Question

Aspirin or acetylsalicylic acid is synthesized by combining salicylic acid with acetic anhydride: $$ \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} $$ \(\begin{array}{l}\text { salicylic acid acetic anhydride } \\ \text { aspirin } & \text { acetic acid }\end{array}\) (a) How much salicylic acid is required to produce \(0.400 \mathrm{~g}\) of aspirin (about the content in a tablet), assuming acetic anhydride is present in excess? (b) Calculate the amount of salicylic acid needed if only 74.9 percent of salicylic is converted to aspirin. (c) In one experiment, \(9.26 \mathrm{~g}\) of salicylic acid reacts with \(8.54 \mathrm{~g}\) of acetic anhydride. Calculate the theoretical yield of aspirin an the percent yield if only \(10.9 \mathrm{~g}\) of aspirin is produced.

Short answer

a) 0.3067 g; b) 0.4094 g; c) Theoretical yield: 12.08 g, Percent yield: 90.2%

Step-by-step solution

Calculate Molar Masses

Find the molar masses of salicylic acid (\(\mathrm{C}_7 \mathrm{H}_6 \mathrm{O}_3\), 138.12 g/mol) and aspirin (\(\mathrm{C}_9 \mathrm{H}_8 \mathrm{O}_4\), 180.16 g/mol) using the periodic table.

Convert Aspirin Mass to Moles

Convert 0.400 g of aspirin into moles using the molar mass: \( n = \frac{0.400 \text{ g}}{180.16 \text{ g/mol}} \approx 0.00222 \text{ mol} \).

Moles of Salicylic Acid Required

Since the reaction is a 1:1 mole ratio, the moles of salicylic acid needed is the same as that of aspirin: 0.00222 mol.

Convert Moles to Mass for Salicylic Acid

Convert moles of salicylic acid to grams: \( m = 0.00222 \text{ mol} \times 138.12 \text{ g/mol} \approx 0.3067 \text{ g} \).

Adjust for Partial Conversion

Calculate for partial conversion: \( \frac{0.3067 \text{ g}}{0.749} \approx 0.4094 \text{ g} \) of salicylic acid are needed when only 74.9% is converted.

Determine Limiting Reactant

Use moles from given masses. Salicylic acid: \( \frac{9.26 \text{ g}}{138.12 \text{ g/mol}} \approx 0.06704 \text{ mol} \). Acetic anhydride: \( \frac{8.54 \text{ g}}{102.09 \text{ g/mol}} \approx 0.08366 \text{ mol} \). Salicylic acid is limiting.

Calculate Theoretical Yield

Theoretical yield of aspirin is \(0.06704 \text{ mol} \times 180.16 \text{ g/mol} = 12.08 \text{ g} \).

Calculate Percent Yield

Percent yield is \( \frac{10.9 \text{ g}}{12.08 \text{ g}} \times 100 \% \approx 90.2 \% \).

Key concepts

Molar Mass Calculation

Molar mass calculation is a fundamental concept in chemistry that helps in converting between grams and moles, which is crucial for stoichiometry. To calculate the molar mass of a compound, you need to sum the atomic masses of all the atoms in its molecular formula as listed in the periodic table.
For instance, the molar mass of salicylic acid (\(\text{C}_7\text{H}_6\text{O}_3\)) is calculated as follows:

• Carbon: 7 atoms \(\times 12.01 \text{ g/mol} = 84.07 \text{ g/mol}\)
• Hydrogen: 6 atoms \(\times 1.01 \text{ g/mol} = 6.06 \text{ g/mol}\)
• Oxygen: 3 atoms \(\times 16.00 \text{ g/mol} = 48.00 \text{ g/mol}\)

Adding these together, the molar mass of salicylic acid is \(84.07 + 6.06 + 48.00 = 138.12 \text{ g/mol}\).
Understanding molar mass is vital because it allows chemists to convert grams to moles and vice versa, enabling accurate measurement and scaling of reactions.

Limiting Reactant

Identifying the limiting reactant is another key concept in chemical stoichiometry. The limiting reactant is the reactant that determines the maximum amount of product that can be formed in a chemical reaction. This occurs because there is not enough of it to completely react with the other reactants.
To determine the limiting reactant, you compare the mole ratio of the reactants used in the reaction with the ratio present in the balanced equation.
For instance, in the synthesis of aspirin from salicylic acid and acetic anhydride given in the problem, calculate the moles of each reactant:

• Salicylic acid: \(\frac{9.26 \text{ g}}{138.12 \text{ g/mol}} \approx 0.06704 \text{ mol}\)
• Acetic anhydride: \(\frac{8.54 \text{ g}}{102.09 \text{ g/mol}} \approx 0.08366 \text{ mol}\)

Here, the molar comparison shows salicylic acid has fewer moles available and is thus the limiting reactant, as it will run out first, stopping the reaction from proceeding further.

Percent Yield

Percent yield is a practical measure of a reaction’s efficiency, comparing the amount of product actually obtained to the theoretical maximum possible (theoretical yield). The percent yield helps identify losses due to reaction inefficiencies or experimental error.
To calculate the percent yield:

• Measure the actual yield of the product obtained.
• Calculate the theoretical yield using stoichiometry.
• Apply the formula: \(\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%\)

In the aspirin synthesis problem, the actual yield is \(10.9 \text{ g}\) and the theoretical yield calculated was \(12.08 \text{ g}\). Thus, the percent yield is \(\frac{10.9}{12.08} \times 100 \approx 90.2\%\). This high yield indicates that the reaction is quite efficient but not perfect.

Theoretical Yield

Theoretical yield is an essential aspect of chemical reaction calculations, representing the maximum amount of product that can be formed from the given quantities of reactants, assuming complete conversion with no losses.
To find the theoretical yield, first, find which reactant is the limiting reactant, as it will dictate the maximum amount of product. Then, use stoichiometry to convert the moles of the limiting reactant to moles of the product, and finally, convert those moles to grams using the product's molar mass.
For example, in our aspirin reaction, since salicylic acid was identified as the limiting reactant with \(0.06704 \text{ mol}\), the theoretical yield of aspirin can be calculated by:

• Moles of aspirin from salicylic acid: \(0.06704 \text{ mol} \times 180.16 \text{ g/mol} = 12.08 \text{ g}\)

It is crucial to predict the theoretical yield for planning chemical reactions and assessing their efficiency.