In the synthesis of aspirin we react salicylic acid with acetic anhydride. The balanced chemical equation is:
2HOOCC6H4OH + C4H6O3 → 2HOOCC6H4O2C2H3 + H2O
salicylic acid acetic
anhydride  acetyl salicylic acid water
If we mix together  27.9 grams of salicylic acid with  14.4 grams of acetic anhydride in this reaction, we obtain 30.7 grams of aspirin.
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What are the theoretical yields of our experiment?ÂÂ
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What are the percentage yields of our experiment?
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The Correct Answer and Explanation is :
To determine the theoretical yield and percentage yield of aspirin in this experiment, we must first identify the limiting reagent and perform stoichiometric calculations based on the balanced chemical equation:
Balanced Chemical Equation:
[ 2 \text{HOOCC}_6\text{H}_4\text{OH (salicylic acid)} + \text{C}_4\text{H}_6\text{O}_3 (\text{acetic anhydride}) \rightarrow 2 \text{HOOCC}_6\text{H}_4\text{O}_2\text{C}_2\text{H}_3 (\text{acetylsalicylic acid}) + \text{H}_2\text{O} ]
Step 1: Molar Masses
- Molar mass of salicylic acid (C₇H₆O₃) = 138.12 g/mol
- Molar mass of acetic anhydride (C₄H₆O₃) = 102.09 g/mol
- Molar mass of aspirin (acetylsalicylic acid, C₉H₈O₄) = 180.16 g/mol
Step 2: Moles of Each Reactant
Moles of salicylic acid:
[
\text{moles of salicylic acid} = \frac{27.9 \, \text{g}}{138.12 \, \text{g/mol}} = 0.202 \, \text{mol}
]
Moles of acetic anhydride:
[
\text{moles of acetic anhydride} = \frac{14.4 \, \text{g}}{102.09 \, \text{g/mol}} = 0.141 \, \text{mol}
]
Step 3: Limiting Reactant
From the balanced equation, we can see that the molar ratio between salicylic acid and acetic anhydride is 2:1. This means that for every 2 moles of salicylic acid, we need 1 mole of acetic anhydride. Let’s check which reactant is limiting.
- The 0.202 moles of salicylic acid would need:
[
\frac{0.202 \, \text{mol}}{2} = 0.101 \, \text{mol of acetic anhydride}
] - We have 0.141 moles of acetic anhydride, which is more than enough to react with the available salicylic acid. Therefore, salicylic acid is the limiting reactant.
Step 4: Theoretical Yield
Since salicylic acid is the limiting reactant, we use its moles to calculate the theoretical yield of aspirin. According to the balanced equation, 2 moles of salicylic acid produce 2 moles of aspirin. Therefore, the moles of aspirin produced will be equal to the moles of salicylic acid:
[
\text{moles of aspirin} = 0.202 \, \text{mol}
]
Now, convert moles of aspirin to grams:
[
\text{mass of aspirin} = 0.202 \, \text{mol} \times 180.16 \, \text{g/mol} = 36.4 \, \text{g}
]
Thus, the theoretical yield of aspirin is 36.4 grams.
Step 5: Percentage Yield
Percentage yield is calculated using the following formula:
[
\text{percentage yield} = \left( \frac{\text{actual yield}}{\text{theoretical yield}} \right) \times 100
]
Given that the actual yield of aspirin is 30.7 grams, the percentage yield is:
[
\text{percentage yield} = \left( \frac{30.7 \, \text{g}}{36.4 \, \text{g}} \right) \times 100 = 84.4\%
]
Conclusion
- The theoretical yield of aspirin is 36.4 grams.
- The percentage yield of aspirin is 84.4%.
The percentage yield represents the efficiency of the reaction. In this case, 84.4% of the theoretical amount of aspirin was obtained, which is a relatively high yield, indicating the reaction was fairly efficient.