Aspirin can be prepared from salicylic acid [tex]$\left( C_7 H_6 O_3 \right)$[/tex], which has a molar mass of [tex]$138.12 \, \text{g/mol}$[/tex], and acetic anhydride [tex]$\left( C_4 H_6 O_3 \right)$[/tex].

The reaction is:
[tex]\[ C_7 H_6 O_3 + C_4 H_6 O_3 \rightarrow C_9 H_8 O_4 + C_2 H_4 O_2 \][/tex]

What is the theoretical yield, in grams, of aspirin [tex]$\left( C_9 H_8 O_4 \right)$[/tex], which has a molar mass of [tex]$180.15 \, \text{g/mol}$[/tex], possible when reacting [tex]$3.04 \, \text{g}$[/tex] of salicylic acid with an excess of acetic anhydride?



Answer :

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.