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Chapter 28: Problem 673

A sample of styrene is polymerized with the help of a little azoisobutyronitrile as initiator. Hydrolysis of the resulting polymer releases \(6 \mathrm{~g}\) of ammonia from \(10 \mathrm{~kg}\) of polymer. If all the end groups are derived from the initiating radical ( \(\alpha\) cyanoisopropyl), what is the average number of styrene units in the chain?

Short Answer

Expert verified
The average number of styrene units in the chain is approximately 272.

Step by step solution

01

(Step 1: Calculate moles of ammonia released)

(Divide the released ammonia by its molar mass: \[ n_{NH_3} = \frac{6 \mathrm{~g}}{17 \mathrm{\frac{g}{mol}}} \])
02

(Step 2: Obtain the moles of the initiating radical)

(The initiating radical provides 1 mol of \(NH_3\) for each mole of initiating radical, so: \[ n_{initiator} = n_{NH_3} \])
03

(Step 3: Calculate total moles of styrene used)

(Divide the given styrene mass by its molar mass: \[ n_{styrene} = \frac{10 \mathrm{~kg}}{104 \mathrm{\frac{g}{mol}}} \times 1000 \mathrm{\frac{g}{kg}} \])
04

(Step 4: Find average number of styrene units per chain)

(Divide the moles of styrene by moles of initiating radical: \[ n_{avg} = \frac{n_{styrene}}{n_{initiator}} \]) Now, we will perform the calculations to find the average number of styrene units per chain:
05

(Step 1: Calculate moles of ammonia released)

(\[ n_{NH_3} = \frac{6 \mathrm{~g}}{17 \mathrm{\frac{g}{mol}}} = 0.353 \mathrm{~mol} \])
06

(Step 2: Obtain the moles of the initiating radical)

(\[ n_{initiator} = n_{NH_3} = 0.353 \mathrm{~mol} \])
07

(Step 3: Calculate total moles of styrene used)

(\[ n_{styrene} = \frac{10 \mathrm{~kg}}{104 \mathrm{\frac{g}{mol}}} \times 1000 \mathrm{\frac{g}{kg}} = 96.154 \mathrm{~mol} \])
08

(Step 4: Find average number of styrene units per chain)

(\[ n_{avg} = \frac{n_{styrene}}{n_{initiator}} = \frac{96.154 \mathrm{~mol}}{0.353 \mathrm{~mol}} = 272.3 \]) The average number of styrene units in the chain is approximately 272.

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Most popular questions from this chapter

Outline all steps in a possible synthesis from non-polymeric starting materials of each of the following polymers. (a) Elastic fibers, used in girdles and bathing suits (Spandex, Lycra). (b) A polyester resin, used in making pipe, boats automobile bodies, etc.

Explain how natural rubber can be made durable for use in hot and cold weather.

Give an example of coordination polymerization. Name the chemists responsible for the discovery of this method of polymerization.

Natural rubber is attacked readily by ozone. If the resulting material is treated with \(\mathrm{H}_{2} \mathrm{O}_{2}\) in acetic acid, the major product isolated is levulinic acid \(\left(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}_{3}\right)\). (a) What is the structure of levulinic acid? (b) If a rubber plant is fed radioactive sodium acetate labeled only at the acetate methyl \(\left({ }^{*} \mathrm{CH}_{3} \mathrm{CO}^{-}{ }_{2} \mathrm{Na}^{+}\right)\), radioactive rubber can be obtained from the latex of the plant after a short time. Degradation of this rubber by ozone yields radioactive levulinic acid. Which specific carbon atoms of the levulinic acid would you expect to be radioactive?

When formaldehyde is polymerized to a linear polymer in heptane solvent, with \(\left(\mathrm{C}_{6} \mathrm{H}_{5}\right){ }_{3} \mathrm{P}\) or a proton as a catalyst, it yields a thermally unstable material (A) that unzips readily to re-form formaldehyde. However, if the end of the polymer is 'capped", the product is a highly crystalline, tough polymer. The example below, \(\mathrm{B}\), is called Delrin and is already replacing nylon as a molding resin. Suggest a reason for the stability gained by capping the polymer.
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