Balance the following redox reaction: Fe$_2$O$_3$ + CO → Fe + CO$_2$

To balance this chemical equation, we need to ensure that the number of atoms of each element is the same on both the reactant side (left) and the product side (right).

1. Analyze the unbalanced equation

Fe$_2$O$_3$ + CO → Fe + CO$_2$

• Reactants: 2 Fe, 4 O (3 from Fe$_2$O$_3$ + 1 from CO), 1 C
• Products: 1 Fe, 2 O (from CO$_2$), 1 C

2. Step-by-step balancing

• Balance Iron (Fe): There are 2 Fe atoms on the left. To balance this, we place a coefficient of 2 before Fe on the right. • Equation: Fe$_2$O$_3$ + CO → 2Fe + CO$_2$
• Balance Carbon (C): There is 1 C on the left and 1 C on the right. Currently, they are balanced.
• Balance Oxygen (O): • On the left, we have 3 (from Fe$_2$O$_3$) + 1 (from CO) = 4 oxygen atoms. • On the right, we have 2 (from CO$_2$). • To get 3 oxygen atoms from CO$_2$ to match the 3 in Fe$_2$O$_3$, we need to adjust the coefficients. Let's try placing a 3 before CO and a 3 before CO$_2$: • Equation: Fe$_2$O$_3$ + 3CO → 2Fe + 3CO$_2$

3. Final Check

• Fe: 2 on the left; 2 on the right. (Balanced)
• C: 3 on the left; 3 on the right. (Balanced)
• O: (3 + 3) = 6 on the left; (3 × 2) = 6 on the right. (Balanced)

The equation is now perfectly balanced.

4. Identify the answer

Comparing our result to the given options, the correct balanced equation is Fe$_2$O$_3$ + 3CO → 2Fe + 3CO$_2$. This matches option D.

Exam Tip

When balancing redox equations involving oxides, always balance the metal atoms first, then the carbon/non-metal atoms, and leave the oxygen atoms for last. If you find yourself stuck with an odd number of oxygens, try doubling your coefficients to clear the fraction!