Problem 99 - Chemistry A Molecular Approach

Question

The foul odor of rancid butter is due largely to butyric acid, a compound containing carbon, hydrogen, and oxygen. Combustion analysis of a \(4.30-\mathrm{g}\) sample of butyric acid produces \(8.59 \mathrm{~g} \mathrm{CO}_{2}\) and \(3.52 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} .\) Determine the empirical formula of butyric acid.

Step-by-Step Solution

Answer

The empirical formula of butyric acid is C4H7O2.

Step 1: Calculate moles of carbon in CO2

To find moles of carbon, first find moles of CO2 using its molar mass. The molar mass of CO2 is approximately 44.01 g/mol. Moles of CO2 = mass of CO2 / molar mass of CO2 = 8.59 g / 44.01 g/mol.

Step 2: Calculate moles of carbon

Each CO2 molecule contains one carbon atom. Moles of carbon = moles of CO2.

Step 3: Calculate moles of hydrogen in H2O

To find moles of hydrogen, first find moles of H2O using its molar mass. The molar mass of H2O is approximately 18.02 g/mol. Moles of H2O = mass of H2O / molar mass of H2O = 3.52 g / 18.02 g/mol.

Step 4: Calculate moles of hydrogen

Each H2O molecule contains two hydrogen atoms. Moles of hydrogen = 2 * moles of H2O.

Step 5: Calculate moles of oxygen in butyric acid

Assuming butyric acid only contains carbon, hydrogen, and oxygen, the mass of oxygen can be found by subtracting the masses of carbon and hydrogen from the total mass of butyric acid. Oxygen's mass = total mass - (mass of carbon + mass of hydrogen).

Step 6: Calculate moles of oxygen

Use molar mass of oxygen (16.00 g/mol) to find moles of oxygen. Moles of oxygen = mass of oxygen / molar mass of oxygen.

Step 7: Determine the mole ratio of C:H:O

Divide the moles of carbon, hydrogen, and oxygen by the smallest number of moles to find the simplest whole number ratio.

Step 8: Write the empirical formula

Use the whole number ratio from Step 7 to write the empirical formula, with each element symbol followed by its corresponding subscript.

Key Concepts

Combustion Analysis

Combustion analysis is a laboratory procedure used to determine the elemental composition of a substance by burning it in excess oxygen and measuring the amounts of resulting compounds. In our example, butyric acid is combusted, producing carbon dioxide (\textbf{CO}\(_2\)) and water (\textbf{H}\(_2\)O). From the known amounts of \textbf{CO}\(_2\) and \textbf{H}\(_2\)O produced, we can determine the number of moles of carbon and hydrogen in the original sample.

First, we convert the measured mass of \textbf{CO}\(_2\) to moles. Since \textbf{CO}\(_2\) contains only one carbon atom, the number of moles of carbon equals the number of moles of \textbf{CO}\(_2\). Similarly, we calculate the moles of \textbf{H}\(_2\)O and then deduce the moles of hydrogen, knowing that each molecule of water contains two hydrogen atoms.

Mole Concept

The mole concept is a fundamental principle in chemistry that relates the mass of a substance to the amount of particles it contains. One mole is equivalent to Avogadro's number (\textbf{6.022} \times \textbf{10}\(^{23}\) particles).

The mass of \textbf{CO}\(_2\) produced is used to calculate the number of moles of \textbf{CO}\(_2\), and therefore moles of carbon since each \textbf{CO}\(_2\) molecule contains exactly one carbon atom. By understanding the relationships between masses, moles, and molar masses, we can deduce the amounts of each element in our sample, which is pivotal for determining the empirical formula.

Molecular Mass

Molecular mass, often referred to as molecular weight, is the sum of the atomic masses of all the atoms in a molecule. For example, the molecular mass of water (\textbf{H}\(_2\)O) is approximately 18.02 grams per mole, calculated by adding together the atomic masses of two hydrogen atoms (1.01 g/mol each) and one oxygen atom (16.00 g/mol).

In our problem, we use the molar masses of \textbf{CO}\(_2\) and \textbf{H}\(_2\)O to convert the masses of these compounds from the combustion analysis into moles. This step is critical in determining the quantities of carbon and hydrogen originally present in butyric acid, which are reflected in the empirical formula.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. In the context of empirical formula determination, stoichiometry is used to calculate the relative number of moles of each element in the compound.

To determine the empirical formula of butyric acid, we calculate the mole ratios of carbon, hydrogen, and oxygen. We do this by dividing the number of moles of each element by the smallest number of moles obtained among the elements. This ratio reflects the simplest whole-number ratio of atoms in the molecule and forms the basis of the empirical formula. Stoichiometric calculations are essential in accurately representing these relationships in the compound's empirical formula.