Alright, let's tackle this step-by-step to determine both the theoretical yield of copper and the percent yield.
### Step 1: Determine the Molar Ratio and Theoretical Yield
From the balanced chemical equation:
[tex]\[ 3 \text{CuCl}_2 + 2 \text{Al} \rightarrow 2 \text{AlCl}_3 + 3 \text{Cu} \][/tex]
The molar ratio between aluminum (Al) and copper (Cu) is 2:3. This means that for every 2 moles of aluminum, 3 moles of copper are produced.
Given:
- Number of moles of aluminum (Al) = 2 moles
Using the stoichiometric ratio:
[tex]\[ \text{Moles of Cu} = \left(\frac{3 \text{moles of Cu}}{2 \text{moles of Al}}\right) \times 2 \text{moles of Al} = 3 \text{moles of Cu} \][/tex]
So, the theoretical yield of copper is 3 moles.
### Step 2: Determine the Percent Yield
Given:
- Actual yield of copper in moles = 0.014 moles
The percent yield is calculated using the formula:
[tex]\[ \text{Percent yield} = \left(\frac{\text{Actual yield}}{\text{Theoretical yield}}\right) \times 100 \][/tex]
Substituting in the values:
[tex]\[ \text{Percent yield} = \left(\frac{0.014 \text{ moles}}{3 \text{ moles}}\right) \times 100 = 0.46666666666666673 \% \][/tex]
Rounding to an appropriate number of significant figures (considering the given precision), the percent yield is approximately:
[tex]\[ \text{Percent yield} \approx 0.47\% \][/tex]
### Summary
- Theoretical yield of copper: 3 moles
- Percent yield of copper: 0.47%
This detailed approach ensures that both the theoretical yield and the percent yield are clearly identified through proper stoichiometric calculations and precise usage of the formula for percent yield.
