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Chapter 14: Problem 16

The number-average molecular weight of a poly(styrene-butadiene) alternating copolymer is \(1,350,000 \mathrm{~g} / \mathrm{mol}\); determine the average number of styrene and butadiene repeat units per molecule.

Short Answer

Expert verified
Answer: There are approximately 8,534 styrene repeat units and 8,534 butadiene repeat units per molecule of the poly(styrene-butadiene) copolymer.

Step by step solution

01

Find the molecular weights of styrene and butadiene repeat units

To solve the problem, we need to know the molecular weights of styrene and butadiene repeat units. The repeat unit of styrene is C8H8 while the repeat unit of butadiene is C4H6. Using the molecular weights of carbon (12.01 g/mol) and hydrogen (1.01 g/mol), we can calculate the molecular weights of styrene and butadiene repeat units. Molecular weight of styrene repeat unit = (8 × 12.01) + (8 × 1.01) = 104.14 g/mol Molecular weight of butadiene repeat unit = (4 × 12.01) + (6 × 1.01) = 54.10 g/mol
02

Calculate the average number of styrene and butadiene repeat units per molecule

Using the molecular weights of styrene and butadiene repeat units, we can determine the average number of these repeat units per molecule. We are given that the number-average molecular weight of the poly(styrene-butadiene) copolymer is 1,350,000 g/mol. Because it is an alternating copolymer, the number of styrene and butadiene repeat units should be equal. Let x be the number of styrene repeat units and y be the number of butadiene repeat units. According to the problem, x = y. So, the total molecular weight of the copolymer, M_n, will be: M_n = (104.14 * x) + (54.10 * y) Since we know that M_n is 1,350,000 g/mol and x = y, we can write the equation as: 1,350,000 = 104.14 * x + 54.10 * x
03

Solve for x to find the average number of styrene repeat units per molecule

Now we need to solve for x in the equation: 1,350,000 = (104.14 + 54.10) * x First, combine the terms in the parentheses: 1,350,000 = (158.24) * x Now, divide both sides by 158.24 to find x: x ≈ 8,534 Since x represents the number of styrene repeat units and x = y, then there are approximately 8,534 styrene repeat units and 8,534 butadiene repeat units per molecule of the poly(styrene-butadiene) copolymer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Polymer Science
Polymer science is the field that studies polymers, large molecules composed of repeating structural units known as monomers. These substances are ubiquitous in daily life—found in everything from plastic bottles to fabrics and even biological systems.

Understanding polymer science is foundational for grasping how different polymers are synthesized, how they behave under various conditions, and how their properties can be tailored for specific needs through molecular modification. It's a multi-disciplinary field overlapping with chemistry, physics, and engineering.
Molecular Weight of Copolymers
Copolymers are polymers formed from two or more different types of monomers, which can result in varied properties. The molecular weight of a copolymer is a crucial parameter as it influences the physical properties such as strength, flexibility, and solubility.

To calculate the molecular weight of a copolymer, we assess the contributions from each type of repeat unit. For instance, in an alternating copolymer where each monomer appears in a regular sequence, the molecular weight can be derived from the sum of the weights of each monomer unit multiplied by their respective occurrence in the polymer chain.
Chemistry of Polymers
The chemistry of polymers involves understanding the reactions and processes that create polymer chains. This includes polymerization methods such as addition and condensation polymerization, and the mechanisms governing them—chain growth versus step growth, for example.

Furthermore, functional groups on the monomers can affect the overall chemistry of the resulting polymer, influencing cross-linking, chain flexibility, and interactions with other molecules. Such considerations are vital when synthesizing polymers with desired characteristics for specific applications.
Stoichiometry
Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. In polymer science, stoichiometry is important when calculating how much of each monomer is needed to achieve a desired molecular weight in a polymer.

This requires balancing the molecular contributions of each monomer within a copolymer's structure, ensuring that the proportions reflect the target weight and functionality desired in the finished polymer. It's a fundamental concept for ensuring that polymer synthesis is both efficient and effective.

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Most popular questions from this chapter

For a linear freely rotating polymer molecule, the total extended chain length \(L\) depends on the bond length between chain atoms \(d\), the total number of bonds in the molecule \(N\), and the angle between adjacent backbone chain atoms \(\theta\), as follows: $$ L=N d \sin \left(\frac{\theta}{2}\right) $$ Furthermore, the average end-to-end distance \(r\) for a randomly winding polymer molecule in Figure \(14.6\) is equal to $$ r=d \sqrt{N} $$ A linear polytetrafluoroethylene has a numberaverage molecular weight of \(500,000 \mathrm{~g} / \mathrm{mol}\); compute average values of \(L\) and \(r\) for this material.

On the basis of the structures presented in this chapter, sketch repeat unit structures for the following polymers: (a) polychlorotrifluoroethylene, and (b) poly(vinyl alcohol).

Argon diffuses through a high-density polyethylene (HDPE) sheet \(40 \mathrm{~mm}\) thick at a rate of \(4.0 \times 10^{-7}\left(\mathrm{~cm}^{3} \mathrm{STP}\right) / \mathrm{cm}^{2} \cdot \mathrm{s}\) at \(325 \mathrm{~K}\). The pressures of argon at the two faces are \(5000 \mathrm{kPa}\) and \(1500 \mathrm{kPa}\), which are maintained constant. Assuming conditions of steady state, what is the permeability coefficient at \(325 \mathrm{~K}\) ?

The density and associated percent crystallinity for two polytetrafluoroethylene materials are as follows: \begin{tabular}{cc} \hline\(\rho\left(\mathrm{g} / \mathrm{cm}^{3}\right)\) & crystallinity \((\%)\) \\\ \hline \(2.144\) & \(51.3\) \\ \(2.215\) & \(74.2\) \\ \hline \end{tabular} (a) Compute the densities of totally crystalline and totally amorphous polytetrafluoroethylene. (b) Determine the percent crystallinity of a specimen having a density of \(2.26 \mathrm{~g} / \mathrm{cm}^{3}\).

(a) Compute the repeat unit molecular weight of polystyrene. (b) Compute the number-average molecular weight for a polystyrene for which the degree of polymerization is 25,000 .
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