Theoretical Yield Worked Problem

This example problem demonstrates how to calculate the amount of reactant needed to produce a product.

Problem

Aspirin is prepared from the reaction of salicylic acid (C₇H₆O₃) and acetic anhydride (C₄H₆O₃) to produce aspirin (C₉H₈O₄) and acetic acid (HC₂H₃O₂). The formula for this reaction is

C₇H₆O₃ + C₄H₆O₃ → C₉H₈O₄ + HC₂H₃O₂

How many grams of salicylic acid are needed to make 1,000 1-gram tablets of aspirin? (Assume 100 percent yield.)

Solution

Step 1: Find the molar mass of aspirin and salicylic acid.

From the periodic table:

Molar Mass of C = 12 grams
Molar Mass of H = 1 grams

Molar Mass of O = 16 grams

MM_aspirin = (9 x 12 grams) + (8 x 1 grams) + (4 x 16 grams)
MM_aspirin = 108 grams + 8 grams + 64 grams
MM_aspirin = 180 grams

MM_sal = (7 x 12 grams) + (6 x 1 grams) + (3 x 16 grams)
MM_sal = 84 grams + 6 grams + 48 grams
MM_sal = 138 grams

Step 2: Find the mole ratio between aspirin and salicylic acid.

For every mole of aspirin produced, 1 mole of salicylic acid was needed. Therefore the mole ratio between the two is one.

Step 3: Find the grams of salicylic acid needed.

The path to solving this problem starts with the number of tablets. Combining this with the number of grams per tablet will give the number of grams of aspirin. Using the molar mass of aspirin, you get the number of moles of aspirin produced. Use this number and the mole ratio to find the number of moles of salicylic acid needed. Use the molar mass of salicylic acid to find the grams needed.

Putting all this together:

grams salicylic acid = 1,000 tablets x 1 g aspirin/1 tablet x 1 mol aspirin/180 g of aspirin x 1 mol sal/1 mol aspirin x 138 g of sal/1 mol sal

grams salicylic acid = 766.67 

Answer

766.67 grams of salicylic acid are needed to produce 1000 1-gram aspirin tablets.