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Chapter 3: Problem 44

Para-cresol ( \(p\) -cresol) is used as a disinfectant and in the manufacture of herbicides. A 0.4039 g sample of this carbon-hydrogen-oxygen compound yields \(1.1518 \mathrm{g} \mathrm{CO}_{2}\) and \(0.2694 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) in combustion analysis. Its molecular mass is 108.1 u. For \(p\) -cresol, determine its (a) mass percent composition; (b) empirical formula; (c) molecular formula.

Short Answer

Expert verified
The p-cresol has a mass percent composition of Carbon: 77.97%; Hydrogen: 7.43%; Oxygen: 14.60%. The empirical formula is \(C_9H_{10}O\), and the molecular formula is \(C_9H_{10}O\)

Step by step solution

01

Determine the moles of CO2 and H2O

By using the molar mass of CO2 (44.01 g/mol) and H2O (18.02 g/mol), we can determine the moles of each in the samples: Moles of \(CO_2 = \frac{1.1518 g}{44.01 g/mol} = 0.0262 mol \) ; Moles of \( H_2O = \frac{0.2694 g}{18.02 g/mol} = 0.0149 mol \)
02

Compute the Mass of Carbon and Hydrogen

Each mole of \(CO_2\) contains 1 mole of carbon and each mole of \(H_2O\) contains 2 moles of hydrogen. Thus, the mass of carbon and hydrogen is calculated as follows: Mass of Carbon = 0.0262 mol x 12.01 g/mol = 0.3148 g. Mass of Hydrogen = 0.0149 mol x 2 x 1.008 g/mol = 0.030 g
03

Find out the Mass of Oxygen

Now we have the masses of carbon and hydrogen, we subtract these from the total mass of p -cresol to find the mass of oxygen: Mass of Oxygen = 0.4039 g (total) - 0.3148 g (C) - 0.030 g (H) = 0.0591 g
04

Calculate the Mass Percent Composition

The mass percent of each element = (mass of element / total mass) x 100%. So, Mass percent of Carbon = (0.3148 g / 0.4039 g) x 100 = 77.97% ; Mass percent of Hydrogen = (0.030 g / 0.4039 g) x 100 = 7.43% ; Mass percent of Oxygen = (0.0591 g / 0.4039 g) x 100 = 14.60%
05

Determine the Empirical Formula

To find the empirical formula, we convert the mass of each element to moles and then divide each by the smallest number of moles to get the mole ratio. Moles of C = 0.3148 g / 12.01 g/mol = 0.0262 mole ; Moles of H = 0.030 g / 1.008 g/mol = 0.0297 mole ; Moles of O = 0.0591 g / 16.00 g/mol = 0.00369 mole. The empirical formula is thus \(C_9H_{10}O\)
06

Determine the Molecular Formula

To get the molecular formula, the molar mass is divided by the mass of the empirical formula. The molecular mass of p-cresol is given as 108.1 g/mol. The empirical formula mass of \( C_9H_{10}O \) is (9 x 12.01) + (10 x 1.008) + (1 x 16.00) = 108.2 g/mol. The ratio is very close to 1, so the molecular formula is the same as the empirical formula, that is \(C_9H_{10}O\)

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Most popular questions from this chapter

Appendix E describes a useful study aid known as concept mapping. Using the method presented in Appendix \(\mathrm{E},\) construct a concept map illustrating the different concepts in Sections \(3-2\) and \(3-3\).

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