Problem 105 - Chemistry The Molecular Science

Question

The fluoridation of city water supplies has been practiced in the United States for several decades because there is scientific evidence that fluoride prevents tooth decay, especially in young children. Fluoridation 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 each person uses 175 gal water per day. Calculate how many tons of sodium fluoride you must add to the water supply each year (365 days) to have the required fluoride concentration of 1 part per million (that is, 1 ton of fluoride per million tons of water). (Sodium fluoride is \(45.0 \%\) fluoride, and U. S. gallon of water has a mass of 8.34 lb.)

Step-by-Step Solution

Answer

88.79 tons of sodium fluoride are needed annually.

Step 1: Calculate Daily Water Consumption

First, we calculate the total daily water consumption for the city. Given that each person uses 175 gallons per day, the total daily consumption is calculated as \(175 \text{ gal/person/day} \times 150,000 \text{ people} = 26,250,000 \text{ gal/day}\).

Step 2: Convert Gallons to Pounds

We need to find the total weight of water used daily in pounds, knowing that 1 gallon of water weighs 8.34 pounds. Thus, daily water usage in pounds is \(26,250,000 \text{ gal} \times 8.34 \text{ lb/gal} = 218,925,000 \text{ lb/day}\).

Step 3: Convert Pounds to Tons

Convert the daily water consumption from pounds to tons (since there are 2,000 pounds in a ton): \(\frac{218,925,000 \text{ lb/day}}{2000 \text{ lb/ton}} = 109,462.5 \text{ tons/day}\).

Step 4: Calculate Annual Water Consumption in Tons

Calculate the annual water consumption in tons by multiplying the daily tonnage by 365 days: \(109,462.5 \text{ tons/day} \times 365 \text{ days} = 39,953,812.5 \text{ tons/year}\).

Step 5: Determine Necessary Fluoride in Tons

For a fluoride concentration of 1 part per million (1 ton of fluoride per million tons of water), we need \(\frac{39,953,812.5}{1,000,000} = 39.954 \text{ tons of fluoride/year}\).

Step 6: Calculate Sodium Fluoride Needed

Since sodium fluoride is only 45% fluoride, calculate the total sodium fluoride required. Divide the amount of fluoride required by 45%: \(\frac{39.954}{0.45} = 88.787 \text{ tons of sodium fluoride/year}\).

Step 7: Round Final Answer

Round the sodium fluoride needed to a reasonable number of decimals for practical purposes: approximately 88.79 tons of sodium fluoride per year.

Key Concepts

Sodium Fluoride

Sodium fluoride is a chemical compound that plays an important role in the process of water fluoridation. It's an ionic compound composed of sodium ions and fluoride ions. The molecular formula for sodium fluoride is NaF. When added to water supplies, sodium fluoride dissociates into sodium and fluoride ions. The fluoride ions are the active agents that help in reducing tooth decay. Fluoride works by strengthening the tooth enamel, making it more resistant to acid attacks from bacteria found in plaque, promoting dental health.
Sodium fluoride is commercially manufactured for different purposes, including dental products and water treatment. In water treatment, it's valued for its solubility and effectiveness in small doses. Sodium fluoride is approximately 45% fluoride by weight. This means, in water fluoridation, the calculation of the amount of sodium fluoride to be added is essential to meet the specific fluoride concentration targets, typically measured in parts per million (ppm). This strategy ensures enough fluoride is available for dental benefits without posing health risks.

Water Treatment

Water treatment refers to the processes used to make water more acceptable for a desired end-use. These uses can include drinking, industrial water supply, or recreational use. Fluoridation is a specific water treatment process aimed at reducing dental cavities. It involves the controlled addition of a fluoride compound, such as sodium fluoride, to public water supplies.
When a city decides to fluoridate its water supply, it considers many factors to determine the correct fluoride dosage. The dosage must be enough to achieve dental benefits but not so high as to cause adverse effects. It's usually expressed in parts per million (ppm). In the practice of water fluoridation, it's crucial to monitor and regulate fluoride levels constantly, to keep them within the safe threshold established by public health guidelines.

• Efficiency: Ensures right fluoride dose for prevention of tooth decay.
• Safety: Monitors fluoride levels to avoid excessive exposure.
• Regulation: Adheres to governmental standards and guidelines.

These procedures guarantee that the added fluoridation is done responsibly, optimizing the health benefits for the community.

Chemical Calculations

Chemical calculations in the context of water fluoridation are critical to achieving the correct concentration of fluoride in the water. This involves multiple steps and unit conversions, ensuring precise and safe dosages. Let's break down the main steps:
Firstly, you'll calculate how much daily water is used by a population. Knowing each person uses a certain gallon of water per day, you'd multiply this by the number of people to get the total daily consumption in gallons. Then, you'd convert these gallons into pounds using the known conversion factor (1 gallon = 8.34 pounds).
Next, convert these pounds into tons, since water fluoridation practices often require measurements in tons. This is done by dividing the total weight in pounds by 2,000 (the number of pounds in a ton).
Following this, calculate annual water consumption by multiplying daily consumption figures by the number of days in a year (365).
Finally, to find out how much sodium fluoride is needed, consider that the target is typically a concentration of 1 ppm. You'll divide the total annual water consumption by 1,000,000 to find the necessary fluoride tonnage. If sodium fluoride is only partly fluoride (45% in this case), further calculations adjust for its actual contribution to fluoride levels in water.
This methodical approach ensures that water fluoridation is both effective and safe, aligning with precise chemical requirements.