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.

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:

\(\text{percentage yield}\)= \(\frac {\text{actual yield}} {\text{theoretical yield}}\times100 \)

Let's illustrate this with an example.

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.

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.

\begin{align} &C_2H_4 +Cl_2\rightarrow C_2H_4Cl_2\\ \text {Start}\qquad &1mole\quad 1mole\\ \text{End}\qquad &0 moles\quad 0moles\quad 1mole\end{align}

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

\begin{align} &C_2H_4 \space +\space Cl_2\rightarrow \quad C_2H_4Cl_2\\ \text {Start}\qquad &1mole\quad 1.5moles\\ \text{End}\qquad &0 moles\quad 0.5moles\quad 1mole\end{align}

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.

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

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