Sure, let's work through this step-by-step based on the given chemical reaction:
We have the balanced chemical equation:
[tex]\[ 3 \text{CuCl}_2 + 2 \text{Al} \rightarrow 2 \text{AlCl}_3 + 3 \text{Cu} \][/tex]
From this equation, we see the molar ratios between the reactants and the products. Specifically, it tells us that 2 moles of aluminum (Al) will react with 3 moles of copper(II) chloride (CuCl[tex]\(_2\)[/tex]) to produce:
- 2 moles of aluminum chloride (AlCl_3)
- 3 moles of copper (Cu)
To determine the theoretical yield of copper using aluminum as the limiting reactant, follow these steps:
1. Identify the mole ratio:
The balanced equation provides the mole ratio of aluminum to copper: [tex]\( 2 \text{ moles Al} : 3 \text{ moles Cu} \)[/tex].
2. Assume starting moles of aluminum:
Let’s assume we start with 1 mole of aluminum (Al).
3. Use the mole ratio to find moles of copper:
According to the mole ratio, for every 2 moles of aluminum, we get 3 moles of copper. Therefore, for 1 mole of aluminum:
[tex]\[
\text{Moles of Cu} = \left( \frac{3 \text{ moles Cu}}{2 \text{ moles Al}} \right) \times 1 \text{ mole Al}
\][/tex]
4. Calculate the moles of copper produced:
Simplifying the ratio:
[tex]\[
\text{Moles of Cu} = 1.5 \text{ moles}
\][/tex]
So, if we start with 1 mole of aluminum and it is the limiting reactant, the theoretical yield of copper would be 1.5 moles.
Therefore, the theoretical yield of copper is:
[tex]\[
1.5 \text{ moles}
\][/tex]
