Problem 44 - Chemistry Matter and Change

Question

Interpret the following equation in terms of particles, moles, and mass. \begin{equation} 4 \mathrm{Al}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s}) \end{equation}

Step-by-Step Solution

Answer

4 Al atoms/moles react with 3 O₂ molecules/moles to form 2 Al₂O₃ molecules/moles, weighing 107.92 g Al, 96.00 g O₂, producing 203.92 g Al₂O₃.

Step 1: Understand the Chemistry Symbols

In the chemical equation, the symbols represent elements and their states. \( \text{Al (s)} \) is solid aluminum; \( \text{O}_2(\text{g}) \) is oxygen gas; \( \text{Al}_2\text{O}_3(\text{s}) \) is solid aluminum oxide.

Step 2: Interpret the Equation in Terms of Particles

The coefficients in the equation (4, 3, and 2) indicate the ratio of individual particles (atoms and molecules) involved. For atoms of aluminum and molecules of oxygen: 4 Al atoms react with 3 \( \text{O}_2 \) molecules to form 2 \( \text{Al}_2\text{O}_3 \) molecules.

Step 3: Relate Coefficients to Moles

The same coefficients apply to moles because moles are a count of particles. Therefore, 4 moles of aluminum react with 3 moles of \( \text{O}_2 \) to produce 2 moles of \( \text{Al}_2\text{O}_3 \).

Step 4: Calculate Mass using Molar Mass

Calculate the molar mass of each substance: Al = 26.98 g/mol, \( \text{O}_2 = 32.00 \) g/mol, and \( \text{Al}_2\text{O}_3 = 101.96 \) g/mol. Using these, 4 moles of Al (107.92 g) react with 3 moles of \( \text{O}_2 \) (96.00 g) to produce 2 moles of \( \text{Al}_2\text{O}_3 \) (203.92 g).

Key Concepts

Chemical Equation Interpretation

When you look at a chemical equation like \( 4 \text{Al (s)} + 3 \text{O}_2(\text{g}) \rightarrow 2 \text{Al}_2\text{O}_3(\text{s}) \), it's important to break it down. A chemical equation represents a chemical reaction using symbols and formulas. Here, the symbols tell us which substances are involved and in what form they exist during the reaction. The letter \( \text{(s)} \) denotes a solid state, and \( \text{(g)} \) represents a gas.
This equation tells a story of how aluminum, a solid, reacts with oxygen, a gas, to form aluminum oxide, another solid. The numbers before these symbols (the coefficients) are crucial; they tell us the exact amount of each substance participating in the reaction process.
This basic interpretation sets the stage for understanding how quantities of substances interact and transform during the reaction.

Mole Concept

The mole concept is a central idea in stoichiometry that connects chemical equations to measurable quantities. One mole of any substance contains Avogadro's number of particles, which is about \( 6.022 \times 10^{23} \) particles. Therefore, in our given reaction, the coefficients not only indicate the number of particles but also the number of moles involved.

• The coefficient 4 before \( \text{Al} \) indicates 4 moles, which means 4 moles of aluminum atoms participate.
• The coefficient 3 before \( \text{O}_2 \) shows 3 moles of oxygen molecules are involved.
• The coefficient 2 before \( \text{Al}_2\text{O}_3 \) tells us that 2 moles of aluminum oxide molecules are produced.

This understanding allows chemists to scale reactions up or down, based on the number of moles, to produce a desired amount of product in the real world.

Molar Mass Calculation

To move from moles to a tangible mass, we use the molar mass, which is the mass of one mole of a substance, usually given in grams per mole (g/mol). Knowing the molar mass of the reactants and products lets us understand how much mass is involved in a reaction.
Let's calculate it for our reaction:

• For Aluminum (Al), the molar mass is 26.98 g/mol, so 4 moles weigh \( 4 \times 26.98 = 107.92 \) g.
• For Oxygen gas (\( \text{O}_2 \)), the molar mass is 32.00 g/mol, so 3 moles weigh \( 3 \times 32.00 = 96.00 \) g.
• For Aluminum Oxide (\( \text{Al}_2\text{O}_3 \)), the molar mass is 101.96 g/mol, so 2 moles weigh \( 2 \times 101.96 = 203.92 \) g.

These calculations help predict how much reactant is needed and how much product can be made.

Particle Ratios

Particle ratios arise directly from the coefficients in a balanced chemical equation. These ratios provide a direct way to relate the number of individual atoms and molecules participating in a reaction. They represent the smallest whole number ratios of the number of atoms and molecules that react and form products.
In our reaction:

• 4 Al atoms react with 3 \( \text{O}_2 \) molecules to form 2 \( \text{Al}_2\text{O}_3 \) molecules.

Understanding these ratios allows chemists to predict amounts of substances required or produced without being dependent on moles or mass, purely on the number of particles. It turns the abstract concept of chemical reactions into tangible predictions about what happens at the molecular level.