chapter5-thermochemistry

55 Thermochemistry

chapter

Thermochemistry

296 Chapter 5 NEL

In this chapter,you will be able to

• compare the energy changesresulting from physical,chemical, and nuclearchanges;

• represent such energychanges usingthermochemical equationsand potential energydiagrams;

• determine enthalpies ofreaction both experimentallyand by calculation fromHess’s law and standardenthalpies of formation;

• compare conventional andalternative sources ofenergy;

• recognize examples oftechnologies that depend onexothermic and endothermicchanges.

Energy transformations are the basis for all of the activities that make up our lives. Whenwe breathe or walk or ride a bicycle, we use the chemical process of respiration and a wholeseries of complex metabolic reactions to convert the chemical energy in food intomechanical energy. Our home furnaces burn fossil fuels such as wood, coal, oil, or nat-ural gas to produce heat that keeps us comfortable in this northern climate. Plants in forestsand our fields take in sunlight and change the solar energy into chemical potential energy— stored carbohydrates — that may be further processed by animals and by ourselves— consider the many transformation necessary to cook corn, for example.

You are already familiar with many energy changes, both chemical and physical. As atennis player sprints for the ball, glucose molecules in muscle cells react to form carbondioxide, water, and energy. At the same time a physical change — the evaporation ofperspiration — consumes energy and helps the player maintain a constant body tem-perature.

Many energy changes have significant effects on our way of life and our future.Transportation, whether in cars or by mass transit, depends to a large extent on thecombustion of fossil fuels. This combustion produces energy of motion but also releasescarbon dioxide, with its possible links to the greenhouse effect, and other pollutants.Even electrically powered vehicles use energy that is generated in part in nuclear or fossilfuel-burning power plants.

Energy is a major factor in decision making on our planet. Most sources of energy arefinite, and using each has its advantages and disadvantages. The control and use of ourpresent energy resources and the decisions that we make for the future will continue tohave far-reaching environmental, economic, social, and political effects for many years.

1. Consider the following changes: ice melting, water evaporating, water vapour con-densing, photosynthesis, respiration, and combustion of gasoline. Classify thesechanges as absorbing or releasing thermal energy.

2. Based on your current understanding of energy, how is electrical power produced inOntario? What are the sources of energy that produce this power?

3. How is nuclear power different from hydroelectric power? How is it similar?

REFLECT on your learning

Thermochemistry 297NEL

TRYTHIS activity Burning Food

Have you heard of fat-burning exercises? Now you are going tonot only burn fat, but also measure how much energy isreleased in the process.

Engineers who design furnaces to heat homes and nutrition-ists who calculate the energy value of different foods need toanalyze the energy-producing ability of different fuels. In experi-ments in which heat is absorbed by water, they use the formula:

heat � (mass of water) � (temperature change of water) � 4.18 J/(g°C)

Materials: eye protection;centigram balance; pecan orother nut; paper clip; small tincan, open at one end andpunctured under the rim onopposite sides; pencil; ther-mometer; measuring cup;matches

• Measure the mass of thenut or assume that anaverage pecan weighsabout 0.5 g.

• Bend a paper clip so that itforms a stand that will sup-port a nut above the labbench (Figure 1).

• Place 50 mL of tap water in the tin can. Measure the temper-ature of the water.

• Suspend the can of water above the nut by putting the pencilthrough the holes under the rim of the can.

• Light the nut and allow the reaction to continue until the nutstops burning. Measure the final temperature of the water.

(a) Calculate how much energy was absorbed by the water.(b) Where did this energy come from?(c) Calculate the amount of heat produced per gram of fuel

(nut) burned.(d) Compare this combustion reaction to the reaction that

would happen if you were to eat the pecan instead ofburning it. Possible areas of comparison could include:reactants and products, total energy production, energystorage, efficiency of energy production, and so on.

(e) What were some sources of experimental error? Howwould you improve this experiment?

Students with extreme sensitivity to nuts or nutproducts should not perform this activity.

Figure 1

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5.15.1 Changes in Matter and EnergyWhat happens when matter undergoes change? Clearly, new substances or states areproduced, but energy changes also occur. If chemistry is the study of matter and itstransformations, then thermochemistry is the study of the energy changes that accom-pany these transformations. Changes that occur in matter may be classified as physical,chemical, or nuclear, depending on whether a change has occurred in the arrangementsof the molecules, their electronic structure, or the nuclei of the atoms involved (Figure 1).Whether ice melts, iron rusts, or an isotope used in medical therapy undergoes radioac-tive decay, changes occur in the energy of chemical substances.

NEL

Figure 1Hydrogen may undergo a physical,chemical, or nuclear change.(a) Physical: Hydrogen boils at

�252°C (or only about 20°Cabove absolute zero): H2( l) → H2(g)

(b) Chemical: Hydrogen is burnedas fuel in the space shuttle’smain engines: 2 H2(g) � O2(g) → 2 H2O( l)

(c) Nuclear: Hydrogen undergoesnuclear fusion in the Sun, pro-ducing helium: H � H → He

thermochemistry the study of theenergy changes that accompanyphysical or chemical changes inmatter

thermal energy energy availablefrom a substance as a result of themotion of its molecules

chemical system a set of reactantsand products under study, usuallyrepresented by a chemical equation

surroundings all matter around thesystem that is capable of absorbingor releasing thermal energy

Heat and Energy ChangesBoth physical and chemical changes are involved in the operation of an oxyacetylenetorch to weld metals together. A chemical reaction, which involves ethyne (or acetylene)and oxygen as reactants, produces carbon dioxide gas, water vapour, and considerableenergy. This energy is released to the surroundings as thermal energy, a form of kineticenergy that results from the motion of molecules. The result is a physical change — themelting of the metal — when the increased vibration of metal particles causes them tobreak out of their ordered solid pattern. When you are studying such transfers of energy,it is important to distinguish between the substances undergoing a change, called thechemical system, and the system’s environment, called the surroundings. A system isoften represented by a chemical equation. For the burning of ethyne, the equation is:

2 C2H2(g) � 5 O2(g) → 4 CO2(g) � 2 H2O(g) � energy

The surroundings in this reaction would include anything that could absorb thethermal energy that has been released, such as metal parts, the air, and the welder’s pro-tective clothing.

