5.6
yield: the amount of product that is
obtained in a chemical reaction
theoretical yield: the amount of product
that we predict will be obtained, calculated
from the equation
actual yield: the amount of product that is
actually obtained at the end of a procedure
Figure 1
Chemicals come in a wide variety of grades
(purities). The purity of a chemical can significantly affect experimental results in a chemical reaction.
percentage yield: the ratio, expressed as
a percentage, of the actual or experimental
quantity of product obtained (actual yield) to
the maximum possible quantity of product
(theoretical yield) derived from a gravimetric
stoichiometry calculation
238 Chapter 5
The Yield of a Chemical Reaction
In all of the predictions of masses of reactants and products so far, we have based
our calculations on the balanced equations for the chemical reactions. We must
remember that the quantities that we calculate in our predictions are theoretical
quantities. They are the quantities of products that should be produced,
according to the numbers in the balanced equation. They are not necessarily the
quantities that we actually get when we carry out the reaction, mixing the reactants and collecting the products.
The amount of product that is obtained in a chemical reaction is called the
yield. It may be measured in mass or in moles. The amount of product that we
predict we should get by stoichiometric calculations using the balanced equation
is called the theoretical yield. When we carry out the reaction, whether it is in a
school or in an industrial laboratory, the amount of product that is obtained and
measured at the end of the procedure is called the actual yield.
Often the actual yield in a chemical reaction turns out to be less than the
theoretical yield. Theoretically, each and every atom, ion, and molecule proceeds
through the reaction according to the balanced equation and is accounted for
and measured in one of the products. In actual practice, there are several reasons
why all of the materials do not end up in the collected product. The most
common loss of product is as a result of experimental procedures, such as in
transferring solutions, filtering precipitates, and splattering during heating.
These losses can be reduced by improving technical skills or the equipment used,
or by reducing the number of steps in the experimental design.
The poor yield could also be due to impurities in the reagents used.
Chemicals come in a wide variety of grades, or purities (Figure 1). Some lowpurity or technical grades may be only 80% to 90% pure; if this factor is not
accounted for in the amount of reactant used, the actual yield will again be less
than the theoretical yield. Impurities may also be a result of other processes. For
example, metals such as magnesium readily react with air to form a layer of metal
oxide on the surface. These impurities are included in the mass of reactants but
do not proceed to form the products collected, thus causing the actual yield to
differ from the theoretical yield.
Another cause of low yield is a side reaction, forming other than the desired
product. When magnesium ribbon is heated in a crucible, it reacts with oxygen
in the air to form magnesium oxide. However, air contains a mixture of gases,
including nitrogen. A side reaction may occur in which some of the magnesium
reacts with nitrogen to form magnesium nitride. If the product collected is presumed to be magnesium oxide, but in fact also contains the nitride, the actual
yield will be different from the theoretical yield. To correct this discrepancy, additional steps can be introduced to convert all products to the desired product.
In yet other cases, the conditions may not be ideal for the reaction to go to
completion. This happens when, as more and more products are formed, the
reverse reaction occurs, in which the products of the reaction become the reactants of the reverse reaction. A certain amount of the products are thus being
used up at the same time that they are being produced. In such cases, the actual
yield is the amount of product present and is always less than the theoretical
yield. To minimize these losses, the conditions for the reaction may need to be
changed to allow the reaction to go to completion.
A comparison of the actual yield and the theoretical yield gives an indication
of the efficiency of a chemical reaction. We can calculate this efficiency as a
percentage yield, by dividing the actual yield by the theoretical yield:
5.6
actual yield
percentage yield = × 100%
theoretical yield
For example, for a certain reaction, if the theoretical yield is 10.0 kg and the
actual yield is 9.0 kg, the percentage yield would be 90%:
9.0 kg
percentage yield = × 100% = 90%
10.0 kg
Sample Problem
Arsenates, used in some pesticides, are compounds of arsenic. The most
common ore of arsenic, FeSAs(s), can be heated to produce arsenic according to
the following equation:
FeSAs(s) → FeS(s) + As(s)
When 250 kg of the ore was processed industrially, 95.3 kg of arsenic was
obtained. Calculate the percentage yield of arsenic in the process.
