Theoretical Yield

In Chemistry, the term theoretical yield relates to the amount of a product that is formed, as and when the reaction completes. The yield further depends on the ideal conditions set for the chemical reaction, considering the risks of unanticipated side reactions, reverse chemical reactions, loss of energy in the process and incomplete conversion of the material used in the chemical process. Hence, for a chemical reaction to happen, it is essential to balance the reaction to mitigate the risks stated above. Also, the reagents (also known as the limiting reagents) need to be determined, to assess their role in the entire chemical reaction. For people who are not aware of what limiting reagent is, here you go: A limiting reagent (also known as limiting reactant) is one of the chemical reactants that help to determine the ability of the chemical reaction to go on, until the energy utilization is complete and the reaction stops.

How to Calculate Theoretical Yield

Before you go about calculating theoretical yield formula, one should know the procedure.

Balancing the Equation
Before proceeding with the practical, first balance the reaction theoretically and determine the ratio of reactants to products. The balancing of a chemical reaction is based on the law of conservation of mass, which states, energy can neither be created, nor destroyed but can only be converted from one form to another. So in a chemical reaction, the number of atoms of the total reactants (which are ideally on the left) should be equal to the number of atoms of the product that is obtained after the reaction is complete. For instance, let's take the example of methane combustion, in presence of oxygen.

Example
CH₄ + O₂ → CO₂ + H₂O

• This is currently an unbalanced chemical formula. So first you need to figure out the smallest whole number coefficients for each of the reactants and the products.
• Let's say the coefficients are a, b, c and d. Multiply each of the reactants and products with these coefficients: a x CH₄ + b x O₂ → c x CO₂ + d x H₂O
• As per the system of equations, it can be observed that the number of carbon atoms is same on the reactant and the product side. So a = c = 1.
• Now the equation is: CH₄ + b x O₂ → CO₂ + d x H₂O. There are 4 hydrogen atoms in the reactant side, however there is only one molecule of methane containing it. Hence, there should be ideally 2 molecules of hydrogen in the product side, which makes it 4 hydrogen atoms there as well. So multiply d by 2.
• Now the equation is: CH₄ + b x O₂ → CO₂ + 2 x H₂O. However, the number of oxygen atoms are still unequal. There are 2 oxygen atoms in the reactant side and 4 oxygen atoms in the product side. So multiply b by 2 and the resultant equation is a balanced chemical equation.
• Resultant equation: CH₄ + 2O₂ → CO₂ + 2H₂O

Determining Limiting Reactant
To determine the limiting reagent, first divide the reactant mass (in gms) by its molecular weight (molar mass) (gms/mole). A mole is a unit of measurement for the amount of reactants used. 1 mole = 12 atoms ~ 6.022 x 10²³ particles - Avogadro's number. 1 mole of ideal gas ~ 22.4 liters at STP (Standard Temperature and Pressure). Another alternative solution is to multiply the amount of reactant (in ml) by its density and then divide by the molar mass. One should know the method to calculate molar mass, before proceeding with calculation of theoretical yield. Now the mass obtained from either of the steps above is to be multiplied by the number of moles of the reactant used in the chemical equation. Based on the capacity of the limiting reagent, calculate the expected moles of the product, assuming the yield to be 100%.

CH₄ + 2O₂ → CO₂ + 2H₂O

Here, 1 mole of methane reacts with 2 moles of oxygen to yield 2 moles of water and 1 mole of carbon dioxide. The stoichiometric ratio would be 1: 2 (for methane : oxygen). Molecular weight of CH₄ is 16.04 gms/mole and of oxygen is 32 gms/mole. So as per the equation, 16 gms of methane reacts with 64 gms of oxygen to yield 44 gms of carbon dioxide and 36 gms of water. So here methane reacts with 4 times the amount of oxygen by weight. So one could say, methane is the limiting agent here.

Calculating Theoretical Yield
The stoichiometric ratio is the theoretical ratio obtained from the chemical equation. However the actual ratio depends on the number of moles of the limiting reagent. To determine theoretical yield, multiply the number of moles of the limiting reagent by the ratio of the limiting reagent and the synthesized product and by the molecular weight of the product. In a chemical reaction, A + B → C, theoretical yield of C can be calculated in 2 ways

• [m(C)/f(C)]/[m(A)/f(A)]
• [m(C)/f(C)]/[m(B)/f(B)]

where A is the limiting reagent, f(A), f(B) and f(C) are formula weights of the reactants and the products respectively and molecular masses of the reactants and the products are m(A), m(B) and m(C) and of these whichever yield is low, the reactant of that chemical equation becomes the limiting reactant.

In the above example, CH₄ + 2O₂ → CO₂ + 2H₂O, if 8 gms of methane were burned with 48 gms of oxygen, to produce 20 gms of carbon dioxide, then the number of moles of methane as per the formula is,

[8 gms of methane x 1 (mole of methane) / 16 (molecular weight of methane)] x [1(mole of CO₂) / 1 (mole of methane)] = 0.5 moles of CO₂
[48 gms of oxygen x 1 (mole of oxygen) / 32 (molecular weight of oxygen)] x [1(mole of CO₂) / 2 (moles of oxygen)] = 0.75 moles of CO₂

Now the theoretical yield formula is, using the smaller number of moles of CO₂ obtained from the reaction 1, where methane is identified as the limiting reagent. Hence, the theoretical yield is : [0.5 (moles of CO₂) x 44 (molecular weight) /1 (mole of CO₂)] = 22 gms CO₂

If the actual yield is 20 gms of CO₂, then the yield percentage can be calculated as,
Actual yield / Theoretical yield x 100 = 20/22 x 100 = 90.9% ~ 91%.

Usually the idea behind calculating theoretical yield is to determine if the chemical reaction was successful or not and if it were, how much was the success percentage. A low percentage indicates that the conditions for the chemical reaction need to be improved, as the above stated risk factors may be responsible for factoring the failure percentage of the chemical reaction. Hope the above theoretical yield example with explanation has helped you understand this formula of theoretical yield. But before you proceed with these calculations, make sure you are well-versed with important chemistry terms and terminologies of Chemistry like, moles and molecular mass. You may take the help of periodic table to calculate the molecular weight. So solve more of these theoretical yield examples and Chemistry will no longer seem a rocket science! What say?