# How To Calculate The Percent Yield

Imagine you work at a paint factory. An experienced chemist like you is always trying new things and, after some years of testing, you are finally able to design a new reactor to produce your company’s flagship product: white paint. How could you convince the board of directors that your reactor is better than the traditional method used for years?

Most factories focus on the efficiency of their processes. This is measured in various ways that depend on the specific production procedures, but it is usually related to the output of a certain process as a function of its input. This means, you compare what you use to execute the production process, like raw materials, energy or human resources, with the amount of good quality product you get at the end. The higher the output of a certain process, executed with a standard input, the more efficient it is.

In the chemical industry, one way to measure the overall efficiency of a chemical reaction is through the percent yield. This value relates the expected maximum amount of product, also called theoretical yield, to the actual amount that is obtained. Let’s discover this simple but powerful method to determine how productive any chemical reaction is.

## How to calculate percent yield

To calculate a reaction’s percent yield follow these steps:

1. Determine the theoretical yield of the reaction, Yt.
2. Precisely measure the resulting amount of your product of interest, M, once the reaction is done.
3. Convert the result obtained in step 2 to the same units as the theoretical yield.
4. Calculate your reaction’s percent yield using this equation:

## What is the percent yield

When you implement a chemical reaction in a laboratory, you usually face some issues that deviate its result from the expected theoretical behavior. Some of the causes of this are the presence of unexpected byproducts, additional reactions taking place simultaneously, reactions occuring slower than expected, remains of unreacted reagents, or a final amount of reaction products different than the one predicted through the corresponding chemical equation.

In many cases, this can happen due to the presence of contaminants, the use of impure reactants, suboptimal reaction conditions, among other reasons. Even if you perform a thorough work, there are fundamental conditions that may affect your results.

In principle, reactant molecules need to interact with each other with enough energy for the reaction to start. They need to come close enough in order to allow electrons to “jump” from one atom to the other, or to relocate within the electronic clouds. This process occurs, mainly, when molecules collide at high speeds. In consequence, even if you have fairly pure reactants, some of the molecules might not even come close enough to react or lose part of their energy due to collisions with their own chemical species.

These basic conditions limit the results you can obtain from a certain reaction. If you look at a reaction’s chemical equation, you can determine the theoretical amount of reactant moles needed to produce a certain amount of product. Let’s use the following example:

Ammonium chloride, a compound commonly used in fertilizers, is produced by mixing ammonia with hydrogen chloride. Since the equation is balanced, we can then conclude we need 1 mol of NH3 and 1 mol of HCl to produce 1 mol of NH4Cl. Since the molar mass of ammonium chloride is 53,5 g/mol, we can say that, theoretically, if we use 1 mol of each of the reactants involved, we will obtain 53,5 g of product. This value is also called the theoretical yield of the reaction under our specific conditions. If you are not sure about how to calculate the theoretical yield, go ahead and read our article about it.

As we saw before, it is very likely that, once we execute this reaction, the resulting amount of product is less than the theoretical yield calculated before. Let’s say you obtain only 40 g of ammonium chloride. The concept of percent yield relates both the expected theoretical yield (53,5 g) and the real amount you obtain (40 g), and serves as a way to measure your reaction’s efficiency. This means, the higher its value, the closer your results will be to the ideal case described by the chemical equation.

## Procedure to calculate a reaction’s percent yield

In order to calculate the percent yield of a given reaction, you must first calculate its theoretical yield. To do this you first need to determine which of the reagents is the limiting reagent based on the amounts you will use and their stoichiometric coefficients in the chemical equation. Then, you need to determine the amount of product you could theoretically obtain by using said amount of limiting reactant. Let’s use a simple reaction to clarify this:

1 mol of propane reacts with 5 moles of molecular oxygen to produce 3 moles of carbon dioxide and 4 moles of water. So, if you were to perform this reaction out in the open, you would not have to worry about your oxygen supply, since there is a huge amount of it available in the air. In this case, for any amount of propane you choose, it is safe to say that all of its molecules will be able to find five other oxygen molecules to react with. So, the limiting reagent in this scenario is propane. Keep in mind this could not be the case if the reaction took place inside a closed vessel under a limited amount of oxygen.

Let’s suppose you decide to use 88 g of propane for your reaction and that the product of interest, meaning the one you want to measure the percent yield for, is carbon dioxide. Since the molar mass of propane is 44 g/mol, your input (88 g) equals 2 moles. With this amount of reagent, you could potentially obtain a maximum of 6 moles of carbon dioxide, assuming all of your reagent is consumed. This is because for every mol of propane, three moles of carbon dioxide are produced, according to equation 3.

Given that the molar mass of your product of interest is also 44 g/mol, those 6 moles equate to a total of 264 g. This is the theoretical yield for the combustion of propane under the conditions described previously. If you want to learn more about this process we invite you to read our article on how to calculate the theoretical yield

Now that you have calculated your reaction’s theoretical yield, you can proceed to execute the reaction. Once it is completed, you must accurately measure the resulting mass of your product of interest, which is also called the actual yield of the reaction. Since there are various ways to do this, we will not go into further detail, but the important thing is that the final amount of product is measured in the same units as the theoretical yield. This means that if you calculate the theoretical yield of your reaction in grams, you need to measure the actual yield also in grams.

Finally, to calculate the resulting percent yield of the reaction you just implemented, you can use the following equation, which simply expresses the portion of the theoretical yield that equals your actual yield as a percentage:

Where M is the resulting mass of your product of interest and Yt the theoretical yield, both in grams. Let’s suppose you measure a final amount of carbon dioxide of 230 g in our previous example. The percent yield in this case would be:

As its name indicates, percent yield takes values from 0% to 100%. A result closer to 100% indicates your reaction tends to the ideal case where the limiting reagent is fully consumed. On the other hand, the lower the value of the percent yield, the less ideal the behavior of the reaction. A result above 100% is not possible, since it would imply you are obtaining an amount of product that would need higher reactant amounts than those you actually used! Nevertheless, you might get a Y% above 100% in some lab experiments, which might be due to errors in the calculation of the actual reactant amounts used.

Exercise 1:

Calculate the percent yield of the reaction described in equation 2, where your theoretical yield was 53,5 g of ammonium chloride. Assume your actual yield was 40 g of said product.

Exercise 2:

Consider the thermal decomposition of calcium carbonate:

1. If you heat up 250 g of calcium carbonate, what is the theoretical yield for calcium oxide?
2. Once the reaction has finished, you measure a total amount of calcium oxide of 120 g. What is the reaction’s percent yield?

Exercise 3:

Assume the following reaction has a typical percent yield of 70%:

1. If you use 124 g of Zn in a sufficient amount of nitric acid, how much zinc nitrate would you most likely obtain?
2. What is the theoretical yield of this reaction?

If you want to test your knowledge or practice what you have learned, use this interactive app by the CK-12 Foundation. You will find questions on both how to calculate the theoretical yield and the percent yield.

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