Step-by-step explanation:
We have to find the percent yield of the reaction, but we don't have the theoretical yield. To find it, we have to calculate the mass of aspirin that will be theoretically produced by 79.8 g of C₇H₆O₃.
First we have to convert 79.8 g of C₇H₆O₃ to moles using its molar mass.
molar mass of C = 12.01 g/mol
molar mass of H = 1.01 g/mol
molar mass of O = 16.00 g/mol
molar mass of C₇H₆O₃ = 7 * 12.01 g/mol + 6 * 1.01 g/mol + 3 * 16.00 g/mol
molar mass of C₇H₆O₃ = 138.13 g/mol
mass of C₇H₆O₃ = 79.8 g
moles of C₇H₆O₃ = 79.8 g * 1 mol/(138.13 g)
moles of C₇H₆O₃ = 0.578 moles
Now we can find the moles of aspirin produced by 0.578 moles of C₇H₆O₃.
C₇H₆O₃ (s) + C₄H₆O₃ (s) ---> C₉H₈O₄ (s) + HC₂H₃O₂ (aq)
According to the coefficients of the equation 1 mol of C₇H₆O₃ will produce 1 mol of aspirin.
1 mol of C₇H₆O₃ = 1 mol of C₉H₈O₄
moles of C₉H₈O₄ = 0.578 moles of C₇H₆O₃ * 1 mol C₉H₈O₄/(1 mol of C₇H₆O₃)
moles of C₉H₈O₄ = 0.578 moles
So we found that 79.8 g of C₇H₆O₃ will yield 0.578 moles of C₉H₈O₄. To get the theoretical yield we have to convert the moles into grams using the molar mass of C₉H₈O₄.
molar mass of C = 12.01 g/mol
molar mass of H = 1.01 g/mol
molar mass of O = 16.00 g/mol
molar mass of C₉H₈O₄ = 9 * 12.01 g/mol + 8 * 1.01 g/mol + 4 * 16.00 g/mol
molar mass of C₉H₈O₄ = 180.17 g/mol
mass of C₉H₈O₄ = 0.578 moles * 180.17 g/mol
mass of C₉H₈O₄ = 104.1 g = theoretical yield
Finally we can find the percent yield of the reaction.
actual yield = 65.9 g
percent yield = actual yield/theoretical yield * 100 %
percent yield = 65.9 g/(104.1 g) * 100 %
percent yield = 63.3 %
Answer: The percent yield of the reaction is 63.3 %.