# How to calculate the theoretical yield of a product in a reaction

Hints on how to calculate the theoretical yield of products are essential and can’t be over-emphasized due to the errors students do in exams.

Theoretical yield is the amount of product based on stoichiometry calculation while the experimental yield (practical yield) is the amount of product gotten from the experiment.

Actually, to get the theoretical yield, you need to understand how to deduce the limiting reagent because the limiting reagent influences the amount of products gotten.

The theoretical yield is otherwise called the assumed or calculated yield. The issue is that we can calculate the amount of product from equations but not based on the actual experiment.

For example, if f 20g of magnesium ribbons react with hydrochloric acid, I can deduce the amount of hydrogen gas liberated from the equation.

## How can I calculate the theoretical yield?

I can easily calculate the theoretical yield of a solid or gaseous product using a balanced chemical equation and stoichiometry concept.

But the theoretical yield most times are bigger than the actual yield (practical or experimental yield). This is due to the fact that the efficiency of an experiment may not be 100% because of some practical errors like materials used, machines involves, measurements, etc

## Can the actual yield be more than the theoretical yield?

The actual sometimes could be bigger than the theoretical yield but this usually emanates from an inaccurate weighing of the product probably because the product has not been fully dried and there is still some moisture or solvent present.

Secondly, the presence of impurity can lead to a higher mass of the product or if the reaction is catalyzed by an unsuspected substance. The substance acting as a catalyst could lead to a higher yield of the product other factors and condones bang ideal.

## Can a reaction ever have 100% or 110% percent yield

Yes, an ideal practical or experiment may give you 100% yield but due to human errors and other inaccurate measurements this may not be obtained easily.,

However, for a reaction to give you 110% yield, there must be issues from the pieces of apparatus used.

To deduce the efficiency of a practical experiment, we use the percentage yield calculation.

In percentage yield calculation, what we do is to weigh the amount of product if it is solid or aqueous and measure the volume of the gaseous product and compare it to the theoretical yield of product and then multiply by a hundred percent.

But how do you find theoretical yield easy? Just by following the steps I have mentioned below and looking at the examples solved to guide you properly and avoid mistakes.

**Mathematically, percent yield = actual yield/theoretical yield x 100%**

**How do you calculate theoretical yield?**

The steps below will actually guide you on how to calculate the theoretical yield and get your answer without stress.

**Step 1: Balance the **c**hemical equatio**n

The balanced chemical equation is a representation of the law of conservation of matter or mass which states that matter cannot be created nor destroyed van be transformed from one form to another.

When you balance a chemical equation, by ensuring you have a number of atoms on both sides of the equation then you can proceed to the calculations.

S**tep 2: Compare the given to the unknown quantity**

In solving stoichiometry problems usually, the reactant is given though not in all cases so you can use it to calculate the product.

You must be able to decipher the reactants or reagents given and then compare the number of moles to the one you are looking for to enable you to solve the equations.

**Step 3: Determine the limiting reagent or reactant**

Before we proceed to examples on calculating theoretical yield, it is pertinent I mention that there are cases where you can be provided with two reactants but one will be given in a limited amount called the limiting reagent while the other reactant will be given in excess called the excess reagent.

It is your duty to determine the limiting reagent and the excess reagent but sometimes the examiner could specify the limiting and excess reagent.

**Examples on Calculating Theoretical Yield**

- Calculate the mass of magnesium chloride produced when 2.5 moles of magnesium reacts with hydrochloric acid.

Mg + 2HCl ==MgCl_{2} + H_{2}

solution

Compare the moles in the balanced equation

1 mole of Mg ====== 1 mole of MgCl_{2}

2.5 moles of Mg ===_{ } x

X = 2.5 x 1 /1 = 2.5 moles of MgCl_{2}

Calculate the mass of MgCl_{2 ===} 24 + 35.5 x 2 = 24 +71 =95

So I mole of MgCl_{2} =====95 g

2.5 moles of MgCl_{2} ==== x

X === 2.5 x 95 = 237.5g

So, the theoretical yield is 237.5 g

- Calculate the volume of carbon IV oxide evolved when 20g of Calcium carbonate reacts with hydrochloric acid.

