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# Percentage Yield

As chemists, if we look closely at any chemical reaction, we ask ourselves 'Does every single reactant turn into product?" Sometimes, yes, this does happen, but sometimes it does not and sometimes not all the reactants have even changed in any way. The way in which we can analyse this is through a concept called percentage yield. Percentage yield allows us to explore how much of a product should be produced, and how much product is actually produced, and this is what we will be exploring within this article.

• We will cover what percentage yield is, the factors that affect it, and also learn how to calculate percentage yield.
• We will consider limiting reactants and how to find the limiting reactant in a chemical reaction.
• Finally, we shall consider percentage errors and how to minimise these.

We can get an idea of how much product (or yield) we will get from a reaction by using the molecular mass of the samples involved.

Let us use the reaction between ethene and water to produce ethanol as an example. Have a look at the molecular masses of ethene, water and ethanol shown below.

Fig. 1 - Percentage yield

## What is percentage yield?

You can see from the balanced equation in the image above that 1 mole of ethene reacts with water to make 1 mole of ethanol. We can guess that if we react 28g of ethene with water, we will make 46g of ethanol. But this mass is only theoretical. In practice, the actual amount of product we get is lower than the amount we predict due to the inefficiency of the reaction process.

If you were to carry out an experiment with exactly 1 mole of ethene and excess water, the amount of product, ethanol, would be less than 1 mole. We can work out how effective a reaction is by comparing the amount of product we get in an experiment to the theoretical amount from the balanced equation. We call this percentage yield.

Percentage yield measures the effectiveness of a chemical reaction. It tells us how much of our reactants (in percent) successfully transformed into a product.

### Factors that affect percentage yield

The reaction process is inefficient due to a number of reasons, some of which are listed below.

• Some of the reactants do not convert into a product.

• Some of the reactants get lost in the air (if it's a gas).

• Unwanted products get produced in side-reactions.

• The reaction reaches equilibrium.

• Impurities stop the reaction.

### Calculating percentage yield

We work out percentage yield using the formula:

$$\text{percentage yield}$$= $$\frac {\text{actual yield}} {\text{theoretical yield}}\times100$$

Actual yield is the amount of product you practically get from an experiment. It is rare to get 100 percent yield in a reaction due to the inefficiency of the reaction process.

Theoretical yield (or predicted yield) is the maximum amount of product you can get from a reaction. It is the yield you would get if all the reactants in your experiment turned into a product.

Let's illustrate this with an example.

In the following reaction, 34g of methane react with excess oxygen to make 73g of carbon dioxide. Find the percentage yield.

$$CH_4+2O_2\rightarrow CO_2+2H_2O$$

1 mole of methane $$CH_4$$ makes 1 mole of carbon dioxide $$CO_2$$

$$CH_4$$ = 16g/mol

34g of methane = 34 ÷ 16 = 2.125 mol since $$n$$ = $$\frac {m} {M}$$

According to the equation, for each mole of $$CH_4$$ we get one mole of $$CO_2$$ , so theoretically we should also produce 2.125 mol of carbon dioxide.

The molecular mass of $$CO_2$$ is 44 g/mol:

M(C) = 12

M(O) = 16

so M($$CO_2$$ ) = 12 + 2 x 16 = 44 g/mol

Remember $$n$$ =$$\frac {m} {M}$$$$\leftrightarrow$$$$m$$=$$\frac {n} {M}$$

By multiplying the molecular mass of $$CO_2$$ with the amount of substance, we can obtain the theoretical yield.

44g x 2.125 = 93.5g

The theoretical (maximal) yield is therefore 93.5g of carbon dioxide.

Actual yield = 73g

Theoretical yield = 93.5g

Percentage yield = (73 ÷ 93.5) x 100 = 78.075%

This means that the percentage yield is 78.075%

## What are limiting reactants?

Sometimes we do not have enough of a reactant to form the amount of product we need.

Imagine you make nine cupcakes for a party but eleven guests show up. You should have made more cupcakes! Now the cupcakes are a limiting factor.

Fig. 2 - Limiting reactant

In the same way, if you do not have enough of a certain reactant for a chemical reaction, the reaction will stop when the reactant is all used up. We call the reactant a limiting reactant.

A limiting reactant is a reactant that is all used up in a chemical reaction. Once the limiting reactant is all used up, the reaction stops.

One or more of the reactants may be in excess. They are not all used up in a chemical reaction. We call them excess reactants.

### How to find the limiting reactant

To figure out which of the reactants in a chemical reaction is the limiting reactant, you must start with the balanced equation for the reaction, then work out the relationship of the reactants in moles or by their mass.

Let's use an example to find the limiting reactant in a chemical reaction.

$$C_2H_4 + Cl_2\rightarrow C_2H_4Cl_2$$

The balanced equation shows 1 mole of ethene reacts with 1 mole of chlorine to produce 1 mole of dichloroethane. Ethene and chlorine are all used up when the reaction stops.

