Question

Cinnamic acid, a compound related to the flavor component of cinnamon, is \(72.96 \%\) carbon, \(5.40 \%\) hydrogen, and the rest is oxygen. What is the empirical formula of this acid?

Short answer

The empirical formula of cinnamic acid is C9H8O2.

Step-by-step solution

Determine the mass of each element

Assuming we have 100 g of the compound, we can use the percentages to find the mass of carbon, hydrogen, and oxygen. Carbon: 72.96 g, Hydrogen: 5.40 g, Oxygen: (100 - 72.96 - 5.40) g = 21.64 g.

Calculate the moles of each element

Using the atomic masses (C: 12.01 g/mol, H: 1.008 g/mol, O: 16.00 g/mol), calculate the number of moles of each element. Moles of Carbon = 72.96 g / 12.01 g/mol, Moles of Hydrogen = 5.40 g / 1.008 g/mol, Moles of Oxygen = 21.64 g / 16.00 g/mol.

Determine the mole ratio

Divide the number of moles of each element by the smallest number of moles calculated in step 2 to get the simplest whole number ratio: Carbon = (72.96 g / 12.01 g/mol) / smallest moles, Hydrogen = (5.40 g / 1.008 g/mol) / smallest moles, Oxygen = (21.64 g / 16.00 g/mol) / smallest moles.

Find the empirical formula

The mole ratios found in step 3 will give you the subscripts for the empirical formula. If necessary, multiply these ratios by a small whole number to make them all whole numbers.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. Essentially, it involves using balanced chemical equations to calculate the amount of reactants needed to produce a certain amount of product, or vice versa. In the context of empirical formula determination, stoichiometry provides the framework for understanding how elements combine in fixed ratios to form compounds.
For learning purposes, it's helpful to see stoichiometry as the 'recipe' for a chemical reaction, where molar amounts of each compound are like the ingredients. By following the 'recipe' accurately, you ensure that your 'dish'—in this case, the compound—is made correctly. The 'mole concept' then, is much like measuring ingredients in terms of cups or tablespoons, giving you a standardized way to express chemical quantities.

Mole Concept

The mole concept is a fundamental principle in chemistry used to measure the amount of substance. One mole of any substance contains Avogadro's number (approximately 6.022×10²³) of entities, be they atoms, molecules, ions, or other particles. In empirical formula determination, the mole concept allows us to convert mass percentages into something that represents the number of particles—the moles, enabling us to compare the ratios of the elements within a compound.
To better visualize this, imagine you have a bag of assorted coins. Determining the number of each type of coin based on percentage weights would be like finding the mole ratio of different elements in a compound. Just as you'd count coins, you'd use the atomic masses (as a proxy to 'coin values') to figure out how many atoms (or 'coins') you have for each element.

Percent Composition

Percent composition refers to the percent by mass of each element in a compound. It's similar to a nutritional label on a food package, which shows what percentage of the product is fat, protein, etc. In chemistry, percent composition is essential in determining the empirical formula since it shows the proportion of each element present in a compound. When given a compound's percent composition, as in our exercise example with cinnamic acid, it simplifies to assuming a 100 gram sample of the compound, since percentages are directly based on mass.
Understanding percent composition is crucial for the calculation steps because it sets the stage for all subsequent conversions—leading from mass to moles, and then to the simple mole ratio that represents the empirical formula of the compound. It's why the first step of our exercise involves distributing the 100 grams into the individual masses of carbon, hydrogen, and oxygen—facilitating a transition into mole calculations that follow.