When the reaction occurs, heat, q, is transferred between substances. (An object pos-sesses thermal energy but cannot possess heat.) When heat transfers between a systemand its surroundings, measurements of the temperature of the surroundings are used toclassify the change as exothermic or endothermic (Figure 2).

The acetylene torch reaction is clearly an exothermic reaction because heat flows intothe surroundings. Chemical potential energy in the system is converted to heat energy,

(a)

(b) (c)


Section 5.1

Thermochemistry 299

which is transferred to the surroundings and used to increase the thermal energy of themolecules of metal and air. Since the molecules in the surroundings have greater kineticenergy, the temperature of the surroundings increases measurably.

Chemical systems may be further classified. A chemical reaction that produces a gasin a solution in a beaker is described as an open system, since both energy and mattercan flow into or out of the system. The surroundings include the beaker itself, the sur-face on which the beaker sits, and the air around the beaker. In the same way, mostexplosive reactions are considered to be open systems because it is so difficult to containthe energy and matter produced. Figure 3 shows an open system. Most calculations ofenergy changes involve systems in which careful measurements of mass and temperaturechanges are made (Figure 4). These are considered to be isolated systems for the pur-pose of calculation. However, it is impossible to completely prevent energy from enteringor leaving any system. In reality, the contents of a calorimeter, or of any container thatprevents movement of matter, form a closed system.

system

Exothermic Endothermic

Figure 2In exothermic changes, energy isreleased from the system, usuallycausing an increase in the tempera-ture of the surroundings. Inendothermic changes, energy isabsorbed by the system, usuallycausing a decrease in the tempera-ture of the surroundings.

heat amount of energy transferredbetween substances

exothermic releasing thermalenergy as heat flows out of thesystem

endothermic absorbing thermalenergy as heat flows into the system

temperature average kineticenergy of the particles in a sampleof matter

open system one in which bothmatter and energy can move in orout

isolated system an ideal system inwhich neither matter nor energy canmove in or out

closed system one in whichenergy can move in or out, but notmatter

Figure 3A burning marshmallow is an example of anopen system. Gases and energy are free toflow out of the system.

Figure 4A bomb calorimeter is a device inwhich a fuel is burned inside aninsulated container to obtain accu-rate measurements of heat transferduring chemical reactions. Becauseneither mass nor energy can escape,the chemical system is described asisolated.

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Measuring Energy Changes: CalorimetryWhen methane reacts with oxygen in a lab burner, enough heat is transferred to thesurroundings to increase the temperature and even to cause a change of state (Figure 5).How is this amount of heat measured? The experimental technique is called calorimetryand it depends on careful measurements of masses and temperature changes. When a fuellike methane burns, heat is transferred from the chemical system into the surroundings(which include the water in the beaker). If more heat is transferred, the observed tem-perature rise in the water is greater. Similarly, given the same amount of heat, a smallamount of water will undergo a greater increase in temperature than a large amount ofwater. Finally, different substances vary in their ability to absorb amounts of heat.

PracticeUnderstanding Concepts

1. Identify each of the following as a physical, chemical, or nuclear change, with reasonsfor your choice:(a) a gas barbecue operating(b) an ice cube melting in someone’s hand(c) white gas burning in a camping lantern(d) wax melting on a hot stove(e) zinc metal added to an acid solution in a beaker(f) ice applied to an athletic injury

2. Identify the system and surroundings in each of the examples in the previous question.

3. Identify the following as examples of open or isolated systems and explain your iden-tification:(a) gasoline burning in an automobile engine(b) snow melting on a lawn in the spring(c) a candle burning on a restaurant table(d) the addition of baking soda to vinegar in a beaker(e) a gas barbecue operating

4. A thimbleful of water at 100°C has a higher temperature than a swimming pool full ofwater at 20°C, but the pool has more thermal energy than the thimble. Explain.

5. Identify each of the following as an exothermic or endothermic reaction:(a) hydrogen undergoes nuclear fusion in the Sun to produce helium atoms;(b) the butane in a lighter burns;(c) the metal on a safety sprinkler on the ceiling of an office melts when a flame is

brought near it.

Making Connections

6. (a) List five changes that you might encounter outside your school laboratory. Createa table to classify each change as physical, chemical, or nuclear; endothermic orexothermic; and occurring in an open or an isolated system.

(b) What are the most commonly encountered types of chemical reactions in termsof energy flow?

7. The energy content of foods is sometimes stated in “calories” rather than the SI unit ofjoules. Physical activity is described as “burning calories”. Research the answers tothe following questions:(a) What are the relationships among a calorie, a Calorie, and a joule?(b) Are calories actually burned? Why is this terminology used?(c) What laboratory methods are used to determine the energy content of foods?

