In the balancing equation for Fe₂O₃ + CO → Fe + CO₂, how many moles of CO are needed?

Steps to Solve

1. Write the unbalanced equation

Start with the unbalanced chemical equation based on the reactants and products involved.

$$ \text{Fe}_2\text{O}_3 + \text{CO} \rightarrow \text{Fe} + \text{CO}_2 $$

2. Identify the number of atoms for each element

Count the number of atoms of each element on both sides of the equation.

• Left side: Fe (2), O (3), C (1)
• Right side: Fe (1), O (2), C (1)

3. Balance the iron (Fe) atoms

To balance the iron atoms, place a coefficient of 2 in front of iron on the product side.

$$ \text{Fe}_2\text{O}_3 + \text{CO} \rightarrow 2\text{Fe} + \text{CO}_2 $$

4. Update the count of atoms

Recount the atoms following the update:

• Left side: Fe (2), O (3), C (1)
• Right side: Fe (2), O (2), C (1)

5. Balance the oxygen (O) atoms

Now we need to balance the oxygen atoms. On the left side, we have 3 oxygen atoms from Fe₂O₃ and on the right, we have 2 from CO₂. We can balance it by adjusting the CO on the reactants side.

To do this efficiently, let's use 3 moles of CO to produce 3 moles of CO₂ and one additional oxygen.

$$ \text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2 $$

6. Recount and confirm all atoms

Now count the atoms again:

• Left side: Fe (2), O (3), C (3)
• Right side: Fe (2), O (3), C (3)

Both sides of the equation are now balanced with 2 iron, 3 carbon, and 3 oxygen atoms.

7. Final balanced equation

The final balanced equation is:

$$ \text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2 $$

This means 3 moles of carbon monoxide are needed.