Question

State whether each of these numbers is a reasonable value for a polymer's molecular weight: \(100 \mathrm{u}, 10,000 \mathrm{u},\) \(100,000 \mathrm{u}, 1,000,000 \mathrm{u} ?\)

Short answer

A 100 u molecular weight is not reasonable for a polymer, as it is smaller than the molecular weight of common monomers. However, 10,000 u, 100,000 u, and 1,000,000 u molecular weights are reasonable for polymers, as they fall within the expected range for various polymer chains and degrees of polymerization.

Step-by-step solution

1) 100 u molecular weight:

When looking at common monomers (e.g., ethylene, styrene), their molecular weights usually range from 25 u to 200 u. Since the molecular weight of a polymer is the sum of the molecular weights of its constituent monomers multiplied by the number of monomers (degree of polymerization), a polymer with a molecular weight smaller than that of a single monomer is not possible. Therefore, a polymer having a 100 u molecular weight is not reasonable.

2) 10,000 u molecular weight:

Considering that a common monomer has a molecular weight between 25 u to 200 u, a polymer with a molecular weight of 10,000 u would result from combining around 50 to 400 monomers, which is a reasonable range for a polymer chain. Consequently, a polymer having a 10,000 u molecular weight is reasonable.

3) 100,000 u molecular weight:

Given the molecular weights of common monomers, a polymer with a 100,000 u molecular weight would mean that it is composed of around 500 to 4,000 monomers. This is still reasonable, as many polymers have large numbers of monomers in their structure. Thus, a polymer having a 100,000 u molecular weight is reasonable.

4) 1,000,000 u molecular weight:

For a polymer with a 1,000,000 u molecular weight, it would have to consist of around 5,000 to 40,000 monomers. This value falls within the range expected for high molecular weight polymers and is still considered reasonable for certain polymers with high degrees of polymerization. Therefore, a polymer having a 1,000,000 u molecular weight is reasonable. In conclusion, among the given molecular weights, 100 u is not a reasonable value for the molecular weight of a polymer, while the others (10,000 u, 100,000 u, and 1,000,000 u) are reasonable values, depending on the type of polymer and its specific application.

Key concepts

Monomers

Monomers are the building blocks of polymers. These are the small, repeating units that link together through chemical bonds to form long chains known as polymers. Think of monomers as the tiny beads that can be strung together to create a necklace. Each monomer has its own molecular weight, typically ranging from 25 u to 200 u, depending on its complexity and structure.

The properties of the polymer, such as flexibility, strength, and thermal resistance, depend heavily on the type of monomers used and how they are arranged in the structure. For example:

• Ethylene, which forms polyethylene, or a simple, repeating carbon chain used in shopping bags.
• Styrene, used for polystyrene, a plastic often employed in packaging material and insulation.

Understanding monomers is key in predicting the behavior and molecular weight of polymers. Each monomer adds its weight to the overall molecular weight of the polymer, so a simple change in monomer type can alter the polymer's properties dramatically.

Degree of Polymerization

The degree of polymerization is a crucial concept in understanding polymer molecular weight. It refers to the number of monomer units present in a polymer chain. Think of it like the number of links in a chain - the more links, the longer and heavier the chain becomes.

The molecular weight of a polymer is directly influenced by its degree of polymerization. To calculate the molecular weight, multiply the molecular weight of a single monomer by the degree of polymerization:

• For a polymer made from ethylene (molecular weight of approximately 28 u), and a degree of polymerization of 1000, the total molecular weight would be 28,000 u.
• In this equation, Polymer MW = Monomer MW × Degree of Polymerization.

This concept allows us to understand how varying the number of monomers changes the molecular weight, impacting the polymer's physical and chemical properties.

Molecular Weight Range

The molecular weight range of a polymer defines its length and size, translating to different functionalities and applications. Molecular weights of polymers can vary widely - from a few thousand to several millions units of molecular weight (u).

A value of 100 u is too small, not exceeding even the molecular weight of a single monomer unit, making it an impractical measure for polymers.

• Molecular weights between 10,000 u and 100,000 u are considered typical for various applications, such as plastic materials.
• Higher molecular weights, like 1,000,000 u, are common in polymers with increased strength and endurance, often used in high-performance applications.

Whether a molecular weight is reasonable depends on the polymer's purpose and the properties it needs to exhibit. High molecular weight polymers generally have better mechanical properties but can become difficult to process due to their size.