To find the percent yield of product [tex]\( Y \)[/tex] in this chemical reaction, follow these steps:
1. Identify the theoretical yield: This is the maximum amount of product that could be formed from the given amount of starting material under perfect conditions. In this case, the theoretical yield is [tex]\( 28.3 \)[/tex] grams of [tex]\( Y \)[/tex].
2. Identify the actual yield: This is the amount of product actually obtained from the experiment. Here, the actual yield is [tex]\( 22.6 \)[/tex] grams of [tex]\( Y \)[/tex].
3. Calculate the percent yield using the formula:
[tex]\[
\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%
\][/tex]
4. Substitute the values:
[tex]\[
\text{Percent Yield} = \left( \frac{22.6 \, \text{g}}{28.3 \, \text{g}} \right) \times 100\%
\][/tex]
5. Compute the division:
[tex]\[
\frac{22.6}{28.3} \approx 0.7985865724381625
\][/tex]
6. Multiply by 100 to convert to percentage:
[tex]\[
0.7985865724381625 \times 100 \approx 79.85865724381625\%
\][/tex]
7. Round to the correct number of significant figures: In this context, we are working with initial values of 3 significant figures (22.6 g has 3 significant figures, and 28.3 g has 3 significant figures). Therefore, the resulting percent yield should also be expressed with 3 significant figures.
[tex]\[
79.85865724381625\% \approx 79.859\%
\][/tex]
So, the percent yield of [tex]\( Y \)[/tex] in the reaction is:
[tex]\[
\boxed{79.859 \, \%}
\][/tex]