GO www.science.nelson.com

Figure 5The fuel in the burner releases heatenergy that is absorbed by the sur-roundings, which include thebeaker, water, and air.

calorimetry the technologicalprocess of measuring energychanges in a chemical system


These three factors — mass (m), temperature change (∆T), and type of substance —are combined in an equation to represent the quantity of heat (q) transferred:

where c is the specific heat capacity, the quantity of heat required to raise the tem-perature of a unit mass (e.g., one gram) of a substance by one degree Celsius or onekelvin. For example, the specific heat capacity of water is 4.18 J/(g•°C). (Recall that theSI unit for energy is the joule, J.) Specific heat capacities vary from substance to sub-stance, and even for different states of the same substance (Table 1).

As the equation indicates, the quantity of heat, q, that flows varies directly with the quan-tity of substance (mass m), the specific heat capacity, c, and the temperature change, ∆T.

Cancelling units in your calculations will help ensure that you have applied the for-mula correctly. In this book, quantities of heat transferred are calculated as absolutevalues by subtracting the lower temperature from the higher temperature.

Section 5.1

q � mc�T

specific heat capacity quantity ofheat required to raise the tempera-ture of a unit mass of a substance1°C or 1K

Table 1 Specific Heat Capacities of Substances

Substance Specific heat capacity, c

ice 2.01 J/(g•°C)

water 4.18 J/(g•°C)

steam 2.01 J/(g•°C)

aluminum 0.900 J/(g•°C)

iron 0.444 J/(g•°C)

methanol 2.918 J/(g•°C)

When 600 mL of water in an electric kettle is heated from 20°C to 85°C to make acup of tea, how much heat flows into the water?

First, use the density formula to calculate the mass of water.

m � dV

� 1.00 g/mL� � 600 mL�

� 600 gUse the heat formula, q � mc�T, to calculate the quantity of heat transferred.

q � ?

m � 600 g

c � 4.18 J/(g•°C) (from Table 1)

�T � 85°C � 20°C � 65°C

q � mc�T

� 600 g� � �(4g�.•1°8C�J)

� � 65°C�

� 1.63 � 105 J or 163 kJ.

163 kJ of heat flows into the water.

ExampleWhat would the final temperature be if 250.0 J of heat were transferred into 10.0 g ofmethanol initially at 20.0°C?

Solutionm � 10.0 g

c � 2.918 J/(g•°C)

T1 � 20.0 °C

�T � T2 – T1 � T2 – 20.0°C

q � 250 J

Calculating Quantity of Heat SAMPLE problem

302 Chapter 5 NEL

q � mc�T

�T � �mqc�

�

� 8.57°C

T2 � 20°C � 8.57°C

T2 � 20.0 � 8.57

T2 � 28.6°C

The final temperature of the methanol is 28.6°C.

250 J��10.0 g� � 2.918 J�/(g�•°C)


8. If the same amount of heat were added to individual 1-g samples of water,methanol, and aluminum, which substance would undergo the greatest tempera-ture change? Explain.

9. There is 1.50 kg of water in a kettle. Calculate the quantity of heat that flows intothe water when it is heated from 18.0°C to 98.7°C.

10. On a mountaineering expedition, a climber heats water from 0°C to 50°C.Calculate the mass of water that could be warmed by the addition of8.00 kJ of heat.

11. Aqueous ethylene glycol is commonly used in car radiators as an antifreeze andcoolant. A 50% ethylene glycol solution in a radiator has a specific heat capacityof 3.5 J/(g•°C). What temperature change would be observed in a solution of4 kg of ethylene glycol if it absorbs 250 kJ of heat?

12. Solar energy can preheat cold water for domestic hot-water tanks.(a) What quantity of heat is obtained from solar energy if 100 kg of water is pre-

heated from 10°C to 45°C?(b) If natural gas costs 0.351¢/MJ, calculate the money saved if the volume of

water in part (a) is heated 1500 times per year.

13. The solar-heated water in the previous question might be heated to the finaltemperature in a natural gas water heater.(a) What quantity of heat flows into 100 L (100 kg) of water heated from 45°C to

70°C?(b) At 0.351¢/MJ, what is the cost of heating 100 kg of water by this amount,

1500 times per year?

Answers

9. 506 kJ

10. 38 g

11. 20ºC

12. (a) 15 M

(b) $77

13. (a) 1.0 � 104 kJ

(b) $55

Heat Transfer and Enthalpy ChangeChemical systems have many different forms of energy, both kinetic and potential. Theseinclude the kinetic energies of

• moving electrons within atoms;

• the vibration of atoms connected by chemical bonds; and

• the rotation and translation of molecules that are made up of these atoms.

More importantly, they also include

• the nuclear potential energy of protons and neutrons in atomic nuclei; and

• the electronic potential energy of atoms connected by chemical bonds.


Researchers have not yet found a way to measure the sum of all these kinetic andpotential energies of a system. For this reason chemists usually study the enthalpychange, or the energy absorbed from or released to the surroundings when a systemchanges from reactants to products.

An enthalpy change is given the symbol ∆H, pronounced “delta H,” and can be deter-mined from the energy changes of the surroundings. A useful assumption that will beapplied in more detail later in this chapter is that the enthalpy change of the systemequals the quantity of heat that flows from the system to its surroundings, or from thesurroundings to the system (Figure 6). This assumption applies as long as there is no sig-nificant production of gas, which is the case in most reactions you will encounter.

This idea is consistent with the law of conservation of energy — energy may be con-verted from one form to another, or transferred from one set of molecules to another,but the total energy of the system and its surroundings remains the same.

For example, consider the reaction that occurs when zinc metal is added to hydrochloricacid in a flask:

Zn(s) � 2 HCl(aq) → H2(g) � ZnCl2(aq)

Some of the chemical potential energy in the system is converted initially to increasedkinetic energy of the products. Eventually, through collisions, this kinetic energy is trans-ferred to particles in the surroundings. The enthalpy change in the system is equal tothe heat released to the surroundings. We can observe this transfer of energy, and canmeasure it by recording the increase in temperature of the surroundings (which includethe solvent water molecules, the flask, and the air around the flask). Our calculations ofthe heat released will involve the masses of the various substances as well as their tem-perature change and specific heat capacities.

