A Simple Guide on How to Calculate Theoretical Yield

Sodium as a limiting reagent
The calculation using the theoretical yield formula is simple, provided it is done in a methodical manner.
In a chemical reaction, the yield or output, i.e. the amount of product that is produced is called the reaction yield.
The maximum amount of product that can be produced in an ideal condition is called the theoretical yield, while the actual amount of product that is produced is called the actual yield.
Actual yield is usually less than the theoretical yield, because some of the reactants are wasted or not used in the reaction.
Related Terms
Limiting Reagent
It is the reactant that gets used up completely in the reaction, therefore, limits the amount of product that can be created as a result of the reaction. Let's take an example of making an egg sandwich using two slices of bread and one egg. If you have 10 slices of bread and just 1 egg, the maximum number of egg sandwiches that you can make would still be one. Therefore, the number of eggs determine how many egg sandwiches can be made. So the egg acts as the limiting reagent here.
Excess Reagent
The reagent which is not completely used up at the end of the reaction is called the excess reagent. In the analogy given above, the bread slices are the excess reagents.
Mole
A mole is a unit of measurement used while dealing with chemical reactions. In chemistry, measuring in terms of grams or kilograms is not always practical. A mole denotes a certain number of particles in a given amount of substance. Speaking in terms of moles of a substance used in a reaction, gives us a precise and reliable method for conversion between number of atoms and molecules, and grams of a substance.
Molar Mass
It is the mass of 1 mole of a substance. It denotes how much 1 mole of an atom or a molecule would weigh.
Steps to Calculate Theoretical Yield
Problem Example
If 4 g of Na (sodium) reacts with 15 g of Cl2 (chlorine) to produce NaCl (common salt), calculate the theoretical yield of NaCl in grams for the reaction.
Step 1: Balance the Chemical Equation
The chemical equation for the reaction is:

Na + Cl2 ➜ NaCl

The first step is to balance the chemical equation. It involves adding numerical coefficients called the stoichiometric coefficients before the reagents and products, so that the number of atoms or molecules on the reactant side and the product side become equal. In the given problem, adding numeral 2 before Na and NaCl, balances the total number of sodium and chlorine atoms on both sides of the equation. Now the balanced equation is:

2Na + Cl2 ➜ 2NaCl
Step 2: Express Mass of the Reactants in Terms of Moles
Here, we have to convert and express the given mass (in grams) of Na and Cl2 in terms of moles. We have learned that molar mass is the mass of 1 mole of a substance. The molar mass of Na is given to be 22.99 g/mole, and the molar mass of Cl2 is given to be 70.90 g/mole.

We have to calculate the number of moles present in 4 grams of Na and 15 grams of Cl2. We can do so by using this formula:

Number of moles of a substance = mass of the reactant ÷ molar mass of the reactant

Number of moles of Na = amount of Na in the reaction (in grams) ÷ molar mass of Na

Number of moles of Na = 4 grams ÷ 22.99 g/mole

Number of moles of Na = 0.17 moles of Na

Similarly:

Number of moles of Cl2 = 15 grams ÷ 70.90 g/mole

Number of moles of Cl2 = 0.21 moles of Cl2
Step 3: Find the Limiting Reagent
Now, the next step is to determine which of the two reactants is the limiting reagent. To do so, we need to find out:
  1. How much product would Na produce, if it were used up completely in the reaction?
  2. How much product would Cl2 produce, if it were used up completely in the reaction?
2Na + Cl2 ➜ 2NaCl

In the balanced equation given above, the stoichiometric coefficient of both Na and NaCl is 2. Therefore, for one mole of Na, you will get 1 mole of NaCl.

For 0.17 moles of Na, you will end up with 0.17 moles of NaCl.

The stoichiometric coefficients of Cl2 is 1 and that of NaCl is 2. Therefore, for one mole of Cl2, you will get 2 moles of NaCl.

For 0.21 moles of Cl2, you will end up with 0.42 moles of NaCl.

Therefore, Na is the limiting reagent in this reaction, as it would produce lesser number of moles, if it were used up fully in the reaction.
Step 4: Find the Theoretical Yield
We have found that Na is the limiting reagent in the reaction, and that for 0.17 moles of Na, 0.17 moles of NaCl are produced. Therefore, the theoretical yield of NaCl in moles is 0.17 moles.

But this value is in terms of moles. In the given problem, we need to find out how many grams of NaCl would be produced in the reaction.

We can convert the value from moles to grams by multiplying it with the molar mass of NaCl, which is equal to 58.44 g/mole.

Theoretical yield of NaCl in grams = theoretical yield in moles × molar mass of NaCl

Theoretical yield of NaCl in grams = 0.17 moles of NaCl × 58.44 g/mole

Theoretical yield of NaCl in grams = 9.93 grams
Step 5: Find the Percentage Yield
If you actually carry out this reaction in a lab, you will be able to find the actual yield of the reaction. Based on that value, you can find the percentage yield by using the ratio of the actual yield and the theoretical yield. The formula for calculating the percent yield is:

Percentage yield = mass of actual yield ÷ mass of theoretical yield × 100%

Let's assume that you obtained an actual yield of 8.50 grams. Then, the percent yield would be:

Percentage yield of NaCl = 8.50 grams ÷ 9.93 grams × 100%

Percentage yield of NaCl = 85.59%

Since the value of actual yield is usually less than the theoretical yield, the percentage yield is always less than 100%.