Problem 27 - General Chemistry: Principles and Modern Applications

Question

Without per frming detailed calculations, determine which of the following compounds has the greatest percent oxygen by mass: dinitrogen tetroxide, aluminum oxide, tetraphosphorus hexoxide, or carbon dioxide.

Step-by-Step Solution

Answer

The compound with the greatest percent oxygen by mass among the provided compounds is Carbon Dioxide (\(CO_2\)).

Step 1: Calculate Oxygen Molecule Proportion

Calculate the proportion of oxygen molecules in each given compound. Dinitrogen tetroxide (\(N_2O_4\)) has 4 out of 6 total atoms as oxygen; aluminum oxide (\(Al_2O_3\)) has 3 out of 5; tetraphosphorus hexoxide (\(P_4O_6\)) has 6 out of 10; carbon dioxide (\(CO_2\)) has 2 out of 3.

Step 2: Compare the Molar Weights and Proportions

Next, you compare the molar weights and proportions. Although \(N_2O_4\) and \(P_4O_6\) have more oxygen atoms, you see that they have larger molar mass due to Nitrogen and Phosphorus. Aluminum oxide (\(Al_2O_3\)) also has sufficient Oxygen Molecules but Aluminum carries a larger molar mass. Carbon Dioxide (\(CO_2\)), on the other hand, only has Oxygen and Carbon contributing to its molar mass. In addition, two out of three atoms in \(CO_2\) are oxygen, which is the highest proportion amongst the four compounds. Thus, without performing detailed calculations, one would suspect that \(CO_2\) has the greatest percentage of Oxygen by Mass.

Step 3: Final Conclusion

So, if we are considering the percentage by mass, Carbon Dioxide should have the largest, due to its low weight and high proportion of Oxygen.

Key Concepts

Molecular Composition

Every chemical compound is made up of different atoms bonded together, forming a specific structure. Understanding molecular composition is crucial when discussing percent composition by mass, especially for oxygen.

Let's break down each compound from the exercise to see their composition:

• Dinitrogen tetroxide ( N_2O_4"): This molecule consists of two nitrogen atoms and four oxygen atoms.
• Aluminum oxide ( Al_2O_3"): Here, you have two aluminum atoms combined with three oxygen atoms.
• Tetraphosphorus hexoxide ( P_4O_6"): Contains four phosphorus atoms and six oxygen atoms.
• Carbon dioxide ( CO_2"): Comprises one carbon atom and two oxygen atoms.

Each compound's unique combination of atoms defines its molecular composition. The number of oxygen atoms relative to the total number of atoms influences the percent oxygen by mass.

Molar Mass

Molar mass is an essential concept in chemistry, representing the mass of one mole of a given substance. It is measured in grams per mole (g/mol) and determined by adding up the atomic masses of all atoms in a molecule.

To find out which compound has the greatest percent oxygen by mass, you need to consider both the number of oxygen atoms and the molar mass:

• Dinitrogen tetroxide ( N_2O_4"): The molar mass involves two nitrogen and four oxygen atoms.
• Aluminum oxide ( Al_2O_3"): The molar mass includes two aluminum and three oxygen atoms.
• Tetraphosphorus hexoxide ( P_4O_6"): Four phosphorus and six oxygen atoms determine its molar mass.
• Carbon dioxide ( CO_2"): The molar mass includes one carbon and two oxygen atoms.

By comparing them, you can identify that despite having fewer oxygen atoms, carbon dioxide's simple composition results in a higher percent oxygen by mass.

Chemical Compounds

Chemical compounds are substances formed from two or more elements, chemically bonded together in fixed proportions. They can exhibit unique properties that depend on their constituents and types of bonds.

In the exercise, you examined four different chemical compounds:

• Dinitrogen tetroxide ( N_2O_4"): An unstable compound with a higher proportion of oxygen atoms, but a large molar mass.
• Aluminum oxide ( Al_2O_3"): A stable compound used in various applications, with considerable molar mass due to aluminum.
• Tetraphosphorus hexoxide ( P_4O_6"): A compound known for its significant number of bonded atoms.
• Carbon dioxide ( CO_2"): A simple, lightweight compound, known for its two oxygen atoms and widespread presence in nature.

Carbon dioxide stands out amongst these due to its minimal non-oxygen mass, which makes it likely to have the highest percent oxygen by mass. Understanding the relationship between molecular structure and properties helps predict such outcomes.