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

Question: Draw a portion of the tetrachloroethylene polymer chain and calculate its molar mass, given that it contains \(3.2 \times 10^{3}\) tetrachloroethylene molecules. Finally, calculate the mass percentages of C and Cl in the polymer. Answer: A portion of the tetrachloroethylene polymer chain can be drawn as: Cl - C - Cl Cl - C - Cl Cl - C - Cl | | | Cl Cl Cl The molar mass of the polymer is 530,624 g/mol. The mass percentages of C and Cl in the polymer are 14.45% and 85.55%, respectively.

Step-by-step solution

(a) Drawing the polymer chain

The formula for the tetrachloroethylene molecule is \(\mathrm{C_2Cl_4}\). One unit of the polymer is made by removing one Cl from each carbon in two tetrachloroethylene molecules and bonding the two carbons together. The structure of a portion of the polymer chain can be drawn as follows: Cl - C - Cl Cl - C - Cl Cl - C - Cl | | | Cl Cl Cl

(b) Calculating the molar mass of the polymer

To find the molar mass of the polymer, we first need to determine the molar mass of one tetrachloroethylene molecule. \(\mathrm{C_2Cl_4}\) contains: - 2 carbon (C) atoms: molar mass = 2 x 12.01 g/mol \(\mathrm{(C)}\) - 4 chlorine (Cl) atoms: molar mass = 4 x 35.45 g/mol \(\mathrm{(Cl)}\) Adding these values, the molar mass of one tetrachloroethylene molecule is \(2\times12.01 + 4\times35.45 = 165.82\) g/mol. Given that the polymer contains \(3.2 \times 10^{3}\) tetrachloroethylene molecules, the molar mass of the polymer is: \(165.82\times 3.2 \times 10^3 = 530,624\) g/mol.

(c) Calculating the mass percents of C and Cl in the polymer

To calculate the mass percents of C and Cl in the polymer, we first look at the mass of carbon and chlorine in one tetrachloroethylene molecule: Mass of carbon (C) in a molecule = 2 x 12.01 g/mol \(\mathrm{(C)}\) Mass of chlorine (Cl) in a molecule= 4 x 35.45 g/mol \(\mathrm{(Cl)}\) Now, let's calculate the mass percentages for C and Cl: Mass percentage of C: \(\frac{2 \times 12.01}{165.82} \times100 = 14.45\%\) Mass percentage of Cl: \(\frac{4 \times 35.45}{165.82} \times100 = 85.55\%\) So, the mass percentages of \(\mathrm{C}\) and \(\mathrm{Cl}\) in the tetrachloroethylene polymer are 14.45% and 85.55%, respectively.

Key concepts

Molar Mass Calculations

When studying polymers, understanding the concept of molar mass calculations is key. Molar mass, expressed in grams per mole (g/mol), tells us how much one mole of a substance weighs. To find the molar mass, we sum up the atomic masses of each atom in a molecule. For instance, in the tetrachloroethylene molecule \(\mathrm{C_2Cl_4}\), you have:

• 2 carbon (\(\mathrm{C}\)) atoms, each with a molar mass of 12.01 g/mol
• 4 chlorine (\(\mathrm{Cl}\)) atoms, each with a molar mass of 35.45 g/mol

Adding these values together gives the molar mass of one tetrachloroethylene molecule as:\[2 \times 12.01 + 4 \times 35.45 = 165.82 \, \text{g/mol}\]To find the molar mass of a polymer chain constructed from these molecules, multiply this molecular mass by the number of repeating units in the polymer chain. Thus, if a polymer contains \(3.2 \times 10^3\) tetrachloroethylene molecules, its molar mass is:\[165.82 \times 3.2 \times 10^3 = 530,624 \, \text{g/mol}\]Compatibility of atomic masses and Avogadro's number ensures that chemical calculations remain consistent across various quantities.

Mass Percentage Calculation

Once you have the molar mass of a molecule, you can calculate how much of that mass is due to each element, known as mass percentage calculation. This involves determining the proportion by mass of each component element in a compound. Using tetrachloroethylene (\(\mathrm{C_2Cl_4}\)) as an example:First, calculate the total mass of each type of atom within one molecule:

• Carbon (\(\mathrm{C}\)) mass: \(2 \times 12.01 = 24.02 \, \text{g/mol}\)
• Chlorine (\(\mathrm{Cl}\)) mass: \(4 \times 35.45 = 141.8 \, \text{g/mol}\)

To find the mass percentage of carbon in the molecule:\[\frac{24.02}{165.82} \times 100 = 14.45\%\]For chlorine, calculate similarly:\[\frac{141.8}{165.82} \times 100 = 85.55\%\]This calculation reveals that carbon constitutes 14.45% of the mass while chlorine accounts for 85.55%. Understanding these percentages can help determine the composition and properties of polymers.

Tetrachloroethylene Polymer

Tetrachloroethylene is a foundational molecule for creating certain types of polymers. Polymerization involves binding individual molecules, like tetrachloroethylene \(\mathrm{C_2Cl_4}\), into long chains or networks.In the case of tetrachloroethylene's polymer, the structure is formed by modifying and connecting these repeating units. Typically, it involves removing a chlorine atom from each tetrachloroethylene molecule and linking the carbon atoms together, resulting in a repetitive sequence, such as:

Cl - C - Cl Cl - C - Cl Cl - C - Cl

This configuration highlights how chlorine atoms remain bonded on the sides of the polymer chain while carbon forms the backbone.Polymers, like those made from tetrachloroethylene, are significant in various applications due to their strong chemical resistance and stability. Understanding the process of polymerization and the resulting structure helps in designing materials with specific properties needed for industrial applications.