Problem 5 - Chemistry The Molecular Science

Question

Write all the possible mole ratios for the reaction $$3 \mathrm{MgO}(\mathrm{s})+2 \mathrm{Fe}(\mathrm{s}) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{Mg}(\mathrm{s})$$

Step-by-Step Solution

Answer

All possible mole ratios are 3:2, 3:1, 3:3, 2:1, 2:3, 1:3.

Step 1: Identify the Reaction Components

For the reaction given \(3 \mathrm{MgO}(\mathrm{s})+2 \mathrm{Fe}(\mathrm{s}) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{Mg}(\mathrm{s})\), identify each compound involved, which are \(\mathrm{MgO}\), \(\mathrm{Fe}\), \(\mathrm{Fe}_2\mathrm{O}_3\), and \(\mathrm{Mg}\).

Step 2: Understand the Coefficients

In the balanced equation, the coefficients are the numbers in front of each compound. These coefficients represent the moles of each substance involved in the reaction. The coefficients are: 3 moles of \(\mathrm{MgO}\), 2 moles of \(\mathrm{Fe}\), 1 mole of \(\mathrm{Fe}_2\mathrm{O}_3\), and 3 moles of \(\mathrm{Mg}\).

Step 3: Determine the Mole Ratios

Mole ratios are derived from the coefficients. They show the ratio of moles of one substance to moles of another. Possible mole ratios from the reaction are:1. 3 moles \(\mathrm{MgO}\) : 2 moles \(\mathrm{Fe}\)2. 3 moles \(\mathrm{MgO}\) : 1 mole \(\mathrm{Fe}_2\mathrm{O}_3\)3. 3 moles \(\mathrm{MgO}\) : 3 moles \(\mathrm{Mg}\)4. 2 moles \(\mathrm{Fe}\) : 1 mole \(\mathrm{Fe}_2\mathrm{O}_3\)5. 2 moles \(\mathrm{Fe}\) : 3 moles \(\mathrm{Mg}\)6. 1 mole \(\mathrm{Fe}_2\mathrm{O}_3\) : 3 moles \(\mathrm{Mg}\)

Step 4: Write Down All Possible Combinations

Based on the coefficients, write down each distinct pair of substances and their mole ratios as found in step 3. Ensure all pairs are covered, including both reactants and products with each other.

Key Concepts

Chemical Reaction Coefficients

When studying chemical reactions, you'll notice numbers in front of the chemical formulas. These are called coefficients. They are vital in understanding how reactions occur.
Coefficients indicate the number of moles, which are very important in chemistry. For example, in the reaction \(3 \mathrm{MgO} + 2 \mathrm{Fe} \rightarrow \mathrm{Fe}_2\mathrm{O}_3 + 3 \mathrm{Mg}\), the coefficients tell you how many moles of each substance take part in the reaction.

• The number 3 in front of \(\mathrm{MgO}\) means 3 moles of magnesium oxide.
• The number 2 in front of \(\mathrm{Fe}\) means 2 moles of iron.
• There is an implied 1 in front of \(\mathrm{Fe}_2\mathrm{O}_3\), representing 1 mole of iron(III) oxide.
• The number 3 in front of \(\mathrm{Mg}\) means 3 moles of magnesium.

These coefficients derive from stoichiometric calculations to ensure the conservation of mass and atoms throughout the reaction.

Balanced Chemical Equations

To understand chemical equations fully, they must be balanced. A balanced chemical equation has equal numbers of each type of atom on both sides of the equation.
Balancing ensures that the Law of Conservation of Mass is obeyed, which states that mass is neither created nor destroyed in a chemical reaction. In essence, the mass of the reactants equals the mass of the products.
For our given reaction, \(3 \mathrm{MgO} + 2 \mathrm{Fe} \rightarrow \mathrm{Fe}_2\mathrm{O}_3 + 3 \mathrm{Mg}\), the equation is set with correct coefficients to achieve this balance.

• Start by counting the atoms of each element on both sides of the equation.
• Adjust the coefficients to get the same number of atoms of each element on both sides.
• The result is a balanced equation that precisely represents the chemical process.

Balancing equations is crucial for accurately calculating reactants and products involved in a reaction.

Stoichiometry

Stoichiometry is a section of chemistry involving the calculation of reactants and products in chemical reactions. It uses the concept of mole ratios derived from the coefficients in a balanced equation.
In our example reaction, different mole ratios can be identified:

• 3 moles of \(\mathrm{MgO}\) to 2 moles of \(\mathrm{Fe}\)
• 3 moles of \(\mathrm{MgO}\) to 1 mole of \(\mathrm{Fe}_2\mathrm{O}_3\)
• 2 moles of \(\mathrm{Fe}\) to 3 moles of \(\mathrm{Mg}\)

These ratios allow you to compute the amounts of substances consumed or produced. Understanding stoichiometry means:

• Predicting how much product you'll get based on known quantities of reactants.
• Determining how much of each reactant is needed to completely react with another.
• Ensuring the reaction has no waste of materials.

It's about the relationship between quantities in a chemical reaction, making stoichiometry one of the fundamental concepts in chemistry.