Question

3\. These compounds are found in many natural favors and scents. Calculate the empirical formula for each compound. (a) ethyl butyrate (pineapple oil): C, 62.04%; H, 10.41%; O, 27.55% (b) methyl butyrate (apple flavor): C, 58.80%; H, 9.87%; O, 31.33% (c) benzyl acetate (oil of jasmine): C, 71.98%; H, 6.71%; O, 21.31%

Short answer

The empirical formulas are (a) C3H6O for ethyl butyrate, (b) C3H6O for methyl butyrate, and (c) C8H8O for benzyl acetate.

Step-by-step solution

Calculate the moles of elements in ethyl butyrate

To find the empirical formula, we start by assuming we have 100 g of the compound. Convert the percentages to grams: C: 62.04 g, H: 10.41 g, O: 27.55 g. Then, divide by their molar masses to find moles: C: 62.04 g / 12.01 g/mol = 5.167 moles, H: 10.41 g / 1.008 g/mol = 10.328 moles, O: 27.55 g / 16.00 g/mol = 1.722 moles.

Determine the mole ratio for ethyl butyrate

To find the mole ratio, divide the moles of each element by the smallest number of moles obtained. For ethyl butyrate: C: 5.167 / 1.722 = 3.001, H: 10.328 / 1.722 = 5.996, O: 1.722 / 1.722 = 1. The empirical formula has whole numbers, so round these to the nearest whole number, yielding C3H6O.

Calculate the moles of elements in methyl butyrate

Assume we have 100 g of methyl butyrate. Convert the percentages to grams: C: 58.80 g, H: 9.87 g, O: 31.33 g. Find moles: C: 58.80 g / 12.01 g/mol = 4.897 moles, H: 9.87 g / 1.008 g/mol = 9.792 moles, O: 31.33 g / 16.00 g/mol = 1.958 moles.

Determine the mole ratio for methyl butyrate

Divide the moles of each element by the smallest number of moles. For methyl butyrate: C: 4.897 / 1.958 = 2.500, H: 9.792 / 1.958 = 5.000, O: 1.958 / 1.958 = 1. Round to the nearest whole numbers to get C3H6O.

Calculate the moles of elements in benzyl acetate

Assume we have 100 g of benzyl acetate. Convert the percentages to grams: C: 71.98 g, H: 6.71 g, O: 21.31 g. Find moles: C: 71.98 g / 12.01 g/mol = 5.994 moles, H: 6.71 g / 1.008 g/mol = 6.657 moles, O: 21.31 g / 16.00 g/mol = 1.332 moles.

Determine the mole ratio for benzyl acetate

Divide the moles of each element by the smallest number of moles. For benzyl acetate: C: 5.994 / 1.332 = 4.501, H: 6.657 / 1.332 = 4.998, O: 1.332 / 1.332 = 1. After rounding, the empirical formula is C8H8O.

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a bridge between the microscopic world of atoms and molecules, and the macroscopic world we can measure and observe. A mole is defined as the amount of any substance that contains as many entities (atoms, molecules, etc.) as there are atoms in exactly 12 grams of pure carbon-12. This number is known as Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities per mole.

Understanding the mole concept is key in determining the empirical formula of compounds. It's because the empirical formula represents the simplest whole-number ratio of atoms within a molecule. By converting mass percentages to moles, as seen in the given examples, it becomes possible to approximate this ratio and thus deduce the empirical formula. Simplifying the mole ratios to the smallest whole numbers reflects the principle that compounds are composed of whole atoms.

Stoichiometry

The concept of stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. It's based on the conservation of mass and the concept of moles. With stoichiometry, we can predict the amounts of substances consumed and produced in a reaction.

In the context of calculating empirical formulas, stoichiometry plays a role in converting mass percentages to moles, as illustrated in the given solution. Once we have the amount of moles for each element, stoichiometry is used to find the mole ratio. This step is critical for determining the simplest ratio of atoms in a compound, and hence its empirical formula. Clear, precise mathematical calculations and adjusting the ratios to whole numbers are vital to stoichiometry, serving as the cornerstone for deeper chemical analysis.

Molecular Composition

The term molecular composition refers to the types and numbers of atoms that constitute a molecule. It reveals the molecule's structure and is described by its chemical formula. The molecular formula provides the exact number of each type of atom in a molecule, whereas the empirical formula gives the simplest whole number ratio of these atoms.

When calculating molecular composition, one must first determine the empirical formula, which acts as a foundational step. As seen in the exercise, understanding the percent composition of each element enables us to calculate the empirical formula. Once obtained, the empirical formula can sometimes be used as is or further modified to find the molecular formula if the molar mass of the compound is known. In depth knowledge of molecular composition, including isomers and molecular structures, can greatly enhance one's comprehension of chemical reactions and properties.