Question

The molecular formula of acetylsalicylic acid (aspirin), one of the most commonly used pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{3} \mathrm{O}_{4}\). a. Calculate the molar mass of aspirin. b. A typical aspirin tablet contains \(500 . \mathrm{mg} \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} .\) 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 \(500 .-\mathrm{mg}\) tablet?

Short answer

a. The molar mass of aspirin can be calculated as: \(Molar~mass~of~aspirin = 9*(12.01~g/mol) + 8*(1.01~g/mol) + 4*(16.00~g/mol) = 180.17~g/mol\) b. The amount (moles) of aspirin in a 500 mg tablet is: \(Amount~(moles)~of~aspirin = 0.5~g / 180.17~g/mol = 2.775 \times 10^{-3}~moles\) The number of molecules of aspirin in the tablet is: \(Number~of~molecules~of~aspirin = 2.775 \times 10^{-3}~moles * 6.022 \times 10^{23}~molecules/mol = 1.67 \times 10^{21}~molecules\)

Step-by-step solution

Calculate the molar mass of aspirin

Using the molecular formula of aspirin, \(C_9H_8O_4\), we can calculate its molar mass using the atomic weights of carbon (C), hydrogen (H), and oxygen (O). The atomic weights can be found in a periodic table: Carbon (C) = 12.01 g/mol, Hydrogen (H) = 1.01 g/mol, Oxygen (O) = 16.00 g/mol. Molar mass of aspirin = 9*(Molar mass of Carbon) + 8*(Molar mass of Hydrogen) + 4*(Molar mass of Oxygen) Molar mass of aspirin = 9*(12.01 g/mol) + 8*(1.01 g/mol) + 4*(16.00 g/mol)

Convert the mass of aspirin from mg to grams

The mass of aspirin in a tablet is given in mg: 500 mg. To calculate the amount (moles), we need to convert it into grams. Since 1g = 1000 mg, we can do this conversion: Mass of aspirin in grams = 500 mg / 1000 mg/g = 0.5 g

Determine the amount (moles) of aspirin in a 500 mg tablet

Now that we have the mass of aspirin in grams and its molar mass, we can calculate the amount (moles) of aspirin in a 500 mg tablet using the formula: moles = mass (g) / molar mass (g/mol) Amount (moles) of aspirin = 0.5 g / Molar mass of aspirin

Calculate the number of molecules of aspirin

Finally, we can determine the number of molecules of aspirin in the tablet using Avogadro's number, which is \(6.022 \times 10^{23}\) molecules per mole. Number of molecules of aspirin = Amount (moles) of aspirin * Avogadro's number By following these steps systematically, we can answer the given questions and find the molar mass, amount (moles), and the number of molecules of aspirin in a 500 mg tablet.

Key concepts

Molecular Formula

The molecular formula of a compound is a notation that indicates the type and number of atoms present in a molecule. In the case of acetylsalicylic acid (commonly known as aspirin), the molecular formula is \(C_9H_8O_4\). This formula tells us that each molecule of aspirin is composed of 9 carbon (C) atoms, 8 hydrogen (H) atoms, and 4 oxygen (O) atoms.
Understanding the molecular formula is crucial for calculating the molar mass, which represents the mass of one mole of a substance. This mass allows us to relate the molecular-level information of a compound to a macroscopic scale. By knowing the molar mass, it is possible to perform further calculations to determine amounts and proportions of the substance in various chemical contexts.

Avogadro's Number

Avogadro's number is a fundamental constant named after Amedeo Avogadro. It represents the number of constituent particles, usually atoms or molecules, contained in one mole of a substance. The value of Avogadro's number is approximately \(6.022 \times 10^{23}\) particles per mole.
In practical terms, Avogadro's number allows chemists to transition from the scale of molecules to the scale of grams. For example, after determining the amount of moles of aspirin in a tablet, Avogadro's number can be employed to find the exact number of aspirin molecules present. This conversion is fundamental in chemistry for dealing with substances at a particle level while using consistent macroscopic measurements.

Conversion of Units

The conversion of units is a fundamental skill in chemistry that allows for the translation of measurements from one unit to another. In this exercise, converting milligrams of aspirin to grams is necessary to determine the amount of moles. Since there are 1000 milligrams in a gram, performing this conversion is straightforward:
- The mass of the aspirin in milligrams (mg) is divided by 1000 to convert it to grams (g).
This basic conversion is essential since molar mass is expressed in grams per mole, and so any mass-related calculations must be in consistent units to ensure accuracy.

Stoichiometry

Stoichiometry is the area of chemistry that deals with reacting quantities of substances. It involves the calculation of the amounts of reactants and products in chemical reactions. This concept hinges on fixed quantitative relationships dictated by the molecular formulas and their respective coefficients in balanced equations.
In this exercise, stoichiometry is employed to calculate the amount of aspirin molecules in a tablet. Through the relationships defined in molecular formulas, molar masses, and Avogadro's number, stoichiometry helps in determining how much of each substance is involved or produced in a given reaction or, as in this case, present in a tablet. Understanding these relationships ensures accurate predictions and interpretations in both laboratory settings and industrial processes.