Calculating Theoretical Yield of Aspirin from Salicylic Acid: A Step-by-Step Guide

Theoretical yield is a crucial concept in chemistry, representing the maximum amount of product that can be generated from a given amount of reactants under ideal conditions. For example, in the synthesis of aspirin (acetylsalicylic acid) from salicylic acid, the theoretical yield helps chemists predict the amount of aspirin that should be produced if the reaction goes to completion without any losses.

Calculating the theoretical yield is important because it allows chemists to:

1. Evaluate Reaction Efficiency: By comparing the actual yield to the theoretical yield, chemists can determine the efficiency of the reaction.
2. Optimize Conditions: Understanding the theoretical yield helps in optimizing reaction conditions to maximize product output.
3. Cost Management: It aids in managing costs by predicting the amount of reactants needed and minimizing waste.

In the case of aspirin synthesis, the reaction involves salicylic acid reacting with acetic anhydride to produce aspirin and acetic acid. The theoretical yield can be calculated based on the stoichiometry of the reaction, ensuring that the process is as efficient and cost-effective as possible.

Would you like to know more about the steps involved in calculating the theoretical yield?

Chemical Reaction

The synthesis of aspirin (acetylsalicylic acid) from salicylic acid involves an esterification reaction. Here is the balanced chemical equation:

$$\text{C}_7\text{H}_6\text{O}_3 + \text{C}_4\text{H}_6\text{O}_3 \rightarrow \text{C}_9\text{H}_8\text{O}_4 + \text{C}_2\text{H}_4\text{O}_2$$C7​H6​O3​+C4​H6​O3​→C9​H8​O4​+C2​H4​O2​

• Salicylic acid (C$_7$H$_6$O$_3$): Provides the phenol group that reacts with acetic anhydride.

• Acetic anhydride (C$_4$H$_6$O$_3$): Acts as the acetylating agent, donating an acetyl group to the salicylic acid.

• Aspirin (C$_9$H$_8$O$_4$): The desired product, formed by the esterification of the phenol group in salicylic acid.

• Acetic acid (C$_2$H$_4$O$_2$): A by-product of the reaction.

The reaction is typically catalyzed by an acid, such as sulfuric acid or phosphoric acid, to increase the reaction rate.

Calculating Theoretical Yield

Here are the steps to calculate the theoretical yield of aspirin from salicylic acid:

1. Write the balanced chemical equation:
   [
   \text{C}_7\text{H}_6\text{O}_3 (\text{salicylic acid}) + \text{C}_4\text{H}_6\text{O}_3 (\text{acetic anhydride}) \rightarrow \text{C}_9\text{H}_8\text{O}_4 (\text{aspirin}) + \text{C}_2\text{H}_4\text{O}_2 (\text{acetic acid})
   ]

2. Calculate the moles of salicylic acid:
   [
   \text{Moles of salicylic acid} = \frac{\text{mass of salicylic acid}}{\text{molar mass of salicylic acid}}
   ]

   • Molar mass of salicylic acid (C(_7)H(_6)O(_3)) = 138.12 g/mol

3. Determine the stoichiometric ratio:

   • The reaction shows a 1:1 molar ratio between salicylic acid and aspirin.

4. Calculate the moles of aspirin:
   [
   \text{Moles of aspirin} = \text{moles of salicylic acid}
   ]

5. Calculate the theoretical yield in grams:
   [
   \text{Theoretical yield} = \text{moles of aspirin} \times \text{molar mass of aspirin}
   ]

   • Molar mass of aspirin (C(_9)H(_8)O(_4)) = 180.16 g/mol

By following these steps, you can determine the theoretical yield of aspirin from a given amount of salicylic acid.

Example Calculation

Let’s calculate the theoretical yield of aspirin (acetylsalicylic acid) from salicylic acid. Here’s a step-by-step example:

Given:

• Mass of salicylic acid: 5.00 grams
• Balanced chemical equation:

  $$\text{C}_7\text{H}_6\text{O}_3 (\text{salicylic acid}) + \text{C}_4\text{H}_6\text{O}_3 (\text{acetic anhydride}) \rightarrow \text{C}_9\text{H}_8\text{O}_4 (\text{aspirin}) + \text{C}_2\text{H}_4\text{O}_2 (\text{acetic acid})$$C7​H6​O3​(salicylic acid)+C4​H6​O3​(acetic anhydride)→C9​H8​O4​(aspirin)+C2​H4​O2​(acetic acid)

Steps:

