Sure! Let's break this problem down step-by-step to find the percent yield.
1. Understanding the Percent Yield Formula:
The percent yield formula is given by:
[tex]\[ \text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100 \][/tex]
2. Identify Values:
- Actual Yield: This is the amount of product you actually recovered from the reaction. For this question, the actual yield of aluminum oxide ([tex]\(Al_2O_3\)[/tex]) is 3.4 grams.
- Theoretical Yield: This is the maximum amount of product that can be formed from the given amounts of reactants, assuming perfect conversion and no losses. For this question, the theoretical yield of aluminum oxide ([tex]\(Al_2O_3\)[/tex]) is 4.7 grams.
3. Substitute the Values into the Formula:
[tex]\[ \text{Percent Yield} = \frac{3.4 \text{ grams}}{4.7 \text{ grams}} \times 100 \][/tex]
4. Calculate the Ratio:
[tex]\[ \frac{3.4 \text{ grams}}{4.7 \text{ grams}} \approx 0.7234042553191489 \][/tex]
5. Multiply by 100 to Convert to Percentage:
[tex]\[ 0.7234042553191489 \times 100 \approx 72.34042553191489 \][/tex]
6. Result:
Therefore, the percent yield for this reaction is approximately:
[tex]\[ 72.34\% \][/tex]
This means that you recovered about 72.34% of the theoretical amount of aluminum oxide.
