Problem 53 - Chemistry: An Atoms-Focused Approach

Question

Do any two of the following compounds, which have been detected in outer space, have the same empirical formula? a. naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\) b. chrysene, \(\mathbf{C}_{18} \mathrm{H}_{12}\) c. anthracene, \(\mathrm{C}_{14} \mathrm{H}_{10}\) d. pyrene, \(\mathrm{C}_{16} \mathrm{H}_{10}\) e. benzoperylene, \(\mathrm{C}_{22} \mathrm{H}_{12}\) f. coronene, \(\mathrm{C}_{24} \mathrm{H}_{12}\)

Step-by-Step Solution

Answer

Answer: No, none of the pairs of compounds have the same empirical formula.

Step 1: Find the ratio of carbon to hydrogen for each compound

Divide the number of carbon atoms by the number of hydrogen atoms for each compound: a. naphthalene, \(\frac{\mathrm{C}_{10}}{\mathrm{H}_{8}}\) b. chrysene, \(\frac{\mathrm{C}_{18}}{\mathrm{H}_{12}}\) c. anthracene, \(\frac{\mathrm{C}_{14}}{\mathrm{H}_{10}}\) d. pyrene, \(\frac{\mathrm{C}_{16}}{\mathrm{H}_{10}}\) e. benzoperylene, \(\frac{\mathrm{C}_{22}}{\mathrm{H}_{12}}\) f. coronene, \(\frac{\mathrm{C}_{24}}{\mathrm{H}_{12}}\)

Step 2: Simplify the ratios

Simplify the ratios to get the simplest whole number ratios: a. naphthalene, \(\frac{10}{8} = \frac{5}{4}\) b. chrysene, \(\frac{18}{12} = \frac{3}{2}\) c. anthracene, \(\frac{14}{10} = \frac{7}{5}\) d. pyrene, \(\frac{16}{10} = \frac{8}{5}\) e. benzoperylene, \(\frac{22}{12} = \frac{11}{6}\) f. coronene, \(\frac{24}{12} = \frac{2}{1}\)

Step 3: Compare the ratios

Now that we have simplified the ratios, let's compare them to see if any two compounds have the same empirical formula: None of the simplified ratios are the same, which means none of these pairs of compounds have the same empirical formula.

Key Concepts

Carbon-Hydrogen Ratio

The carbon-hydrogen ratio is a way to express the proportion of carbon atoms to hydrogen atoms in a molecule. This ratio is crucial in determining the empirical formula of a compound, which reflects the simplest whole-number ratio of these atoms. To find this ratio, one must divide the number of carbon atoms by the number of hydrogen atoms present in the molecule.
For example, in naphthalene, this would be calculated as \(\frac{10}{8} = \frac{5}{4}\). Understanding the carbon-hydrogen ratio helps identify relationships between different organic compounds and determine similarities in their composition.

Outer Space Molecules

Outer space molecules are fascinating chemical entities that exist beyond the confines of Earth. Many of these molecules, such as naphthalene and chrysene, have been detected in space through spectral analysis. These molecules float around in interstellar clouds, often found in areas with significant carbon deposits.
The study of such molecular compounds in outer space gives scientists insights into the complex chemical processes that occur in space, providing clues about the formation of stars and planets.

Organic Compounds

Organic compounds are chemicals that primarily consist of carbon and hydrogen atoms. These compounds form the basis of all life on Earth, span millions of unique molecular structures, and are also found abundantly in outer space.
Among organic compounds detected in space, polycyclic aromatic hydrocarbons (PAHs) like naphthalene and coronene are notable for their stability and intricate ring structures. The study of organic compounds in different environments helps in understanding chemical processes and the history of molecular evolution.

Naphthalene

Naphthalene is one of the simplest polycyclic aromatic hydrocarbons (PAHs), consisting of two fused benzene rings. Its formula is \(\mathrm{C}_{10}\mathrm{H}_{8}\).
Widely used in mothballs and as a precursor for other chemicals, naphthalene's relatively simple structure makes it an ideal molecule for study in outer space. Its carbon-hydrogen ratio of \(\frac{5}{4}\) does not match any others in the exercise, indicating its unique empirical formula among the listed compounds.

Chrysene

Chrysene is an important PAH that contains four fused aromatic rings and has the molecular formula \(\mathrm{C}_{18}\mathrm{H}_{12}\).
Chrysene is typically recognized for its presence in fossil fuels and tobacco smoke. It has a carbon-hydrogen ratio of \(\frac{3}{2}\), distinguishing it from the other aromatic compounds in the exercise. This shows its unique composition and serves as a marker for identifying it among other PAHs.

Anthracene

Anthracene is a compound with a molecular formula of \(\mathrm{C}_{14}\mathrm{H}_{10}\), characterized by three linearly-fused benzene rings. It is known for its applications in dyes and in the study of fluorescence.
With a carbon-hydrogen ratio of \(\frac{7}{5}\), anthracene stands out with its distinct empirical formula. Despite sharing some structural similarities with other PAHs, this ratio highlights its unique chemical identity in comparative analyses.

Pyrene

Pyrene is a PAH with four benzene rings arranged in a compact cluster, enjoying a rich history in industrial applications and scientific research. Its formula is \(\mathrm{C}_{16}\mathrm{H}_{10}\).
The carbon-hydrogen ratio of \(\frac{8}{5}\) distinguishes pyrene's empirical formula from others in the list, underscoring its individual structure. This precise ratio is essential for distinguishing pyrene from closely related PAHs and ensuring accurate identification in research and application.

Benzoperylene

Benzoperylene is a larger and more complex PAH, with a formula \(\mathrm{C}_{22}\mathrm{H}_{12}\). Found in diesel exhausts and other combustion processes, benzoperylene is recognized for its unique planar structure.
This compound has a carbon-hydrogen ratio of \(\frac{11}{6}\), highlighting its complex structure compared to simpler PAHs. This particular ratio indicates a greater number of carbon rings which contribute to its higher molecular weight and stability in hydrocarbon-rich environments.

Coronene

Coronene, known as super benzene, showcases six benzene rings fused in a hexagonal shape. It has the molecular formula \(\mathrm{C}_{24}\mathrm{H}_{12}\).
With a carbon-hydrogen ratio of \(\frac{2}{1}\), coronene's unique symmetry and stability make it a subject of interest for both theoretical chemistry and material science. This distinct ratio reveals much about its structure's aromatic properties, setting it apart from other PAHs mentioned in this exercise.