Problem 127 - Chemistry The Science in Context

Question

Composition of Over-the-Counter Medicines Calculate the number of molecules or formula units of compound in each of the following common, over-the-counter medications: a. ibuprofen, a pain reliever and fever reducer that contains \(200.0 \mathrm{mg}\) of the active ingredient, \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2}\) b. an antacid containing 500.0 mg of calcium carbonate c. an allergy tablet containing 4 mg of chlorpheniramine $$\left(\mathrm{C}_{16} \mathrm{H}_{19} \mathrm{ClN}_{2}\right)$$.

Step-by-Step Solution

Answer

Question: Calculate the number of molecules or formula units of the active ingredient in each over-the-counter medication, given the following information: a. Ibuprofen: 200.0 mg b. Calcium carbonate: 500.0 mg c. Chlorpheniramine: 4 mg Answer: a. Ibuprofen: 5.84 * 10^20 molecules b. Calcium carbonate: 3.01 * 10^21 formula units c. Chlorpheniramine: 8.79 * 10^18 molecules

Step 1: Calculate the moles of the active ingredient in each medication

First, we will find the molar mass of each active ingredient and then calculate the moles: a. Ibuprofen: \(\mathrm{C}_{13}\mathrm{H}_{18}\mathrm{O}_{2}\) Molar mass: 13 * 12.01 + 18 * 1.01 + 2 * 16.00 = 206.37 g/mol Moles in 200.0 mg: (200.0 mg) * (1 g/1000 mg) * (1 mol/206.37 g) = 9.70 * 10^{-4} mol b. Calcium carbonate: \(\mathrm{CaCO}_{3}\) Molar mass: 40.08 + 12.01 + 3 * 16.00 = 100.09 g/mol Moles in 500.0 mg: (500.0 mg) * (1 g/1000 mg) * (1 mol/100.09 g) = 4.999 * 10^{-3} mol c. Chlorpheniramine: \(\left(\mathrm{C}_{16}\mathrm{H}_{19}\mathrm{ClN}_{2}\right)\) Molar mass: 16 * 12.01 + 19 * 1.01 + 35.45 + 2 * 14.01 = 274.86 g/mol Moles in 4 mg: (4 mg) * (1 g/1000 mg) * (1 mol/274.86 g) = 1.460 * 10^{-5} mol

Step 2: Calculate the number of molecules or formula units using Avogadro's number

Now, we will use Avogadro's number (6.022 * 10^{23} entities/mol) to calculate the number of molecules or formula units for each medication. a. Ibuprofen: Number of molecules = (9.70 * 10^{-4} mol) * (6.022 * 10^{23} molecules/mol) = 5.84 * 10^{20} molecules b. Calcium carbonate: Number of formula units = (4.999 * 10^{-3} mol) * (6.022 * 10^{23} units/mol) = 3.01 * 10^{21} formula units c. Chlorpheniramine: Number of molecules = (1.460 * 10^{-5} mol) * (6.022 * 10^{23} molecules/mol) = 8.79 * 10^{18} molecules In conclusion, the number of molecules or formula units in each medication are: a. Ibuprofen: 5.84 * 10^{20} molecules b. Calcium carbonate: 3.01 * 10^{21} formula units c. Chlorpheniramine: 8.79 * 10^{18} molecules

Key Concepts

Molar Mass Calculation

Understanding molar mass is fundamental in solving many chemistry problems, especially when dealing with substances in various medications, like ibuprofen or calcium carbonate. Molar mass refers to the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It is calculated by adding up the atomic masses of all atoms in a molecule.

• For instance, the molar mass of ibuprofen (C₁₃H₁₈O₂) is found by summing up the atomic masses: 13 carbon (C) atoms at 12.01 g/mol each, 18 hydrogen (H) atoms at 1.01 g/mol each, and 2 oxygen (O) atoms at 16.00 g/mol each.
• In another example, the molar mass of calcium carbonate (CaCO₃) requires adding the masses of 1 calcium (Ca) atom, 1 carbon (C) atom, and 3 oxygen atoms.

Once the molar mass is identified, it is used to convert between mass and the number of moles, simplifying chemical calculations. By understanding the molar mass, one can easily find out the quantity of a compound, even when it is present in very small amounts, such as in medicines.

Avogadro's Number

Avogadro's number is a key concept that allows chemists to connect the macroscopic world (what we see) with the molecular world (what we can't see). This constant, approximately 6.022 × 10²³, represents the number of entities in one mole of a substance, whether they are atoms, molecules, or formula units.

• This number is crucial in counting particles because they are only measurable in large quantities.
• For example, once the number of moles of ibuprofen in a tablet is known, Avogadro's number helps us calculate the huge number of individual ibuprofen molecules within.

This concept is so integral that it permeates various aspects of chemistry, like determining the amount of reactant needed or calculating the yield in reactions. Essentially, it bridges the microscopic and macroscopic worlds, making chemical quantification feasible and understandable.

Mole Concept

The mole is one of the core concepts in chemistry, providing a grounding framework to assess amounts of chemical substances easily. Defined as a unit that contains exactly 6.022 × 10²³ entities, the mole allows chemists to measure out substances in a way that's practical for laboratory work and theoretical calculations.

• The concept of the mole is particularly useful when dealing with small amounts of a chemical, such as the few milligrams of active ingredient in a medication, offering a way to translate those weights into countable entities.
• In practical terms, the mole is used to convert masses into numbers of particles, made feasible through using molar mass and Avogadro's number.

To fully grasp the size and scope of chemical reactions, the mole concept is applied to convert between mass of a substance and the number of atoms or molecules it contains. This ultimately simplifies understanding complex reactions and substances, facilitating more precise and meaningful experimentation and results in chemistry.