(C4H6O3): C7H6O3 + C4H6O3 --> C9H8O4 + HC2H3O2

Question

Aspirin (C9H8O4) is produced from salicylic acid (C7H6O3) and acetic anhydride (C4H6O3): C7H6O3 + C4H6O3 --> C9H8O4 + HC2H3O2. What is the percent yield of the reaction where 0.185 Mg of salicylic acid and 125 kg of acetic anhydride react to form 1.82 x 1020 fg of aspirin?

Answer 1

C7H6O3 + C4H6O3 --> C9H8O4 + HC2H3O2 ... balanced equation

SA................AA.............Aspirin..........acetic acid

In this problem, we have several different units of mass, such as Mg (megagrams), kg( kilograms) and fg (femtograms). We will convert them to a more common unit of g (grams).

1 Mg = 1000 kg = 10³ kg

1 kg = 1000 g = 10³ g

1 fg = 10^-15 g 

molar mass SA = 138 g/mol

molar mass AA = 102 g/mol

molar mass aspirin = 180 g/mol

Using dimensional analysis and the balanced equation we have the following:

moles SA present = 0.185 Mg x 10³ kg/Mg x 10³ g/kg x 1 mol/138 g = 1.34x10³ moles

moles AA present = 125 kg x 10³ g/kg x 1 mol/102 g = 1.23x10³ moles

AA (acetic anhydride) is limiting

Theoretical yield: 

1.23x10³ moles AA x 1 mole aspirin/mol AA x 180 g aspirin/mole = 2.21x10⁵ g aspirin

% yield = actual yield/theoretical yield (x100%)

actual yield = 1.82x10²⁰ fg x 1 g/10¹⁵ fg = 1.82x10⁵ g

% yield = 1.82x10⁵ g / 2.21x10⁵ g (x100%) = 82.4% yield