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Chapter 15: Problem 25

For the vulcanization of polyisoprene, compute the weight percent of sulfur that must be added to ensure that \(10 \%\) of possible sites will be crosslinked; assume that, on the average, 3.5 sulfur atoms are associated with each crosslink.

Short Answer

Expert verified
Answer: Approximately 56.87% of sulfur must be added.

Step by step solution

01

Calculate the molecular weight of polyisoprene and sulfur

We need to find the molecular weight of polyisoprene (C5H8) and sulfur (S8) in order to proceed with our calculations. The molecular weights of chemical elements are: C = 12.01 g/mol, H = 1.01 g/mol, and S = 32.07 g/mol. Using these values, we can find the molecular weights of polyisoprene and sulfur: - Molecular weight of polyisoprene: \((5 \times 12.01) + (8 \times 1.01) = 60.05 + 8.08 = 68.13 \frac {g}{mol}\) - Molecular weight of sulfur: 8 × 32.07= 256.56 \(\frac {g}{mol}\)
02

Determine the number of sites being crosslinked

Given that 10% of the possible sites will be crosslinked, we'll use the given information to determine the number of crosslinked sites: - 1 mole of polyisoprene has 10% crosslinked sites. - Number of crosslinked moles = \(0.10 \times 1 \, mole\)
03

Calculate the weight of sulfur required for the crosslinked sites

Since 3.5 sulfur atoms are associated with each crosslink, we can calculate the required weight of sulfur for the crosslinked sites: - Number of sulfur moles required = 0.10 × 3.5 = 0.35 moles - Weight of required sulfur = 0.35 moles × 256.56 \(\frac {g}{mol}\) = 89.79g
04

Compute the weight percent of sulfur to be added

Now, we compute the weight percent of sulfur to be added: - Weight of 1 mole of polyisoprene = 68.13g - Total weight including polyisoprene and sulfur = 68.13 + 89.79 = 157.92g - Weight percent of sulfur = \(\frac {89.79}{157.92} \times 100 \% \approx 56.87 \%\) Thus, approximately \(56.87 \%\) of sulfur must be added to ensure that \(10 \%\) of possible sites will be crosslinked in the vulcanization of polyisoprene, assuming that, on average, 3.5 sulfur atoms are associated with each crosslink.

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Most popular questions from this chapter

Fifteen kilogram of polychloroprene is vulcanized with \(5.2 \mathrm{kg}\) sulfur. What fraction of the possible crosslink sites is bonded to sulfur crosslinks, assuming that, on the average, 5.5 sulfur atoms participate in each crosslink?

Demonstrate, in a manner similar to Equation \(15.4,\) how vulcanization may occur in a chloroprene rubber.

Briefly explain how each of the following influences the tensile or yield strength of a semicrystalline polymer and why: (a) Molecular weight (b) Degree of crystallinity (c) Deformation by drawing (d) Annealing of an undeformed material

For each of the following pairs of polymers, do the following: (1) state whether or not it is possible to decide whether one polymer has a higher tensile strength than the other; (2) if this is possible, note which has the higher tensile strength and then cite the reason(s) for your choice; and (3) if it is not possible to decide, then state why. (a) Linear and isotactic poly(vinyl chloride) with a weight-average molecular weight of \(100,000 \mathrm{g} / \mathrm{mol} ;\) branched and atactic poly \((\) vinyl chloride) having a weight-average molecular weight of \(75,000 \mathrm{g} / \mathrm{mol}\) (b) Graft acrylonitrile-butadiene copolymer with \(10 \%\) of possible sites crosslinked; alternating acrylonitrile-butadiene copolymer with \(5 \%\) of possible sites crosslinked (c) Network polyester; lightly branched polytetrafluoroethylene

Normal butane and isobutane have boiling temperatures of -0.5 and \(-12.3^{\circ} \mathrm{C}(31.1\) and \(\left.9.9^{\circ} \mathrm{F}\right),\) respectively. Briefly explain this behavior on the basis of their molecular structures, as presented in Section 14.2.
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