Calculation of Theoretical Yield
The theoretical yield of a reaction is the amount of product that would be formed if the reaction went to completion. It is based on the stoichiometry of the reaction and ideal conditions in which starting material is completely consumed, undesired side reactions do not occur, the reverse reaction does not occur, and there no losses in the work-up procedure.
In order to calculate the theoretical yield, you must first balance the reaction. Then, look closely to determine which reagents are being used in excess and which is the limiting reagent. The overall yield of product depends on the limiting reagent. Remember that catalysts, solvents, or any compounds that are not part of the actual chemical reaction cannot be the limiting reagent. Theoretical yield calculations are carried out in the same way as they were in general chemistry: the moles of limiting reactant determines the moles of product.
After your laboratory reaction is complete, you will isolate and measure the amount of product, then compare the actual yield to the theoretical yield to determine the percent yield:
In the laboratory, the percent yield has the practical aspect of telling you how successful was your synthesis scheme. A low percentage yield means that the conditions were not optimal and could be improved. Perhaps there are competing reactions occurring or some of the product is being lost in the purification steps.
To calculate theoretical yield:
Four Examples
Helpful Nomenclature and Relationships
The calculation of the number of moles of acetic acid (Example 2) brings up several questions which students often ask when encountering physical data involving acids. For acetic acid, you find in the table the MW, normality of concentrated reagent, the percent by weight, and the specific gravity.
What is normality?
Normality is the number of equivalents per liter, for an acid, an equivalent is the mass of acid that can furnish exactly 1 mole of H+ ions. The relationship between molarity and normality for several acids is summarized in the table below.
| acid | name | relationship of molarity and normality |
| HCl | hydrochloric acid | 1 M = 1 N |
| H2SO4 | sulfuric acid | 1 M = 2 N |
| H3PO4 | phosphoric acid | 1 M = 3 N |
| CH3CO2H | acetic acid | 1 M = 1 N |
What is specific gravity?
Specific gravity is the ratio of the density (in g/mL) of the compound at standard conditions relative to the density of water at the same conditions. Practically, you can assume that specific gravity equals density, therefore if concentrated acetic acid has a specific gravity of 1.05, it has a density of 1.05 g/mL
What is percent by weight?
The percent by weight is the number of grams of the compound in a particular mass of the concentrated solution. If you have 100 g of concentrated acetic acid, you have 99.8 g of acetic acid. From this, you can calculate the number of moles using the molecular weight.
Which values should I use to calculate the number of moles of the acid in question?
The answer to this is: Whichever values you find more convenient, depending on which values you are given in the experimental procedure or measured in your experiment. If you are given a volume measurement, it is easiest to use the normality as in example 2 above. You could also use the specific gravity and the molecular weight to calculate moles from a volume measurement. If you are given a number of grams, you can calculate the moles from the % by weight and the molecular weight.
How do I calculate the number of grams when given the number of milliliters?
The answer is to convert using the following relationship of mass, volume, and density:
mass = volume x density
Density values are listed as grams per milliliter. For example, if you have 25 mL of a compound and its density is 0.97 g/mL, the number of grams is found by the following calculation:
mass = 25 mL x 0.97 g/mL = 24.2 g