In order to control variables and allow comparisons, energy changes in chemical sys-tems are measured at standard conditions of temperature and pressure, such as SATP,before and after the reaction. Under these conditions, the enthalpy change of a chemical

Section 5.1

Medical Cold Packs (p. 347)Can you identify the active chemicalin a medical cold pack?

INVESTIGATION 5.1.1

enthalpy change (�H) the differ-ence in enthalpies of reactants andproducts during a change

�Hsystem � � qsurroundings

In searching through referencesyou may find the terms enthalpy ofreaction, heat of reaction, changein heat content, enthalpy change,and �H. They all mean the samething.

LEARNING TIP

Reaction Progress

Changes in Kinetic and Potential Energy

Energy

high kinetic energyhigh potential energy

low potential energylow kinetic energy

Figure 6In this example of an exothermicchange, the change in potentialenergy of the system (�H ) equalsthe change in kinetic energy of thesurroundings (q). This is consistentwith the law of conservation ofenergy.

Setting HardThe setting of concrete is quiteexothermic, and the rate at whichit sets or cures determines thehardness of the concrete. If theconcrete sets too quickly (forexample, if the heat of reaction isnot dissipated quickly enough intothe air), the concrete may expandand crack.

DID YOU KNOW ??

system is the change in the chemical potential energy of the system because the kineticenergies of the system’s molecules stay constant (for our purposes at this stage).

We can observe enthalpy changes during phase changes, chemical reactions, or nuclearreactions. Although the magnitudes of the enthalpy changes that accompany these eventsvary considerably (Table 2 and Figure 7), the basic concepts of enthalpy change andheat transfer apply. Notice how much more energy is produced in a nuclear change thanin a chemical change, and in a chemical change than in a physical change.

304 Chapter 5 NEL

Table 2 Types of Enthalpy Changes

Physical changes

• Energy is used to overcome or allow intermolecular forces to act.

• Fundamental particles remain unchanged at the molecular level.

• Temperature remains constant during changes of state (e.g., water vapour sublimes to form frost: H2O(g) → H2O(s) + heat).

• Temperature changes during dissolving of pure solutes (e.g., potassium chloride dissolves: KCl(s) + heat → KCl(aq)).

• Typical enthalpy changes are in the range �H � 100 � 102 kJ/mol.

Chemical changes

• Energy changes overcome the electronic structure and chemical bonds within the particles (atoms or ions).

• New substances with new chemical bonding are formed

(e.g., combustion of propane in a barbecue: C3H8(g) � 5 O2(g) → 3 CO2(g) + 4 H2O(g) � heat);

(e.g., calcium reacts with water: Ca(s) � 2 H2O(l) → H2(g) � Ca(OH)2(aq) � heat).

• Typical enthalpy changes are in the range �H � 102 – 104 kJ/mol.

Nuclear changes

• Energy changes overcome the forces between protons and neutrons in nuclei.

• New atoms, with different numbers of protons or neutrons, are formed (e.g., nuclear decay of uranium-238: 238

92 U → 42He � 234

90 Th � heat).

• Typical enthalpy changes are in the range �H � 1010 � 1012 kJ/mol. The magnitude of the energy change is a consequence of Einstein’s equation (Figure 8).

physical change a change in theform of a substance, in which nochemical bonds are broken

chemical change a change in thechemical bonds between atoms,resulting in the rearrangement ofatoms into new substances

nuclear change a change in theprotons or neutrons in an atom,resulting in the formation of newatoms

Figure 7Log scale of the enthalpy changesresulting from a variety of physical,chemical, and nuclear changes

1024 J

daily solar energyfalling on Earth

10–21 J

10–18 J

10–15 J

10–12 J

10–9 J

10–6 J

10–3 J

energy of a strongearthquake

1 kilowatt-hour ofelectrical energy

heat released fromcombustion of 1 molglucose

1000 tonnes ofcoal burned

1 tonne of TNT exploded

heat absorbed duringdivision of one bacterial cell

average kinetic energy ofa molecule in air at 300 K

energy from fission ofone 235U atom

1 calorie (4.184 J)

daily electricaloutput of hydroelectric plant

100 J

103 J

106 J

109 J

1012 J

1015 J

1018 J

1021 J


14. Explain how �Hsystem and qsurroundings are different and how they are similar.

15. How do enthalpy changes of physical, chemical, and nuclear changes compare?

Applying Inquiry Skills

16. Design an experiment to determine the identity of an unknown metal, clearlydescribing the set of observations that you would make and the calculations that youwould perform (including units), given the following information:• The metal is zinc, magnesium, or aluminum, all of which are shiny, silvery metals.• These metals react when placed in dilute acid solution.• Dilute acid has the same density and specific heat capacity as water.• A Chemical Handbook provides values for the heat (in J) released per unit mass

(g) of metal reacting in acid.


Section 5.1

Section 5.1 QuestionsUnderstanding Concepts

1. For the three states of matter (solid, liquid, and gas), thereare six possible changes of state. Which changes of stateare exothermic? Which are endothermic?

