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Chapter 12: Problem 83

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

Expert verified
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

01

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.
02

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.
03

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.
04

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.

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