Question

Write all the mole-mole factors for each of the following equations: a. \(2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s)\) b. \(4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

Reaction (a) mole ratios: 2:3, 2:2, 3:2; Reaction (b) mole ratios: 4:1, 4:2, 4:2, 1:2, 1:2, 2:2.

Step-by-step solution

Identify the reactants and products

For each chemical reaction, identify the reactants and products along with their stoichiometric coefficients.

Write mole ratios for Reaction (a)

For Reaction (a): \(2 \text{Al}(s) + 3 \text{Cl}_{2}(g) \rightarrow 2 \text{AlCl}_{3}(s)\) List the mole ratios: - \(2 \text{mol Al}\text{ : }3 \text{mol Cl}_{2}\) - \(2 \text{mol Al}\text{ : }2 \text{mol AlCl}_{3}\) - \(3 \text{mol Cl}_{2}\text{ : }2 \text{mol AlCl}_{3}\)

Write mole ratios for Reaction (b)

For Reaction (b): \(4 \text{HCl}(g) + \text{O}_{2}(g) \rightarrow 2 \text{Cl}_{2}(g) + 2 \text{H}_{2}\text{O}(g)\) List the mole ratios: - \(4 \text{mol HCl}\text{ : }1 \text{mol O}_{2}\) - \(4 \text{mol HCl}\text{ : }2 \text{mol Cl}_{2}\) - \(4 \text{mol HCl}\text{ : }2 \text{mol H}_{2}\text{O}\) - \(1 \text{mol O}_{2}\text{ : }2 \text{mol Cl}_{2}\) - \(1 \text{mol O}_{2}\text{ : }2 \text{mol H}_{2}\text{O}\) - \(2 \text{mol Cl}_{2}\text{ : }2 \text{mol H}_{2}\text{O}\)

Key concepts

stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is like a recipe for chemistry, specifying the exact amount of ingredients needed and the amount of product that will be produced. This process relies heavily on understanding and using mole ratios derived from balanced chemical equations. These mole ratios allow chemists to predict the amounts of substances consumed and produced in any given reaction.

The balanced chemical equation serves as the foundation in stoichiometry. It tells us the number of moles of each reactant that react to form a certain number of moles of each product. For instance, in the equation: \(2 \text{Al} + 3 \text{Cl}_2 \rightarrow 2 \text{AlCl}_3\)
we can see that 2 moles of aluminum react with 3 moles of chlorine to produce 2 moles of aluminum chloride. This gives us several possible mole ratios we can use to solve problems.

mole-mole factors

Mole-mole factors are derived from the coefficients of a balanced chemical equation. These coefficients are the numbers in front of the chemical formulas within the equation, indicating the ratio of moles of each substance involved. The mole-mole factors are used to convert between moles of different substances in a chemical reaction.

Let's look at the example equation again: \(2 \text{Al} + 3 \text{Cl}_2 \rightarrow 2 \text{AlCl}_3\)
To find the mole-mole factors:

• \text{2 mol Al : 3 mol Cl}_2
• \text{2 mol Al : 2 mol AlCl}_3
• \text{3 mol Cl}_2\text{ : 2 mol AlCl}_3

Each pair gives a mole ratio we can use. These ratios act like conversion factors that allow us to predict how much of one substance is needed or produced when given the quantity of another.

chemical equations

Chemical equations represent chemical reactions by using symbols and formulas to describe the reactants and products. A balanced chemical equation ensures that the number of atoms for each element is the same on both sides of the equation. This balance reflects the conservation of mass in chemical reactions, where the total mass of reactants equals the total mass of products.

For example, consider the equation: \(4 \text{HCl} + \text{O}_2 \rightarrow 2 \text{Cl}_2 + 2 \text{H}_2\text{O}\)
Here, we have:
\text{4 moles of hydrogen chloride gas} reacting with \text{1 mole of oxygen gas} to produce \text{2 moles of chlorine gas} and \text{2 moles of water vapor}.
This balanced equation is essential for determining the mole ratios:

• \text{4 mol HCl : 1 mol O}_2
• \text{4 mol HCl : 2 mol Cl}_2
• \text{4 mol HCl : 2 mol H}_2\text{O}
• \text{1 mol O}_2\text{ : 2 mol Cl}_2
• \text{1 mol O}_2\text{ : 2 mol H}_2\text{O}
• \text{2 mol Cl}_2\text{ : 2 mol H}_2\text{O}

Understanding how to balance chemical equations and use them to determine mole-mole factors is a fundamental skill in chemistry.