Percentage Yield Formula: In chemistry, the product that we obtain after a chemical reaction is known as the yield. We can measure this obtained yield in grams or moles. It is the ‘actual yield’ that we get after the completion of a chemical reaction. Apart from this, based on our calculation, we calculate the expected yield of a reaction known as the ‘theoretical yield.’ In this article, we have discussed the percentage yield formula in detail along with some tips to increase the annual yield.

The percent ratio of the ‘actual yield’ to the ‘theoretical yield’ is known as the ‘percentage yield.’ This Percentage Yield is mostly lower than \(100\%\) because the actual yield is mostly lower than the theoretical yield because of the incomplete reaction or loss of the product during recovery. Percentage yield can only be \(100\%\) when the actual yield is equal to the theoretical yield. It is a positive value. In this article, we will learn about the percentage yield and the various factors governing it in detail.

Percentage Yield Definition

In reality, chemical reactions do not always go exactly as planned by the chemists on paper. During an experiment, many factors often contribute to the formation of less product than the expected one. Some of these factors may include incomplete reactions, undesirable side reactions, spills, or other experimental errors. To measure how successful a reaction has been, chemists need a measurement which is called the percentage yield. The percentage yield is the ratio of the actual yield to the theoretical yield multiplied by \(100\).

Percentage Yield Formula in Chemistry

In order to calculate the percentage yield, it is primarily necessary to determine how much of the product should be formed based on stoichiometric calculations. This is known as the theoretical yield, which is the maximum amount of product that could be formed from the given amounts of reactants.

For calculating the theoretical yield, first, the limiting reagent is determined because the number of moles of products obtained is dependent on the molar amount of the limiting reagent. Then, the possible number of moles of the product is multiplied by the molecular weight of the product to convert to grams.

The actual yield is the amount of product that is formed when the reaction is actually carried out in the laboratory. Percentage yield can be expressed as follows:

\({\rm{Percentage}}\,{\rm{Yield}} = \frac{{{\rm{Actual}}\,{\rm{Yield}}}}{{{\rm{Theoretical}}\,{\rm{Yield}}}} \times 100\)

Percentage yield is very important in the manufacture of products in industries. In multi-step chemical synthesis, a low percentage yield in even a single step may cause a huge loss of time and money due to the unnecessary wastage of the reactants. So, industries spend lots of resources on increasing their percentage yield. Percentage yield can only be \(100\%\) when the actual yield is equal to the theoretical yield, which is a rare case. Percentage yield is mostly less than \(100\%\) because actual yield is mostly lower than the theoretical yield because of the incomplete reaction or loss of the product during recovery.

Calculation of Percentage Yield with Example

Let us take the example of a chemical reaction to calculate the percentage yield. One of the best percentage yield calculation examples is the reaction between hydrogen and oxygen that leads to the formation of water.

\(\underset{2\mathrm g}{2{\mathrm H}_2+}\underset{16\mathrm g}{{\mathrm O}_2}\rightarrow\underset{18\mathrm g}{2{\mathrm H}_2\mathrm O}\)

We can calculate the theoretical yield of \(18\,{\rm{g}}\) of water molecules from \(2\,{\rm{g}}\) hydrogen and \(16\,{\rm{g}}\) oxygen. But actually, only \(15\,{\rm{g}}\) of water molecules are obtained at the end of the reaction. Thus, for the above equation:

Theoretical Yield \( = 18\;{\rm{g}}\)

Actual Yield \( = 15\;{\rm{g}}\)

Using the formula:

\({\rm{Percentage}}\,{\rm{Yield}} = \frac{{{\rm{Actual}}\,{\rm{Yield}}}}{{{\rm{Theoretical}}\,{\rm{Yield}}}} \times 100\)
\({\rm{Percentage}}\,{\rm{Yield}} = \frac{{{\rm{15}}\,{\rm{g}}}}{{{\rm{18}}\,{\rm{g}}}} \times 100\)

Percentage Yield \({\rm{ = 83}}{\rm{.3}}\,{\rm{\% }}\)

Thus, it can be said that the percentage yield of the formation of water from hydrogen and oxygen is \({\rm{83}}{\rm{.3}}\,{\rm{\% }}\).

What is Percentage Yield Calculator?

An annual percentage yield calculator will teach you how to calculate percent yield as well as the formula and definition of percent yield annually. The percent yield equation converts your experimental yields into a measure of how successfully you carried out your reaction, hence finding the yield is an important aspect of any synthetic lab work.