2HCl + CaCO_{3} == CaCl_{2} + H_{2}O + CO_{2}

Solution

I mole of calcium carbonate yields 100g of calcium carbonate

Using the balanced equation

I mole of CaCO_{3} ==== 1 mole of carbon IV oxide

Therefore 100g of CaCO_{3} === 22.4 dm^{3}

20g of CaCO_{3} === X

X = 20 X 22.4 /100

X= 4.48 dm^{3}

**Alternatively**

We can solve the number of moles

Number of moles (n) = mass/molar mass

n=20/100 = 0.2 mole

Therefore 1 mole of CaCO_{3} === 22.4 dm^{3}

0.2 of CaCO_{3} === X

X = 20 X 22.4 /100

X= 4.48 dm^{3}

- What mass of zinc chloride will be produced if 40g of zinc reacted with 200cm
^{3}of 0.45 mol/dm^{3 }HCl?

Solution

In this case, you need to determine the limiting reagent. The limiting reagent is the reagent or reactant that will finish first.

Let’s deduce the limiting reagent though I have a full post on how to deduce limiting reagent.

Zn + 2HCl ==ZnCl_{2} + H_{2}

_{ } For Zinc granules and hydrochloric acid you need to deduce calculate the nu,nber of

moles

ZnCl_{2} | HCl |

n = m/M = 40/65 n =0.615 moles | n=CV n=0.45 x 200/1000 n=0.09 moles |

Recall that the examiner did not mention the limiting reagent or reactant in excess.

The limiting reagent is 0.09 moles of HCl, s you use it in the calculations.

Comparing HCl and ZnCl_{2}

_{ }If 2 moles of HCl ===== I mole of ZnCl_{2}

0.09 mole of HCl ===== x

X = 0.09 x 1 /2 = 0.045 moles of ZnCl_{2}

_{ } Therefore if I mole === 136g

0.045 mole ===x

X = 0.045 x 136 =6.12g

**What is the relationship between the limiting reagent and theoretical yield?**

What is the relationship between the limiting reactant and theoretical yield? Actually, the limiting reagent determines the extent of a reaction. A reaction stops when the limiting reagent finishes and ultimately determines the amount of product gotten.

The reactant in excess is not actually used in the calculation of the theoretical yield. The limiting reagent is the stoichiometric mole used in the calculation of the amount of products gotten.

**Percentage yield Calculations**

Percentage yield in Chemistry is important because it helps us deduce the efficiency of our experiments and precautions to take to improve the efficiency and even helps us decode if there are errors encountered.

Examples on percentage yield calculations in Chemistry

**Example 1**

- A student reacts 15g of Aluminium powder with excess oxygen. The amount of Aluminium Oxide produced is 24.6g.

Calculate the theoretical yield and percent yield of Alumium oxide

Solution

4Al + 3O_{2} ===2Al_{2}O_{3}

4 moles of Al ==== 2 moles of Al_{2}O_{3}

Changing to mass

4 x 27g ===== 2 x (27 x2+ 16 x3)

108g of Al =====2 x102 g of Al_{2}O_{3}

108g of Al =====204 g of Al_{2}O_{3}

15g of Al ========x

X = 15 x 204 /108

X = 28.33g

The theoretical yield is 28.33g

How do I calculate the percent yield of the reaction?

Use the percent yield Formula = actual yield/theoretical yield x 100%

Percent yield = 24.6/28.33 x 100%

Percent yield = 86.8%

Example 2

This question is on the percent yield of aspirin.

If the synthesis of aspirin uses 10 cm^{3} in 1.0g/cm^{3} of acetic anhydride against 7.5g of salicylic acid according to the reaction of acetic anhydride and salicylic acid below, calculate the theoretical yield and percentage yield of aspirin if 8.4g of Aspirin was obtained.

C_{7}H_{6}O_{3 }+ (CH_{3}CO)_{2}CO ===C_{9}H_{8}O_{4} +CH3COOH

Solution

The limiting reagent for the synthesis of aspirin in this case is the salicyclic acid.

So we compare the moles or mass of salicyclic acid against the noles or mass of aspirin

1 mole of (CH_{3}CO)_{2}CO ==== I mole of C_{9}H_{8}O_{4}

_{ } (12+1 x3 +12+16)2+12+16 ===== 12 x9+1 x 8+16 x 4

(12+3+12+116) x 2 +12 +16======180g of C_{9}H_{8}O_{4}

114g of (CH_{3}CO)_{2}CO =======180g of C_{9}H_{8}O_{4}

_{ } 7.5g of (CH_{3}CO)_{2}CO ======= x

X = 11.84 g of aspirin

Percent yield of Aspirin = 8.4/11.84 x 100 = 70.94% yield of Aspirin.

**Which equation shows the relationship between Percent yield, theoretical yield and actual yield.**

**Percent yield is the ratio of actual yield or experimental yield multiplied by 100%.**

**Percent yield = actual yield/theoretical yield x 100%**