Problem 155 - Chemistry An Atoms First Approach

Question

Para-cresol, a substance used as a disinfectant and in the manufacture of several herbicides, is a molecule that contains the elements carbon, hydrogen, and oxygen. Complete combustion of a 0.345-g sample of \(p\)-cresol produced 0.983 g carbon dioxide and \(0.230 \mathrm{g}\) water. Determine the empirical formula for \(p\)-cresol.

Step-by-Step Solution

Answer

The empirical formula for para-cresol is \( C_7H_8O \).

Step 1: Calculate the moles of carbon and hydrogen

Using the molar masses of carbon dioxide (\(CO_2\), 44.01 g/mol) and water (\(H_2O\), 18.02 g/mol), we find the moles of carbon and hydrogen present in the produced compounds. Moles of carbon in \(CO_2\): \((0.983 \, g \, CO_2) \times (\frac{1 \, mol \, CO_2}{ 44.01 \, g}) \times \frac{1 \, mol \, C}{1 \, mol \, CO_2} = 0.0223 \, mol \, C\). Moles of hydrogen in \(H_2O\): \((0.230 \, g \, H_2O) \times (\frac{1 \, mol \, H_2O}{18.02 \, g}) \times \frac{2 \, mol \, H}{1 \, mol \, H_2O} = 0.0255 \, mol \, H\).

Step 2: Find the moles of oxygen in the sample

Using mole conservation, the moles of oxygen in para-cresol can be found by subtracting the moles of carbon and hydrogen from the total moles of para-cresol. Total moles of para-cresol = \(\frac{0.345 g}{\textit{molar mass of para-cresol}}\). Let \(x\) be the moles of oxygen in para-cresol. Then, Total moles of para-cresol = moles of \(C +\) moles of \(H +\) moles of \(O\). \(\frac{0.345 \, g}{\textit{molar mass of para-cresol}} = 0.0223 \, mol \, C + 0.0255 \, mol \,H + x \, mol \, O\). Proceed to find the value of \(x\). Since we do not yet know the molecular formula of \(p\)-cresol, we will calculate the oxygen mass using the percent proportion: \(\dfrac{0.345 g - (0.0223 mol \times 12.01 g/mol \, C + 0.0255 mol \times 1.008 g/mol \, H)}{0.345 g} \times 100\%\). Oxygen mass = \(0.345\, g - (0.267 \, g \, C + 0.0255 \, g \, H)\). Oxygen mass = \(0.345 \, g - 0.2925 \, g = 0.0525 \, g \, O\). Moles of oxygen = \(\dfrac{0.0525 \, g}{16.00 \, g/mol \, O} = 0.00328 \, mol\, O\).

Step 3: Convert the ratio of moles to the simplest whole number ratio

Now that we have the moles of each element, finding the ratio of the moles will help to determine the empirical formula. Moles ratio: \(\dfrac{C}{0.0223}\): \(\dfrac{H}{0.0255}\): \(\dfrac{O}{0.00328}\). To simplify the ratio, divide each mole count by the smallest mole count (0.00328): \(C:H:O \approx 6.8 : 7.8 : 1\) Rounding the ratios to the nearest whole numbers, we find the empirical formula: \(C_7H_8O\) Therefore, the empirical formula for para-cresol is \( C_7H_8O \).

Key Concepts

Combustion Analysis

Combustion analysis is a laboratory technique commonly used in chemistry to determine the elemental composition of a substance by burning it. In the case of organic compounds, combustion in excess oxygen results in the formation of carbon dioxide and water, which are then measured. From the amounts of these products, one can calculate the amount of carbon and hydrogen present in the original compound.

For example, when para-cresol is burned, the carbon is all converted into carbon dioxide, and the hydrogen is converted into water. By knowing the masses of carbon dioxide and water produced, and using their molar masses (44.01 g/mol for carbon dioxide and 18.02 g/mol for water), we can work backwards to find the moles of carbon and hydrogen in the original sample. This step is crucial for determining the empirical formula, as it reveals how much of each element was present in the original substance.

Mole Concept

The mole concept is the cornerstone of chemistry, as it allows chemists to count particles by weighing. One mole of any substance contains the same number of entities (e.g., atoms or molecules) as there are atoms in 12 grams of carbon-12, which is approximately 6.022 x 10^23, according to Avogadro's number.

In the context of our exercise, moles provide a crucial link between the mass of substances (like the 0.983 g of CO2 and the 0.230 g of H2O from the combustion of para-cresol) and the number of atoms they contain. Calculating the number of moles of carbon from the carbon dioxide and hydrogen from the water involves simple division by their respective molar masses.

Stoichiometry

Stoichiometry is the aspect of chemistry that relates to the quantitative relationships between reactants and products in a chemical reaction. It's based on the conservation of mass and the concept of moles, enabling the calculation of quantities required or produced in a reaction.

When applying stoichiometry to our problem, you should first note the proportions of elements in the products of combustion (carbon dioxide and water) and relate them back to the original compound. By applying the stoichiometric coefficients from the balanced combustion equation, we determine the exact number of moles of each element that combined to form para-cresol. In the solution steps, the mole to mole conversions adhere to these fixed ratios defined by the chemical equation of the combustion process.

Molecular Composition

Molecular composition refers to the types and numbers of atoms that make up a molecule. The empirical formula is the simplest whole-number ratio of these atoms. To find the empirical formula, one must know the moles of each element in the compound, as this ratio directly corresponds to the ratio of atoms in the molecule.

In the case of para-cresol, after determining the moles of carbon, hydrogen, and oxygen, these values were then used to calculate the simplest mole ratio of the elements, which resulted in the empirical formula of C7H8O. This formula provides valuable information about the molecular composition of para-cresol—the most simplified representation of its constituent elements.