Solution
mole ratio FeSAs:As = 1:1
actual yield of As(s) = 95.3 kg
1 mol
nFeSAs = 250 000 g × 162.83 g
= 1535 mol
nAs = 1535 mol
74.92 g
mAs = 1535 mol × 1
mol
mAs = 115.0 kg
95.3 kg
percentage yield = × 100% = 82.8%
115.0 kg
The percentage yield of arsenic in the process was 82.8%.
Practice
Understanding Concepts
1. Describe the distinction between the terms actual yield and
theoretical yield.
2. Can the actual yield ever be greater than the theoretical yield?
Explain.
3. In an experiment, 5.00 g of silver nitrate is added to a solution containing an excess of sodium bromide. It was found that 5.03 g of
silver bromide is obtained.
(a) Write a balanced equation for the reaction.
(b) What is the theoretical yield of silver bromide?
(c) What is the actual yield of silver bromide in the experiment?
(d) What is the percentage yield of the experiment?
Answers
3. (b) 5.53 g
(c) 5.03 g
(d) 91.0%
4. (a) FeS(s)
4. In an experiment, when 16.1 g of FeS reacted with 10.8 g of O2,
14.1 g of Fe2O3(g) was produced. The balanced equation for the reaction is given below:
4 FeS(s) + 7 O2(g) → 2 Fe2O3(s) + 4 SO2(g)
(a) Identify the limiting reagent in the experiment.
Quantities in Chemical Equations 239
Answers
4. (b) 14.6 g
(c) 96.6%
5. 90.8%
6. 74.9%
(a)
(b) Calculate the theoretical yield.
(c) Calculate the percentage yield of Fe2O3(s) in the experiment.
5. Iron is produced from its ore, hematite, Fe2O3(s), by heating with
carbon monoxide in a blast furnace. If the industrial process produced 635 kg of iron from 1000 kg of hematite, what is the percentage yield of iron in the process? The equation for the reaction is
given below:
Fe2O3(s) + 3 CO(g) → 2 Fe(s) + 3 CO2(g)
6. Methyl salicylate, C8H8O3(l), is the chemical responsible for the wintergreen flavouring. It can be prepared by heating salicylic acid, C7H6O3(s),
with methanol, CH3OH(l), according to the equation below:
C7H6O3(s) + CH3OH(l) → C8H8O3(l) + H2O(l)
If 2.00 g of salicylic acid is reacted with excess methanol, and the
yield of oil of wintergreen is 1.65 g, what is the percentage yield?
Applying Inquiry Skills
(b)
7. In an experiment to recover a precipitate that was formed in a chemical reaction, a chemistry student followed this procedure:
•
The mass of a reactant is determined using weighing paper on a
centigram balance.
•
The reactant is transferred to a large beaker.
•
A second aqueous reactant, used in excess, is measured using a
graduated cylinder and added to the beaker.
•
The mixture is stirred and heated to dryness in an evaporating
dish over a laboratory burner.
•
The precipitate is transferred from the evaporating dish to
weighing paper and the mass is determined.
Suggest ways in which the procedure can be modified to improve the
yield.
Making Connections
(c)
8. When you drink a beverage or eat a candy artificially coloured with
red food dye, you may be ingesting a chemical that was produced by
a tiny red insect and extracted by a process developed by two
Canadian chemists. Several synthetic red dyes have been found to be
carcinogenic (cancer-causing), but a vivid red dye called carmine,
which is made from the cochineal insect (Figure 2), has been
approved for use in foods, drugs, and cosmetics. The method of production has been improved to increase the purity and the yield of the
product. Use the Internet to research the following and summarize
your findings in a one-page report:
(a) the modifications in the procedure for producing the dye carmine
from the insects, thus increasing yield;
(b) the effect that the industrial production of carmine has had on
the people of Peru, where the insects are found.
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Figure 2
(a) The cochineal lives in prickly pear cacti in the high desert
plains of the Peruvian Andes.
(b) (c) A vivid red dye is made of the dried and crushed
bodies of female cochineal insects.
