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.

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

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

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

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.