4.5 Yields of Reactions

The yield of the reaction depends on stoichiometric amounts of the reactant(s) present in the balanced chemical reaction.

Most chemical reactions that take place in the real world begin with more or less arbitrary amounts of the various reactants; we usually have to make a special effort if we want to ensure that stoichiometric amounts of the reactants are combined. This means that one or more reactant will usually be present in excess; there will be more present than can react, and some will remain after the reaction is over. At the same time, one reactant will be completely used up; we call this the limiting reactant because the amount of this substance present will control, or limit, the quantities of the other reactants that are consumed as well as the amounts of products produced.

The Limiting Reactant: is the reactant which will be consumed completely during the chemical reaction. The reaction will stop when all of the limiting reactant is consumed.

Excess Reactant: is the reactant that stays present when the reaction stops when the limiting reactant is completely consumed.

Theoretical Yield is a calculated yield of the product of the chemical reaction based on the limiting reactant calculated amount. It is pure calculation and there is no experiment involved in this calculation, therefore such yield is called theoretical yield.

Actual Yield is a calculated yield of the product based on an experiment that carried out in an actual chemistry laboratory.

Overall Yield is the percent ratio between the actual yield over the theoretical yield.

Limiting reactant problems are handled in the same way as ordinary stoichiometry problems with one additional preliminary step: you must first determine which of the reactants is limiting— that is, which one will be completely used up. To start you off, consider the following very simple example

The figure below illustrates the concept of limiting reactant as well the theoretical yield of reaction:

Figure 4.22 Limiting Reagent & Theoretical Yield

Reference: https://slideplayer.com/slide/12627403/

The videos below illustrate also the concept of limiting react and the percent yield:

Introduction to Limiting Reactant and Excess Reactant

Limiting Reactant Practice Problems

Limiting Reagents and Percent Yield

Limiting reactants in everyday life

The concept of limiting reactants touches us all in our everyday lives — and as we will show in the second example below, even in the maintenance of life itself!

Aerobic and anaerobic respiration

Our bodies require a continual supply of energy in order to maintain neural activity, synthesize proteins and other essential biochemical components, replace cells, and to power muscular action. The “fuel” — the carrier of chemical energy — glucose, a simple sugar which is released as needed from the starch-like polymer glycogen, the form in which the energy we derive from food is stored.

Arterial blood carries dissolved glucose along with hemoglobin-bound dioxygen to individual cells which are the sites of glucose “combustion”:

C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O

The net reaction and the quantity of energy released are the same as if the glucose were burned in the open air, but within the cells the reaction proceeds in a series of tiny steps which capture most of this energy for the body’s use, liberating only a small fraction of it as thermal energy (heat).

Because this process utilizes oxygen from the air we breath, it is known as aerobic respiration. And as with any efficient combustion process, glucose is the limiting reactant here.

But there are times when vigorous physical activity causes muscles to consume glucose at a rate that exceeds the capacity of the blood to deliver the required quantity of oxygen. Under these conditions, cellular respiration shifts to an alternative anaerobic mode:

C₆H₁₂O₆ → 2 CH₃CH(OH)COOH

As you can see from this equation, glucose is only partially broken down (into lactic acid), and thus only part of its chemical energy is captured by the body.

There are numerous health benefits to aerobic exercise, including increased ability of the body to maintain an aerobic condition. But if you are into short-distance running (sprinting) or being pursued by a tiger, the reduced efficiency of anaerobic exercise may be a small price to pay.

Percent Yield

It is often important to calculate percent yield in a chemical reaction to estimate the efficiency of a chemical reaction. Percent yield is defined as

Percent yield= (actual/theoretical)*100%. The actual yield is the amount of product in a chemical reaction, determined by weighing a product on a balance. Theoretical yield is a quantity calculated from a balanced chemical equation, using mole ratios and molar masses. The theoretical yield is the maximum amount of product formed in a chemical reaction from the amount of reactants used.

When we perform stoichiometric calculations to determine the amount of product produced – that is a theoretical yield. But when we actually perform the experiment in a lab setting, we usually find we do not get as much product, we usually get a smaller actual yield due to human error or other experimental error.

To calculate the percent yield, the actual yield and theoretical yield are needed. You prepared cookie dough to make 5 dozen cookies. The phone rings and you answer. While talking, a sheet of 12 cookies burn and you have to throw them out. The rest of the cookies are okay. What is the percent yield of edible cookies?

Theoretical yield 60 cookies possible

Actual yield 48 cookies to eat

Percent yield 48 cookies x 100 = 80% yield

Stoichiometry – Limiting & Excess Reactant, Theoretical & Percent Yield – Chemistry

The following simulation illustrates in detail about the leftover and excess reactant for any reaction.

