To determine the theoretical yield of aspirin, follow these steps:
1. Determine the moles of salicylic acid:
Use the molar mass of salicylic acid [tex]\(C_7H_6O_3\)[/tex] and the given mass to calculate the number of moles.
[tex]\[
\text{Molar mass of salicylic acid} = 138.12 \, \text{g/mol}
\][/tex]
[tex]\[
\text{Mass of salicylic acid} = 3.04 \, \text{g}
\][/tex]
The number of moles of salicylic acid can be calculated using the formula:
[tex]\[
\text{Moles of salicylic acid} = \frac{\text{Mass of salicylic acid}}{\text{Molar mass of salicylic acid}}
\][/tex]
[tex]\[
\text{Moles of salicylic acid} = \frac{3.04 \, \text{g}}{138.12 \, \text{g/mol}} = 0.022009846510280914 \, \text{mol}
\][/tex]
2. Determine the moles of aspirin:
According to the balanced chemical equation, the reaction ratio of salicylic acid to aspirin is 1:1. Therefore, the number of moles of aspirin formed is equal to the number of moles of salicylic acid.
[tex]\[
\text{Moles of aspirin} = 0.022009846510280914 \, \text{mol}
\][/tex]
3. Calculate the theoretical yield of aspirin:
Use the molar mass of aspirin [tex]\(C_9H_8O_4\)[/tex] and the number of moles of aspirin to find the theoretical yield in grams.
[tex]\[
\text{Molar mass of aspirin} = 180.15 \, \text{g/mol}
\][/tex]
The theoretical yield of aspirin can be calculated using the formula:
[tex]\[
\text{Theoretical yield of aspirin} = \text{Moles of aspirin} \times \text{Molar mass of aspirin}
\][/tex]
[tex]\[
\text{Theoretical yield of aspirin} = 0.022009846510280914 \, \text{mol} \times 180.15 \, \text{g/mol} = 3.9650738488271067 \, \text{g}
\][/tex]
Thus, the theoretical yield of aspirin when reacting 3.04 g of salicylic acid with an excess of acetic anhydride is approximately 3.97 grams.
