Question

In small amounts, the fluoride ion (often consumed as NaF) prevents tooth decay. According to the American Dental Association, an adult female should consume 3.0 mg of fluorine per day. Calculate the amount of sodium fluoride (45.24% F) that a woman should consume to get the recommended amount of fluorine.

Short answer

To get 3.0 mg of fluorine, an adult female should consume approximately 6.63 mg of sodium fluoride.

Step-by-step solution

Understand the Percentage of Fluoride in Sodium Fluoride

Determine the fraction of fluorine in sodium fluoride (NaF). Given the percentage of fluorine is 45.24%, this means that in 100 g of NaF, there are 45.24 g of fluorine.

Calculate the Mass of NaF Needed for the Required Fluorine

Use the percentage to find the mass of NaF that contains 3.0 mg of fluorine. Set up the proportion: (3.0 mg fluorine / x mg NaF) = (45.24 g fluorine / 100 g NaF).

Solve for the Mass of Sodium Fluoride

Cross-multiply and solve for x to find the mass of NaF that provides 3.0 mg of fluorine. x = (3.0 mg fluorine * 100 g NaF) / 45.24 g fluorine.

Convert the Mass to the Appropriate Units

Ensure the mass of NaF is in milligrams. Convert grams to milligrams if necessary (1 g = 1000 mg).

Key concepts

Chemical Composition

Understanding the chemical composition of substances is fundamental in chemistry. In the case of sodium fluoride (NaF), which is often used in small amounts to prevent tooth decay, we are specifically interested in its composition in terms of fluoride content. The chemical formula of sodium fluoride tells us that it consists of sodium (Na) and fluoride (F) ions. This binary compound is formed by the transfer of an electron from a sodium atom to a fluoride atom, creating a stable ionic bond between them.

Knowing the chemical composition helps in determining how much of a substance is needed for a specific purpose, like how much NaF should be consumed to meet the fluoride intake recommended by the American Dental Association. It is essential to look at the percentage of fluoride within NaF to calculate the proper amount needed to reach the desired fluoride intake.

Molar Mass Calculation

Molar mass calculation is a crucial step in stoichiometry that involves determining the mass of one mole of a substance. The molar mass of a compound is the sum of the total mass in grams of all the atoms in one mole of the compound. For sodium fluoride (NaF), this consists of the atomic mass of sodium (approximately 22.99 g/mol) and the atomic mass of fluoride (approximately 19.00 g/mol).

The molar mass calculation for NaF is therefore performed by adding these two values, which gives us approximately 41.99 g/mol. This molar mass allows scientists and health professionals to calculate the amount of NaF required to achieve a specific number of moles, or in our case, to obtain the necessary intake of fluoride.

Percentage by Mass

Percentage by mass is a way of expressing the concentration of a component in a mixture or compound. In this scenario, sodium fluoride (NaF) consists of fluoride ions that make up 45.24% of its mass. This means that for every 100 grams of NaF, there are 45.24 grams of fluoride.

To calculate the amount of sodium fluoride an adult female should consume, we use the percentage by mass of fluoride. With this concentration and the recommended fluoride intake, we can determine the necessary weight of NaF that must be ingested. This straightforward calculation involves setting up a ratio based on the percentage concentration and solving for the unknown quantity.

Daily Nutrient Requirements

Daily nutrient requirements are guidelines set by health organizations to indicate the amount of nutrients an individual should consume each day for optimal health. Fluoride, while not a traditional nutrient, is considered important for dental health. According to the American Dental Association, an adult female should consume 3.0 mg of fluorine each day to prevent tooth decay.

To ensure proper intake, the total mass of the sodium fluoride consumed needs to align with the recommended fluoride dose. This calculation is based on the known mass percentage of fluoride in NaF and requires stoichiometric conversions to ensure that when a person ingests the prescribed mass of sodium fluoride, they are indeed getting 3.0 mg of pure fluoride for their daily requirement.