240 Chapter 5
5.6
Investigation 5.6.1
Determining Percentage Yield in a Chemical
Reaction
In this investigation, mass relationships in a chemical reaction will be studied by
performing an experiment, collecting and recording evidence, and analyzing the
evidence. The actual yield, theoretical yield, and percentage yield of copper in a
single displacement reaction are determined and the experimental procedure
evaluated.
Write a report to present the Prediction, Evidence, Analysis, and
Evaluation.
Question
What mass of copper is formed when excess aluminum is reacted with a given
mass of copper(II) chloride dihydrate?
Prediction
(a) Calculate the theoretical yield for this experiment.
INQUIRY SKILLS
Questioning
Hypothesizing
Predicting
Planning
Conducting
Recording
Analyzing
Evaluating
Communicating
Copper chloride dihydrate is
toxic and must not be
ingested.
Care must be taken when
handling hot equipment.
Eye protection and lab
aprons must be worn.
Experimental Design
A known mass of a copper salt is dissolved in water and is reacted with an excess
of aluminum. The mass of copper formed in the reaction is determined.
Percentage yield is calculated.
The reaction is represented by this balanced equation:
3 CuCl2•2H2O(aq) + 2 Al(s) → 3 Cu(s) + 2 AlCl3(aq) + 6 H2O(l)
Materials
eye protection
aluminum foil, 8 cm × 8 cm
copper(II) chloride dihydrate, 2.00 g
two 150-mL beakers
50-mL graduated cylinder
stirring rod
ruler
forceps
hot plate
ring stand
iron ring
wire gauze
watch glass
crucible tongs
centigram balance
Quantities in Chemical Equations 241
Procedure
1. Measure a mass of 2.00 g of the copper salt, to 0.01 g, and dissolve in 50 mL
of water in a beaker.
2. Fold the aluminum foil lengthwise to make a strip 2 cm × 8 cm. Coil the
strip loosely to fit into the copper chloride solution in the beaker, making
sure that the strip is entirely immersed.
3. Heat the beaker gently on the hot plate for 5 min or longer, until all blue
colour in the solution has disappeared. Continue heating gently for
another 5 min. Allow to cool.
4. Use the forceps to shake loose all copper formed on the aluminum foil.
Carefully transfer the copper to a weighed beaker and rinse the copper
with water.
5. Pour off as much of the rinse water as possible. Spread the copper on the
bottom of the beaker.
6. Cover the beaker containing the wet copper with a watch glass and gently
heat the beaker to drive off the water. Reduce heat if the copper begins to
turn black.
7. When the copper is dry, determine the mass of copper.
8. Wash hands thoroughly after the experiment, and follow your teacher’s
instructions for disposal of the waste materials.
Analysis
(b) Answer the Question.
(c) Identify the limiting reagent and the excess reagent in this reaction. What
visible evidence is there to confirm your identification?
(d) Determine the actual yield of copper.
(e) Determine the percentage yield of copper in this experiment.
Evaluation
(f) If your percentage yield is less than 100%, suggest specific techniques or
equipment that may account for the loss of product.
Synthesis
Figure 3
The spruce budworm survives harsh Canadian
winters by producing an antifreeze protein
that lowers the freezing point of its body
fluids. Scientists are interested in the possible use of these antifreeze proteins to help
preserve organs at low temperatures prior to
transplant operations. To increase the yield of
these antifreeze proteins, biochemists have
isolated the spruce budworm gene responsible for making the proteins and incorporated it into bacteria. Since bacteria grow
rapidly, they are ideal “factories” for mass
production of the selected proteins.
242 Chapter 5
(g) Suppose that the percentage yield was greater than 100%. Suggest one or
more specific factors in this experiment that may account for this.
(h) What steps did you take to ensure that the reaction went to completion?
(i) If you wanted to use aluminum as the limiting reagent, what changes in the
procedure would be needed? What visible evidence would you look for to
ensure that the reaction had gone to completion?
Yield in Industrial Chemical Reactions
In industrial applications, it is important for manufacturers of a product to
achieve as close to 100% yield as possible (Figure 3). The chemists or engineers
must first determine the percentage yield of the operation and analyze all aspects
of the process to look for ways of improving efficiency. This may require
changing the conditions of the reaction, such as the temperature or pressure,
which would in turn change the final equilibrium conditions of the reaction. It
may require changing some steps in the procedure to reduce loss due to inadequate equipment or poor technique. The final decision will rest on an analysis of
the costs of the changes required to improve the yield as well as the increased
5.6
profit from an improved yield. The decision may also depend on whether byproducts or unused reactants can be recycled or used in other profitable processes.
