For each of the following pairs of polymers, do the following: (1) state whether it is possible to decide whether one polymer has a higher tensile modulus than the other; (2) if his is possible, note which has the higher ensile modulus and then cite the reason(s) or your choice; and (3) if it is not possible o decide, then state why. a) Random acrylonitrile-butadiene copolyner with \(10 \%\) of possible sites crosslinked; ilternating acrylonitrile-butadiene copolymer with \(5 \%\) of possible sites crosslinked (b) Branched and syndiotactic polypropylene with a degree of polymerization of 5000 ; linear and isotactic polypropylene with a degree of polymerization of 3000 (c) Branched polyethylene with a numberaverage molecular weight of \(250,000 \mathrm{~g} / \mathrm{mol}\); linear and isotactic poly(vinyl chloride) with a number-average molecular weight of \(200,000 \mathrm{~g} / \mathrm{mol}\)

Step by step solution

01

Comparison of crosslinking percentages

Compare the crosslinking percentages: random acrylonitrile-butadiene copolymer has 10% of possible sites crosslinked while the alternating acrylonitrile-butadiene copolymer has 5% of possible sites crosslinked.

02

Deciding the higher tensile modulus

It's possible to decide which polymer has a higher tensile modulus. The random acrylonitrile-butadiene copolymer with 10% of possible sites crosslinked has a higher tensile modulus than the alternating acrylonitrile-butadiene copolymer with 5% of possible sites crosslinked.

03

Explanation

The reason for this conclusion is that a higher amount of crosslinking leads to a stronger and stiffer material, giving it a higher tensile modulus. #b) Branched syndiotactic polypropylene vs Linear isotactic polypropylene#

04

Comparison of degree of polymerization

Compare the degree of polymerization for both polymers: branched syndiotactic polypropylene (5000) and linear isotactic polypropylene (3000).

05

Deciding the higher tensile modulus

It's possible to decide which polymer has a higher tensile modulus. The linear isotactic polypropylene with a degree of polymerization of 3000 has a higher tensile modulus than the branched syndiotactic polypropylene with a degree of polymerization of 5000.

06

Explanation

The reason for this conclusion is that linear isotactic polymers have a more regular structure that allows for better packing and stronger intermolecular forces, which contributes to a higher tensile modulus. #c) Branched polyethylene vs linear isotactic poly(vinyl chloride)#

07

Comparison of molecular weight

Compare the molecular weight for both polymers: branched polyethylene (\(250,000 \mathrm{~g} / \mathrm{mol}\)) and linear isotactic poly(vinyl chloride) (\(200,000 \mathrm{~g} / \mathrm{mol}\)).

08

Deciding the higher tensile modulus

It's not possible to decide which polymer has a higher tensile modulus based on the given information.

09

Explanation

The reason for this conclusion is that we are comparing two different types of polymers with different molecular structures and arrangements. The given information about molecular weights is not sufficient to determine the tensile modulus in this case. Other factors, such as crystallinity and intermolecular forces, should also be considered.

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