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 \(0.345-\mathrm{g}\) sample of \(p\) -cresol produced 0.983 g carbon dioxide and 0.230 \(\mathrm{g}\) water. Determine the empirical formula for \(p\) -cresol.

Short answer

The empirical formula of p-cresol is \(C_7H_8O\).

Step-by-step solution

Determine the moles of CO_2 and H_2O produced

Given: Mass of CO_2 produced = 0.983 g Mass of H_2O produced = 0.230 g Molar mass of CO_2 = 12.01 (Carbon) + 2 * 16.00 (Oxygen) = 44.01 g/mol Molar mass of H_2O = 2 * 1.01 (Hydrogen) + 16.00 (Oxygen) = 18.02 g/mol Moles of CO_2 produced = mass of CO_2 / molar mass of CO_2 = 0.983 g / 44.01 g/mol ≈ 0.0223 mol Moles of H_2O produced = mass of H_2O / molar mass of H_2O = 0.230 g / 18.02 g/mol ≈ 0.0128 mol

Determine the moles of C, H, and O in p-cresol

In one mole of CO_2, there is one mole of Carbon. Thus, moles of Carbon in p-cresol = moles of CO_2 produced = 0.0223 mol In one mole of H_2O, there are two moles of Hydrogen. Thus, moles of Hydrogen in p-cresol = 2 * moles of H_2O produced = 2 * 0.0128 mol = 0.0256 mol Now we need to find the moles of Oxygen in p-cresol. From the initial mass of p-cresol given (0.345 g), we can find the mass of Oxygen by subtracting the mass of Carbon and Hydrogen present: Mass of Carbon = moles of Carbon * molar mass of Carbon = 0.0223 mol * 12.01 g/mol ≈ 0.267 g Mass of Hydrogen = moles of Hydrogen * molar mass of Hydrogen = 0.0256 mol * 1.01 g/mol ≈ 0.0258 g Mass of Oxygen = mass of p-cresol - mass of Carbon - mass of Hydrogen = 0.345 g - 0.267 g - 0.0258 g ≈ 0.052 g Now we can find the moles of Oxygen: Moles of Oxygen = mass of Oxygen / molar mass of Oxygen = 0.052 g / 16.00 g/mol ≈ 0.00325 mol

Find the ratio of C: H: O moles

To find the empirical formula, we need to find the simplest whole number ratio of C: H: O atoms in the molecule. First, divide all the moles by the lowest number of moles: Carbon = 0.0223 / 0.00325 ≈ 6.86 Hydrogen = 0.0256 / 0.00325 ≈ 7.87 Oxygen = 0.00325 / 0.00325 ≈ 1 We observe that all the ratios are close to whole numbers. We can round them to the nearest whole number to obtain: C: H: O ≈ 7:8:1

Write the empirical formula for p-cresol

The empirical formula is written using the whole number ratio of atoms. Therefore, the empirical formula of p-cresol is: \(C_7H_8O\) And that is the final answer.

Key concepts

Combustion Reaction

Often in chemistry, to analyze compounds containing carbon, a combustion reaction is used. This reaction involves burning a substance in the presence of oxygen to produce certain products. In the case of organic compounds like para-cresol, the main products are carbon dioxide (CO_2) and water (H_2O). By measuring the amounts of CO_2 and H_2O, we can gain insight into the original compound’s structure. During combustion, the carbon atoms in para-cresol become part of the carbon dioxide molecules, and hydrogen atoms form water molecules. The oxygen atoms, meanwhile, come from both the para-cresol and the O_2 in the air used to support combustion. This transformation provides a way to determine the empirical formula as it reflects the number of atoms in the smallest unit of the compound.

Mole Calculation

In chemical equations, counting the exact number of molecules isn't feasible due to their tininess, so we use moles. A mole is a standard unit in chemistry that represents a specific number, about 6.022 x 10^{23}, of particles, be it atoms, molecules, or ions. For example, once we have the mass of the combustion products, CO_2 and H_2O, we convert these masses into moles using their respective molar masses. The details are:

• For CO_2, the molar mass is 44.01 g/mol, and for H_2O, it is 18.02 g/mol.
• Using the provided masses from the problem ( 0.983 g CO_2 and 0.230 g H_2O), we find there are approximately 0.0223 moles of CO_2 and 0.0128 moles of H_2O.

This step is crucial because it sets the stage for determining the proportions of each element in the empirical formula.

Chemical Stoichiometry

Stoichiometry is the field of chemistry that deals with the relative quantities of reactants and products in chemical reactions. By examining these relationships, we can understand how much of each substance is consumed or produced in a reaction. In our context, stoichiometry helps to calculate the number of moles of each type of atom in para-cresol. Here’s how:

• Every mole of CO_2 corresponds to one mole of carbon atoms.
• Each mole of H_2O provides two moles of hydrogen atoms.
• Using the mass difference from the initial mass, we calculate the moles of oxygen.

These computations enable us to deduce the simplest whole number ratio of each element, crucial for establishing the empirical formula.

Organic Compounds

Organic compounds, primarily composed of carbon, hydrogen, and, sometimes, oxygen, form the backbone of living organisms and various industrial materials. Para-cresol, like many organic substances, can be analyzed by breaking it down into these basic elements via combustion.To determine its empirical formula from its combustion products, consider these aspects:

• The empirical formula gives the simplest ratio of these elements.
• Understanding organic compounds involves looking at both their structural formula (or how atoms are bonded together) and their empirical formula (or the simplified version).
• In our example of para-cresol, we use elemental analysis through combustion to solve for its empirical formula: \(C_7H_8O\).

This step-by-step breakdown is vital for chemistry students to understand how to derive empirical formulas from organic combustion reactions.