Question

Propenoic acid is a reactive organic liquid used in the manufacture of plastics, coatings, and adhesives. An unlabeled container is thought to contain this acid. A 0.2033-g sample is combusted in an apparatus such as that shown in Figure 3.14. The gain in mass of the \(\mathrm{H}_{2} \mathrm{O}\) absorber is \(0.102 \mathrm{~g}\), whereas that of the \(\mathrm{CO}_{2}\) absorber is \(0.374 \mathrm{~g}\). What is the empirical formula of propenoic acid?

Short answer

The empirical formula of the compound in the unlabeled container is \(H_{3}C_{2}O\), which confirms that it contains propenoic acid.

Step-by-step solution

Converting masses to moles

To convert the masses of water and carbon dioxide to moles, divide each mass by its respective molar mass. The molar mass of water is 18.015 g/mol, and the molar mass of carbon dioxide is 44.01 g/mol. Moles of water: \(\frac{0.102\,\text{g}}{18.015\,\text{g/mol}} = 0.00567\,\text{mol}\) Moles of carbon dioxide: \(\frac{0.374\,\text{g}}{44.01\,\text{g/mol}} = 0.00850\,\text{mol}\)

Deduce moles of hydrogen and carbon

Since water is formed by the reaction of hydrogen and oxygen, the moles of hydrogen in the original compound can be deduced from the moles of water produced, considering that each water molecule contains two hydrogen atoms: Moles of hydrogen: \(0.00567\,\text{mol} \times 2 = 0.0113\,\text{mol}\) Similarly, carbon dioxide is formed by the reaction of carbon and oxygen, so the moles of carbon in the original compound can be deduced from the moles of carbon dioxide produced: Moles of carbon: \(0.00850\,\text{mol}\)

Determine moles of oxygen

To find the moles of oxygen in the original compound, we'll use the mass conservation principle. The mass of the original compound is the sum of the masses of hydrogen, carbon, and oxygen, which can be expressed as: \(0.2033\,\text{g} = n_{H} \times m_{H} + n_{C} \times m_{C} + n_{O} \times m_{O}\) Where n represents moles and m represents molar mass. We know the values for hydrogen and carbon moles, as well as the molar mass of hydrogen (1.008 g/mol), carbon (12.01 g/mol), and oxygen (16.00 g/mol). By solving for the moles of oxygen (nO), we find: \(n_{O} = \frac{0.2033\,\text{g} - (0.0113\,\text{mol} \times 1.008\,\text{g/mol}) - (0.00850\,\text{mol} \times 12.01\,\text{g/mol})}{16\,\text{g/mol}} = 0.00415\,\text{mol}\)

Calculate the empirical formula

To find the empirical formula, we'll divide the moles of each element by the smallest number of moles: Minimum moles ratio: \( H: C: O \approx \frac{0.0113\,\text{mol}}{0.00415\,\text{mol}} : \frac{0.00850\,\text{mol}}{0.00415\,\text{mol}} : \frac{0.00415\,\text{mol}}{0.00415\,\text{mol}} = 2.72 : 2.05 : 1\) Because the moles are almost in a whole number ratio, rounding to the nearest whole number will give the empirical formula: Empirical formula: \(H_{3}C_{2}O_{1}\), or simply, \(H_{3}C_{2}O\). In conclusion, based on the combustion analysis, the empirical formula of the compound is \(H_{3}C_{2}O\), which confirms that the unlabeled container contains propenoic acid.

Key concepts

Combustion Analysis

Combustion analysis is a laboratory technique often used to determine the elemental composition of a chemical compound, especially when the compound is organic. In this method, the unknown compound is burned, or combusted, which means reacting it with oxygen. This process forms simpler compounds, typically carbon dioxide \(\(\text{CO}_2\)\) and water \(\(\text{H}_2\text{O}\)\).
When performing combustion analysis, the goal is to determine how much carbon and hydrogen are present in a sample. By accurately measuring the amounts of \(\(\text{CO}_2\)\) and \(\(\text{H}_2\text{O}\)\) produced in the reaction, we can back-calculate to find the proportions of carbon and hydrogen in the original compound.
Let's take a closer look at what happens during the combustion process. When you combust an organic compound, each carbon atom will pair up with oxygen to form \(\(\text{CO}_2\)\). Similarly, every two hydrogen atoms will connect with oxygen to make one molecule of \(\(\text{H}_2\text{O}\)\). By capturing the products of combustion with absorbers and measuring the increase in their mass, scientists can deduce the initial content in the sample. This quantitative analysis allows chemists to piece together a clearer picture of the compound's makeup.

Molecular Composition

Molecular composition refers to the specific amounts and types of atoms that make up a molecule. Understanding the molecular composition is crucial in identifying unknown compounds and can provide insights into the chemical behavior of a substance.
For example, when analyzing the molecular composition of propenoic acid through combustion analysis, we first convert the absorbed masses of water and carbon dioxide to moles. This calculation is a key step because it shifts our perspective from mass to moles, aligning with Avogadro's principle which considers chemical reactions in terms of atoms and molecules, not grams.

• Water ((\(\text{H}_2\text{O}\)) contains two hydrogen atoms.
• Carbon dioxide ((\(\text{CO}_2\)) contains one carbon atom.

By determining the number of moles of \(\(\text{H}_2\text{O}\)\) and \(\(\text{CO}_2\)\), we gain valuable information about how many hydrogen and carbon atoms are present. This information is critical in constructing the empirical formula of the compound and helps cross-verify its identity.

Chemical Formula Determination

Chemical formula determination is the process of figuring out the ratios of atoms in a compound. The empirical formula is derived from these ratios and reflects the simplest whole-number ratio of atoms within a molecule.
To determine a chemical formula, the calculated moles of each element, deduced from combustion products, are divided by the smallest amount present among them. This division yields a relative number of moles for each element, allowing the formulation of a whole-number ratio that translates directly into an empirical formula.

• If necessary, these ratios are adjusted to the nearest whole numbers to provide clarity and consistency.
• In complex cases, multiplication might be needed to eliminate fractions.

For example, in finding the empirical formula of propenoic acid, the analysis showed approximately 2.72, 2.05, and 1.00 for hydrogen, carbon, and oxygen, respectively. Simplifying these figures gives a clear formula, adjusting as needed to the nearest whole number reveals the empirical formula provided as \(\(\text{C}_2\text{H}_3\text{O}\)\), which can be used for further characterization and application determination.