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# Theoretical Yield Worked Problem

## Calculate the Amount of Reagent Needed to Yield a Specified Product

You can calculate how much reactant you need to obtain an amount of product.

Steve McAlister, Getty Images

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 1000 1-gram tablets of aspirin? (Assume 100% yield)

Solution

Step 1 - Find molar mass of aspirin and salicylic acid

From the periodic table:

Molar Mass of C = 12 g
Molar Mass of H = 1 g
Molar Mass of O = 16 g

MMaspirin = (9 x 12 g) + (8 x 1 g) + (4 x 16 g)
MMaspirin = 108 g + 8 g + 64 g
MMaspirin = 180 g

MMsal = (7 x 12 g) + (6 x 1 g) + (3 x 16 g)
MMsal = 84 g + 6 g + 48 g
MMsal = 138 g

Step 2 - Find 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 1.

Step 3 - Find 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 = 1000 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 g sal

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