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. Draw two repeating units of ABS plastic assuming that the three monomer units react in a \(1: 1: 1\) mole ratio and react in the same order as the monomers listed above. b. A sample of ABS plastic contains \(8.80 \% \mathrm{~N}\) by mass. It took \(0.605 \mathrm{~g} \mathrm{Br}_{2}\) to react completely with a \(1.20\) -g sample of ABS plastic. What is the percent by mass of acrylonitrile, butadiene, and styrene in this polymer sample? c. ABS plastic does not react in a \(1: 1: 1\) mole ratio among the three monomer units. Using the results from part b, determine the relative numbers of the monomer units in this sample of ABS plastic.

Step by step solution

01

Draw repeating units of an ABS plastic

According to the 1:1:1 mole ratio, a monomer of acrylonitrile would bind to a monomer of butadiene, which would then bind to a monomer of styrene. This reaction chain would continue on and on, creating the polymer, ABS. Following this reaction order, two repeating units would represent the chain formed by the combination of these monomers in the order twice.

02

Calculate Molar Masses

Calculate molar masses of each monomer, as well as bromine (Br2). The molar mass of acrylonitrile (C3H3N) is 53.06 g/mol. The molar mass of butadiene (C4H6) is 54.09 g/mol. The molar mass of styrene (C8H8) is 104.15 g/mol. Lastly, the molar mass of bromine (Br2) is 159.8 g/mol.

03

Identify the Percent Nitrogen

First, it's important to remember that only acrylonitrile contains nitrogen. Therefore, 8.8% of the mass of ABS is due to acrylonitrile. This means that out of the original 1.20 g sample, 0.1056 g is due to acrylonitrile.

04

Use Bromine to Find Acrylonitrile Content

The fact that 0.605 g Br2 reacted with the ABS indicates that there was enough acrylonitrile to react with all of it. Given that the acrylonitrile-Br2 reaction occurs in a 1:1 molar ratio, we can determine that 0.605 g of Br2 is equivalent to 0.605 g/159.8 g/mol = 0.003785 moles. Thus, the ABS sample must contain 0.003785 moles of acrylonitrile which is equal to 0.003785 moles x 53.06 g/mol = 0.2008 g of acrylonitrile.

05

Determine Content of Butadiene and Styrene

Now that the mass of acrylonitrile in the sample is known, the combined mass of butadiene and styrene can be found by subtracting the mass of acrylonitrile from the total mass of the ABS sample:1.20 g - 0.2008 g = 0.9992 g. We can use percentage composition to calculate the mass of butadiene and styrene, given that in the 1:1:1 ratio, one third of polymer is each of butadiene and styrene. Thus the amount of butadiene and styrene each, in the sample is \(0.9992 g * \frac{1}{2} = 0.4996 g\).

06

Find Percent by Mass for Acrylonitrile, Butadiene, and Styrene

With the masses of acrylonitrile, butadiene, and styrene found, their percent by mass in the sample can be calculated as: \[\frac{Mass_{monomer}}{Mass_{sample}} \times 100\%.\] Percent by mass for acrylonitrile = \(\frac{0.2008 g}{1.20 g} \times 100\% = 16.73\%\), percent by mass for butadiene = \(\frac{0.4996 g}{1.20 g} \times 100\% = 41.63\%\), percent by mass for styrene = \(\frac{0.4996 g}{1.20 g} \times 100\% = 41.63\%\).

07

Determine Mole Ratios of Monomers

From the results of part b, the mass of each monomer in the ABS sample is known. These can be converted to moles by dividing by their respective molar masses and then a ratio of those amounts can be found. The number of moles of acrylonitrile = \(\frac{0.2008 g}{53.06 g/mol} = 0.003785 mol\), the number of moles of butadiene = \(\frac{0.4996 g}{54.09 g/mol} = 0.00924 mol\), the number of moles of styrene = \(\frac{0.4996 g}{104.15 g/mol} = 0.004797 mol\). Using the amount of acrylonitrile as the standard (1), the ratio of acrylonitrile:butadiene:styrene = 1: \(\frac{0.00924}{0.003785}\): \(\frac{0.004797}{0.003785}\) = 1:2.44:1.27 This indicates that for every mole of acrylonitrile, there are approximately 2.44 moles of butadiene and 1.27 moles of styrene in this particular sample of ABS plastic. This ratio will vary for different samples.

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