Problem 77 - Chemistry: An Atoms-Focused Approach

Question

Which substance in each of the following pairs of quantities contains more moles of oxygen? a. \(1 \mathrm{mol} \mathrm{Al}_{2} \mathrm{O}_{3}\) or \(1 \mathrm{mol} \mathrm{Fe}_{2} \mathrm{O}_{3}\) b. \(1 \mathrm{mol} \mathrm{SiO}_{2}\) or \(1 \mathrm{mol} \mathrm{N}_{2} \mathrm{O}_{4}\) c. 3 mol \(\mathrm{CO}\) or \(2 \mathrm{mol} \mathrm{CO}_{2}\)

Step-by-Step Solution

Answer

a. Al2O3 or Fe2O3 Answer: Neither. Both substances have the same number of moles of oxygen. b. SiO2 or N2O4 Answer: N2O4 has more moles of oxygen than SiO2. c. 3 moles of CO or 2 moles of CO2 Answer: 2 moles of CO2 contain more moles of oxygen than 3 moles of CO.

Step 1: a. \(\mathrm{Al}_{2}\mathrm{O}_{3}\) vs \(\mathrm{Fe}_{2}\mathrm{O}_{3}\)

In \(\mathrm{Al}_{2}\mathrm{O}_{3}\), there are 3 moles of oxygen, as indicated by the subscript 3. In \(\mathrm{Fe}_{2}\mathrm{O}_{3}\), there are also 3 moles of oxygen, as indicated by the subscript 3. Since both substances have the same number of moles of oxygen, neither contains more moles of oxygen than the other.

Step 2: b. \(\mathrm{SiO}_{2}\) vs \(\mathrm{N}_{2}\mathrm{O}_{4}\)

In \(\mathrm{SiO}_{2}\), there are 2 moles of oxygen, as indicated by the subscript 2. In \(\mathrm{N}_{2}\mathrm{O}_{4}\), there are 4 moles of oxygen, as indicated by the subscript 4. Since 4 is greater than 2, \(\mathrm{N}_{2}\mathrm{O}_{4}\) contains more moles of oxygen than \(\mathrm{SiO}_{2}\).

Step 3: c. 3 mol \(\mathrm{CO}\) vs 2 mol \(\mathrm{CO}_{2}\)

In \(\mathrm{CO}\), there is 1 mole of oxygen. Since we have 3 moles of \(\mathrm{CO}\), the total number of moles of oxygen is 3 * 1 = 3 moles. In \(\mathrm{CO}_{2}\), there are 2 moles of oxygen. Since we have 2 moles of \(\mathrm{CO}_{2}\), the total number of moles of oxygen is 2 * 2 = 4 moles. Since 4 is greater than 3, 2 moles of \(\mathrm{CO}_{2}\) contain more moles of oxygen than 3 moles of \(\mathrm{CO}\).

Key Concepts

Chemical Formulas

Chemical formulas are a type of shorthand notation that convey the composition of chemical compounds. In this notation, elements are represented by their chemical symbols, and subscripts are used to indicate the number of atoms of each element in a molecule. Taking \(\text{Al}_2\text{O}_3\) as an example, this formula tells us there are two aluminum (Al) atoms and three oxygen (O) atoms in one molecule of aluminum oxide. This coding method is essential for easily sharing information about substances on a chemical level.

Let's consider how subscripts work. The subscript in a chemical formula shows the count of atoms per molecule. For instance, in \(\text{N}_2\text{O}_4\), the subscript '2' following nitrogen (N) means there are two nitrogen atoms, while '4' following oxygen (O) denotes there are four oxygen atoms in each molecule of dinitrogen tetroxide.

• It quantifies atoms precisely.
• Helps predict reactions and product formation.
• Enables calculation of molar masses.

Understanding chemical formulas equips us to better grasp the intricacies of chemical reactions, molecular behavior, and even the physical properties of materials.

Molecular Composition

Molecular composition describes the types and numbers of atoms that make up a molecule. This insight is directly derived from chemical formulas, which serve as blueprints for these compositions. For example, examining \(\text{SiO}_2\), which is silicon dioxide, we conclude it consist of one silicon (Si) atom and two oxygen (O) atoms per molecule.

The composition of a molecule influences its properties and functionality. For instance:

• \(\text{CO}\): Contains one carbon and one oxygen atom. It's a simple molecule but is known as poisonous carbon monoxide.
• \(\text{CO}_2\): Comprises one carbon and two oxygen atoms, forming carbon dioxide—a crucial component of Earth's atmosphere.

The number of atoms in specific elements can determine not only the molecule’s mass but also its chemical reactivity and interaction with other substances. This differentiation fosters our ability to engage in complex discussions about environmental science, medicine, and industry.

Quantitative Analysis

Quantitative analysis in chemistry focuses on determining the amounts or concentrations of substances. This process often involves calculations using the mole concept, which is a standard unit in chemistry that quantifies the amount of a substance. Each mole contains Avogadro's number of entities, \(6.022 \times 10^{23}\) units.

This concept helps us compare amounts on a macroscopic scale. In problems like deciding between the number of oxygen moles in different substances, quantitative analysis proves crucial. As seen:

• For \(\text{Al}_2\text{O}_3\) and \(\text{Fe}_2\text{O}_3\), analysis shows both have equivalent oxygen mole counts.
• Comparing \(\text{SiO}_2\) with \(\text{N}_2\text{O}_4\), it reveals the latter contains more moles of oxygen.
• Between 3 mol \(\text{CO}\) and 2 mol \(\text{CO}_2\), \(\text{CO}_2\) emerges with a higher oxygen mole content due to its chemical composition.

Quantitative analysis lets chemists effectively quantify and control reactants and products in a chemical reaction. It underpins technology developments and scientific advancements, facilitating precise calculations and experimental planning.