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Explanation:

Step1: Balance Fe atoms

There are 2 Fe atoms on the left, so add coefficient 2 to Fe on the right:
$\text{CO} + \text{Fe}_2\text{O}_3
ightarrow 2\text{Fe} + \text{CO}_2$

Step2: Balance O atoms

Left side has 3 O from $\text{Fe}_2\text{O}_3$ + 1 O from $\text{CO}$; right side has 2 O from $\text{CO}_2$. To balance, add coefficient 3 to $\text{CO}$ and $\text{CO}_2$ (each $\text{CO}$ gains 1 O to become $\text{CO}_2$, 3 O atoms need 3 $\text{CO}$):
$3\text{CO} + \text{Fe}_2\text{O}_3
ightarrow 2\text{Fe} + 3\text{CO}_2$

Step3: Verify all atoms

Count atoms:

  • C: 3 on left, 3 on right
  • O: $3+3=6$ on left, $3\times2=6$ on right
  • Fe: 2 on left, 2 on right

All atoms are balanced.

Answer:

$3\text{CO} + \text{Fe}_2\text{O}_3
ightarrow 2\text{Fe} + 3\text{CO}_2$
(The coefficients in order are 3, 1, 2, 3)