Question

Consider a polymer made from tetrachloroethylene. (a) Draw a portion of the polymer chain. (b) What is the molar mass of the polymer if it contains \(3.2 \times 10^{3}\) tetrachloroethylene molecules? (c) What are the mass percents of \(\mathrm{C}\) and \(\mathrm{Cl}\) in the polymer?

Short answer

Answer: The mass percents of carbon and chlorine in the polymer are 14.48% C and 85.52% Cl.

Step-by-step solution

Draw a portion of the polymer chain

For tetrachloroethylene, the chemical formula is \(\mathrm{C_2Cl_4}\) which contains two carbon atoms and four chlorine atoms. A portion of the polymer chain is represented by a series of tetrachloroethylene molecules connected by single bonds between carbon atoms: \(\mathrm{Cl-} \underset{\smile}{\mathrm{C}}\overset{\mathrm{Cl}}{} - \overset{\smile }{\mathrm{C}} {\mathrm{- }} \underset{\mathrm{Cl}}{} - \overset{\smile }{\mathrm{C}} {\mathrm{- }} \underset{\mathrm{Cl}}{} - ...\) Note that two of the chlorine atoms are connected to each carbon atom, and the polymer chain continues in a similar pattern.

Calculate the molar mass of the polymer chain

To determine the molar mass of the polymer, first find out the molar mass of a single tetrachloroethylene molecule. Molar mass of tetrachloroethylene = (2 × Molar mass \(\mathrm{C}\)) + (4 × Molar mass \(\mathrm{Cl}\)) = (2 × 12.01 g/mol) + (4 × 35.45 g/mol) = 24.02 g/mol + 141.8 g/mol = 165.82 g/mol Since the polymer contains \(3.2 × 10^3\) tetrachloroethylene molecules, the molar mass of the polymer chain is: Molar mass of polymer chain = (Number of tetrachloroethylene molecules) × (Molar mass of tetrachloroethylene) = \(3.2 × 10^3\) × 165.82 g/mol = 530,624 g/mol

Calculate mass percents of carbon and chlorine

Finally, we need to find out the mass percents of carbon and chlorine in the polymer. Mass percent of \(\mathrm{C}\) = \(\frac{\text{(Number of carbon atoms × Molar mass of C)}}{\text{Molar mass of tetrachloroethylene}}\) × 100% = \(\frac{(2 × 12.01 \, \text{g/mol})}{165.82 \, \text{g/mol}}\) × 100% = 14.48% Mass percent of \(\mathrm{Cl}\) = \(\frac{\text{(Number of chlorine atoms × Molar mass of Cl)}}{\text{Molar mass of tetrachloroethylene}}\) × 100% = \(\frac{(4 × 35.45 \, \text{g/mol})}{165.82 \, \text{g/mol}}\) × 100% = 85.52% To summarize: (a) The portion of the polymer chain is as follows: \(\mathrm{Cl-} \underset{\smile}{\mathrm{C}}\overset{\mathrm{Cl}}{} - \overset{\smile }{\mathrm{C}} {\mathrm{- }} \underset{\mathrm{Cl}}{} - \overset{\smile }{\mathrm{C}} {\mathrm{- }} \underset{\mathrm{Cl}}{} - ...\) (b) The molar mass of the polymer if it contains \(3.2 × 10^3\) tetrachloroethylene molecules is 530,624 g/mol. (c) The mass percents of carbon and chlorine in the polymer are 14.48% \(\mathrm{C}\) and 85.52% \(\mathrm{Cl}\).