Problem 49 - Chemistry: An Atoms-Focused Approach

Question

Organic Compounds in Space The following compounds have been detected in space. Which contains the greatest percentage of carbon by mass? a. naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\) b. chrysene, \(\mathrm{C}_{18} \mathrm{H}_{12}\) c. pentacene, \(\mathrm{C}_{22} \mathrm{H}_{14}\) d. pyrene, \(C_{16} H_{10}\)

Step-by-Step Solution

Answer

Answer: Pyrene (\(C_{16} H_{10}\)) has the greatest percentage of carbon by mass (95.02%).

Step 1: Calculate molar mass of Carbon and Hydrogen

First, we need to calculate the molar mass of Carbon and Hydrogen. From the periodic table, we have the molar mass of Carbon (C) as 12.01 g/mol and Hydrogen (H) as 1.01 g/mol.

Step 2: Calculate the molar mass of each compound

In this step, we will calculate the molar mass of each compound by multiplying the molar mass of each element with its number of atoms and then summing the results. - Naphthalene: \(\mathrm{C}_{10} \mathrm{H}_{8}\) Molar mass = (10 x 12.01) + (8 x 1.01) = 128.17 g/mol - Chrysene: \(\mathrm{C}_{18} \mathrm{H}_{12}\) Molar mass = (18 x 12.01) + (12 x 1.01) = 228.29 g/mol - Pentacene: \(\mathrm{C}_{22} \mathrm{H}_{14}\) Molar mass = (22 x 12.01) + (14 x 1.01) = 278.35 g/mol - Pyrene: \(\mathrm{C}_{16} \mathrm{H}_{10}\) Molar mass = (16 x 12.01) + (10 x 1.01) = 202.26 g/mol

Step 3: Calculate the percentage of Carbon by mass for each compound

Now, we will calculate the percentage of carbon by mass for each compound using the following formula: Percentage of carbon = \(\frac{\text{mass of carbon}}{\text{total mass}} \times 100\) - Naphthalene: Percentage of Carbon = \(\frac{10 \times 12.01}{128.17} \times 100\) = 93.75% - Chrysene: Percentage of Carbon = \(\frac{18 \times 12.01}{228.29} \times 100\) = 94.54% - Pentacene: Percentage of Carbon = \(\frac{22 \times 12.01}{278.35} \times 100\) = 94.94% - Pyrene: Percentage of Carbon = \(\frac{16 \times 12.01}{202.26} \times 100\) = 95.02%

Step 4: Identify the compound with the greatest percentage of Carbon

By comparing the calculated percentages, we find that Pyrene (d) has the greatest percentage of carbon by mass (95.02%). Therefore, the answer is Pyrene, \(C_{16} H_{10}\).

Key Concepts

Percentage Composition

Understanding percentage composition is essential in chemistry, especially when analyzing organic compounds. It gives us a way to compare how much of each element is present in a compound relative to its total mass. In the context of the given exercise, the percentage composition focuses solely on the carbon content of the compounds.

• First, calculate the molar mass of the compound.
• Next, find the mass of the carbon within the molecule by multiplying the number of carbon atoms by the molar mass of carbon.
• Finally, calculate the percentage of carbon by dividing the mass of carbon by the total molar mass of the compound and multiplying by 100.

This method allows us to identify which compound has the highest proportion of carbon, an essential factor when studying the chemical properties of organic molecules found in space.

Molar Mass Calculation

Calculating the molar mass of a compound is a crucial step in determining its chemical characteristics. The molar mass is the sum of the masses of all the atoms in a single molecule of that compound.

• Start by identifying the number of each type of atom in the formula of the compound.
• Multiply the number of each atom by its respective atomic mass (from the periodic table).
• Add all these values together to obtain the molar mass.

For example, naphthalene, \(C_{10}H_{8}\), has a molar mass calculated by \( (10 \times 12.01) + (8 \times 1.01) = 128.17\) g/mol. This process is repeated for each compound to find their unique molar masses.

Carbon Content

The carbon content in organic compounds is particularly important in both terrestrial and extraterrestrial chemistry. It not only dictates the structure and properties of a molecule but also its chemical reactivity and stability. When calculating the carbon content percentage:

• First, determine the total mass of carbon in the molecule by multiplying the number of carbon atoms by their atomic mass.
• Divide this value by the total molar mass of the compound.
• Multiply the result by 100 to convert it to a percentage.

In the context of space exploration and astrochemistry, identifying the carbon content can help scientists understand potential chemical pathways and origins of organic matter identified in the cosmos.

Astrochemistry

Astrochemistry is an exciting and vast field that combines the principles of chemistry with astronomy to study the chemical composition of the universe. Organic compounds like naphthalene, chrysene, pentacene, and pyrene have been detected in space, providing clues about the chemical processes occurring beyond Earth.

• Understanding the composition and distribution of organic molecules helps researchers speculate about the potential for life elsewhere in the universe.
• Molecules with significant carbon content, such as pyrene which has the highest percentage among the given options, are particularly intriguing because they resemble basic building blocks of life.
• The discovery and analysis of these compounds inform our understanding of chemical evolution in space.

The study of astrochemistry is a crucial part of developing a holistic view of our universe, from its smallest particles to its grandest galaxies.