Problem 95 - Chemistry The Science in Context

Question

Toothpaste Chemistry Most of the toothpaste sold in the United States contains about 1.00 mg of fluoride per gram of toothpaste. The fluoride compound that is most often used in toothpaste is sodium fluoride, NaF, which is \(45 \%\) fluoride by mass. How many milligrams of NaF are in a typical 8.2 -ounce tube of toothpaste?

Step-by-Step Solution

Answer

Answer: Approximately 516.6 milligrams of sodium fluoride is present in a typical 8.2-ounce tube of toothpaste.

Step 1: Convert the weight of toothpaste from ounces to grams

Given that 1 ounce is approximately equal to 28.35 grams, we can convert the total weight of toothpaste from ounces to grams: Weight of toothpaste (in grams) = 8.2 ounces * 28.35 grams/ounce

Step 2: Calculate the total fluoride in the toothpaste

Now that we have the weight of the toothpaste in grams, we can calculate the amount of fluoride: Total fluoride (in mg) = Weight of toothpaste (in grams) * 1.00 mg of fluoride / gram of toothpaste

Step 3: Determine the amount of sodium fluoride (NaF)

We know that sodium fluoride is \(45 \%\) fluoride by mass. So, we can find the amount of sodium fluoride in the toothpaste as follows: Total NaF (in mg) = Total fluoride (in mg) / (0.45) Now, let's calculate the values: Weight of toothpaste (in grams) = 8.2 * 28.35 = 232.47 g Total fluoride (in mg) = 232.47 * 1.00 = 232.47 mg Total NaF (in mg) = 232.47 / 0.45 = 516.6 mg So, there are approximately 516.6 milligrams of sodium fluoride in a typical 8.2-ounce tube of toothpaste.

Key Concepts

Toothpaste Composition

Toothpaste is more than just a daily hygiene product; it's a carefully crafted blend of ingredients designed for oral health.
One of its main purposes is to clean teeth and prevent cavities.
This is why it often includes active ingredients like fluoride.

• Abrasives: These help scrub away food particles and plaque.
• Fluoride: Provides protection against tooth decay by strengthening enamel.
• Humectants: Keeps the toothpaste moist and prevents it from drying out.
• Binders: Give toothpaste its texture and consistency.
• Flavors and Sweeteners: Make the toothpaste taste pleasant without promoting tooth decay.

In the United States, many toothpastes include about 1.00 mg of fluoride per gram, which makes them effective at preventing cavities.

Sodium Fluoride

Sodium fluoride (NaF) is a common fluoride compound used in toothpaste. This ingredient is chosen for its effectiveness in promoting dental health.
NaF offers several benefits:

• Cavity Prevention: Sodium fluoride helps to rebuild weakened tooth enamel, a process known as remineralization.
• Accessibility: It's easily added to toothpaste and remains stable over time.

Specifically, sodium fluoride is about 45% fluoride by mass.
This means that in any given amount of NaF, nearly half is pure fluoride, making it an efficient source of fluoride for oral care.

Mass Conversion

Understanding mass conversion is crucial when solving problems involving weight and measurements.
In the case of toothpaste, converting from ounces to grams allows for accurate calculations related to its chemical components.
Here's a simple breakdown of the conversion process:

• 1 ounce is approximately 28.35 grams.
• To convert, multiply the number of ounces by 28.35.

For example, if you have 8.2 ounces of toothpaste, converting it to grams would be:
\[8.2 \, ext{ounces} \times 28.35 \, \frac{\text{grams}}{\text{ounce}} = 232.47 \, \text{grams}\]
Accurate mass conversion is essential for determining the correct amount of fluoride in toothpaste.

Fluoride Concentration

Fluoride concentration in toothpaste is a vital factor for dental health.
It refers to the amount of fluoride present in the toothpaste, typically measured in milligrams per gram.
Here's how to calculate and understand it:

• Total Fluoride Calculation: Multiply the weight of the toothpaste in grams by the fluoride concentration. For an 8.2-ounce tube which converts to 232.47 grams, and 1 mg of fluoride per gram, the total fluoride is:\[232.47 \, \text{grams} \times 1 \, \frac{\text{mg of fluoride}}{\text{gram}} = 232.47 \, \text{mg}\]
• Relation to Sodium Fluoride: Since NaF is 45% fluoride by mass, use the calculated fluoride to find the total NaF:\[\frac{232.47 \, \text{mg}}{0.45} = 516.6 \, \text{mg NaF}\]

Understanding fluoride concentration is key to ensuring the toothpaste is effective for oral health.