What if we use 1.5 moles of chlorine? How much of the reactants are left over?

1 mole of ethene and one mole of chlorine react to make 1 mole of dichloroethane. 0.5 moles of chlorine is left over. Ethene is the limiting reactant in this case as it is all used up at the end of the reaction.

You can also use the trick of dividing the number of moles of each reactant by its stoichiometric coefficient to determine which reactant is limiting. The reactant with the smallest mole ratio is limiting.

For the above example:

$$C_2H_4 + Cl_2\rightarrow C_2H_4Cl_2$$

Stoichiometric coefficient of $$C_2H_4$$ = 1

Number of moles = 1

1 ÷ 1 = 1

Stoichiometric coefficient of $$Cl_2$$ = 1

Number of moles = 1.5

1.5 ÷ 1 = 1.5

1 < 1.5, therefore,$$C_2H_4$$ is the limiting reactant.

## Percentage errors

When we carry out an experiment, we use different apparatus to measure things. For example, a balance or a measuring cylinder. Now, when using these to measure they are not entirely accurate and instead have something called a percentage error, and when we carry out experiments we need to be able to calculate percentage error. So how do we do this?

1. First we need to find the margin of error of the apparatus and we then need to see how many times we used the apparatus for a single measurement.

2. Then we need to see how much of a substance we measured.

3. Lastly, we use the figures and plug them into the following equation: maximum error/measured value x 100

1. A burette has a margin of error of 0.05cm3 and when we use this apparatus to record a measurement we use it twice. So we do 0.05 x 2 = 0.10, this is the margin error

2. Let us say we have measured 5.00 cm3 of a solution. This is the amount of substance we measured.

3. Now, we can put the figures into the equation:

0.10/5 x 100 = 2%

So this has a 2% error.

### How to minimise percentage error?

So, now that we know how to calculate percentage error, let us explore how to reduce it.

1. Increasing the amount measured: the margin of error of an apparatus is set, so the only factor we can change is the amount measured. So if we increase it, the percentage error will be smaller.

2. Using an apparatus with smaller divisions: if an apparatus has smaller divisions, it is less likely to have a bigger marginal error

## Percentage Yield - Key takeaways

• Factors that affect percentage yield: the reactants do not convert to a product, some reactants get lost in the air, unwanted products get produced in side-reactions, the reaction reaches equilibrium, and impurities stop the reaction.
• Percentage yield measures the effectiveness of a chemical reaction. It tells us how much of our reactants (in percentage terms) are successfully turned into a product.
• The formula for percentage yield (actual yield/theoretical yield) is 100.
• Theoretical yield (or predicted yield) is the maximum amount of product that you can get from a reaction.
• Actual yield is the amount of product you practically get from an experiment. It is rare to get the 100 percent yield in a reaction.
• A limiting reactant is a reactant that is all used up at the end of a chemical reaction. Once the limiting reactant is all used up, the reaction stops.
• One or more of the reactants may be in excess. They are not all used up in a chemical reaction. We call them excess reactants.

We work out percentage yield using the formula below:

actual yield/ theoretical yield x 100

Percentage yield measures the effectiveness of a chemical reaction. It tells us how much of our reactants (in percent) successfully turned into a product.

A high percentage yield lets us know how effective our reaction was. We usually only care about one of the products in a chemical reaction. Percentage yield lets us know how much of our reactants turned into a desired product.

## Final Percentage Yield Quiz

Question

Select factors that affect percentage yield?

Some reactants get lost in the air

Show question

Question

What is the percentage yield?

Percentage yield measures the effectiveness of a chemical reaction. It tells us how much of our reactants (in percent) successfully turned into a product.

Show question

Question

What is theoretical yield?

Theoretical yield (A.K.A. predicted yield) is the maximum amount of product that you can get from a reaction.

Show question

Question

What is actual yield?

Actual yield is the amount of product you practically get from an experiment. It is rare to get 100 percent yield in a reaction due to the inefficiency of the reaction process.

Show question

Question

What is a limiting reactant?

A limiting reactant is a reactant that is all used up at the end of a chemical reaction. Once the limiting reactant is all used up, the reaction stops.

Show question

Question

What is an excess reactant?

One or more of the reactants may be in excess. They are not all used up in a chemical reaction.

Show question

Question

Find the limiting reactant in the reaction below?

5 g of iron and 5 g of sulfur were used to make iron sulphide

Fe(s) + S(s) → FeS(s)

Iron (Fe) is the limiting reactant.

(1 mole of iron reacts with 1 mole of sulfur to make 1 mole of iron sulphide.

Fe = 56/5 = 0.089 mol. Fe

S = 32/5 = 0.156 mol. S

There is not enough iron to react with the sulfur.)

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