2. What three factors are involved in calculations of theamount of heat absorbed or released in a chemical reac-tion?

3. Identify each of the following as a physical, chemical, ornuclear change, giving reasons for your choice:(a) gasoline burning in a car engine(b) water evaporating from a lake(c) uranium fuel encased in concrete in a reactor

4. Identify the chemical system and the surroundings in eachof the examples in question 3.

5. Identify each of the examples in question 3 as an open oran isolated system. Explain your classifications.

6. Describe the chemical system in each of the examples inquestion 3. Compare the relative amounts of energy per

mole that would be transferred in each of the changes ofstate (to the nearest power of ten).

Making Connections

7. The bomb calorimeter is a commonly used laboratory apparatus. Research and write a brief report describing theapplications of this technology.

8. Hot packs and cold packs use chemical reactions to produce or absorb energy. Write a brief report describingthe chemical systems used in these products and theirusefulness.

Figure 8In Einstein’s famous equation, largeamounts of energy, E, are producedwhen a small amount of mass, m, isdestroyed because c, the speed oflight, is such a large value(3.0 � 108 m/s).



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5.25.2When we write an equation to represent changes in matter, the chemical symbols mayrepresent individual particles but usually they represent numbers of moles of particles.Thus, the thermochemical equation

1 H2(g) � �12

� O2(g) → 1 H2O(g) � 241.8 kJ

represents the combustion reaction of 1 mol of hydrogen with 0.5 mol of oxygen toform 1 mol of water vapour. The enthalpy change per mole of a substance undergoinga change is called the molar enthalpy and is represented by the symbol ∆Hx, where x isa letter or a combination of letters to indicate the type of change that is occurring. Thus,the molar enthalpy of combustion of hydrogen is

�Hcomb � �241.8 kJ/mol

Note the negative sign in the value of ∆H. Changes in matter may be either endothermicor exothermic. The following sign convention has been adopted.

Stating the molar enthalpy is a convenient way of describing the energy changesinvolved in a variety of physical and chemical changes involving 1 mol of a particular reac-tant or product. Table 1 shows some examples.

We can express the molar enthalpy of a physical change, such as the vaporization ofwater, as follows:

H2O(l) � 40.8 kJ → H2O(g)

What we may think of as the change in potential energy in the system, the molarenthalpy of vaporization for water, is

�Hvap � 40.8 kJ/mol

Molar Enthalpies

molar enthalpy, �Hx the enthalpychange associated with a physical,chemical, or nuclear changeinvolving one mole of a substance

Table 1 Some Molar Enthalpies of Reaction (�Hx)

Type of molar enthalpy Example of change

solution (�Hsol) NaBr(s) → Na+(aq) � Br�

(aq)

combustion (�Hcomb) CH4(g) � 2 O2(g) → CO2(g) � H2O(l)

vaporization (�Hvap) CH3OH(l) → CH3OH(g)

freezing (�Hfr) H2O(l) → H2O(s)

neutralization (�Hneut)* 2 NaOH(aq) � H2SO4(aq) → 2 Na2SO4(aq) � 2 H2O(l)

neutralization (�Hneut)* NaOH(aq) � 1/2 H2SO4(aq) → 1/2 Na2SO4(aq) � H2O(l)

formation (�Hf)** C(s) � 2 H2(g) � 1/2 O2(g) → CH3OH(l)

* Enthalpy of neutralization can be expressed per mole of either base or acid consumed.

** Molar enthalpy of formation will be discussed in more detail in Section 5.5.

• Enthalpy changes for exothermic reactions are given anegative sign.

• Enthalpy changes for endothermic reactions are given apositive sign.


Molar enthalpy values are obtained empirically and are listed in reference books in tablessuch as Table 2.

The amount of energy involved in a change (the enthalpy change ∆H, expressed in kJ)depends on the quantity of matter undergoing that change. This is logical: twice themass of ice will require twice the amount of energy to melt. To calculate an enthalpychange ∆H for some amount of substance other than a mole, you need to obtain the molar enthalpy value ∆Hx from a reference source, and then use the formula ∆H � n∆Hx. Note the cancellation of units in the following problem.

Section 5.2

A common refrigerant (Freon-12, molar mass 120.91 g/mol) is alternately vaporized in tubes inside a refrigerator, absorbing heat, and condensed in tubesoutside the refrigerator, releasing heat. This results in energy being transferredfrom the inside to the outside of the refrigerator. The molar enthalpy of vaporiza-tion for the refrigerant is 34.99 kJ/mol. If 500.0 g of the refrigerant is vaporized,what is the expected enthalpy change �H?

�Hvap � 34.99 kJ/mol

�H � ?

First, find the amount of refrigerant, n, in moles. From the problem statement,

Mrefrigerant � 120.91 g/mol, and mrefrigerant � 500.0 g, so

nrefrigerant � 500.0 g� � �1210m.9

o1lg�

�

� 4.35 mol

Then calculate the enthalpy change, �H.

�H � n�Hvap

� 4.35 mol� � �341.9m9okl�J

�

�H � 144.7 kJ

Because the refrigerant vaporizes by absorbing heat, the enthalpy change is positive.

Using Molar Enthalpies in Heat Calculations SAMPLE problem

Table 2 Molar Enthalpies for Changes in State of Selected Substances

Molar enthalpy of Molar enthalpy of

Chemical Name Formula fusion (kJ/mol) vaporization (kJ/mol)

sodium Na 2.6 101

chlorine Cl2 6.40 20.4

sodium chloride NaCl 28 171

water H2O 6.03 40.8

ammonia NH3 — 1.37

freon-12 CCl2F2 — 34.99

methanol CH3OH — 39.23

ethylene glycol C2H4(OH)2 — 58.8

In calculations involving molarenthalpies, we assume that thenumber of moles indicated in thechemical equation is exact (hasinfinite certainty) and so does notaffect the number of significantdigits in the answer.

