To determine the theoretical yield of copper (Cu) from the given reaction:
[tex]\[
3 \, \text{CuCl}_2 + 2 \, \text{Al} \rightarrow 2 \, \text{AlCl}_3 + 3 \, \text{Cu}
\][/tex]
we start by analyzing the balanced chemical equation.
1. Identify the limiting reactant and the product of interest.
- In this reaction, we focus on aluminum (Al) as the limiting reactant and copper (Cu) as the product of interest.
2. Determine the molar ratio between the limiting reactant (Al) and the product (Cu).
- From the balanced chemical equation, 2 moles of aluminum produce 3 moles of copper.
3. Calculate the moles of copper produced per mole of aluminum used.
- For every 2 moles of aluminum, we get 3 moles of copper. Therefore, if we consider 1 mole of aluminum:
[tex]\[
\text{Moles of Cu from Al} = \frac{3 \text{ moles Cu}}{2 \text{ moles Al}} \times \text{moles of Al}
\][/tex]
- Since the number of moles of aluminum used is 2:
[tex]\[
\text{Moles of Cu from Al} = 2 \text{ moles Al} \times \frac{3 \text{ moles Cu}}{2 \text{ moles Al}} = 3 \text{ moles Cu}
\][/tex]
4. Therefore, the theoretical yield of copper is:
[tex]\[
\text{Theoretical yield} = 3.0 \, \text{moles}
\][/tex]
This means that the theoretical yield of copper, based on the limiting reactant aluminum, is 3.0 moles.