1. Calculate the molar mass of salicylic acid (C$_7$H$_6$O$_3$):

   • C: 7 atoms × 12.01 g/mol = 84.07 g/mol
   • H: 6 atoms × 1.01 g/mol = 6.06 g/mol
   • O: 3 atoms × 16.00 g/mol = 48.00 g/mol
   • Total molar mass = 84.07 + 6.06 + 48.00 = 138.13 g/mol

2. Calculate the moles of salicylic acid:

   $$\text{Moles of salicylic acid} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{5.00 \text{ g}}{138.13 \text{ g/mol}} = 0.0362 \text{ moles}$$Moles of salicylic acid=Molar massMass​=138.13 g/mol5.00 g​=0.0362 moles

3. Determine the mole ratio from the balanced equation:

   • 1 mole of salicylic acid produces 1 mole of aspirin.

4. Calculate the moles of aspirin produced:

   $$\text{Moles of aspirin} = 0.0362 \text{ moles (same as salicylic acid)}$$Moles of aspirin=0.0362 moles (same as salicylic acid)

5. Calculate the molar mass of aspirin (C$_9$H$_8$O$_4$):

   • C: 9 atoms × 12.01 g/mol = 108.09 g/mol
   • H: 8 atoms × 1.01 g/mol = 8.08 g/mol
   • O: 4 atoms × 16.00 g/mol = 64.00 g/mol
   • Total molar mass = 108.09 + 8.08 + 64.00 = 180.17 g/mol

6. Calculate the theoretical yield of aspirin in grams:

   $$\text{Theoretical yield} = \text{Moles of aspirin} \times \text{Molar mass of aspirin} = 0.0362 \text{ moles} \times 180.17 \text{ g/mol} = 6.52 \text{ grams}$$Theoretical yield=Moles of aspirin×Molar mass of aspirin=0.0362 moles×180.17 g/mol=6.52 grams

So, the theoretical yield of aspirin from 5.00 grams of salicylic acid is 6.52 grams.

Factors Affecting Theoretical Yield

Here are some key factors that can affect the theoretical yield of aspirin from salicylic acid:

1. Purity of Reactants:

   • Impurities in Salicylic Acid: Impurities can react with acetic anhydride, reducing the amount available to form aspirin.
   • Impurities in Acetic Anhydride: Contaminants can interfere with the reaction, leading to side products.

2. Reaction Conditions:

   • Temperature: Too high or too low temperatures can affect the reaction rate and yield. Optimal temperature ensures maximum conversion.
   • Catalyst: The presence and concentration of a catalyst (like sulfuric acid) can significantly speed up the reaction and improve yield.
   • Reaction Time: Insufficient reaction time can lead to incomplete conversion of salicylic acid to aspirin.
   • Mixing: Proper mixing ensures that reactants are evenly distributed, promoting a more complete reaction.

3. Measurement Accuracy:

   • Reactant Quantities: Accurate measurement of salicylic acid and acetic anhydride is crucial. Any deviation can affect the stoichiometry and yield.

4. Post-Reaction Processing:

   • Purification: Incomplete purification can lead to a higher measured yield due to the presence of impurities.
   • Drying: Inadequate drying can result in a higher apparent yield due to residual solvents.

These factors collectively influence the efficiency and outcome of the synthesis process.

Understanding Theoretical Yield of Aspirin from Salicylic Acid

Understanding and calculating the theoretical yield of aspirin from salicylic acid is crucial in laboratory settings as it allows chemists to predict and optimize the amount of product obtained from a given reaction. This knowledge has significant implications for practical applications, such as large-scale production of aspirin, where maximizing yield can lead to cost savings and improved efficiency.

The Importance of Theoretical Yield Calculation

The theoretical yield calculation provides a benchmark against which actual yields can be compared, helping researchers identify potential issues with the synthesis process. By understanding the factors that affect the theoretical yield, chemists can take steps to optimize reaction conditions, improve reactant purity, and enhance post-reaction processing techniques.

Practical Applications of Theoretical Yield Calculations

In practical applications, accurate calculations of theoretical yield are essential for scaling up production processes, ensuring consistent product quality, and meeting regulatory requirements. Moreover, understanding the limitations and potential pitfalls in aspirin synthesis can inform the development of more efficient and environmentally friendly methods, ultimately contributing to improved public health outcomes.

Driving Progress in Pharmaceutical Research

By grasping the importance of theoretical yield calculations, chemists can refine their experimental design, troubleshoot issues, and develop innovative solutions that drive progress in pharmaceutical research and production.