A model case of striving for maximum yield is that of the synthesis of
ibuprofen, an analgesic (painkiller) sold under several brand names, such as
Motrin and Advil (Figure 4). The company that manufactures ibuprofen, BHC
Company, researched and refined its chemical process to produce a more efficient synthesis, creating less waste and fewer byproducts.
The traditional industrial synthesis of ibuprofen was developed in the 1960s
and involved a six-step process that resulted in large quantities of unwanted chemicals that needed to be disposed of. Even if the percentage yield was at an acceptable level, the yield of products from raw materials was low due to the reactions
used in the experimental design. In this process, dubbed the “brown” process, 40%
of the total atoms present in the reactants were recovered in the desired product.
In 1991, a new three-step process was implemented that dramatically
reduced the quantities of waste chemicals produced and increased to 77% the
recovery of atoms from reactants to desired product. The shorter “green” process
also offered the advantage of producing larger quantities of ibuprofen in less
time and with less capital expenditure. These improvements not only increased
profitability for the company, but benefited the environment also by reducing the
need to dispose of millions of kilograms of waste materials.
Practice
Figure 4
The analgesic ibuprofen is part of a booming
pharmaceutical business with estimated
sales of U.S. $124.6 billion in 1998.
Understanding Concepts
9. What are some factors that may contribute to less than 100% percentage yield in a chemical reaction?
10. One of the reactions used in the smelting of copper ores to produce
copper involves reacting copper(I) oxide with copper(I) sulfide. The
balanced equation for the reaction is given below:
2 Cu2O(s) + Cu2S(s) → 6 Cu(s) + SO2(g)
Answers
10. (a) Cu2S
(b) 309 kg
(c) 92.2%
11. (a) 31.4%
(b) 78.6%
When 250 kg of copper(I) oxide is heated with 129 kg of copper(I) sulfide, 285 kg of copper is recovered.
(a) Determine the limiting reagent.
(b) Calculate the theoretical yield of copper.
(c) Determine the percentage yield of copper.
11. The carbon in coal can be converted into methane, CH4(g), by first
heating the coal powder with steam and oxygen, followed by heating
with carbon monoxide and hydrogen. The overall process is summarized below:
C(s) + 2 H2(g) → CH4(g)
(a) When 10.0 kg of coal is used in the process, 4.20 kg of methane is
produced. What is the percentage yield of methane, assuming
the coal is pure carbon?
(b) Further analysis shows that the coal contains only 40.0% carbon
by mass. Recalculate the percentage yield of methane, taking into
account the purity of the coal.
Making Connections
12. Maximizing percentage yield is not the only factor to consider in
designing a chemical process. A reaction must be assessed for its
efficiency, potential effect on the environment, and many other factors. For each of the following factors, select the “greener” option
and give reasons for your selection.
Quantities in Chemical Equations 243
(a) a reaction that requires the use of an organic solvent versus one
that uses water as a solvent
(b) a reaction that takes place at high temperature versus one that
takes place at room temperature
(c) a reaction that requires the product to be dried versus one that
does not require a drying agent
(d) a reaction that requires the product to be purified versus one that
requires no purification of the product
(e) a reaction that uses starting material derived from crude oil
versus one that uses material derived from plant or animal
matter
Section 5.6 Questions
Understanding Concepts
1. What are some ways of improving percentage yield in
(a) a school chemistry experiment?
(b) an industrial chemical process?
2. Acetylsalicylic acid (ASA), C9H8O4(s), is the chemical name for an
analgesic whose common name is Aspirin. It is manufactured by
heating salicylic acid, C7H6O3(s), with acetic anhydride, C4H6O3(s),
according to the equation below:
C7H6O3(s) + C4H6O3(s) → C9H8O4(s) + C2H4O2(s)
(a) If 2.00 g of salicylic acid is heated with 4.00 g of acetic anhydride, what is the theoretical yield?
(b) If the actual yield is 2.09 g, what is the percentage yield?
