Question 3.13: Aspirin, acetylsalicylic acid (C9H8O4), is the most commonly...
Aspirin, acetylsalicylic acid (C9H8O4), is the most commonly used pain reliever in the world. It is produced by the reaction of salicylic acid (C7H6O3) and acetic anhydride (C4H6O3) according to the following equation:
\underset{salicylic acid}{C_{7}H_{6}O_{3}} + \underset{acetic anhydride}{C_{4}H_{6}O_{3}} → \underset{ acetylsalicylic acid}{C_{9}H_{8}O_{4}} + \underset{acetic acid}{HC_{2}H_{3}O_{2}}
In a certain aspirin synthesis, 104.8 g of salicylic acid and 110.9 g of acetic anhydride are combined. Calculate the percent yield of the reaction if 105.6 g of aspirin are produced.
Strategy Convert reactant grams to moles, and determine which is the limiting reactant. Use the balanced equation to determine the number of moles of aspirin that can be produced, and convert this number of moles to grams for the theoretical yield. Use the actual yield (given in the problem) and the calculated theoretical yield to calculate the percent yield.
Setup The necessary molar masses are 138.12 g/mol for salicylic acid, 102.09 g/mol for acetic anhydride, and 180.15 g/mol for aspirin.
104.8 \cancel{g C_{7}H_{6}O_{3}} × \frac{1 mol C_{7}H_{6}O_{3}}{138.12 \cancel{g C_{7}H_{6}O_{3}}} = 0.7588 mol C_{7}H_{6}O_{3}
110.9 \cancel{g C_{4}H_{6}O_{3}} × \frac{1 mol C_{4}H_{6}O_{3}}{102.09 \cancel{g C_{4}H_{6}O_{3}}} = 1.086 mol C_{4}H_{6}O_{3}
Because the two reactants combine in a 1:1 mole ratio, the reactant present in the smallest number of moles (in this case, salicylic acid) is the limiting reactant. According to the balanced equation, one mole of aspirin is produced for every mole of salicylic acid consumed.
1 mol salicylic acid (C7H6O3) \bumpeq 1 mol aspirin (C9H8O4)
Therefore, the theoretical yield of aspirin is 0.7588 mol. We convert this to grams using the molar mass of aspirin:
0.7588 \cancel{mol C_{9}H_{8}O_{4}} × \frac{180.15 g C_{9}H_{8}O_{4}}{1 \cancel{mol C_{9}H_{8}O_{4}}} = 136.7 g C_{9}H_{8}O_{4}
Thus, the theoretical yield is 136.7 g. If the actual yield is 105.6 g, the percent yield is
\% yield = \frac{105.6 g}{136.7 g} × 100\% = 77.25\% yield