1.Go to the activity and click on the 2^nd option “Molecules”

2. Choose the reaction “Making Ammonia. A screen like below should appear.

• Try with 2 molecules of N₂ and 4 molecules of H₂.

• How many molecules of NH3 are formed?

• What is(are) the excess reactant(s)?

• Explain your results.

Problem Example:

For the hypothetical reaction 3 A + 4 B → products, determine which reactant will be completely consumed when we combine
a) equimolar quantities of A and B;
b) 0.57 mol of A and 0.68 mol of B.

Solution:

a) Simple inspection of the equation shows clearly that more moles of B are required, so this component will be consumed (and is thus the limiting reactant), leaving behind ¾ as many moles of A.

b) How many moles of B will react with .57 mol of A? The answer will be
(4/3 × 0.57 mol). If this comes to less than 0.68 mol, then B will be the limiting reactant, and you must continue the problem on the basis of the amount of B present. If the limiting reactant is A, then all 0.57 mol of A will react, leaving some of the B in excess. Work it out!

Practice Problem#1: CO    +   2 H₂     à     CH₃OH 

If 12.0 g H₂ and 74.5 g CO are used determine the limiting reactant.

Number of moles of the product CH₃OH based on CO as reactant = [74.5 g CO] x [mol CO / 28.0 g CO] x [1 mol CH₃OH / 1 mol CO]  =  2.66 moles of CH₃OH

[Note: molar mass of CO is used to be 28.0 g/mol]

Number of moles of the product CH₃OH based on H₂ as reactant = [12.0 g H₂] x [mol H₂ / 2.00 g H₂] x [1 mol CH₃OH / 2 mol H₂]  = 3.00 moles of CH₃OH

[Note: molar mass of H₂ is used to be 2.00 g/mol]

Since 2.66 moles is smaller than 3.00  à  CO is the limiting reactant and H₂ is said to be the excess reactant.

Now we can determine (calculate) the theoretical yield based on the limiting reactant CO

Theoretical yield = [2.66 mol CH₃OH] x [32.0 g CH₃OH / mol CH₃OH] = 85.1 g CH₃OH

[Note: molar mass of CH₃OH is used to be 32.0 g/mol]

Example:

Limiting Reactants, Theoretical Yield, Actual Yield and the Overall Yield:

C₃H₈ +     5 O₂     à      3 CO₂     +      4 H₂O

If 0.550 g C₃H₈ is reacting with 0.550 g O₂. Calculate:

1. The amount moles of CO₂ produced based on the limiting reactant
2. Theoretical yield (based on the limiting reactant)
3. The overall yield if the actual yield of is 0.550 g CO₂
4. The % error of the yield

a) The amount of CO₂ produced based on the limiting reactant

Number of CO₂ moles based on C₃H₈ = [0.550 g C₃H₈] x [1 mol C₃H₈ / 44.0 g C₃H₈] x [ 3 mol CO₂ / 1 mol C₃H₈]  =  0.0375 moles CO₂

[Note that molar mass of C₃H₈ is used to be 44.0 g/mol]

[Note that molar mass of CO₂ is used to be 44.0 g/mol]

[Note that molar mass of O₂ is used to be 32.0 g/mol]

Number of CO₂ moles based on O₂ = [0.550 g O₂] x [mol O₂ / 32.0 g O₂] x [3 mol CO₂ / 5 mol O₂] = 0.0103 moles CO₂

• moles are less than 0.0375 moles. Therefore, O₂ is the limiting reactant.

 b) Theoretical yield (based on the limiting reactant)

Theoretical yield of CO₂ based on the limiting reactant = [0.0103 mol CO₂] x [44.0 g CO₂ / mol CO₂] = 0.572 g CO₂

c) The overall yield if the actual yield of is 0.550 g CO₂

The overall yield = [Actual Yield / Theoretical Yield] x 100%

The overall yield = [0.550 g CO₂ / 0.572 g CO₂] x 100%   =   96.2 %

d) The % error of the yield = | {[Theoretical Yield – Actual Yield] / [Theoretical Yield]} | x 100%

The % error of the yield = | {[0.572 g – 0.550 g] / [0.572 g]} | x 100% = 3.85 %

The videos below show more examples for the actual yield, theoretical yield and the percent yield:

How to Find Actual Yield, Theoretical Yield, and Percent Yield Examples, Practice Problems

Calculate the Theoretical Yield to determine the % yield in a chemical reaction