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Chapter 14: Problem 20

Crosslinked copolymers consisting of 35 wt \(\%\) ethylene and 65 wt\% propylene may have elastic properties similar to those for natural rubber. For a copolymer of this composition, determine the fraction of both repeat unit types.

Short Answer

Expert verified
Question: Determine the mole fractions of ethylene and propylene in a crosslinked copolymer consisting of 35 wt% ethylene and 65 wt% propylene, which has elastic properties similar to natural rubber. Answer: The mole fraction of ethylene in the copolymer is approximately 44.7%, and the mole fraction of propylene is approximately 55.3%.

Step by step solution

01

Determine the molecular weight of ethylene and propylene

For this, we need to know the molecular formula for both compounds. Ethylene (C2H4) has 2 carbon atoms and 4 hydrogen atoms, whereas propylene (C3H6) has 3 carbon atoms and 6 hydrogen atoms. The atomic weights of carbon and hydrogen are 12 g/mol and 1 g/mol, respectively. Thus, the molecular weights of ethylene and propylene are: Ethylene (C2H4) = (2 × 12) + (4 × 1) = 28 g/mol Propylene (C3H6) = (3 × 12) + (6 × 1) = 42 g/mol
02

Calculate the mass-to-mole conversion factors for ethylene and propylene

Now that we know the molecular weights of both ethylene and propylene, we can calculate their respective mass-to-mole conversion factors: Conversion factor for ethylene = 1 mole / 28 g Conversion factor for propylene = 1 mole / 42 g
03

Convert the weight percentages to moles for both compounds

We will now convert the given weight percentages of 35 wt% ethylene and 65 wt% propylene to moles using the conversion factors derived in the previous step: Moles of ethylene = 35 g * (1 mole / 28 g) = 1.25 moles Moles of propylene = 65 g * (1 mole / 42 g) = 1.548 moles
04

Calculate the total moles of both compounds

To determine the mole fractions of both ethylene and propylene, we first need to calculate the total moles of the mixture: Total moles = Moles of ethylene + Moles of propylene = 1.25 moles + 1.548 moles = 2.798 moles
05

Calculate the mole fractions of ethylene and propylene

Now, we will calculate the mole fractions of both ethylene and propylene by dividing the moles of each compound by the total moles: Mole fraction of ethylene = (1.25 moles) / (2.798 moles) = 0.447 Mole fraction of propylene = (1.548 moles) / (2.798 moles) = 0.553 So, the fraction of ethylene repeat units in the crosslinked copolymer is about 44.7% and that of propylene repeat units is about 55.3%.

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Most popular questions from this chapter

The density and associated percent crystallinity for two polypropylene materials are as follows: $$\begin{array}{cc} \hline \rho\left(g / c m^{3}\right) & \text {Crystallinity (\%)} \\ \hline 0.904 & 62.8 \\ 0.895 & 54.4 \\ \hline \end{array}$$ (a) Compute the densities of totally crystalline and totally amorphous polypropylene. (b) Determine the density of a specimen having \(74.6 \%\) crystallinity.

Is it possible to have a poly(vinyl chloride) homopolymer with the following molecular weight data, and a degree of polymerization of \(1120 ?\) Why or why not? $$\begin{array}{ccc} \hline \text {Molecular Weight} & & \\ \text {Range }(\mathrm{g} / \mathrm{mol}) & \boldsymbol{w}_{\boldsymbol{i}} & \boldsymbol{x}_{\boldsymbol{i}} \\ \hline 8,000-20,000 & 0.02 & 0.05 \\ 20,000-32,000 & 0.08 & 0.15 \\ 32,000-44,000 & 0.17 & 0.21 \\ 44,000-56,000 & 0.29 & 0.28 \\ 56,000-68,000 & 0.23 & 0.18 \\ 68,000-80,000 & 0.16 & 0.10 \\ 80,000-92,000 & 0.05 & 0.03 \\ \hline \end{array}$$

Sketch cis and trans structures for (a) butadiene, and (b) chloroprene.

Carbon dioxide diffuses through a high density polyethylene (HDPE) sheet \(50 \mathrm{mm}\) thick at a rate of \(2.2 \times 10^{-8}\left(\mathrm{cm}^{3} \mathrm{STP}\right) / \mathrm{cm}^{2}-\mathrm{s}\) at 325 K. The pressures of carbon dioxide at the two faces are \(4000 \mathrm{kPa}\) and \(2500 \mathrm{kPa}\), which are maintained constant. Assuming conditions of steady state, what is the permeability coefficient at \(325 \mathrm{K} ?\)

For each of the following pairs of polymers, do the following: (1) state whether or not it is possible to determine whether one polymer is more likely to crystallize than the other; (2) if it is possible, note which is the more likely and then cite reason(s) for your choice; and (3) if it is not possible to decide, then state why. (a) Linear and atactic poly(vinyl chloride); linear and isotactic polypropylene. (b) Linear and syndiotactic polypropylene; crosslinked cis-isoprene. (c) Network phenol-formaldehyde; linear and isotactic polystyrene. (d) Block poly(acrylonitrile-isoprene) copolymer; graft poly(chloroprene- isobutylene) copolymer.
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