Problem 3 - Chemistry Matter and Change

Question

Determine all possible mole ratios for the following balanced chemical equations. \begin{equation} \begin{array}{l}{\text { a. } 4 \mathrm{Al}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})} \\ {\text { b. } 3 \mathrm{Fe}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}\left(\mathrm{l} \rightarrow \mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})+4 \mathrm{H}_{2}(\mathrm{g})\right.} \\ {\text { c. } 2 \mathrm{HgO}(\mathrm{s}) \rightarrow 2 \mathrm{Hg}(1)+\mathrm{O}_{2}(\mathrm{g})}\end{array} \end{equation}

Step-by-Step Solution

Answer

The mole ratios are: a. Al:O2:Al2O3 as 4:3:2; b. Fe:H2O:Fe3O4:H2 as 3:4:1:4; c. HgO:Hg:O2 as 1:1:2.

Step 1: Identify the Chemical Equation

We have three balanced chemical equations: a. \(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\) b. \(3 \text{Fe} + 4 \text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + 4 \text{H}_2\) c. \(2 \text{HgO} \rightarrow 2 \text{Hg} + \text{O}_2\)

Step 2: Determine the Mole Ratios for Reaction a

In the chemical equation \(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\):- The mole ratio of Al to O_2 is \(\frac{4}{3}\)- The mole ratio of Al to Al_2O_3 is \(\frac{4}{2} = 2 \)- The mole ratio of O_2 to Al_2O_3 is \(\frac{3}{2}\).

Step 3: Determine the Mole Ratios for Reaction b

In the chemical equation \(3 \text{Fe} + 4 \text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + 4 \text{H}_2\):- The mole ratio of Fe to H_2O is \(\frac{3}{4}\)- The mole ratio of Fe to Fe_3O_4 is \(\frac{3}{1} = 3\)- The mole ratio of Fe to H_2 is \(\frac{3}{4}\)- The mole ratio of H_2O to Fe_3O_4 is \(\frac{4}{1} = 4\)- The mole ratio of H_2O to H_2 is \(\frac{4}{4} = 1\)- The mole ratio of Fe_3O_4 to H_2 is \(\frac{1}{4}\).

Step 4: Determine the Mole Ratios for Reaction c

In the chemical equation \(2 \text{HgO} \rightarrow 2 \text{Hg} + \text{O}_2\):- The mole ratio of HgO to Hg is \(\frac{2}{2} = 1\)- The mole ratio of HgO to O_2 is \(\frac{2}{1} = 2\)- The mole ratio of Hg to O_2 is \(\frac{2}{1} = 2\).

Key Concepts

Balanced Chemical Equations

Balanced chemical equations depict how substances react together to form new products. Each side of the equation holds equal numbers of each type of atom, reflecting the conservation of mass. When balancing, you adjust coefficients, not subscripts. For example, in the equation \(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\), the coefficients ensure that the number of Al and O atoms on both sides is balanced.
In this case:

• 4 atoms of Al on the left balance with those combined in 2 \(\text{Al}_2\text{O}_3\) on the right, since \(2 \text{Al}_2\text{O}_3\) implies 4 Al atoms.
• 6 oxygen atoms in the form of 3 \(\text{O}_2\) molecules balance with the 6 oxygen atoms in 2 \(\text{Al}_2\text{O}_3\) molecules.

Balanced equations are vital for accurate stoichiometry calculations, as using unbalanced ones leads to misplaced predictions about the quantities of products formed.

Stoichiometry

Stoichiometry involves quantifying the relationships between reactants and products in chemical reactions. It's like a recipe, where ingredients measure out to make a dish. Mole ratios, derived from the balanced chemical equation, help determine how much of one substance reacts with or forms from another. For instance, in \(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\), the mole ratio of Al to \(\text{O}_2\) is \(\frac{4}{3}\), indicating that 4 moles of Al react with 3 moles of \(\text{O}_2\).
This bridges theory and reality since it calculates how much of each substance you need methodically and predicts the outputs from a reaction accurately. Learning stoichiometry allows for mastering critical thinking and problem-solving skills specific to chemistry.

Chemical Reactions

Chemical reactions transform substances via breaking and forming chemical bonds. Their representation through equations provides a fundamental communication tool in chemistry. For instance, the reaction \(3 \text{Fe} + 4 \text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + 4 \text{H}_2\) explains how elemental iron reacts with water to form iron(II, III) oxide and hydrogen gas.
Key Points about Reactions:

• Reactions involve reactants converting into products through rearranging atoms.
• Types of reactions include synthesis, decomposition, single replacement, and double replacement.
• Reactions must adhere to the law of conservation of mass, ensuring total mass of reactants equals the mass of products.

Understanding how reactions proceed allows chemists and researchers to manipulate and create materials aimed at specific uses in industry, medicine, or research.

Mole Concept

The mole concept connects mass and numbers of particles, making it easier to quantify chemical substances. One mole, aligning with Avogadro’s number \(6.022 \times 10^{23}\), represents a large quantity of particles, like atoms or molecules, akin to counting by dozens but on a much larger scale. For example, in \(2 \text{HgO} \rightarrow 2 \text{Hg} + \text{O}_2\), the equation signifies 2 moles of \(\text{HgO}\) decomposing into 2 moles of \(\text{Hg}\) and 1 mole of \(\text{O}_2\).
The mole supports practical laboratory activities since substances are measured more feasibly in moles rather than enormous numbers. The conversion between moles and grams facilitates the use of weighable quantities in experiments, maintaining precision and simplicity in chemical analysis.