Problem 125 - Chemistry

Question

Aspirin or acetyl salicylic acid is synthesized by reacting salicylic acid with aceticanhydride:$$\mathrm{C}_{7}\mathrm{H}_{6}\mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \quad \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8}\mathrm{O}_{4}+\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$$ (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 acid is converted to aspirin. (c) In one experiment, \(9.26 \mathrm{~g}\) of salicylic acid is reacted with \(8.54 \mathrm{~g}\) of acetic anhydride. Calculate the theoretical yield of aspirin and the percent yield if only \(10.9 \mathrm{~g}\) of aspirin is produced.

Step-by-Step Solution

Answer

a) 0.306 g salicylic acid b) 0.408 g salicylic acid c) Theoretical yield = 12.07 g, Percent yield = 90.3%

Step 1: Calculating the Molar Mass of the Compounds

To find out the molar mass of the compounds, sum up the molar masses of each atom involved. For salicylic acid \(\mathrm{C}_{7}\mathrm{H}_{6}\mathrm{O}_{3}\), the molar mass is \(7(12.01) + 6(1.01) + 3(16.00) = 138.12 \mathrm{~g/mol}\) and for the product, acetylsalicylic acid \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\), \(9(12.01) + 8(1.01) + 4(16.00) = 180.16 \mathrm{~g/mol}\).

Step 2: Stoichiometric Calculations

We take advantage of the stoichiometry of the reaction 1 mole of salicylic acid reacts with 1 mole of acetic anhydride to produce 1 mole of acetylsalicylic acid. (a) Therefore, to produce \(0.400 \mathrm{~g}\) of acetylsalicylic acid, convert the grams to moles using the molar mass, we get \(0.400 \mathrm{~g} / 180.16 \mathrm{~g/mol} = 0.00222 \mathrm{~mol}\). Since this reaction is 1:1, we need the same amount of moles of salicylic acid, so multiply it by the molar mass, we get \(0.00222 \mathrm{~mol} * 138.12 \mathrm{~g/mol} = 0.306 \mathrm{~g}\) of salicylic acid required.

Step 3: Considering the Percent Conversion

(b) If the conversion efficiency is 74.9 percent, we have to account for the unconverted salicylic acid by dividing the required amount by the percent conversion, so, \(0.306 \mathrm{~g} / 0.749 = 0.408 \mathrm{~g}\).

Step 4: Theoretical Yield and Percent Yield Calculation

(c) The theoretical yield can be calculated from the salicylic acid, its amount in moles is \(9.26 \mathrm{~g} / 138.12 \mathrm{~g/mol} = 0.0670 \mathrm{~mol}\). The theoretical yield is \(0.0670 \mathrm{~mol} * 180.16 \mathrm{~g/mol} = 12.07 \mathrm{~g}\). The percent yield is the actual yield divided by the theoretical yield times 100 percent, so \(10.9 \mathrm{~g} / 12.07 \mathrm{~g} * 100% = 90.3%\).

Key Concepts

Salicylic Acid

Salicylic acid is an organic compound, commonly recognized by its formula \(\mathrm{C}_7\mathrm{H}_6\mathrm{O}_3\). It occurs naturally in plants and is a key ingredient in many skincare products. However, its most notable application is as a precursor for the synthesis of aspirin (also known as acetylsalicylic acid). Salicylic acid is slightly acidic and it's categorized as a beta hydroxy acid (BHA), making it soluble in oil, which helps it penetrate the skin. In the context of chemical reactions, specifically stoichiometry, it acts as the reactant to produce aspirin in a 1:1 molar ratio. This means that one mole of salicylic acid reacts with one mole of acetic anhydride to produce one mole of aspirin. This property is crucial when calculating the amount of salicylic acid required for a certain yield of aspirin, allowing chemists to predict the outcomes of their experiments accurately.

• Formula: \(\mathrm{C}_7\mathrm{H}_6\mathrm{O}_3\)
• Molar Mass: 138.12 g/mol
• Used in skincare and aspirin synthesis

Acetylsalicylic Acid

Acetylsalicylic acid, commonly known as aspirin, is a widely used pharmaceutical compound with the formula \(\mathrm{C}_9\mathrm{H}_8\mathrm{O}_4\). It is renowned for its anti-inflammatory, pain-relieving, and fever-reducing properties. Aspirin works by inhibiting certain enzymes in the body, which reduces the production of molecules involved in inflammation and pain transmission. In terms of chemical synthesis, aspirin is produced through the acetylation of salicylic acid using acetic anhydride. This reaction proceeds with a 1:1 stoichiometry, meaning one mole of each reactant produces one mole of aspirin. Consequently, understanding the molar mass and the stoichiometric ratio is vital for determining how much salicylic acid is necessary for a desired amount of aspirin. Additionally, when performing experiments, calculating the theoretical yield is essential for assessing the efficiency of the synthesis.

• Formula: \(\mathrm{C}_9\mathrm{H}_8\mathrm{O}_4\)
• Molar Mass: 180.16 g/mol
• Used for reducing inflammation, pain, and fever

Percent Yield

Percent yield is an important concept in chemical reactions, as it measures the efficiency of a reaction. It is the ratio of the actual yield (the amount of product obtained from the reaction) to the theoretical yield (the amount of product expected based on stoichiometric calculations), expressed as a percentage. In the process of producing aspirin from salicylic acid, calculating the percent yield helps chemists understand how much of the reactants were successfully converted to the desired product. A high percent yield indicates an efficient reaction, while a low percent yield suggests either inefficiencies in the reaction process or measurement errors. To calculate percent yield, divide the actual yield by the theoretical yield and multiply by 100%. For example, if the theoretical yield of aspirin is 12.07 g, and 10.9 g is produced, the percent yield is \( \frac{10.9}{12.07} \times 100\% = 90.3\% \). Understanding percent yield is crucial for optimizing chemical processes and maximizing production efficiency in both research and industrial settings.