(b) Menthol, the substance we can smell in mentholated cough drops, is composed of C, H, and O. A 0.1005-g sample of menthol is combusted, producing 0.2829 g of CO₂ and 0.1159 g of H₂O. What is the empirical formula for menthol? If menthol has a molar mass of 156 g/mol, what is its molecular formula?

Verified step by step guidance

1. 1. The first step is to determine the moles of carbon and hydrogen in the sample. This can be done by using the mass of CO₂ and H₂O produced and the molar mass of these compounds. The molar mass of CO₂ is approximately 44.01 g/mol and the molar mass of H₂O is approximately 18.02 g/mol. The moles of carbon can be calculated by multiplying the mass of CO₂ by the ratio of the molar mass of carbon to the molar mass of CO₂. The moles of hydrogen can be calculated by multiplying the mass of H₂O by the ratio of twice the molar mass of hydrogen to the molar mass of H₂O.
2. 2. The next step is to calculate the mass of oxygen in the sample. This can be done by subtracting the mass of carbon and hydrogen from the total mass of the sample. The molar mass of carbon is approximately 12.01 g/mol and the molar mass of hydrogen is approximately 1.01 g/mol. The mass of oxygen can be calculated by subtracting the product of the moles of carbon and the molar mass of carbon and the product of the moles of hydrogen and the molar mass of hydrogen from the total mass of the sample.
3. 3. The moles of oxygen can then be calculated by dividing the mass of oxygen by the molar mass of oxygen, which is approximately 16.00 g/mol.
4. 4. The empirical formula can be determined by dividing the moles of each element by the smallest number of moles calculated. This will give the ratio of the elements in the compound.
5. 5. The molecular formula can be determined by dividing the molar mass of the compound by the molar mass of the empirical formula. The result is the number of empirical formula units in the molecule. Multiply the subscripts in the empirical formula by this number to get the molecular formula.

Key Concepts

Combustion Analysis

Combustion analysis is a technique used to determine the elemental composition of organic compounds. In this process, a sample is burned in excess oxygen, producing carbon dioxide (CO2) and water (H2O). By measuring the mass of these products, one can calculate the amounts of carbon and hydrogen in the original sample, which are essential for determining the empirical formula.

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. It is derived from the moles of each element present in the sample, calculated from the mass of the combustion products. For menthol, the empirical formula can be determined by converting the masses of CO2 and H2O produced into moles of carbon and hydrogen, respectively, and then finding the simplest ratio.

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 comparing the molar mass of the compound to the molar mass of the empirical formula. If the molar mass of menthol is known (156 g/mol), and the empirical formula's molar mass is calculated, the molecular formula can be determined by finding the ratio of these two values.