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 \(\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)\) 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.

Short answer

In this problem, we analyze the composition of an ABS plastic sample. To summarize the findings: a. The two repeating units of ABS plastic in a 1:1:1 mole ratio consist of monomers acrylonitrile, butadiene, and styrene in the given order. b. In the provided ABS plastic sample, the percent by mass of each monomer is: - Acrylonitrile: 16.73% - Butadiene: 41.63% - Styrene: 41.63% c. Based on the calculations from Part b, the relative mole ratio of monomer units in the ABS plastic sample is approximately 1:2.44:1.27 for acrylonitrile, butadiene, and styrene, respectively. This ratio will vary for different ABS samples.

Step-by-step solution

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.

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.

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.

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.

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 \(0.9992 g * \frac{1}{2} = 0.4996 g\).

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 = \(\frac{0.4996 g}{1.20 g} \times 100\% = 41.63\%\).

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.

Key concepts

Polymer Chemistry

Polymer chemistry is the study of large, repeating molecules known as polymers. These are formed by the chemical bonding of numerous smaller units called monomers. The properties of polymers, such as strength, flexibility, and resistance, depend heavily on the types and arrangements of these monomers.
ABS plastic, a well-known polymer, is valued for its toughness and impact resistance. It consists of three different monomer units: acrylonitrile, butadiene, and styrene. By understanding how these monomers connect, you can grasp why ABS plastic is so durable and versatile.
In the case of ABS plastic, the monomers are believed to ideally bond in a 1:1:1 ratio, though experimental results may illustrate different proportions. This ratio gives the material its distinct characteristics by balancing the contributions of each monomer. Acrylonitrile provides chemical resistance and strength, butadiene offers toughness, and styrene provides rigidity and processability.

Molar Mass Calculation

Molar mass is a critical concept in chemistry that refers to the mass of a given substance (a chemical element or chemical compound) divided by its amount of substance. It is usually expressed in units of grams per mole (g/mol).
To determine the molar mass of a polymer like ABS, each monomer's molar mass must first be calculated. For acrylonitrile (\( C_3H_3N \)), it is calculated as the sum of the atomic masses of its constituent atoms, resulting in 53.06 g/mol. Butadiene (\( C_4H_6 \)) has a molar mass of 54.09 g/mol, and styrene (\( C_8H_8 \)) has 104.15 g/mol.
This understanding allows us to quantify how much of each monomer contributes to the overall polymer. Additionally, if a reagent like bromine (\( Br_2 \)) reacts with the polymer sample, calculating its molar mass (159.8 g/mol) is necessary to further analyze the reaction and the polymer composition.

Monomer Units

Monomer units are individual molecules that can bind together to form a polymer. In ABS plastic, the monomers are acrylonitrile, butadiene, and styrene.
Each monomer adds certain qualities to the polymer:

• Acrylonitrile (\( C_3H_3N \)): Provides strength and chemical resistance due to its nitrile group.
• Butadiene (\( C_4H_6 \)): Adds flexibility and impact resistance.
• Styrene (\( C_8H_8 \)): Contributes hardness and stability.

With these in mind, creating a polymer like ABS involves linking the monomers in a specific sequence. Changes in the sequence or the amount of each monomer can affect the polymer's properties. Experiments, like determining nitrogen content or reactivity with bromine, reveal which monomers are present in what quantities, offering insight into the structural formula of the polymer.

Percent Composition

Percent composition is a way of describing the relative amounts of each element or monomer in a compound based on their mass. This concept helps us understand the makeup of complex materials like polymers.
In the provided exercise, percent composition was key to finding the individual contributions of each monomer to the mass of ABS plastic. For instance, knowing that the ABS sample contains 8.8% nitrogen allowed us to calculate that acrylonitrile (the only nitrogen-containing monomer) makes up a specific part of the sample.
By determining the mass of bromine that reacted with the ABS and using known molar masses, we were able to deduce the masses of each monomer in the polymer. The calculations showed that acrylonitrile made up 16.73% of the sample, and that butadiene and styrene each made up 41.63% in the assumed ideal conditions. Understanding percent composition is crucial for accurately determining the physical and chemical properties of the polymer as a whole.