To determine how many moles of FeO are produced if 8 moles of [tex]\( SO_2 \)[/tex] are produced, we need to use the stoichiometric relationship provided by the balanced chemical equation:
[tex]\[ 2 \, \text{CuFeS}_2 + 5 \, \text{O}_2 \rightarrow 2 \, \text{Cu} + 2 \, \text{FeO} + 4 \, \text{SO}_2 \][/tex]
1. From the balanced equation, we observe that for every 2 moles of FeO produced, 4 moles of [tex]\( SO_2 \)[/tex] are produced. This simplifies to a 1:2 stoichiometric ratio between FeO and [tex]\( SO_2 \)[/tex].
2. We are given that 8 moles of [tex]\( SO_2 \)[/tex] are produced. Based on the stoichiometric ratio (1 mole of FeO for every 2 moles of [tex]\( SO_2 \)[/tex]):
[tex]\[ \text{Moles of FeO} = 8 \, \text{moles of SO}_2 \times \left( \frac{1 \, \text{mole of FeO}}{2 \, \text{moles of SO}_2} \right) \][/tex]
3. Simplifying this calculation:
[tex]\[ \text{Moles of FeO} = 8 \times 0.5 = 4.0 \][/tex]
Therefore, if 8 moles of [tex]\( SO_2 \)[/tex] are produced, 4.0 moles of FeO are also produced.
