Problem 90 - Chemistry: The Central Science

Question

(a) The molecular formula of acetylsalicylic acid (aspirin), one of the most common pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\). How many moles of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in a \(0.500-\mathrm{g}\) tablet of aspirin? (b) How many molecules of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in this tablet? (c) How many carbon atoms are in the tablet?

Step-by-Step Solution

Answer

(a) There are approximately 0.00278 moles of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) in a 0.500 g tablet of aspirin. (b) There are approximately \(1.67 \times 10^{21}\) molecules of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) in the tablet. (c) There are approximately \(1.50 \times 10^{22}\) carbon atoms in the tablet.

Step 1: Calculate the molar mass of aspirin

To calculate the molar mass of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\), we need to multiply the number of atoms of each element by their respective molar masses and add the results: Molar mass of aspirin = 9(molar mass of C) + 8(molar mass of H) + 4(molar mass of O) Using the molar masses of the elements (C: 12 g/mol, H: 1 g/mol, O: 16 g/mol), we get: Molar mass of aspirin = 9(12 g/mol) + 8(1 g/mol) + 4(16 g/mol) = 108 + 8 + 64 = 180 g/mol

Step 2: Calculate the moles of aspirin in the tablet

Now we can use the given mass of aspirin (0.500 g) and the molar mass we calculated in Step 1 to find the number of moles. Moles of aspirin = mass / molar mass = 0.500g / 180 g/mol ≈ 0.00278 mol

Step 3: Calculate the number of molecules in the tablet

To find the number of molecules in the tablet, we will multiply the moles of aspirin by Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol). Number of molecules = moles * Avogadro's number ≈ 0.00278 mol * \(6.022 \times 10^{23}\) molecules/mol ≈ \(1.67 \times 10^{21}\) molecules of aspirin

Step 4: Calculate the number of carbon atoms in the tablet

In one molecule of aspirin, there are 9 carbon atoms. To find the total number of carbon atoms in the tablet, multiply the number of molecules calculated in Step 3 by 9. Number of carbon atoms = 9 * \(1.67 \times 10^{21}\) molecules ≈ \(1.50 \times 10^{22}\) carbon atoms

Key Concepts

Molecular Formula

The molecular formula is a way to express the number and type of atoms in a molecule. For acetylsalicylic acid, commonly known as aspirin, the molecular formula is \( \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} \). This formula tells us that each molecule consists of:

• 9 carbon atoms (\( \mathrm{C} \)),
• 8 hydrogen atoms (\( \mathrm{H} \)), and
• 4 oxygen atoms (\( \mathrm{O} \)).

Understanding the molecular formula helps us determine the molar mass and the composition of a substance. We use these formulas to perform various calculations such as determining the number of molecules and atoms present in a given quantity of a substance.
By knowing the combination and number of atoms, we can better understand the chemical properties and how this compound might interact with others.

Avogadro's Number

Avogadro's number, \( 6.022 \times 10^{23} \), is a fundamental constant in chemistry. It represents the number of atoms, molecules, or particles in one mole of a substance. The concept is crucial for converting between moles and the actual number of particles.
In our aspirin tablet, once we have calculated the number of moles, we use Avogadro's number to find out how many molecules are present. For instance, multiplying the moles of acetylsalicylic acid by Avogadro's number gives us the total number of molecules in the tablet.

• Why is Avogadro's number important? It allows chemists to relate quantities of substances at the macroscopic level to the number of particles involved, facilitating stoichiometric calculations.

This number assists in bridging the gap between the amount we weigh on a scale and the microscopic world of atoms and molecules.

Carbon Atoms

Carbon atoms play a crucial role in organic chemistry as they form the backbone of organic molecules, including acetylsalicylic acid. The presence of 9 carbon atoms in each aspirin molecule defines much of its structure and properties.
To determine the number of carbon atoms in a tablet of aspirin, after calculating the number of molecules, we simply multiply by the number of carbon atoms per molecule.

• If one molecule of aspirin has 9 carbon atoms, then the total number of carbon atoms would be 9 times the number of aspirin molecules.

This multiplicative approach gives us an accurate count of carbon atoms in any given sample, which can be critical for understanding chemical reactions that may involve this element specifically.

Acetylsalicylic Acid

Acetylsalicylic acid, often casually referred to as aspirin, is a widely used medication for relieving pain and reducing fever. From a chemical perspective, its formula, \( \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} \), describes a molecule formed by the combination of carbon, hydrogen, and oxygen atoms.
Aspirin is an interesting compound as it represents a simple yet effective combination of organic chemistry principles.

• The acetyl part of the name refers to the attached acetyl group, which plays a significant role in its biological activity.
• The salicylic part refers to its origin from salicylic acid, a compound known for its anti-inflammatory properties.

Understanding its chemical makeup helps us appreciate how it works on a microscopic level and continues to be a staple in medical treatments worldwide.