LEARNING TIP

308 Chapter 5 NEL

Calorimetry of Physical ChangesSo far, you have been provided with values for molar enthalpies. How are these valuesobtained? Studying energy changes requires an isolated system, that is, one in whichneither matter nor energy can move in or out. Carefully designed experiments and pre-cise measurements are also needed. Two nested disposable polystyrene cups are a fairlyeffective calorimeter for making such measurements (Figure 1).

When we investigate energy changes we base our analysis on the law of conservationof energy: the total energy change of the chemical system is equal to the total energychange of the surroundings.

�Hsystem � � qsurroundings

ExampleWhat amount of ethylene glycol would vaporize while absorbing 200.0 kJ of heat?

Solution�H � 200.0 kJ

�Hvap � 58.8 kJ/mol (from Table 2)

n � ?

�H � n�Hvap

n � ��

�

HH

vap�

� �582.080k.0J�mkJ�

ol�

n � 3.40 mol

The amount of ethylene glycol that would vaporize is 3.40 mol.


1. Calculate the enthalpy change �H for the vaporization of 100.0 g of water at100.0°C (Table 2).

2. Ethylene glycol is used in automobile coolant systems because its aqueous solutions lower the freezing point of the coolant liquid and prevent freezing ofthe system during Canadian winters. What is the enthalpy change needed to completely vaporize 500.0 g of ethylene glycol? (See Table 2)

3. Under certain atmospheric conditions, the temperature of the surrounding air risesas a snowfall begins, because energy is released to the atmosphere as waterchanges to snow. What is the enthalpy change �H for the freezing of 1.00 t ofwater at 0.0°C to 1.00 t of snow at 0.0°C? (Recall that 1 t � 1000 kg.)

Answers

1. 227 kJ

2. 474 kJ

3. 3.4 � 105 kJ


There are three simplifying assumptions often used in calorimetry:

• no heat is transferred between the calorimeter and the outside environment;

• any heat absorbed or released by the calorimeter materials, such as thecontainer, is negligible; and

• a dilute aqueous solution is assumed to have a density and specific heatcapacity equal to that of pure water (1.00 g/mL and 4.18 J/g•°C or 4.18 kJ/kg • °C).

Section 5.2

Figure 1A simple laboratory calorimeter consists of an insulated container made oftwo nested polystyrene cups, a measured quantity of water, and a ther-mometer. The chemical system is placed in or dissolved in the water of thecalorimeter. A third cup, with a hole punched in the bottom, can beinverted and used as a lid. Energy transfers between the chemical systemand the surrounding water are monitored by measuring changes in thetemperature of the water.

In a calorimetry experiment, 7.46 g of potassium chloride is dissolved in 100.0 mL(100.0 g) of water at an initial temperature of 24.1°C. The final temperature of thesolution is 20.0°C. What is the molar enthalpy of solution of potassium chloride?

First, calculate the amount of potassium chloride.

mKCl � 7.46 g

MKCl � 74.6 g/mol

nKCl � 7.46 g� � �714m.6

og�l

�

nKCl � 0.100 mol KCl

The next step is to recognize the law of conservation of energy.

�H � q

(KCl dissolving) (calorimeter water)

By combining this with the mathematical formulas used earlier in this chapter,

�H � n�Hsol and q � mc�T,

we can derive a formula to determine the enthalpy change of potassium chloride dis-solving to form a solution:

n�Hsol � mc�T

Assuming that the dilute solution has the same physical properties as pure water, wecan now find the molar enthalpy of solution by rearranging this new equation to isolatethe quantity we wish to solve for and substituting the given information and the appro-priate constants. Note that the mass quantity we are considering is the mass of water inthe solution.

mwater � 100.0 g

cwater � 4.18 J/(g•°C)

�T � 24.1°C � 20.0°C � 4.1°C

Using Calorimetry to Find Molar Enthalpies SAMPLE problem

Chemical systemdissolved in surroundingwater

KEY EQUATION

n�Hsol � mc�T

where n and �Hsol refer tothe solute, and m, c, and�T refer to the solvent(assuming the solution hasthe same physical proper-ties as the solvent — as itwill if it is dilute).

310 Chapter 5 NEL

n�Hsol � mc�T

�Hsol(KCl) � �mc

n�T�

�

�Hsol(KCl) � 1.7 � 104 J/mol or 17 kJ/mol

The enthalpy change for each mole of potassium chloride that dissolves is 17 kJ/mol.Because the reaction is endothermic, the molar enthalpy of solution for potassiumchloride is reported as �17 kJ/mol. Note that the certainty of the final answer (two significant digits) is determined by the certainty of the temperature change, 4.1°C.

ExampleWhat mass of lithium chloride must have dissolved if the temperature of 200.0 g ofwater increased by 6.0°C? The molar enthalpy of solution of lithium chloride is �37 kJ/mol.

Solutionmwater � 200.0 g

�T � 6.0°C

�Hsol � 37 kJ/mol

cwater � 4.18 kJ/kg•°C

MLiCl � 42.4 g/mol

mLiCl � ?

n�Hsol � qwater

n�Hsol � mc�T

nLiCl � �m�H

c�

so

T

l�

nLiCl �

� 0.14 mol

mLiCl � 0.14 mol� � �412m.4

ogl�

�

mLiCl � 5.7 g

The mass of lithium chloride required to raise the temperature of the water 6.0°C is 5.7 g.

