Question

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

Short answer

The possible mole ratios for the given balanced chemical equations are: a) \(\frac{4}{3}\), \(\frac{4}{2}\), \(\frac{3}{2}\) b) \(\frac{3}{4}\), \(\frac{3}{1}\), \(\frac{3}{4}\), \(\frac{4}{1}\), \(\frac{4}{4}\), \(\frac{1}{4}\) c) \(\frac{2}{2}\), \(\frac{2}{1}\), \(\frac{2}{1}\)

Step-by-step solution

Identify participating substances

In this balanced chemical equation, we have: 1. 4 moles of Aluminum (Al) 2. 3 moles of Oxygen gas (O2) 3. 2 moles of Aluminum oxide (Al2O3)

Create mole ratios between the substances

We will now create fractions that represent the mole ratios between each substance and every other substance in the reaction. 1. \(\frac{4 \: \text{moles} \: \text{Al}}{3 \: \text{moles} \: \text{O}_2}\) 2. \(\frac{4 \: \text{moles} \: \text{Al}}{2 \: \text{moles} \: \text{Al}_2 \text{O}_3}\) 3. \(\frac{3 \: \text{moles} \: \text{O}_2}{2 \: \text{moles} \: \text{Al}_2 \text{O}_3}\) Thus, the possible mole ratios for equation (a) are: \(\frac{4}{3}\), \(\frac{4}{2}\), \(\frac{3}{2}\) #System:b)#

Identify participating substances

In this balanced chemical equation, we have: 1. 3 moles of Iron (Fe) 2. 4 moles of Water (H2O) 3. 1 mole of Iron(III) oxide (Fe3O4) 4. 4 moles of Hydrogen gas (H2)

Create mole ratios between the substances

We will now create fractions that represent the mole ratios between each substance and every other substance in the reaction. 1. \(\frac{3 \: \text{moles} \: \text{Fe}}{4 \: \text{moles} \: \text{H}_2 \text{O}}\) 2. \(\frac{3 \: \text{moles} \: \text{Fe}}{1 \: \text{mole} \: \text{Fe}_3 \text{O}_4}\) 3. \(\frac{3 \: \text{moles} \: \text{Fe}}{4 \: \text{moles} \: \text{H}_2}\) 4. \(\frac{4 \: \text{moles} \: \text{H}_2 \text{O}}{1 \: \text{mole} \: \text{Fe}_3 \text{O}_4}\) 5. \(\frac{4 \: \text{moles} \: \text{H}_2 \text{O}}{4 \: \text{moles} \: \text{H}_2}\) 6. \(\frac{1 \: \text{mole} \: \text{Fe}_3 \text{O}_4}{4 \: \text{moles} \: \text{H}_2}\) Thus, the possible mole ratios for equation (b) are: \(\frac{3}{4}\), \(\frac{3}{1}\), \(\frac{3}{4}\), \(\frac{4}{1}\), \(\frac{4}{4}\), and \(\frac{1}{4}\) #System:c)#

Identify participating substances

In this balanced chemical equation, we have: 1. 2 moles of Mercury (II) oxide (HgO) 2. 2 moles of Mercury (Hg) 3. 1 mole of Oxygen gas (O2)

Create mole ratios between the substances

We will now create fractions that represent the mole ratios between each substance and every other substance in the reaction. 1. \(\frac{2 \: \text{moles} \: \text{HgO}}{2 \: \text{moles} \: \text{Hg}}\) 2. \(\frac{2 \: \text{moles} \: \text{HgO}}{1 \: \text{mole} \: \text{O}_2}\) 3. \(\frac{2 \: \text{moles} \: \text{Hg}}{1 \: \text{mole} \: \text{O}_2}\) Thus, the possible mole ratios for equation (c) are: \(\frac{2}{2}\), \(\frac{2}{1}\), \(\frac{2}{1}\)

Key concepts

Balanced Chemical Equations

Understanding balanced chemical equations is essential for describing chemical reactions. In a balanced equation, the number of atoms for each element is the same on both sides of the equation. This follows the law of conservation of mass, which asserts that mass cannot be created or destroyed in a chemical reaction.
These equations help in determining the proportions of reactants and products involved in a reaction. For instance, in the equation \( 4 \text{Al (s)} + 3 \text{O}_2 \text{(g)} \rightarrow 2 \text{Al}_2\text{O}_3 \text{(s)} \), the coefficients indicate that 4 moles of aluminum react with 3 moles of oxygen gas to produce 2 moles of aluminum oxide.

• It's vital to first identify all the substances involved and their quantities in moles.
• The coefficients in the balanced equation represent these mole amounts, guiding the stoichiometric calculations.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with measuring relationships between reactants and products in a chemical reaction. It uses the coefficients from a balanced chemical equation to determine how much of each substance is involved or needed.
In stoichiometry, the mole ratio from the balanced equation helps predict quantities based on known amounts. Consider part b of our exercise: \(3 \text{Fe (s)} + 4 \text{H}_2\text{O (l)} \rightarrow \text{Fe}_3\text{O}_4 \text{(s)} + 4 \text{H}_2 \text{(g)}\). Here, 3 moles of iron always react with 4 moles of water to produce 1 mole of iron(III) oxide and 4 moles of hydrogen gas.

• By interpreting these ratios, one can solve problems related to measuring reactants and products.
• Stoichiometry is fundamental for understanding chemical processes and for scaling reactions for practical applications.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, involving rearrangement of atoms. They can be represented by balanced chemical equations that provide insights into the process. Different types of reactions such as synthesis, decomposition, single and double replacement exist, each with distinct patterns and outcomes.
For example, in exercise part c: \(2 \text{HgO (s)} \rightarrow 2 \text{Hg(l)} + \text{O}_2\text{(g)}\), we see a decomposition reaction, where mercury(II) oxide breaks down into its elemental form of mercury and oxygen gas.

• In decompositions, typically a single compound breaks down into two or more simpler substances.
• Understanding the type of reaction aids in predicting the behavior and products involved.

Moles in Chemistry

Moles are a fundamental unit in chemistry, representing a quantity of substance. One mole contains Avogadro's number, \(6.022 \times 10^{23}\), of entities (usually atoms or molecules) and helps relate the macroscopic scale to the atomic scale.
Within a chemical equation, determining the number of moles is crucial for quantifying reactions and stoichiometry. For example, in the reaction \(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\), having 4 moles of aluminum means you have \(4 \times 6.022 \times 10^{23}\) atoms of aluminum.

• Moles facilitate the conversion between mass of substances and the number of atoms or molecules.
• They act as a bridge in calculations, enabling conversion between grams, molecules, and volume of gases.