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Chapter 3: Problem 125

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.

Short Answer

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

Step by step solution

01

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 \(\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}\), \(9(12.01) + 8(1.01) + 4(16.00) = 180.16 \mathrm{~g/mol}\).
02

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.
03

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, \(0.306 \mathrm{~g} / 0.749 = 0.408 \mathrm{~g}\).
04

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 \(10.9 \mathrm{~g} / 12.07 \mathrm{~g} * 100% = 90.3%\).

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