Question

Hexachlorophene, a compound made up of atoms of carbon, hydrogen, chlorine, and oxygen, is an ingredient in germicidal soaps. Combustion of a 1.000 -g sample yields \(1.407 \mathrm{~g}\) of carbon dioxide, \(0.134 \mathrm{~g}\) of water, and \(0.523 \mathrm{~g}\) of chlorine gas. What are the mass percents of carbon, hydrogen, oxygen, and chlorine in hexachlorophene?

Short answer

Answer: To find the mass percentages of carbon, hydrogen, oxygen, and chlorine in the hexachlorophene sample, follow the steps in the provided solution to calculate the mass of each element in the sample. Then, calculate the mass percentages by dividing the mass of each element by the total mass of the sample and multiplying by 100.

Step-by-step solution

Determine the mass of carbon from the mass of carbon dioxide

Since complete combustion of the sample yields carbon dioxide (CO₂), we can obtain the mass of carbon by using the mass ratio of carbon to carbon dioxide. This ratio is $$\frac{m_\text{C}}{m_\text{CO₂}} = \frac{12.01 \,\text{g/mol}}{44.01 \,\text{g/mol}}.$$ Given that the mass of carbon dioxide is \(1.407 \,\text{g}\), we can then find the mass of carbon in the sample as $$m_\text{C} = \frac{12.01}{44.01} \times 1.407 \,\text{g}.$$

Determine the mass of hydrogen from the mass of water

Similarly, we can obtain the mass of hydrogen by using the mass ratio of hydrogen to water. This ratio is $$\frac{2 \times m_\text{H}}{m_\text{H₂O}} = \frac{2 \times 1.01\, \text{g/mol}}{18.02\, \text{g/mol}}.$$ Given that the mass of water is \(0.134 \,\text{g}\), we can then find the mass of hydrogen in the sample as $$m_\text{H} = \frac{2 \times 1.01}{18.02} \times 0.134 \,\text{g}.$$

Determine the mass of chlorine from the mass of chlorine gas

The mass of chlorine can be determined directly from the mass of chlorine gas, since chlorine gas is a diatomic molecule (Cl₂) and consists only of chlorine atoms. Therefore, \(m_\text{Cl} =0.523 \,\text{g}\).

Determine the mass of oxygen

To find the mass of oxygen in the sample, we will subtract the sum of the masses of carbon, hydrogen, and chlorine from the initial mass of the sample. Thus, $$m_\text{O} = 1.000\, \text{g} - (m_\text{C} + m_\text{H} + m_\text{Cl}).$$

Calculate the mass percentages

Finally, we will calculate the mass percentages of carbon, hydrogen, oxygen, and chlorine by dividing their respective masses by the initial mass of the sample and multiplying by 100. This will give us the following: $$\%_\text{C} = \frac{m_\text{C}}{1.000}\times 100,\%_\text{H} =\frac{m_\text{H}}{1.000}\times 100,\%_\text{O} =\frac{m_\text{O}}{1.000}\times 100,\%_\text{Cl} = \frac{m_\text{Cl}}{1.000}\times 100.$$ Compute these percentages using the masses obtained in Steps 1 - 4.