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Chapter 15: Problem 27

The vulcanization of polyisoprene is accomplished with sulfur atoms according to Equation 15.4. If \(57 \mathrm{wt} \%\) sulfur is combined with polyisoprene, how many crosslinks will be associated with each isoprene repeat unit if it is assumed that, on the average, six sulfur atoms participate in each crosslink?

Short Answer

Expert verified
Answer: Approximately 0.02551 crosslinks are associated with each isoprene repeat unit.

Step by step solution

01

Calculate the molar mass of sulfur and polyisoprene

First, we need to find the molar mass of sulfur and polyisoprene. The molar mass of sulfur (S) is 32 g/mol. For polyisoprene, we need to consider the isoprene (C5H8) unit, which has a molar mass of (5(12.01) + 8(1.01)) g/mol = 68.07 g/mol.
02

Calculate the mass of sulfur and polyisoprene in 100 grams of the compound

Since we know that 45.3 wt% of sulfur is combined with polyisoprene, this means that in 100 grams of the compound, we have 45.3 grams of sulfur and (100-45.3) grams of polyisoprene.
03

Calculate the moles of sulfur and polyisoprene

To find the moles of sulfur and polyisoprene, we will use their molar masses and the mass of each component in 100 grams of the compound. Moles of sulfur = \(\frac{45.3 \text{ g}}{32 \text{ g/mol}}\) = 1.415625 mol Moles of polyisoprene = \(\frac{100-45.3 \text{ g}}{68.07 \text{ g/mol}}\) = 0.803625 mol
04

Calculate the mol percentage of sulfur atoms

Now we can find the mol percentage of sulfur atoms in the compound: Mol percent of sulfur = \(\frac{1.415625 \text{ mol}}{1.415625 \text{ mol} + 0.803625 \text{ mol}} \times 100 \%\) = 63.77 %
05

Calculate the number of sulfur atoms per isoprene repeat unit

Since we know that five sulfur atoms participate in each crosslink, and the mol percentage of sulfur atoms is 63.77%, we can find the number of sulfur atoms per isoprene repeat unit: Number of sulfur atoms per isoprene repeat unit = \(\frac{63.77 \%}{100 \%} \div 5\) = 0.12754 sulfur atoms
06

Determine the number of crosslinks per isoprene repeat unit

Finally, we can find the number of crosslinks associated with each isoprene repeat unit: Number of crosslinks per isoprene repeat unit = \(\frac{0.12754 \text{ sulfur atoms}}{5 \text{ sulfur atoms/crosslink}}\) = 0.02551 crosslinks Thus, there will be approximately 0.02551 crosslinks associated with each isoprene repeat unit.

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Most popular questions from this chapter

Ten kilograms of polybutadiene is vulcanized with \(4.8 \mathrm{~kg}\) sulfur. What fraction of the possible crosslink sites is bonded to sulfur crosslinks, assuming that, on the average, \(4.5\) sulfur atoms participate in each crosslink?

Make two schematic plots of the logarithm of relaxation modulus versus temperature for an amorphous polymer (curve \(C\) in Figure 15.8). (a) On one of these plots demonstrate how the behavior changes with increasing molecular weight. (b) On the other plot, indicate the change in behavior with increasing crosslinking.

List the two molecular characteristics that are essential for elastomers.

For thermoplastic polymers, cite five factors that favor brittle fracture.

In Figure 15.28, the logarithm of \(E_{r}(t)\) versus the logarithm of time is plotted for polyisobutylene at a variety of temperatures. Make a plot of \(E_{r}(10)\) versus temperature and then estimate its \(T_{g}\).
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