Applying Inquiry Skills
3. In this lab exercise, iron(III) silicate, Fe2(SiO3)3(s), is to be synthesized in a chemical reaction, in a simulation of an industrial
process. Iron(III) silicate is produced as a yellow-orange precipitate in the reaction of sodium silicate and excess iron(III) nitrate.
(a) Design an experiment to determine the actual yield of iron(III)
silicate using this reaction. Write a report that includes the
procedure, safety procedures, and an evaluation of the chemical process used in the synthesis.
(b) Assume that the percentage yield in the experiment is 80.0%.
Evaluate the experimental process with regard to maximizing
yield.
Making Connections
4. The efforts of the BHC Company in improving its process in the
manufacture of ibuprofen were recognized and the company
received several awards. Industrial designs of products and
processes that are efficient and benign to the environment and to
human health are referred to as “green” chemistry. Using the
Internet, research other “green” chemistry projects and briefly
summarize the major features of one such project.
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5. Chemical engineering is a discipline that was developed when
the discovery of oil led to the need for engineers who understood
its chemistry and who could convert the chemicals from oil into
244 Chapter 5
5.7
useful products. Chemical engineers now work in many areas of
science, especially in industry. They design and develop industrial processes to make different consumer goods; they scale up
laboratory experiments into industrial-size operations; they analyze data using electronics and computers. They are also responsible for the design of an efficient and safe chemical plant that
protects the natural environment. Overall, a chemical engineer is
a versatile problem-solver.
Research some specific fields in chemical engineering and
the university courses that lead to a degree in chemical engineering. If possible, interview a chemical engineer to learn more
about a career in this field. Prepare a report on your findings.
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DID YOU KNOW ?
5.7
Chemistry in Technology
What is the difference between science and technology? Are they the same thing?
How are they related? Science is the study of the natural world to describe, predict, and explain changes and substances; technology encompasses the skills,
processes, and equipment required to make useful products or to perform useful
tasks. Sometimes technology is a practical application of science. However, often
a certain technology existed long before the scientific principles behind it were
understood. In this section we will look at the technology of glassmaking and
how a scientific understanding of chemical reactions led to the industrial production of one of its key ingredients.
Glass is formed by heating a mixture of sand, sodium carbonate (soda), and calcium oxide (lime) to a high temperature—1425°C to 1600°C, depending upon the
exact composition—at which point the mixture takes on a molten (liquid) state.
The sand provides silicon dioxide (silica), which makes up the largest percentage of
the mixture. Sodium carbonate lowers the temperature at which the sand will melt,
and calcium oxide makes the glass strong and water-resistant. The percentage composition of this glass mixture determines the properties of the resultant glass. When
cooled, the molten glass mixture becomes a “supercooled” liquid that retains its
liquid shape as a solid. Glass making is known to have begun in Egypt about 5000
years ago, long before chemical formulas and reactions were understood, a case of
technology preceding scientific knowledge. In Canada, glass making dates back to
the 1800s, with the production of mostly industrial glassware, such as lantern and
streetlight globes, lenses for railway and ship lanterns, and telephone line insulators.
The advances in atomic theory and the development of systematic quantitative analysis in the early 1800s brought with them an understanding of chemical
formulas and equations. The application of chemical analysis and calculations
led to improved properties of glass as well as the establishment of industrial
chemical processes (Figure 1).
Science in Glass Making
The development of systematic quantitative
chemical analysis in the early 19th century,
followed by chemical formulas and equations, contributed a great deal to the largescale industrial supply of raw materials such
as soda ash, used in glass making. In 1830,
the French chemist Jean-Baptiste-André
Dumas (1800–1884) showed that soda-limesilica glass was most durable when the mass
ratio of the three was 1:1:6, a ratio that is
still used in modern soda-lime-silica glass.
The LeBlanc Process
At the beginning of this chapter we talked about the LeBlanc process used during
the 1700s and 1800s to produce sodium carbonate. Not only was the process
inefficient but it was harmful also to the environment. The LeBlanc process
begins with the reaction of salt and sulfuric acid, releasing hydrogen chloride:
Figure 1
Glass-making technology has changed greatly
in the last two centuries.
Quantities in Chemical Equations 245