Question

The molecular formula of acetylsalicylic acid (aspirin), one of the most commonly used pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} .\) a. Calculate the molar mass of aspirin. b. A typical aspirin tablet contains 500 . mg \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) . What amount (moles) of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) molecules and what number of molecules of acetylsalicylic acid are in a 500 -mg tablet?

Short answer

The molar mass of aspirin (acetylsalicylic acid) is 180.17 g/mol. In a 500-mg tablet, there are 0.002774 moles and \(1.67 \times 10^{21}\) molecules of acetylsalicylic acid.

Step-by-step solution

a. Calculate the molar mass of aspirin

To calculate the molar mass, we first need to find the molar mass of each element in the molecular formula, which we can find from the periodic table. Then, we will multiply each element's molar mass by its number of atoms in the molecule and sum all values. Molar mass of C: 12.01 g/mol Molar mass of H: 1.01 g/mol Molar mass of O: 16.00 g/mol Molar mass of aspirin = (9 × 12.01) + (8 × 1.01) + (4 × 16.00) = \(108.09 + 8.08 + 64\) g/mol = 180.17 g/mol Molar mass of acetylsalicylic acid is 180.17 g/mol.

b. Calculate moles and number of molecules of acetylsalicylic acid in the 500-mg tablet

Firstly, to calculate the moles of C9H8O4 in the 500-mg tablet, we need to convert the mass of the tablet from mg to g (500 mg = 0.500 g) and divide it by the molar mass of aspirin. Moles of acetylsalicylic acid = mass of tablet (in g) / molar mass Moles = \(0.500 \div 180.17\) Moles = 0.002774 mol Now, we need to find the number of molecules of acetylsalicylic acid in the tablet. We will use Avogadro's number (6.022 × 10^23) for this calculation. Number of molecules = moles × Avogadro's number Number of molecules = 0.002774 × \(6.022 \times 10^{23}\) Number of molecules = \(1.67 \times 10^{21}\) In a 500-mg tablet, there are 0.002774 moles and \(1.67 \times 10^{21}\) molecules of acetylsalicylic acid.

Key concepts

Molecular Formula

Understanding the molecular formula is crucial in chemical calculations and identifying compounds. A molecular formula shows the actual number of each type of atom in a molecule. For acetylsalicylic acid (aspirin), the molecular formula is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\). It tells us that each molecule contains:

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

This kind of formula is different from the empirical formula, which shows the simplest whole-number ratio of atoms in a compound. However, in aspirin, the molecular formula is often the same as the empirical formula.
Using the periodic table, we can find the molar mass of each element. Then, multiplying each by the number of atoms in the molecular formula yields the molar mass of the compound. This process is essential for converting between mass and moles.

Avogadro's Number

Avogadro's number is a fundamental concept in chemistry that allows chemists to count atoms, molecules, and ions by weighing them. Named after the scientist Amedeo Avogadro, it is defined as \(6.022 \times 10^{23}\). This large number is the number of atoms or molecules in one mole of a substance.
Avogadro's number links the macroscopic world (what we can see and measure) to the microscopic world of atoms and molecules. When we say one mole of aspirin contains \(6.022 \times 10^{23}\) molecules, it gives chemists a scale to work with for practical calculations.

• For example, if you know the number of moles of a compound, you can easily find out how many molecules you have by multiplying the number of moles by Avogadro's number.
• This is useful for chemists who need precise measurements to ensure reactions happen as expected.

In the case of aspirin, knowing the number of moles in a tablet lets us calculate the number of individual molecules present, which is crucial for dosage and efficacy.

Chemical Calculations

Chemical calculations involve determining quantities like mass, moles, and number of molecules. These calculations start with the molecular formula and depend on accurately performing conversions and using constants effectively.
For aspirin, we use its molecular formula \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) to calculate the molar mass. From there, if we want to find how much aspirin is in a tablet, we perform the following steps:

• First, convert the mass in milligrams to grams because chemists typically use grams in calculations. For example, 500 mg = 0.500 g.
• Next, use the molar mass to convert the mass in grams to moles using the formula: \(\text{Moles} = \frac{\text{mass (in g)}}{\text{molar mass (in g/mol)}}\).
• Finally, to find the exact number of molecules, multiply the moles by Avogadro's number.

Being able to perform these steps is a critical skill in chemistry, enabling the practical application of theoretical knowledge. It ensures accurate preparation, measurement, and analysis in chemical experimentation.