ABS plastic is a tough, hard plastic used in applications requiring shock resistance. The polymer consists of three monomer units: acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\right),\) butadiene \(\left(\mathrm{C}_{4} \mathrm{H}_{6}\right),\) and styrene \(\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)\) a. A sample of ABS plastic contains \(8.80 \% \mathrm{N}\) by mass. It took \(0.605 \mathrm{g}\) of \(\mathrm{Br}_{2}\) to react completely with a \(1.20-\mathrm{g}\) sample of ABS plastic. Bromine reacts 1: 1 (by moles) with the butadiene molecules in the polymer and nothing else. What is the percent by mass of acrylonitrile and butadiene in this polymer? b. What are the relative numbers of each of the monomer units in this polymer?

Step by step solution

01

1. Calculate the mass of Nitrogen in the sample

Since the ABS sample contains 8.8% of Nitrogen by mass, we can calculate the mass of Nitrogen by multiplying the sample mass by the percentage. \(Mass \, of \, Nitrogen = \frac{8.8}{100} \times 1.20 g = 0.1056\,g\)

02

2. Find the mass of acrylonitrile

Since the molecular formula of acrylonitrile is \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\), there is one Nitrogen atom in each molecule. We can calculate the number of moles of Nitrogen in the sample: \(moles \, of \, Nitrogen = \frac{0.1056\,g}{14.01\,g/mol} = 0.00754\,mol\) Then the mass of acrylonitrile will be: \(Mass \, of \, acrylonitrile = 0.00754\,mol \times 53.06\,g/mol = 0.40\,g\)

03

3. Calculate the amount of butadiene that reacted with Bromine

Since Bromine reacts 1:1 (by moles) with the butadiene molecules in the polymer, we can calculate the number of moles of butadiene that reacted with given Bromine: \(moles \, of \, butadiene= \frac{0.605\,g\, \mathrm{Br}_{2}}{159.81\,g/mol\, \mathrm{Br}_{2}} = 0.00379 mol\)

04

4. Find the mass of butadiene

To find the mass of butadiene, we can multiply the number of moles of butadiene with the molar mass of butadiene: \(Mass \, of \, butadiene = 0.00379\,mol \times 54.09\,g/mol = 0.205\,g\)

05

5. Calculate the mass of styrene

Since we now know the mass of acrylonitrile and butadiene, we can find the mass of styrene in the ABS sample by subtraction: \(Mass \, of \, styrene = Total\, mass - (mass \, of \, acrylonitrile + mass \, of \, butadiene)\) \(Mass \, of \, styrene = 1.20\,g - (0.40\,g + 0.205\,g) = 0.595\,g\)

06

6. Determine the mole ratios of acrylonitrile, butadiene, and styrene

Mole ratios can be determined by calculating the moles of each monomer unit and finding the smallest whole number ratio among them: \(Mole\, ratio\, acrylonitrile:butadiene:styrene \newline = \frac{0.00754\,mol \, acrylonitrile}{0.00379\,mol \, butadiene}: \frac{0.00379\,mol \, butadiene}{0.00379\,mol \, butadiene}: \frac{0.00523\,mol \, styrene}{0.00379\,mol \, butadiene} \newline = 1.99: 1: 1.38 \approx 2:1:1\) a. The percent by mass of acrylonitrile in the polymer is \(\frac{0.40\,g}{1.20\,g}\times 100 = 33.33 \%\) and the percent by mass of butadiene is \(\frac{0.205\,g}{1.20\,g} \times 100 = 17.08 \%\). b. The relative numbers of each monomer units in the polymer are approximately 2 molecules of acrylonitrile, 1 molecule of butadiene, and 1 molecule of styrene.

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