Reasons for getting Lower Percentage Yield

1. All reactants might not react – If a chemical reaction is very slow, then some of the reactants might not react and will remain as reactants only till the end of the reaction.
2. Reversible reaction – In a reversible reaction, the reaction reaches equilibrium when the products undergo a backward reaction to form the reactants again which would reduce the yield. For example, in Haber’s process, the ammonia formed as the product may turn back to nitrogen and hydrogen gas.
   \({{\rm{N}}_2} + 3{{\rm{H}}_2}⇌2{\rm{N}}{{\rm{H}}_3}\)
3. Side reactions – Many chemical reactions are accompanied by side reactions. For example, in the formation of ammonia, nitrogen may react with oxygen present in the air to form nitrogen dioxide. This would decrease the yield of ammonia.
   \({{\rm{N}}_2} + 3{{\rm{H}}_2}⇌2{\rm{N}}{{\rm{H}}_3}\)
   Instead of the above reaction, a side reaction may occur:
   \({{\rm{N}}_2} + 2{{\rm{O}}_2} \to 2{\rm{N}}{{\rm{O}}_2}\)
4. Loss of products during the reaction – Some of the gaseous products may escape during the reaction procedure itself. This would also decrease the yield of the product.
5. Loss of products during recovery – After the reaction is completed, in the process of recovery of products such as filtration, the product loss may happen by spilling, or the filter paper may not be able to capture the liquid or solid.

How to Increase the Percentage Yield of a Reaction?

1. Increase the temperature: At higher temperatures, the kinetic energy of the reactant molecules will increase, and this would lead to maximum collisions between the molecules to form sufficient products as all the reactant molecules would undergo a complete reaction at the end.
2. Increase the concentration of reactants: If reactant concentration is increased, the product concentration will automatically increase to a great extent.
3. Increase the surface area of the reactants: The greater surface area ensures that more particles are exposed to the other reactant molecules which would lead to a greater chance of particles colliding. Thus, due to more successful collisions per second, the rate of reaction increases, and ultimately the yield also increases.
4. Remove the product as it is formed: Mostly, in case of reversible reactions, the products should be readily removed to avoid reformation of the reactants. Also, sometimes products get oxidized to form undesired substances. Thus, by removing the products at the end of the reaction, we may get a proper yield.

Summary

The percentage yield is the ratio of the actual yield to the theoretical yield multiplied by 100. Actual yield is the real data obtained in the laboratory, while theoretical yield is the desired data obtained by stoichiometric calculations. In industrial chemistry, especially in the pharmaceutical and drug industries, this percentage yield is of topmost priority because if the yield of the chemical synthesized is not satisfactory, it may cause a huge loss to the company.

In organic reactions, mostly multi-step chemical reactions take place, so a good yield should be maintained to avoid the loss of the reactants in between the reactions themselves which may lead to lower yield. Some of the factors that reduce the percentage yield of the products in a chemical reaction include side reactions, reversible reactions, loss of products during the reactions, as well as during workup after the completion of the reaction to recover the products. By putting attention on some points like maintaining the desired temperature, increasing the surface area of the reactants, using a catalyst, etc., the percentage yield of a chemical reaction may increase.

FAQs on Percentage Yield Formula

Q.1: What is the percentage yield formula?
Ans: The percentage yield is the ratio of the actual yield to the theoretical yield multiplied by \(100\). Its formula is:

\({\rm{Percentage}}\,{\rm{Yield}} = \frac{{{\rm{Actual}}\,{\rm{Yield}}}}{{{\rm{Theoretical}}\,{\rm{Yield}}}} \times 100\)

Q.2: How do you calculate percentage yield?
Ans: For calculating the percentage yield of a chemical reaction, it is primarily necessary to determine how much of the product should be formed based on stoichiometric calculations. This is known as the theoretical yield, which is the maximum amount of product that could be formed from the given amounts of reactants. The actual yield is the amount of product that is formed when the reaction is carried out in the laboratory. Then by taking the ratio of the actual yield to the theoretical yield and then multiplying it by \(100\), we can calculate the percentage yield.

Q.3: How do you find theoretical yield and percentage yield?
Ans: For calculating the theoretical yield, first, the limiting reagent is determined because the number of moles of products obtained is dependent on the molar amount of the limiting reagent. Then, the possible number of moles of the product is multiplied by the molecular weight of the product to convert to grams. Then by dividing the actual yield by the calculated yield and multiplying it by \(100\), we get the percentage yield.

Q.4: How do you calculate percentage yield in organic chemistry?
Ans: In organic chemistry, many complex reactions occur that are multi-step also. To calculate the overall percentage yield of a multi-step organic reaction, multiply the individual percentage yields of every step by each other (for example, for \(3\) steps, \(30\%\) yield in every step, we can calculate \(0.30 \times 0.30 \times 0.30 = 0.27 \times 100 = 27\% \) overall percentage yield). On the other hand, we can take the limiting reagent molar amount of the first step of the organic reaction and find the molar amount of the final product according to stoichiometry and then multiply it by the molecular weight of the final product obtained. In these two manners, we can calculate percentage yield in organic chemistry.

Q.5: How to calculate the actual yield from percentage yield?
Ans: To find the actual yield, we can multiply the percentage and theoretical yields together as the percentage yield is the ratio of the actual yield to the theoretical yield.

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