Question

The monomer of poly(vinyl chloride) has the formula \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl} .\) If there are 1565 repeat units in a single chain of the polymer, what is the molecular mass (in amu) of that chain?

Short answer

97812.5 amu

Step-by-step solution

Identify the Monomer's Formula

The formula for the monomer is \(\text{C}_2\text{H}_3\text{Cl}\).

Determine the Atomic Masses

Find the atomic masses of each element: Carbon (C) is approximately \(\text{12 amu}\), Hydrogen (H) is approximately \(\text{1 amu}\), and Chlorine (Cl) is approximately \(\text{35.5 amu}\).

Calculate the Molecular Mass of the Monomer

The molecular mass of the monomer \(\text{C}_2\text{H}_3\text{Cl}\) is calculated as follows: \[2 \times \text{C} + 3 \times \text{H} + 1 \times \text{Cl} = 2 \times 12 + 3 \times 1 + 35.5 = 24 + 3 + 35.5 = 62.5 \text{ amu}\]

Calculate the Total Molecular Mass

The total molecular mass of the polymer chain is given by multiplying the molecular mass of the monomer by the number of repeat units: \[1565 \times 62.5 \text{ amu} = 97812.5 \text{ amu}\]

Key concepts

Polymer Chemistry

Polymer chemistry involves the study of large molecules made up of repeating structural units called monomers. These monomers are linked together in a chain-like fashion. Common polymers include plastics, rubber, and DNA. For instance, in the exercise, the polymer is poly(vinyl chloride), abbreviated as PVC. PVC is widely used in pipes, cables, and many other products due to its durability and resistance to environmental degradation. Understanding the structure of these polymers allows chemists to predict and manipulate their properties for various applications. By analyzing a polymer's repeating molecular structure, such as \(\text{C}_2\text{H}_3\text{Cl}\) in PVC, we can calculate essential characteristics like molecular mass, which is critical for industrial processing and product formation.

Atomic Masses

Atomic masses are essential in chemistry for calculating molecular masses of compounds. Each element has a unique atomic mass, usually measured in atomic mass units (amu). Here are some typical atomic masses:

• Carbon (C): approximately 12 amu
• Hydrogen (H): approximately 1 amu
• Chlorine (Cl): approximately 35.5 amu

To find the molecular mass of a compound, we sum the atomic masses of its constituent elements according to their ratios given by the formula. For example, the atomic mass of monomer \(\text{C}_2\text{H}_3\text{Cl}\) is calculated by adding the masses of 2 carbon atoms, 3 hydrogen atoms, and 1 chlorine atom:
\[2 \times 12 + 3 \times 1 + 35.5 = 62.5 \text{ amu}\]
The precise weights of atoms in a molecule provide the foundation for a wide range of chemical calculations, from stoichiometry to complex reaction mechanisms.

Monomer Molecular Mass

The molecular mass of a monomer is the sum of the atomic masses of all the atoms in a single molecule of that monomer. This value is critical in understanding polymers because it allows us to determine the total molecular mass of the polymer. In our example, the monomer of PVC (\(\text{C}_2\text{H}_3\text{Cl}\)) has a molecular mass calculated as:
\[2 \times 12 + 3 \times 1 + 35.5 = 62.5 \text{ amu}\]
Once we have the molecular mass of a single monomer, we can extend this to find the molecular mass of the entire polymer. For a polymer with 1565 repeat units, the calculation is:
\[1565 \times 62.5 \text{ amu} = 97812.5 \text{ amu}\]
Thus, knowing the monomer molecular mass helps in scaling up to predict the properties and behaviors of the entire polymer macromolecule. This is essential for material science and engineering applications.