Question

Which of the following correctly describes the balanced chemical equation given below? There may be more than one true statement. If a statement is incorrect, explain why it is incorrect. $$ 4 \mathrm{Al}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3} $$ a. For every 4 atoms of aluminum that react with 6 atoms of oxygen, 2 molecules of aluminum oxide are produced. b. For every 4 moles of aluminum that reacts with 3 moles of oxygen, 2 moles of aluminum (III) oxide is produced. c. For every 4 grams of aluminum that reacts with 3 grams of oxygen, 2 grams of aluminum oxide is produced.

Short answer

Statements a and b are correct. Statement a: For every 4 atoms of aluminum that react with 6 atoms of oxygen, 2 molecules of aluminum oxide are produced. Statement b: For every 4 moles of aluminum that reacts with 3 moles of oxygen, 2 moles of aluminum (III) oxide are produced. Statement c is incorrect because it gives the relationship in grams, which doesn't respect the stoichiometry based on moles in the balanced equation.

Step-by-step solution

Statement a: Interpretation

Statement a says that for every 4 atoms of aluminum that react with 6 atoms of oxygen, 2 molecules of aluminum oxide are produced. This can be represented as: \(4 \mathrm{Al} + 6 \mathrm{O} \rightarrow 2 \mathrm{Al}_2 \mathrm{O}_3\)

Statement a: Analysis

Comparing statement a with the given balanced equation: \(4 \mathrm{Al} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}\) we notice that the only difference is how oxygen is represented (6 O atoms instead of 3 O2). This doesn't change the ratios between the elements as the coefficients represent stoichiometric quantities. Therefore, statement a is correct.

Statement b: Interpretation

Statement b says that for every 4 moles of aluminum that react with 3 moles of oxygen, 2 moles of aluminum (III) oxide are produced. This statement corresponds exactly to the balanced equation: \(4 \mathrm{Al} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}\)

Statement b: Analysis

Since statement b precisely matches the given balanced equation and respects its stoichiometry, statement b is correct.

Statement c: Interpretation

Statement c says that for every 4 grams of aluminum that react with 3 grams of oxygen, 2 grams of aluminum oxide are produced.

Statement c: Analysis

Using the chemical equation, we should analyze the relationships based on moles and not grams. If we check the statement in grams: - 4 grams of Al corresponds to \(\frac{4 \, \text{g}}{26.98 \, \text{g/mol}} \approx 0.148 \, \text{moles}\) of Al. - 3 grams of O2 corresponds to \(\frac{3 \, \text{g}}{32.00 \, \text{g/mol}} \approx 0.094 \, \text{moles}\) of O2. Now, looking at mole ratios in the equation: \(4 \mathrm{Al} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}\) The ratio of reactants is 4:3, but in grams, the moles ratio is approximately 0.148:0.094, which is not the same proportion (4:3). Therefore, statement c is incorrect.

Key concepts

Stoichiometry

Understanding stoichiometry is akin to understanding a recipe for a chemical reaction. Just as a recipe specifies the exact amount of each ingredient needed to make a cake, a balanced chemical equation indicates the precise ratios of reactants that combine to form products.

In our exercise, the balanced equation \[4 \mathrm{Al} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}\] communicates that 4 moles of aluminum (Al) react with 3 moles of oxygen (O2) to produce 2 moles of aluminum oxide (Al2O3). This relationship is what stoichiometry is all about—the calculation of the quantities of reactants and products involved in a chemical reaction based on the mole ratios provided by the balanced chemical equation.

To help students better visualize these proportions, consider using analogies or creating visual aids like pie charts or bar graphs that represent the mole ratios. This can make the abstract concept of stoichiometry more relatable and easier to grasp.

Chemical Reaction

At the heart of every chemical process is a chemical reaction, a transformation where substances called reactants convert into different substances called products. The balanced chemical equation \[4 \mathrm{Al} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}\] describes a reaction where aluminum and oxygen combine to form aluminum oxide.

Chemical equations are not just symbolic representations; they express the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. This means that the amount of matter present in the reactants must equal the amount in the products, a concept that helps explain why balancing chemical equations is crucial. An imbalanced equation suggests that atoms have been lost or gained, which is not possible in reality.

Encouraging students to perform simple experiments that demonstrate a chemical reaction can greatly aid in understanding. For instance, the decomposition of hydrogen peroxide into water and oxygen gas can be easily observed and connected back to the theoretical aspects discussed in class.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world we observe. Just as a dozen refers to a specific quantity—12—no matter what object you're talking about, a mole represents a set number of particles, specifically Avogadro’s number (\(6.022 \times 10^{23}\)) particles, be it atoms, ions, or molecules.

This concept comes to life in our chemical reaction example, as the moles indicate how many molecules or atoms will react. It's essential to recognize that moles account for quantities of particles, not grams. While 4 moles of aluminum react with 3 moles of oxygen, we cannot say that 4 grams of aluminum react with 3 grams of oxygen to produce 2 grams of aluminum oxide, as statement c wrongly suggests.

Using interactive simulations that allow students to visualize and manipulate atoms and molecules can significantly deepen their understanding of the mole concept. Also, hands-on activities like measuring a mole of various substances help make the abstract notion of moles more tangible.