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 compositions by mass for the compounds are: a. Acrylic Acid: \(50.00\% \ \mathrm{C}, 5.58\% \ \mathrm{H}, 44.42\% \ \mathrm{O}\) b. Methyl Acrylate: \(55.82\% \ \mathrm{C}, 7.03\% \ \mathrm{H}, 37.15\% \ \mathrm{O}\) c. Acrylonitrile: \(67.76\% \ \mathrm{C}, 5.70\% \ \mathrm{H}, 26.54\% \ \mathrm{N}\)

Step-by-step solution

Find the molar mass of \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2}\)

From the periodic table, the atomic masses of Carbon, Hydrogen, and Oxygen are \(12.01\,\text{g/mol}\), \(1.01\,\text{g/mol}\), and \(16.00\,\text{g/mol}\), respectively. The molar mass of \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2}\) is: \[3(12.01)+4(1.01)+2(16.00)=72.06\,\text{g/mol}\]

Find the percent composition by mass of each element

To find the percent composition by mass of each element, divide the mass contribution of each element by the total molar mass and multiply by 100. Carbon: \(\frac{3(12.01)}{72.06} \times 100 = 50.00\%\) Hydrogen: \(\frac{4(1.01)}{72.06} \times 100 = 5.58\%\) Oxygen: \(\frac{2(16.00)}{72.06} \times 100 = 44.42\%\) Acrylic Acid Percent Composition: \(50.00\% \ \mathrm{C}, 5.58\% \ \mathrm{H}, 44.42\% \ \mathrm{O}\) b. Methyl Acrylate:

Find the molar mass of \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\)

The molar mass of \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\) is: \[4(12.01)+6(1.01)+2(16.00)=86.08\,\text{g/mol}\]

Find the percent composition by mass of each element

To find the percent composition by mass of each element, divide the mass contribution of each element by the total molar mass and multiply by 100. Carbon: \(\frac{4(12.01)}{86.08} \times 100 = 55.82\%\) Hydrogen: \(\frac{6(1.01)}{86.08} \times 100 = 7.03\%\) Oxygen: \(\frac{2(16.00)}{86.08} \times 100 = 37.15\%\) Methyl Acrylate Percent Composition: \(55.82\% \ \mathrm{C}, 7.03\% \ \mathrm{H}, 37.15\% \ \mathrm{O}\) c. Acrylonitrile:

Find the molar mass of \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\)

From the periodic table, the atomic mass of Nitrogen is \(14.01\,\text{g/mol}\). The molar mass of \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\) is: \[3(12.01)+3(1.01)+1(14.01)=53.08\,\text{g/mol}\]

Find the percent composition by mass of each element

To find the percent composition by mass of each element, divide the mass contribution of each element by the total molar mass and multiply by 100. Carbon: \(\frac{3(12.01)}{53.08} \times 100 = 67.76\%\) Hydrogen: \(\frac{3(1.01)}{53.08} \times 100 = 5.70\%\) Nitrogen: \(\frac{1(14.01)}{53.08} \times 100 = 26.54\%\) Acrylonitrile Percent Composition: \(67.76\% \ \mathrm{C}, 5.70\% \ \mathrm{H}, 26.54\% \ \mathrm{N}\)

Key concepts

Molar Mass Calculation

Understanding molar mass is essential in chemistry as it helps in determining the mass of individual elements in a compound. The molar mass of a compound is the sum of the atomic masses of all the atoms in its chemical formula. To calculate it, you'll need the atomic masses of the elements, which can be found on the periodic table.
For example, in acrylic acid with the formula \(\mathrm{C}_3\mathrm{H}_4\mathrm{O}_2\), the molar mass is calculated by:

• Multiplying the atomic mass of carbon (12.01 g/mol) by the number of carbon atoms (3)
• Adding the result to the total mass of hydrogen atoms: 4 x 1.01 g/mol
• Finally, adding the total mass of oxygen atoms: 2 x 16.00 g/mol

This results in a total molar mass of \(72.06\,\text{g/mol}\). Molar mass is an integral part of finding the percent composition, which tells us how much of each element is in a compound.

Synthetic Polymers

Synthetic polymers are large, complex molecules created from simpler units known as monomers. These materials are crucial in manufacturing a wide range of products, from plastics to fibers, because they can be customized for different properties.
Examples include acrylic acid, methyl acrylate, and acrylonitrile. Acrylic acid is used to make acrylic plastics, which are known for their transparency and resistance to breaking. Methyl acrylate serves as a building block for Plexiglas, a material widely used for making windows and lenses. Acrylonitrile is a key component in Orlon, a lightweight, strong fiber used for textiles.

• Acrylic plastics: durable and resistant
• Plexiglas: clear and shatter-resistant
• Orlon: strong and flexible fiber

These polymers have a profound impact on our daily lives and advancements in technology, enhancing both utilities and aesthetics of countless products.

Elemental Analysis

Elemental analysis involves determining the percentage of each element in a compound. It is an essential analytical chemistry method used in both quality control and research.
Here, percent composition refers to the mass percentage each element contributes to the total mass of the compound. The formula for finding percent composition by mass is:

• Compute the mass contribution of each element: # of atoms \(\times\) atomic mass
• Divide the result by the compound's total molar mass
• Multiply by 100 to convert it to a percentage

For instance, in acrylic acid, carbon has a percent composition of 50.00%. This process highlights which elements predominate in a compound, which is critical in determining its properties. By understanding these ratios, chemists can infer how a compound will behave in reactions or in product formulations.