Learn how to calculate theoretical yield

The theoretical yield of a chemical reaction is the maximum quantity of products that could be obtained by said reaction from known quantities of reactants, assuming that the reaction proceeds until the limiting reactant is completely exhausted. It is called theoretical yield because in practice the amount of product predicted by this yield is never obtained, a smaller quantity is always obtained. This is due to various reasons, including:

• Experimental errors in the determination of masses and volumes.
• The presence of impurities in the reagents.
• Side reactions that may occur.
• Formation of chemical equilibria.
• Stopping the reaction prematurely (which is particularly problematic when dealing with slow reactions).

In the calculation of the theoretical yield it is assumed that the reaction is irreversible, so it does not reach an equilibrium state. Furthermore, it is assumed that the reagents involved only react by means of the reaction in question, and there is no other parallel reaction that could reduce the availability of reagents.

Calculation of theoretical yield is one of the basic skills of any chemistry student and it is also one of the most frequent stoichiometric calculation procedures that you will come across during your studies.

The limiting reagent

The concept of limiting reagent is central to the calculation of theoretical yield. This is defined as the reactant that is found in the smallest proportion, which is why it is the first to be consumed during the course of a chemical reaction.

Since a chemical reaction cannot occur if one of its reactants is not present, then the moment the limiting reactant is finished, the reaction stops. This means that all products are no longer produced and all other reactants are no longer consumed. For this reason, the limiting reagent determines how far a reaction can go; it is the one that limits the amount of products that can be produced and of reactants that can be consumed, and hence its name.

everyday example of limiting reagent

To better understand the concept of limiting reagent, let’s consider the preparation of a cake. This preparation could be considered as a chemical reaction in which the ingredients are the reactants and the cake is the only product.

The preparation of a cake requires a specific number of ingredients, in the same way that a chemical reaction requires a specific number of molecules of each reactant. Let’s imagine that a very simple cake recipe calls for 2 cups of flour, 5 eggs, and 1 cup of sugar. This could be written as:

Now let’s ask ourselves the following question: how many cakes can we prepare if, when we open the refrigerator, we find that there are 30 eggs, 10 cups of flour and 8 cups of sugar?

We can deduce this by determining separately the number of cakes that we could prepare with each ingredient:

• With 30 eggs we could make 6 cakes, since each one requires 5 eggs.
• With 10 cups of flour we could prepare 5 cakes.
• 8 cups of sugar are enough for 8 cakes

Now we ask ourselves, how many cakes can we really make, 5, 6 or 8? The answer, of course, is 5. The reasoning is that with the amount of flour we have we cannot make more than 5 cakes. All the other ingredients are enough for even more, but after the fifth cake is made, there will be no more flour to make another one and it doesn’t matter how much extra sugar or eggs we may have, since without that ingredient we will not be able to follow the recipe.

In this case, the flour is the limiting ingredient (understood as the limiting reagent), because it limited the maximum number of cakes that can be produced to 5.

By the way, these 5 cakes that can be produced from the ingredients we have would come to represent the theoretical yield. In other words, we could theoretically make 5 cakes, but if we crack an egg in the process, spill sugar, or burn one of the cakes, the number of cakes we can actually produce will be reduced.

Procedure for calculating theoretical yield

To calculate the theoretical yield, one must start from the amount of the limiting reagent since, as explained above, when finished first, this reagent limits the amount of products that can be produced and the other reagents that can be consumed.

Below is a practical and quick way to determine which is the limiting reactant and which is or are the reactants in excess.

Determination of the limiting reagent

There are several ways to identify the limiting reactant. One way is like we did in the pie example: by determining the amount of product we can get from each amount of reactant, and then selecting the reactant that produces the least amount. However, there is another more practical and mechanical way to do it.

By definition, the limiting reactant is the one that is in the lowest stoichiometric proportion. This means that all we have to do to identify the limiting reactant is determine the stoichiometric ratio in which all the reactants are and then select the smallest.

Determining the stoichiometric ratio is as simple as calculating the number of moles of each reactant and dividing it by the stoichiometric coefficient of the balanced reaction.

Example

Suppose 20g of iron is reacted with 20g of oxygen gas to produce ferric oxide (Fe ₂ O ₃ ). Determine the limiting reactant of the reaction. The molar mass of iron is 56g/mol, of oxygen gas it is 32g/mol, and of iron oxide it is 160g/mol.

The first step is to write the balanced chemical equation, which, in this case, is:

Now, we calculate the number of moles from the mass, and then the stoichiometric ratio. This can be organized in a table to make the process easier, especially when there are numerous reagents:

As can be seen, the reactant that is in a smaller proportion in this case is iron, so it is the limiting reactant.

Calculation of theoretical yield

Once we know what the limiting reactant is, we can use it to carry out all other stoichiometric calculations. This includes calculating the amounts of excess reactants that can actually be consumed, thereby determining how much of them will remain in excess (unreacted), and, of course, calculating the amounts of products that will be consumed. can produce, that is, the theoretical yield.

All these calculations are carried out using the different stoichiometric relationships that can be established between the limiting reagent and each of the other substances involved in the reaction.

It should be noted that if a reaction generates more than one product, then there will be a yield for each of the products, but not for all the products as a whole.

Example

Continuing with the previous example, we now want to calculate how much (in grams) of ferric oxide can be produced from 20g of iron and 20g of oxygen gas.

What is asked is to determine the amount of product that can be produced given the amounts of reactants, so what you want to calculate is the theoretical yield of the reaction. In the previous example we determined that the limiting reagent in this case is iron, so the amount of ferric oxide will be determined from it. This means that the calculation starts with the amount of iron and ends with an amount of ferric oxide, as shown below:

References

• Brown, T. (2021). Chemistry: The Central Science (11th ed.). London, England: Pearson Education.
• Chang, R., Manzo, Á. R., Lopez, PS, & Herranz, ZR (2020). Chemistry (10th ed.). New York City, NY: MCGRAW-HILL.
• Flowers, P., Theopold, K., Langley, R., & Robinson, WR (2019c, February 14). 4.4 Reaction Yields – Chemistry 2e | OpenStax . Retrieved from https://openstax.org/books/chemistry-2e/pages/4-4-reaction-yields
• The stoichiometry of chemical reactions. (2020, October 29). Retrieved on August 7 from https://espanol.libretexts.org/@go/page/1816
• The yields of the reactions . (2020, October 30). Retrieved on August 7, 2021 from https://espanol.libretexts.org/@go/page/1822