Consider the reaction Fe2O3(s) + CO(g) → Fe(s) + CO2(g). When this chemical equation is balanced, what will be the correct set of coefficients a, b, c and d respectively in aFe2O3 + bCO → cFe + dCO2?

Introduction / Context:
This question tests your skill in balancing chemical equations, a fundamental technique in chemistry. The reaction given represents the reduction of iron(III) oxide by carbon monoxide to produce metallic iron and carbon dioxide, a process related to iron extraction in a blast furnace. You are asked to determine the correct set of coefficients a, b, c and d that balance the reaction aFe2O3 + bCO → cFe + dCO2. Balancing ensures that the law of conservation of mass is satisfied, with the same number of each type of atom on both sides of the equation.

Given Data / Assumptions:
The unbalanced reaction is Fe2O3(s) + CO(g) → Fe(s) + CO2(g).
The coefficients a, b, c and d are positive integers to be determined.
We must balance the number of Fe, C and O atoms on both sides of the equation.
No side reactions are considered, and the reaction is taken as a single step overall process.

Concept / Approach:
To balance a chemical equation, we equate the total number of atoms of each element on the reactant and product sides. We usually start with the metal or the most complex compound and then balance other elements like oxygen and carbon. In this case, Fe2O3 contains two iron atoms and three oxygen atoms per formula unit. Each CO molecule contains one carbon and one oxygen, while each CO2 molecule contains one carbon and two oxygen atoms. The goal is to find integer coefficients that satisfy these atom counts simultaneously.

Step-by-Step Solution:
Step 1: Begin with iron. Fe2O3 contains two iron atoms, so we need two Fe atoms on the product side. This suggests setting c = 2 in the balanced equation. Step 2: With a single Fe2O3 on the reactant side, set a = 1. Now we have one Fe2O3 providing two Fe atoms and three O atoms. Step 3: Next, consider carbon. Suppose we use three molecules of CO, so set b = 3. This introduces three carbon atoms and three oxygen atoms from CO on the reactant side. Step 4: The total oxygen atoms on the reactant side are now three from Fe2O3 and three from CO, giving six oxygen atoms in total. On the product side, each CO2 has two oxygen atoms, so to match six oxygens we need three CO2 molecules. This sets d = 3. Step 5: Check carbon balance. With b = 3, we have three carbon atoms from CO on the reactant side, and with d = 3, we have three carbon atoms in three CO2 molecules on the product side. Iron is already balanced with two atoms on each side, and oxygen is balanced with six atoms on each side. Therefore the correct coefficients are a = 1, b = 3, c = 2 and d = 3.

Verification / Alternative check:
Write the fully balanced equation as Fe2O3 + 3CO → 2Fe + 3CO2. Counting atoms on both sides gives two Fe, three C and six O atoms on each side, confirming that the equation is balanced. This is the standard form of the reaction used in discussions of iron extraction in metallurgy. Comparing this to the answer choices, the correct set of coefficients corresponds to 1, 3, 2, 3 for a, b, c and d respectively. No other set given in the options will produce the same balanced atom counts without introducing fractions or inconsistencies.

Why Other Options Are Wrong:
The set 3, 2, 3, 1 is wrong because it does not balance the number of oxygen and carbon atoms on both sides; using these coefficients would lead to mismatched totals.

The set 2, 3, 3, 1 is incorrect because the number of oxygen atoms and carbon atoms would not be equal on reactant and product sides when these coefficients are applied.

The set 3, 3, 2, 1 is also incorrect, as the atoms of oxygen and carbon would again not be balanced simultaneously, violating conservation of mass.

Common Pitfalls:
A common mistake is to balance one element but forget to recheck others after adjusting coefficients, leading to partially balanced equations. Another pitfall is accepting fractional coefficients as final answers instead of scaling the equation to obtain whole numbers. Students may also confuse this reaction with similar ones involving carbon or carbon monoxide and misremember the coefficient pattern. Systematically balancing one element at a time and verifying all elements at the end helps prevent these errors.

Final Answer:
The correctly balanced equation is Fe2O3 + 3CO → 2Fe + 3CO2, so the coefficients are 1, 3, 2, 3 for a, b, c and d respectively.