Alright, let's solve this step-by-step:
1. Write the balanced chemical equation:
[tex]\[
3 \text{CuCl}_2 + 2 \text{Al} \rightarrow 2 \text{AlCl}_3 + 3 \text{Cu}
\][/tex]
2. Identify the molar ratio:
The balanced equation indicates that 2 moles of aluminum ([tex]\(\text{Al}\)[/tex]) react with 3 moles of copper(II) chloride ([tex]\(\text{CuCl}_2\)[/tex]) to produce 3 moles of copper ([tex]\(\text{Cu}\)[/tex]).
3. Determine the molar ratio relevant to our question:
The molar ratio of aluminum to copper is derived from the coefficients in the balanced equation:
[tex]\[
\text{Molar ratio of Al to Cu} = \frac{3 \text{ moles of Cu}}{2 \text{ moles of Al}} = 1.5
\][/tex]
4. Assume 1 mole of aluminum (as a limiting reactant):
We need to calculate the theoretical yield of copper produced if we start with 1 mole of aluminum.
5. Calculate the theoretical yield:
Using the molar ratio calculated, if we have 1 mole of aluminum, we can calculate the amount of copper produced:
[tex]\[
\text{Theoretical yield of Cu} = 1 \text{ mole of Al} \times \text{molar ratio of Cu to Al}
\][/tex]
[tex]\[
\text{Theoretical yield of Cu} = 1 \text{ mole of Al} \times 1.5 = 1.5 \text{ moles of Cu}
\][/tex]
Thus, the theoretical yield of copper is [tex]\(1.5\)[/tex] moles.
