Percent Yield

[danny89]

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Given: Ca3(PO4)2 + 3H2SO4--->2H3PO4 + 3CaSO4

Problem: 10 moles of calcium phosphate are combined with 30 moles of sulfuric acid. The reaction produces 18 moles of phosphoric acid and 27 moles of calcium sulfate. What is the percent yield of the reaction?

 

[Paean1]

Percent yield = (Actual Yield/Theoretical Yield) x 100.

First of all, which reactant is limiting? We know from the equation that the mole ratio between the reactants should be 1:3. The actual ratio we have is 10:30. Since both reactants should theoretically be fully used up, you can take either one as the limiting reactant.

Now calculate theoretical yield:
For each mole of calcium phosphate that reacts we expect 2 moles of phosphoric acid to be produced. Since we start with 10 moles of calcium phosphate we expect 20 moles of phosphoric acid to be produced (10 moles calcium phosphate * 2 moles phosphoric acid/1 mole calcium phosphate).
Our theoretical yield, therefore, is 20 moles of H3PO4.

Actual yield:
18 moles of H3PO4.

Percent yield:
(18/20) * 100 = 90%

Obviously this can be done much faster in your head once you understand the concept.

 

[danny89]

Great explanation. Thanks!