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How many moles of [tex]\( CuFeS_2 \)[/tex] are used to produce 16 moles of Cu?

Given the reaction:
[tex]\[ 2 CuFeS_2 + 5 O_2 \rightarrow 2 Cu + 2 FeO + 4 SO_2 \][/tex]

[tex]\[ \text{? mol } CuFeS_2 \][/tex]


Sagot :

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].
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