water treatment lies in its ability to release fluoride ions when dissolved, which is essential for dental health.
In the context of the exercise, sodium fluoride is used to achieve a specific fluoride concentration in the water supply. Since sodium fluoride is only 45.0% fluoride by mass, we need to calculate the total mass of sodium fluoride required to ensure the desired amount of fluoride is provided. This consideration is essential for precise chemical calculations in water treatment processes.

parts per million (ppm)

Parts per million, abbreviated as ppm, is a unit of measurement used to denote very dilute concentrations of substances. In the fluoridation of water, ppm is particularly significant because it allows us to measure the concentration of fluoride with a high degree of accuracy.
1 ppm is the equivalent of 1 milligram of a substance per liter of water, which also translates to 1 kilogram of fluoride per 1,000,000 kilograms of water. This measurement is crucial when ensuring safe levels of a substance, like fluoride, are present in drinking water.
Understanding ppm is necessary for accurately determining the right levels of chemicals added to the water supply. This ensures that the concentrations are both safe for human consumption and effective for preventing tooth decay. Fluoride levels in drinking water are often maintained at around 1 ppm, as seen in the exercise, to balance efficacy and safety.

water treatment

Water treatment refers to the process of improving the quality of water to make it suitable for a specific end-use such as drinking, industrial water supply, or irrigation. In terms of fluoridation, water treatment involves adding sodium fluoride to achieve a target fluoride concentration.
Fluoridation is an integral part of water treatment in many communities. It involves controlled addition of fluoride to prevent dental cavities across populations. The exercise shows a practical application of this process by calculating the quantity of sodium fluoride needed to maintain the fluoride concentration at the desired level of 1 ppm.
In the broader context of water treatment, ensuring the correct dosage of additives like sodium fluoride is vital. This prevents over-fluoridation, which can lead to adverse health effects, while also ensuring enough fluoride is present to be beneficial for dental health. Proper water treatment practices help maintain public health and safety.

chemical calculations

Chemical calculations are an essential part of ensuring correct dosing in processes like water fluoridation. They involve using mathematical formulas to determine the precise amounts of chemicals needed to achieve desired concentrations.
In the exercise, several crucial calculations take place:

• Total water consumption is calculated by considering the daily water usage of 150,000 people over a year.
• The mass of water is determined using the density of water, simplifying conversions between volume and mass.
• The required fluoride mass is calculated to maintain a concentration of 1 ppm in the total water volume.
• Finally, the mass of sodium fluoride required is determined by considering its percentage composition of fluoride.

These chemical calculations ensure accuracy and safety in water treatment. They are fundamental skills in chemistry, applicable in various fields beyond water treatment, such as pharmaceuticals and environmental science.