0.2000 kg� � �4k.1g�8•°

kC�J�

� � 6.0°C��

37 kJ�/mol

100.0 g� � 4.18 J/g�•°C� � 4.1°C��

0.100 mol


4. In a chemistry experiment to investigate the properties of a fertilizer, 10.0 g of urea,NH2CONH2(s), is dissolved in 150 mL of water in a simple calorimeter. A tempera-ture change from 20.4°C to 16.7°C is measured. Calculate the molar enthalpy ofsolution for the fertilizer urea.

5. A 10.0-g sample of liquid gallium metal, at its melting point, is added to 50.0 g of waterin a polystyrene calorimeter. The temperature of the water changes from 24.0°C to27.8°C as the gallium solidifies. Calculate the molar enthalpy of solidification for gallium.

Answers

4. �13.9 kJ/mol

5. �5.54 kJ/mol


Calorimetry of Chemical ChangesChemical reactions that occur in aqueous solutions can also be studied using a poly-styrene calorimeter. The chemical system usually involves aqueous reactant solutions thatare considered to be equivalent to water. The assumptions and formulas applied are iden-tical to those used in the analysis of energy changes during state changes and dissolving.

When aqueous solutions of acids and bases react, they undergo a neutralization reac-tion. For example, potassium hydroxide and hydrobromic acid solutions react to formwater and aqueous potassium bromide:

KOH(aq) � HBr(aq) → H2O(l) � KBr(aq)

The molar enthalpy of reaction for systems such as this is sometimes called the heatof neutralization, or enthalpy of neutralization.

Section 5.2

Molar Enthalpy of a ChemicalChange (p. 348)How are molar enthalpies deter-mined? Use the equations and gen-eralizations you’ve learned todetermine a value for the molarenthalpy of neutralization of sodiumhydroxide by sulfuric acid.

INVESTIGATION 5.2.1


6. List three assumptions made in student investigations involving simple calorimeters.

7. The energy involved in the process H2O(g) → H2O(l) could be described as a molarenthalpy of condensation. Describe the type of molar enthalpy that would be associ-ated with each of the following reactions:

(a) Br2(l) → Br2(g)

(b) CO2(g) → CO2(s)

(c) LiBr(s) → Li+(aq) + Br–(aq)

(d) C3H8(g) � 5 O2(g) → 3 CO2(g) + 4 H2O(l)

(e) NaOH(aq) + HCl(aq) → 2 NaCl(aq) + H2O(l)


8. In a calorimetry experiment in which you are measuring mass and temperature usingequipment available to you in your school lab, which measurements limit the certaintyof the experimental result? Explain.

9. (a) A laboratory technician adds 43.1 mL of concentrated, 11.6 mol/L hydrochloricacid to water to form 500.0 mL of dilute solution. The temperature of the solutionchanges from 19.2°C to 21.8°C. Calculate the molar enthalpy of dilution ofhydrochloric acid.

(b) What effect would there be on the calculated value for the molar enthalpy of dilu-tion if the technician accidentally used too much water so that the total volumewas actually more than 500.0 mL? Explain.

(c) The dissolving of an acid in water is a very exothermic process. Dilute acid solu-tions should always be made by adding acid to water. Explain why adding waterto acid is very dangerous.

10. In a laboratory investigation into the reaction

Ba(NO3)2(s) � K2SO4(aq) → BaSO4(s) � 2 KNO3(aq)

a researcher adds a 261-g sample of barium nitrate to 2.0 L of potassium sulfate solu-tion in a polystyrene calorimeter.

Evidence

As the barium nitrate dissolves, a precipitate is immediately formed.

T1 � 26.0°C

T2 � 29.1°C

Analysis

(a) Calculate the molar enthalpy of reaction of barium nitrate.

Answers

9. (a) �10.9 kJ/mol

10. (a) �26 kJ/mol

312 Chapter 5 NEL


1. If the molar enthalpy of combustion of ethane is �1.56MJ/mol, how much heat is produced in the burning of(a) 5.0 mol of ethane?(b) 40.0 g of ethane?

2. The molar enthalpy of solution of ammonium chloride is+14.8 kJ/mol. What would be the final temperature of asolution in which 40.0 g of ammonium chloride is added to200.0 mL of water, initially at 25°C?

3. The molar enthalpy of combustion of decane (C10H22) is–6.78 MJ/mol. What mass of decane would have to beburned in order to raise the temperature of 500.0 mL ofwater from 20.0°C to 55.0°C?

4. During sunny days, chemicals can store solar energy inhomes for later release. Certain hydrated salts dissolve in their water of hydration when heated and release heat when they solidify. For example, Glauber’s salt, Na2SO4•10 H2O(s), solidifies at 32°C, releasing 78.0 kJ/molof salt. What is the enthalpy change for the solidification of1.00 kg of Glauber’s salt used to supply energy to a home(Figure 2)?


5. In a laboratory investigation into the neutralization reaction

HNO3(aq) � KOH(s) → KNO3(aq) + H2O(l)

a researcher adds solid potassium hydroxide to nitric acidsolution in a polystyrene calorimeter.

Evaluationmass KOH � 5.2 gvolume of nitric acid solution � 200 mLT1 � 21.0°CT2 � 28.1°C

Analysis(a) Calculate the molar enthapy of neutralization of

potassium hydroxide.

6. A student noticed that chewing fast-energy dextrosetablets made her mouth feel cold. Design an investigation,including a Question, Hypothesis, Experimental Design,Materials list, and Procedure, to find out whether therereally is a temperature change.

Making Connections

7. The propane refrigerator seems to be a contradiction interms: the exothermic combustion of a hydrocarbon is usedto cool food.(a) Find out how this device functions and what changes

in matter occur in its operation.(b) Calculate enthalpy changes expected in a typical

example.


