Ibuprofen, an anti-inflammatory drug in Advil, has the formula C₁₃H₁₈O₂.
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d. How many moles of ibuprofen contain 1.22 × 10²³ atoms of C?

Verified step by step guidance

1. Step 1: Begin by identifying the molecular formula of ibuprofen, which is C₁₃H₁₈O₂. This indicates that each molecule of ibuprofen contains 13 carbon (C) atoms.
2. Step 2: Use the given number of carbon atoms (1.22 × 10²³ atoms of C) and determine how many molecules of ibuprofen correspond to this number of carbon atoms. Divide the total number of carbon atoms by the number of carbon atoms per molecule (13). The formula for this step is: \( \text{Number of molecules of ibuprofen} = \frac{\text{Total carbon atoms}}{\text{Carbon atoms per molecule}} \).
3. Step 3: Convert the number of molecules of ibuprofen into moles using Avogadro's number (6.022 × 10²³ molecules/mol). The formula for this step is: \( \text{Moles of ibuprofen} = \frac{\text{Number of molecules of ibuprofen}}{\text{Avogadro's number}} \).
4. Step 4: Perform dimensional analysis to ensure that the units cancel appropriately, leaving the result in moles of ibuprofen.
5. Step 5: Summarize the process: Divide the total carbon atoms by 13 to find the number of ibuprofen molecules, then divide this result by Avogadro's number to find the moles of ibuprofen.

Key Concepts

Moles and Avogadro's Number

A mole is a unit in chemistry that represents 6.022 x 10²³ entities, such as atoms or molecules. This number, known as Avogadro's number, allows chemists to convert between the mass of a substance and the number of particles it contains. Understanding this concept is crucial for solving problems involving quantities of substances in chemical reactions.

Molecular Formula

The molecular formula of a compound indicates the number and type of atoms present in a molecule. For ibuprofen, C₁₃H₁₈O₂ shows that each molecule contains 13 carbon (C) atoms, 18 hydrogen (H) atoms, and 2 oxygen (O) atoms. This information is essential for determining the number of moles based on the number of atoms.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows for the calculation of how much of one substance is needed or produced based on the amounts of others. In this context, stoichiometry helps in converting the number of carbon atoms into moles of ibuprofen.