Question

Calculate the percent composition by mass of the following compounds that are important starting materials for synthetic polymers: a. \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2}\) (acrylic acid, from which acrylic plastics are made) b. \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\) (methyl acrylate, from which Plexiglas is made) c. \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\) (acrylonitrile, from which Orlon is made)

Short answer

The percent composition by mass of the compounds is as follows: a. Acrylic acid \((\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2})\): Percent composition of C \(= 54.5 \% \), H \(= 6.1 \% \), and O \(= 39.4 \% \). b. Methyl acrylate \((\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2})\): Percent composition of C \(= 53.5 \% \), H \(= 8.1 \% \), and O \(= 38.4 \% \). c. Acrylonitrile \((\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N})\): Percent composition of C \(= 58.3 \% \), H \(= 5.1 \% \), and N \(= 36.6 \% \).

Step-by-step solution

Determine the molar mass of the compounds

To find the molar mass of the compounds, we'll need to use the periodic table to look up the molar mass of each individual element and then multiply it by the number of times it appears in the compound's formula. a. Acrylic acid \((\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2})\): Molar mass \(= (3 \times \text{molar mass of C}) + (4 \times \text{molar mass of H}) + (2\times \text{molar mass of O})\) b. Methyl acrylate \((\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2})\): Molar mass = \((4 \times \text{molar mass of C}) + (6\times \text{molar mass of H}) + (2\times \text{molar mass of O})\) c. Acrylonitrile \((\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N})\): Molar mass \(= (3\times \text{molar mass of C}) + (3\times \text{molar mass of H}) + (\times\text{molar mass of N})\) Use the periodic table to find the molar masses of C, H, O, and N, and then plug them into the above equations.

Calculate the percent composition by mass for each element in the compounds

To calculate the percent composition by mass of an element in a compound, divide the total mass of that element in the compound by the total molar mass of the compound and multiply the result by 100. a. Acrylic acid \((\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2})\): Percent composition of C \(= \frac{(3\times \text{molar mass of C})}{(\text{total molar mass of compound})} \times 100\) Percent composition of H \(= \frac{(4\times \text{molar mass of H})}{(\text{total molar mass of compound})} \times 100\) Percent composition of O \(= \frac{(2\times \text{molar mass of O})}{(\text{total molar mass of compound})} \times 100\) b. Methyl acrylate \((\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2})\): Percent composition of C \(= \frac{(4\times \text{molar mass of C})}{(\text{total molar mass of compound})} \times 100\) Percent composition of H \(= \frac{(6\times \text{molar mass of H})}{(\text{total molar mass of compound})} \times 100\) Percent composition of O \(= \frac{(2\times \text{molar mass of O})}{(\text{total molar mass of compound})} \times 100\) c. Acrylonitrile \((\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N})\): Percent composition of C \(= \frac{(3\times \text{molar mass of C})}{(\text{total molar mass of compound})} \times 100\) Percent composition of H \(= \frac{(3\times \text{molar mass of H})}{(\text{total molar mass of compound})} \times 100\) Percent composition of N \(= \frac{(\text{molar mass of N})}{(\text{total molar mass of compound})} \times 100\) Finally, plug in the molar mass values from Step 1 and calculate the percent compositions.

Key concepts

Understanding Molar Mass

Grasping the concept of molar mass is pivotal when analyzing the percent composition by mass of compounds, especially those involved in the creation of synthetic polymers. The molar mass represents the mass of one mole of a substance (be it an element or a compound) and is typically expressed in grams per mole (g/mol). It's calculated by summing up the atomic masses of all the atoms present in a single molecule of the substance.

For instance, if we take acrylic acid with the chemical formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2}\), we would determine the molar mass by multiplying the atomic mass of carbon (C) by 3, hydrogen (H) by 4, and oxygen (O) by 2, and then adding all these values together. Utilizing the average atomic masses from the periodic table, carbon has a molar mass of approximately 12 g/mol, hydrogen is about 1 g/mol, and oxygen is around 16 g/mol.

Practical Application in Calculating Percent Composition

In the step-by-step solution provided, after the molar mass of the compound is determined, it forms the basis for calculating the percent composition by mass. This not only aids in comprehending the compound's chemical makeup but also plays an essential role in formulating and adjusting the synthesis of polymers like Plexiglas, ensuring the desired physical and chemical properties are achieved.

Deciphering the Chemical Formula

A chemical formula is not just a string of letters and numbers; it’s the blueprint of a compound, revealing the types and quantities of atoms present. From glancing at the formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2}\) for acrylic acid, we immediately discern that there are 3 carbon atoms, 4 hydrogen atoms, and 2 oxygen atoms in one molecule of the compound.

The chemical formula thus conveys detailed information which is crucial for understanding the structure of a compound and predicting its reactivity. For synthetic polymers, the chemical formula of the monomers (the building blocks of polymers) is essential. It allows chemists to predict the properties of the polymer, be it the toughness of acrylic plastics or the resilience of Orlon fibers.

Role in Percent Composition Calculations

When calculating the percent composition by mass, the chemical formula serves as the skeletal frame from which we extract the number of atoms needed to compute the mass contributions of each constituent element. This is particularly beneficial for students and professionals in fields such as material science and chemistry, where precise formulations are necessary.

Synthetic Polymers and Their Importance

Synthetic polymers, such as the ones referenced in the exercise, are monumental in modern industry and day-to-day life. From acrylic plastics to fabrics like Orlon, polymers are an eclectic group of long chain-like molecules made of repeating units called monomers. Understanding the percent composition by mass of the starting materials of these polymers is crucial for several reasons.

For one, the percent composition can affect the physical properties of the polymer, like its strength, flexibility, and resistance to heat and chemicals. It also has implications for the polymer's environmental impact and recyclability. The meticulous control of composition is vital in applications requiring specific performance characteristics, such as in aerospace or medical devices.

Advancements in Polymer Chemistry

Significant advancements in polymer chemistry come from tweaking the percent compositions of starting materials. These changes at the molecular level can lead to the production of new materials with desirable traits for specialized uses. Therefore, a clear understanding of the mass contribution of each element within the monomers guides chemists in synthesizing the next generation of synthetic polymers with precise and improved features.