Problem 63 - Chemistry The Molecular Science

Question

Iron reacts with oxygen to give iron(III) oxide, \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). (a) Write a balanced equation for this reaction. (b) An ordinary iron nail (assumed to be pure iron) has a mass of \(5.58 \mathrm{~g} ;\) calculate the mass (in grams) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) that is produced when the nail is converted completely to \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) (c) Calculate the mass of \(\mathrm{O}_{2}\) (in grams) required for the reaction.

Step-by-Step Solution

Answer

(a) Balanced equation: \(4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3\). (b) Mass of \(\text{Fe}_2\text{O}_3\): 7.98 g. (c) Mass of \(\text{O}_2\): 2.40 g.

Step 1: Write the Unbalanced Equation

Identify the reactants and products. Iron (Fe) reacts with oxygen (O₂) to form iron(III) oxide (Fe₂O₃). The unbalanced equation is:\[\text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3\]

Step 2: Balance the Chemical Equation

Balance the equation by adjusting the coefficients of the reactants and products to ensure the number of each type of atom is the same on both sides.The balanced equation is:\[4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3\]

Step 3: Calculate Moles of Iron

Calculate the number of moles of iron using the molar mass of iron (55.85 g/mol).\[\text{Moles of Fe} = \frac{5.58 \text{ g}}{55.85 \text{ g/mol}} \approx 0.10 \text{ moles}\]

Step 4: Determine Moles of Fe₂O₃ Produced

Use the mole ratio from the balanced equation (2 moles of Fe for 1 mole of Fe₂O₃) to find the moles of Fe₂O₃ produced.\[\text{Moles of Fe}_2\text{O}_3 = \frac{0.10 \text{ moles Fe}}{4/2} = 0.05 \text{ moles}\]

Step 5: Calculate Mass of Fe₂O₃

Multiply the moles of Fe₂O₃ by its molar mass (159.69 g/mol) to calculate its mass. \[\text{Mass of Fe}_2\text{O}_3 = 0.05 \text{ moles} \times 159.69 \text{ g/mol} = 7.98 \text{ g}\]

Step 6: Calculate Moles of O₂ Required

Use the balanced equation to find the moles of O₂ required (3 moles of O₂ are needed for every 4 moles of Fe).\[\text{Moles of O}_2 = \frac{0.10 \text{ moles Fe} }{4} \times 3 = 0.075 \text{ moles}\]

Step 7: Calculate Mass of O₂ Required

Calculate the mass of O₂ using its molar mass (32.00 g/mol).\[\text{Mass of O}_2 = 0.075 \text{ moles} \times 32.00 \text{ g/mol} = 2.40 \text{ g}\]

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is essential in stoichiometry because it ensures that the same number of each type of atom appears on both sides of the equation. This reflects the law of conservation of mass, meaning mass cannot be created or destroyed in a chemical reaction. When reacting iron with oxygen to form iron(III) oxide, we begin with the unbalanced equation:\[ \text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3 \]To balance this, we adjust the coefficients—the numbers in front of the chemical formulas—until we have the same quantity of atoms for each element on both the reactant and product sides. For this reaction, the balanced equation is:\[ 4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3 \]Here’s how this works:

• Iron (Fe) atoms: 4 on both sides.
• Oxygen (O) atoms: 6 from O₂ (3 x 2) on the left and 6 (2 x 3) in Fe₂O₃ on the right.

Balancing equations might seem tricky at first, but a systematic approach ensures success. You often balance atoms that appear less frequently first, like iron, before tackling those in polyatomic molecules like oxygen.

Moles Calculation

Moles are the bridge between the atomic world and the macro world in chemistry, allowing us to count entities like atoms based on mass. To determine the moles of a substance, we use the formula:\[\text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]For iron, with a given mass of 5.58 grams and a molar mass of 55.85 g/mol, the calculation is:

• \( \text{Moles of Fe} = \frac{5.58 \text{ g}}{55.85 \text{ g/mol}} \approx 0.10 \text{ moles} \)

Once the moles of iron are known, we can use the balanced chemical equation to find the moles of other substances. According to the reaction:

• 4 moles of Fe produce 2 moles of Fe₂O₃.
• Therefore, 0.10 moles of Fe will produce \( \frac{0.10}{4} \times 2 = 0.05 \) moles of Fe₂O₃.

Mole ratios are vital because they allow chemists to relate amounts of reactants to products in a reaction, much like a recipe.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol), and is used to convert grams to moles or vice versa. Each element has a molar mass listed on the periodic table. Here’s how you apply molar mass to our example reaction:

• Iron (Fe): 55.85 g/mol
• Iron(III) Oxide (Fe₂O₃): Add up the masses of 2 Fe atoms (2 x 55.85 g/mol) and 3 O atoms (3 x 16.00 g/mol) = 159.69 g/mol
• Oxygen (O₂): 32.00 g/mol (because each O is 16.00 g/mol and O₂ has two oxygen atoms)

Knowing the molar mass, we can switch between mass and moles in calculations:- For Fe₂O₃, if you have 0.05 moles, then the mass is:\[\text{Mass of Fe}_2\text{O}_3 = 0.05 \text{ moles} \times 159.69 \text{ g/mol} = 7.98 \text{ g}\]Molar mass thus serves as a crucial tool for converting between moles and mass, enabling calculations that predict the amounts of substances consumed and produced in a chemical reaction.