Certainly! Let's solve this problem step-by-step.
1. Analyze the chemical reaction:
The balanced chemical equation given is:
[tex]\[
2 \text{CuFeS}_2 + 5 \text{O}_2 \rightarrow 2 \text{Cu} + 2 \text{FeO} + 4 \text{SO}_2
\][/tex]
2. Identify the relationship between reactants and products:
From the balanced equation, we observe that:
- 2 moles of [tex]\(\text{CuFeS}_2\)[/tex] produce 2 moles of [tex]\(\text{Cu}\)[/tex].
3. Set up the proportion:
We need to find out how many moles of [tex]\(\text{CuFeS}_2\)[/tex] are required to produce 16 moles of [tex]\(\text{Cu}\)[/tex].
Since the stoichiometric ratio between [tex]\(\text{CuFeS}_2\)[/tex] and [tex]\(\text{Cu}\)[/tex] is 1:1 (2 moles of [tex]\(\text{CuFeS}_2\)[/tex] produce 2 moles of [tex]\(\text{Cu}\)[/tex]), we can directly use this ratio to determine the moles of [tex]\(\text{CuFeS}_2\)[/tex] needed.
4. Calculate the moles of [tex]\(\text{CuFeS}_2\)[/tex]:
Using the stoichiometric ratio, the number of moles of [tex]\(\text{CuFeS}_2\)[/tex] required to produce 16 moles of [tex]\(\text{Cu}\)[/tex] will be the same as the number of moles of [tex]\(\text{Cu}\)[/tex] produced since the ratio is 1:1.
Therefore:
[tex]\[
\text{Moles of } \text{CuFeS}_2 = \text{Moles of } \text{Cu} = 16 \text{ moles}
\][/tex]
5. Final Result:
Thus, to produce 16 moles of [tex]\(\text{Cu}\)[/tex], you need 16 moles of [tex]\(\text{CuFeS}_2\)[/tex].
Therefore, the answer is 16 moles of [tex]\(\text{CuFeS}_2\)[/tex].
