Determine the empirical and molecular formulas of each of the following substances: (a) Ibuprofen, a headache remedy, contains 75.69% C, 8.80% H, and 15.51% O by mass and has a molar mass of 206 g/mol.

Verified step by step guidance

1. Step 1: Assume you have 100 g of the substance, which makes it easy to convert percentages to grams. This means you have 75.69 g of C, 8.80 g of H, and 15.51 g of O.
2. Step 2: Convert the mass of each element to moles by dividing by their respective atomic masses: C (12.01 g/mol), H (1.008 g/mol), and O (16.00 g/mol).
3. Step 3: Determine the mole ratio of the elements by dividing each element's mole value by the smallest number of moles calculated in Step 2.
4. Step 4: If necessary, multiply the ratios by a whole number to get whole numbers for each element, which gives you the empirical formula.
5. Step 5: Calculate the empirical formula mass and divide the given molar mass (206 g/mol) by the empirical formula mass to find the ratio. Multiply the subscripts in the empirical formula by this ratio to get the molecular formula.

Key Concepts

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. To determine it, the percentage composition of each element is converted to moles, and then the mole ratios are simplified to the smallest integers. For example, if a compound contains 2 moles of carbon and 1 mole of oxygen, its empirical formula would be CO.

Molecular Formula

The molecular formula indicates the actual number of atoms of each element in a molecule of a compound. It can be derived from the empirical formula by multiplying the subscripts by a whole number, which is determined by dividing the compound's molar mass by the molar mass of the empirical formula. For instance, if the empirical formula is CH2 and the molar mass is 28 g/mol, the molecular formula would be C2H4.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in the molecular formula. Understanding molar mass is crucial for converting between grams and moles, which is essential for determining both empirical and molecular formulas in chemical analysis.