Problem 38 - General Chemistry: Principles and Modern Applications

Question

In many communities, water is fluoridated to prevent tooth decay. In the United States, for example, more than half of the population served by public water systems has access to water that is fluoridated at approximately \(1 \mathrm{mg} \mathrm{F}^{-}\) per liter. (a) What is the molarity of \(\mathrm{F}^{-}\) in water if it contains \(1.2 \mathrm{mg} \mathrm{F}^{-}\) per liter? (b) How many grams of solid KF should be added to a \(1.6 \times 10^{8}\) L water reservoir to give a fluoride concentration of \(1.2 \mathrm{mg} \mathrm{F}^{-}\) per liter?

Step-by-Step Solution

Answer

The molarity of F- in water is \(6.32 \times 10^{-5} \, M\) and the amount of KF required to achieve the desired fluoride ion concentration is 586.59 g

Step 1: Convert mass to moles

To calculate molarity, the amount of F- should be in moles, not in milligrams. Thus, first we will convert the given mass (1.2 mg) of F- to moles. The molar mass of F is around 18.998 g/mol.\nSo, \(1.2 \, mg = 1.2 \times 10^{-3} \, g\), and number of moles = \(\frac{1.2 \times 10^{-3} \, g}{18.998 \, g/mol} = 6.32 \times 10^{-5} \, mol\)

Step 2: Calculate Molarity

Now we use the molarity formula which is number of moles divided by volume in liters. Here the amount of water is 1 liter. So, molarity of F- is \( \frac{6.32 \times 10^{-5} \, mol}{1 \, L} = 6.32 \times 10^{-5} \, M\)

Step 3: Calculate the amount of KF

To answer the second part of the question, we must first calculate the total amount of F- needed for the reservoir, then calculate the equivalent amount of KF. We have the molarity and the volume of water hence we can find the amount of F- in moles required. The volume is given in liters so we must convert it to liters first: \(1.6 \times 10^{8} \, L\). Now the number of moles of F- required can be found by multiplying the molarity with volume: \(6.32 \times 10^{-5} \, mol/L \times 1.6 \times 10^{8} \, L = 10.1 \, mol\). \nWe know that in KF, for each molecule of KF there is one ion of F-. So the moles of KF required will be the same as the moles of F-. The molar mass of KF is (39.1 + 18.998) = 58.098 g/mol. So to get the mass in grams we multiply the moles with molar mass: \(10.1 \, mol \times 58.098 \, g/mol = 586.59 \, g\) which is the amount of KF required

Key Concepts

Water fluoridation

Water fluoridation is a public health measure aimed at reducing tooth decay by adding fluoride to drinking water. This process was first introduced in the early 20th century and has been widely adopted across the globe, especially in the United States. Fluoride, in regulated amounts, contributes to the remineralization of tooth enamel, making it more resistant to acid attacks from bacteria, plaque, and sugar.

• In the United States, the recommended concentration of fluoride in water is typically around 0.7 to 1.2 milligrams per liter.
• The goal is to achieve an optimal balance where fluoride levels are high enough to protect teeth, yet low enough to avoid dental fluorosis, which is mild discoloration of the teeth.

With this process, communities benefit from cost-effective dental health improvements as it reduces cavities and other oral health issues.

Tooth decay prevention

Tooth decay prevention is a critical aspect of maintaining oral health and hygiene. Cavities are caused by bacteria in the mouth which produce acids that erode teeth. Fluoride, a naturally occurring mineral, plays a significant role in minimizing this risk.

• When fluoridated water is consumed, fluoride becomes incorporated into the enamel, creating a barrier against bacterial acids.
• It also helps repair weak areas on teeth, reversing early decay.

Fluoride works alongside other oral hygiene practices such as brushing, flossing, and regular dental check-ups. Together, these strategies significantly reduce the prevalence of cavities and tooth decay.

Molar mass calculation

Molar mass calculation is crucial when determining the amount of a substance present in a given sample. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). For calculations involving water fluoridation, understanding molar mass helps in converting between mass and moles, which is essential in chemistry.

• The molar mass of an element or compound is found by summing the average atomic masses of its constituent atoms.
• For example, the molar mass of fluoride ion (F-) is approximately 18.998 g/mol.
• For potassium fluoride (KF), the molar mass is calculated by adding the atomic masses of potassium (K, approximately 39.1 g/mol) and fluoride (F-, approximately 18.998 g/mol), which gives about 58.098 g/mol.

Applying these values, one can calculate the number of moles from a given mass and vice versa, crucial for tasks like determining the amount of KF needed for water treatment.

Fluoride ion concentration

Fluoride ion concentration in water is a key metric used to ensure water fluoridation is both safe and effective. It is typically expressed in terms of molarity, which is the number of moles of solute (in this case, fluoride ions, \( F^- \)) per liter of solution.

• To calculate fluoride ion concentration, first convert the mass of fluoride provided (e.g., in milligrams) into grams, and then to moles using its molar mass.
• The formula for molarity is \( C = \frac{n}{V} \), where \( n \) is the number of moles and \( V \) is the volume in liters.

By following these steps, you can determine how much fluoride is present in a water supply. Monitoring and adjusting this concentration is essential for effective tooth decay prevention while ensuring water safety standards are maintained.