Question

A tablet of Tylenol \(^{\text {m }}\) has a mass of \(0.611 \mathrm{~g}\). It contains \(251 \mathrm{mg}\) of its active ingredient, acetaminophen, \(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{NO}_{2}\). (a) What is the mass percent of acetaminophen in a tablet of Tylenol? (b) Assume that all the nitrogen in the tablet is in the acetaminophen. How many grams of nitrogen are present in a tablet of Tylenol?

Short answer

= (0.251/0.611) x 100% = 0.4108 x 100% = 41.08% Therefore, the mass percent of acetaminophen in a tablet of Tylenol is 41.08%. #tag_title#Step 2: Calculate the mass of nitrogen in the tablet#tag_content# To calculate the mass of nitrogen in the tablet, we will need to find the proportion of nitrogen in acetaminophen and then multiply it by the mass of acetaminophen. The molecular formula of acetaminophen is C8H9NO2. To find the proportion of nitrogen in the compound, we need to divide the molar mass of nitrogen by the molar mass of acetaminophen. The molar mass of nitrogen (N) is 14.01 g/mol. The molar mass of acetaminophen is (8 × 12.01) + (9 × 1.01) + (14.01) + (2 × 16.00) = 151.17 g/mol. Now, we can find the proportion of nitrogen as follows: Proportion of nitrogen = Molar mass of nitrogen / Molar mass of acetaminophen = 14.01 g/mol / 151.17 g/mol = 0.0926 Finally, we can find the mass of nitrogen in the tablet by multiplying the proportion of nitrogen by the mass of acetaminophen: Mass of nitrogen = Proportion of nitrogen x Mass of acetaminophen = 0.0926 × 0.251 g = 0.0232 g Therefore, the mass of nitrogen in a tablet of Tylenol is approximately 0.0232 g. Short Answer: The mass percent of acetaminophen in a tablet of Tylenol is 41.08%, and the mass of nitrogen in the tablet is approximately 0.0232 g.

Step-by-step solution

Calculate the mass percent of acetaminophen in a tablet of Tylenol

To calculate the mass percent of acetaminophen, we can use the following formula: Mass percent = (Mass of acetaminophen / Total mass of tablet) x 100% First, we need to convert the mass of acetaminophen from milligrams to grams: 251 mg = 0.251 g Next, we plug the values into the formula: Mass percent = (0.251 g / 0.611 g) x 100%

Key concepts

Acetaminophen Composition

Acetaminophen, known for its pain-relieving properties, is the active ingredient in many over-the-counter medications, including Tylenol. To understand its composition, we first look at its chemical formula: \( C_{8}H_{9}NO_{2} \). This indicates that each molecule of acetaminophen consists of 8 carbon (C) atoms, 9 hydrogen (H) atoms, 1 nitrogen (N) atom, and 2 oxygen (O) atoms.

In a pharmaceutical context, knowing the exact composition of a drug is crucial. It helps in determining the dosage and understanding how the medication interacts with the body. For example, in a Tylenol tablet, the quantity of acetaminophen directly affects its effectiveness and safety for consumption. In our exercise, the tablet contains 251 mg of acetaminophen. This amount is essential in calculating the mass percent, which indicates the concentration of the active ingredient in the tablet.

Mass percent calculations are not just important in pharmacy but also in chemistry and other sciences where the analysis of mixtures and solutions is needed. To grasp this concept, students should also be comfortable with unit conversion, as doses and measurements can come in various units.

Chemical Formula Interpretation

The ability to interpret a chemical formula is fundamental in understanding the composition of compounds. The formula itself is a shorthand representation of the types and number of atoms in a molecule. For example, acetaminophen's formula, \( C_{8}H_{9}NO_{2} \), tells us not only the kinds of atoms present but also their ratios within one molecule.

Let's dive a little deeper. Each element symbol corresponds to a unique type of atom. The subscript numbers indicate how many of each atom are present. If there's no subscript, it means there's just one atom of that element in the molecule. Understanding this allows students to delve into concepts such as molecular mass, which is the sum of the atomic masses of all atoms in the molecule. This is particularly important when quantifying substances or converting between moles and grams—a key skill in stoichiometry and thermodynamics.

Unit Conversion

Unit conversion is an indispensable tool across all sciences and everyday life, allowing quantities expressed in different units to be compared and manipulated appropriately. In the context of our exercise, the mass of acetaminophen is provided in milligrams (mg), while the mass of the Tylenol tablet is in grams (g). To perform calculations, we need these units to match.

The conversion is straightforward: 1 gram is equivalent to 1000 milligrams. Therefore, to convert 251 mg of acetaminophen to grams, we divide by 1000, which gives us 0.251 g. This skill is critical, as precision in measurements is imperative, especially in pharmacology where incorrect dosages can have serious implications. It's also worth noting that conversions are not limited to mass; they may include volumes, lengths, and various other units depending on the context of the problem at hand.

Strengthening unit conversion skills ensures a solid foundation when dealing with mathematical equations and scientific analyses. Teaching this concept can be enhanced through practical examples and repetition, allowing students to become confident and efficient in converting units.