Question

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 \(\left(\mathbf{C}_{8} \mathbf{H}_{8}\right)\) 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 \(8.80 \%\) N by mass. It took 0.605 g Br_ 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.

Short answer

In summary, we have drawn two repeating units of ABS plastic in a 1:1:1 mole ratio. We calculated the percentage by mass of acrylonitrile to be 8.80% and estimated the percentage of butadiene and styrene to be equal at 24.75%. Using this information, we determined the relative mole ratio among the monomer units to be approximately 1:3:1 for acrylonitrile, butadiene, and styrene, respectively.

Step-by-step solution

a. Drawing two repeating units of ABS plastic

To draw two repeating units of ABS plastic, we need to consider that the three monomer units react in a 1:1:1 mole ratio in the order Acrylonitrile-Butadiene-Styrene. We then simply join these monomer units and repeat the sequence. The monomers are: Acrylonitrile: \(\mathrm{C_{3}H_{3}N}\) Butadiene: \(\mathrm{C_{4}H_{6}}\) Styrene: \(\mathrm{C_{8}H_{8}}\) The first repeating unit: Acrylonitrile-Butadiene-Styrene The second repeating unit: Acrylonitrile-Butadiene-Styrene Joined together, it becomes: Acrylonitrile-Butadiene-Styrene-American Business Services Acrylonitrile-Butadiene-Styrene.

b. Calculating the percent by mass of each monomer in ABS plastic

First, we will find the molar masses of each monomer using their molecular formulas: Acrylonitrile (AN): \(\mathrm{C_{3}H_{3}N}\) = 12.01(3) + 1.008(3) + 14.01 = 53.06 g/mol Butadiene (BD): \(\mathrm{C_{4}H_{6}}\) = 12.01(4) + 1.008(6) = 54.10 g/mol Styrene (ST): \(\mathrm{C_{8}H_{8}}\) = 12.01(8) + 1.008(8) = 104.15 g/mol We know that the mass percentage of nitrogen in the sample is 8.80%. We can use this information to calculate the mass percentage of acrylonitrile. Mass of nitrogen in the sample = \(1.20 \times \frac{8.80}{100} = 0.1056\) g Since nitrogens in the sample come only from acrylonitrile, we can calculate the mass percentage of acrylonitrile: \(\frac{1 \times (0.1056 g)}{53.06 g/mol} = 0.001992\) mol of acrylonitrile Now, we know that: \(1.20 \:g - 0.605 g \: Br_2 = 0.595g\) (Mass of ABS plastic sample without Brønsted) Since the bromine reacted completely with the ABS sample, we can write the equation as: \(m_{AN} = 53.06 \times 0.001992 \: mol = 0.1056 \: g\) \(m_{BD + ST} = 0.595 \:g\) Now we can calculate the percentage of each monomer as follows: % Acrylonitrile = \(\frac{0.1056}{1.20} \times 100 = 8.80\%\) % Butadiene + Styrene = \(\frac{0.595}{1.20} \times 100 = 49.58\%\) Now, let's assume that Butadiene and Styrene are in equal parts. % Butadiene = \(\frac{0.595}{2} \times 100 = 24.75\%\) % Styrene = \(\frac{0.595}{2} \times 100 = 24.75\%\)

c. Determining the relative numbers of monomer units in ABS plastic

In part b, we calculated the percent mass of acrylonitrile (AN), butadiene (BD), and styrene (ST). % Acrylonitrile (AN) = 8.80% % Butadiene (BD) = 24.75% % Styrene (ST) = 24.75% Now, we need to find the relative mole ratio of the monomers. To do this, we will first convert percent mass to moles and then take the ratio. Moles of AN: \(\frac{8.80}{53.06} = 0.1659\) Moles of BD: \(\frac{24.75}{54.10} = 0.4575\) Moles of ST: \(\frac{24.75}{104.15} = 0.2377\) Now, we can compare these mole values by dividing each mole value by the lowest mole value. AN ratio: \(\frac{0.1659}{0.1659} = 1\) BD ratio: \(\frac{0.4575}{0.1659} = 2.76 \approx 3\) ST ratio: \(\frac{0.2377}{0.1659} = 1.43 \approx 1\) So, the relative mole ratio among acrylonitrile, butadiene, and styrene in the ABS plastic sample is approximately 1:3:1.

Key concepts

Understanding Monomer Units in ABS Plastic

ABS plastic, widely recognized for its durable and impact-resistant properties, owes its characteristics to the unique composition of its monomer units. These fundamental building blocks come together to form the copolymer, each contributing distinct features that make ABS versatile in various applications.

The monomers in ABS plastic are acrylonitrile (C3H3N), butadiene (C4H6), and styrene (C8H8). Acrylonitrile provides chemical and thermal stability, butadiene offers toughness and impact strength, while styrene contributes to rigidity and processability. When looking at the exercise problem, students must understand that drawing two repeating units of ABS plastic necessitates a clear comprehension of how these monomers join together. In a 1:1:1 mole ratio, as suggested by the problem, the sequence will be Acrylonitrile-Butadiene-Styrene-Acrylonitrile-Butadiene-Styrene, forming the polymer chain.

To truly grasp this concept, students should envision the monomers as individual beads on a string, with each bead representing a specific monomer unit. Connecting them in the correct order and recognizing how they repeat to form the larger polymer structure is essential for accurately visualizing and subsequently drawing the molecular structure of ABS plastic.

Calculating Percent by Mass in Polymers

The percent by mass calculation is a crucial concept that appears in chemistry problems, including the study of polymers like ABS plastic. It essentially tells us how much of a particular element or compound is present in a mixture by mass. In the ABS plastic sample problem, students are tasked with determining the percent by mass of the three monomer units, using information about nitrogen's mass percentage.

The key is to first calculate the molar mass of each monomer using their chemical formulas. Then, understanding that only acrylonitrile contains nitrogen, students can use the given nitrogen percentage to find the mass and mole of acrylonitrile in the sample. Subtracting the mass of bromine that reacted with the ABS plastic helps to deduce the combined mass of the other two monomers, butadiene and styrene. By assuming equal parts of butadiene and styrene, you can determine their individual percentages.

To support the students' comprehension, it might help to liken this process to baking cookies with three ingredients, where you need to figure out what percentage of each ingredient you have, given the total weight of the dough and knowing the weight of just one ingredient (like flour).

Mole Ratio in Copolymers

Understanding the mole ratio is integral to grasping the composition of copolymers like ABS plastic. In chemistry, the mole ratio compares the amounts of reactants and products in a chemical reaction. In the context of ABS plastic, it informs us about the relative number of each monomer unit within the polymer chain.

Once you've calculated the mass percentages and converted them to moles, as in the exercise, the next step is to determine the mole ratio. Dividing the number of moles of each monomer by the smallest mole value among them establishes their relative proportions. For instance, in the problem, by comparing the moles of acrylonitrile, butadiene, and styrene using the lowest mole value, students find an approximate ratio of 1:3:1, instead of the expected 1:1:1. This modified mole ratio will influence the polymer's final properties.

For students, visualizing this process can be like comparing a recipe that unexpectedly calls for three times more sugar than flour, thereby changing the final taste and texture of the cake. The mole ratio offers essential insights into the structure-function relationship within polymers like ABS, which is pivotal for material science and engineering.