Using percentage yield to determine the amount of reactant needed

Percentage yield is defined as the actual mass of product divided by the theoretical maximum mass of product, multiplied by 100%. We can similarly express percentage yield in terms of moles.

There are essentially three types of questions:

1. Calculate the % yield for a reaction

Here, you would divide the actual moles of product by the theoretical maximum moles of product, and multiply by 100%.

e.g., The actual moles of product was 10 mol and the theoretical maximum moles of product was 20 mols.

Percentage yield = 10 / 20 x 100% = 50%

2. Calculate the actual moles of product

Here, you would multiply the theoretical maximum moles by the percentage yield, and divide by 100%

e.g., The theoretical maximum moles of product was 20 mols and the percentage yield was 50%.

Actual moles of product = 20 x 50% / 100 = 10 mols.

3. Calculate the theoretical maximum moles of product

Here, you would multiply the actual moles of product and 100%, and divide by the percentage yield.

e.g., The actual moles of product was 10 mol and the percentage yield was 50%.

Theoretical maximum moles of product = 10 x 100% / 50% = 20 mol

The final type of calculation is especially interesting because, when combined with a balanced symbol equation it allows us to work out how much reactant is required to make a given actual amount of product!

Question: Buta-1,3-diene can be formed by the reaction of 2,3-dibromobutane with NaOH. 

Reaction: C4H8Br2 + 2 NaOH -> C4H6 + 2 NaBr + 2 H2O

The percentage yield for the reaction is 80% and the chemist needs to make 10.8 g of buta-1,3-diene. Determine the masses of 2,3-dibromobutane and NaOH required.

Answer

A useful first step would be to work out the Mr of C4H6 (54) and C4H8Br2 (216).

n C4H6 =10.8 / 54 = 0.2 mol (i.e., actual moles of product)

n C4H6 =0.2 x 100% / 80% = 0.25 mol (i.e., theoretical maximum)

Using the balanced symbol equation, the initial moles of C4H8Br2 and NaOH can now be calculated:

n C4H8Br2 =1 x 0.25 = 0.25 mol

n NaOH =2 x 0.25 = 0.50 mol

Using the Mr of C4H8Br2 (216) and NaOH (40), we can now work out the required masses.

m C4H8Br2 = 0.25 x 216 = 54 g

n NaOH =0.50 x 40 = 20 g