Aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) is synthesized by reacting salicylic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) with acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right) .\) The balanced equation is $$\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}$$ a. What mass of acetic anhydride is needed to completely consume \(1.00 \times 10^{2}\) g salicylic acid? b. What is the maximum mass of aspirin (the theoretical yield) that could be produced in this reaction?

Step by step solution

01

Calculate the moles of salicylic acid given

Using the molar mass of salicylic acid (C7H6O3), we can find the moles of salicylic acid in the given mass: Molar mass of salicylic acid = \(7 \times 12.01\) (for C) \(+ 6 \times 1.01\) (for H) \(+ 3 \times 16.00\) (for O) = 138.12 g/mol Given mass of salicylic acid = 100 g Moles of salicylic acid = \(\frac{\text{Given mass}}{\text{Molar mass}}\) Moles of salicylic acid = \(\frac{100\,\text{g}}{138.12\,\text{g/mol}}\) = 0.724 moles

02

Calculate the moles of acetic anhydride required

From the balanced equation, 1 mole of salicylic acid reacts with 1 mole of acetic anhydride. Therefore, we can find the moles of acetic anhydride required: Moles of acetic anhydride = moles of salicylic acid = 0.724 moles

03

Calculate the mass of acetic anhydride required

Using the molar mass of acetic anhydride (C4H6O3), we can find the mass of acetic anhydride required: Molar mass of acetic anhydride = \(4 \times 12.01\) (for C) \(+ 6 \times 1.01\) (for H) \(+ 3 \times 16.00\) (for O) = 102.09 g/mol Mass of acetic anhydride = moles of acetic anhydride × molar mass of acetic anhydride Mass of acetic anhydride = \(0.724\, \text{moles} \times 102.09\, \text{g/mol}\) = 73.91 g a. The mass of acetic anhydride needed to completely consume 100 g of salicylic acid is 73.91 g.

04

Calculate the moles of aspirin produced

From the balanced equation, 1 mole of salicylic acid produces 1 mole of aspirin. Therefore, we can find the moles of aspirin produced: Moles of aspirin = moles of salicylic acid = 0.724 moles

05

Calculate the maximum mass of aspirin produced

Using the molar mass of aspirin (C9H8O4), we can find the maximum mass of aspirin produced: Molar mass of aspirin = \(9 \times 12.01\) (for C) \(+ 8 \times 1.01\) (for H) \(+ 4 \times 16.00\) (for O) = 180.16 g/mol Mass of aspirin = moles of aspirin × molar mass of aspirin Mass of aspirin = \(0.724\, \text{moles} \times 180.16\, \text{g/mol}\) = 130.44 g b. The maximum mass of aspirin (theoretical yield) that could be produced in this reaction is 130.44 g.

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