Figure 2Glauber’s salt is an ideal medium for storing solar energyduring the day and releasing it at night. Its melting point isconvenient, at 32°C, and it has a high enthalpy of fusion, so alot of energy can be stored by a small mass of salt. Tubes filledwith this salt are part of the heat system in a solar-heatedhome.


5.35.3How do scientists communicate to each other the size of enthalpy changesand determine whether they are endothermic or exothermic? Combustionreactions are often spectacular and are obviously exothermic. However,it is usually not obvious whether a chemical change will absorb or releaseenergy, so, when we are discussing thermochemical reactions, we mustindicate this information clearly. The equations we use to do this arecalled themochemical equations.

You have already seen that the value of an enthalpy change, ∆H, dependson the quantity of a substance that undergoes a change. For example,one mole of hydrogen as it burns has an enthalpy change of –285.8 kJ, andthe enthalpy change for two moles of hydrogen is twice that: –571.6 kJ.You have also learned that a sign convention identifies reactions asendothermic or exothermic:

• endothermic enthalpy changes are reported as positive values; and

• exothermic enthalpy changes are reported as negative values.

When water decomposes, the system gains energy from the surroundingsand so the molar enthalpy is reported as a positive quantity to indicate anendothermic change:

H2O(l) → H2(g) � �12

� O2(g) �Hdecomp � � 285.8 kJ/mol H2O

The law of conservation of energy implies that the reverse process (combustion ofhydrogen) has an equal and opposite energy change.

H2(g) � �12

� O2(g) → H2O(l) �Hcomb � –285.8 kJ/mol H2

The sign convention represents the change from the perspective of the chemical systemitself, not from that of the surroundings. An increase in the temperature of the sur-roundings implies a decrease in the enthalpy of the chemical system, because the changewas exothermic.

Most information about energy changes, for example, the enthalpy change that accom-panies the burning of methanol (Figure 1), comes from the experimental technique ofcalorimetry. We can communicate the energy changes, obtained from these empiricalstudies, in four different ways. Three use thermochemical equations and one uses a diagram:

• by including an energy value as a term in the thermochemical equation

e.g., CH3OH(l) + �32

� O2(g) → CO2(g) + 2 H2O(g) + 726 kJ

• by writing a chemical equation and stating its enthalpy change

e.g., CH3OH(l) + �32

� O2(g) → CO2(g) + 2 H2O(g) �H � –726 kJ

• by stating the molar enthalpy of a specific reaction

e.g., �Hcombustion or �Hc � –726 kJ/mol CH3OH

• by drawing a chemical potential energy diagram (Figure 2)

All four of these methods of expressing energy changes are equivalent and are describedin more detail as follows.

Representing Enthalpy Changes

Figure 1Hydrocarbons such as acetone burnwith a readily visible flame. Theflame produced by combustingmethanol (right) is difficult to see,and so more dangerous.

Reaction Progress

Potential Energy Diagram foran Exothermic Reaction

Ep

CH3OH(l) + O2(g)

CO2(g) + H2O(l)

∆H

Figure 2

314 Chapter 5 NEL

Method 1: Thermochemical Equations with Energy TermsYou are already familiar, from your grade 11 Chemistry course, with the first way todescribe the enthalpy change in a chemical reaction: include it as a term in a thermo-chemical equation. If a reaction is endothermic, it requires a certain quantity of energyto be supplied to the reactants. This energy (like the reactants) is “consumed” as thereaction progresses and is listed along with the reactants.

For example, in the electrolysis of water, energy is absorbed. For our purposes, SATPconditions are usually assumed for all equations.

H2O(l) + 285.8 kJ → H2(g) + �12

� O2(g)

If a reaction is exothermic, energy is released as the reaction proceeds (Figure 3) andis listed along with the products. For example, magnesium burns in oxygen as follows:

Mg(s) + �12

� O2(g) → MgO(s) + 601.6 kJ

Fractions are convenient in manythermochemical equations. Notethat these apply to fractions of

moles of substances (e.g., �32

� mol

represents 1.5 mol) rather thanfractions of actual molecules.

LEARNING TIP

Figure 3Combustion reactions are the mostfamiliar exothermic reactions. Thesearing heat produced by a burningbuilding is a formidable obstaclefacing firefighters.

Oxygen is often the reactant givena fractional coefficient in combus-tion equations because it occursas a diatomic molecule and thetotal numbers of oxygen atoms inthe products are often odd numbers.

LEARNING TIP

Write a thermochemical equation to represent the exothermic reaction thatoccurs when two moles of butane burn in excess oxygen gas. The molar enthalpyof combustion of butane is –2871 kJ/mol.

First, write the equation for the combustion of butane:

2 C4H10(g) � 13 O2(g) → 8 CO2(g) � 10 H2O(l)

Then obtain the amount of butane, n , from the balanced equation. In this case, n � 2 mol.From the problem, �Hc � –2871 kJ/mol,

�H � n�Hc

� 2 mol� � ��

128

m71ol�

kJ�

�H � –5742 kJ

The reaction is exothermic, so the energy term must be a product. Report the enthalpychange for the reaction by writing it as a product in the thermochemical equation, as follows:

2 C4H10(g) � 13 O2(g) → 8 CO2(g) � 10 H2O(l) � 5742 kJ

Writing Thermochemical Equations with Energy TermsSAMPLE problem


Method 2: Thermochemical Equations with �H ValuesA second way to describe the enthalpy change in a reaction is to write a balanced chem-ical equation and then the ∆H value beside it, making sure that �H is given the correctsign. Thus, the production of methanol from carbon monoxide and hydrogen could bewritten as:

CO(g) + 2 H2(g) → CH3OH(l) �H � –128.6 kJ

Note that the units for the enthalpy change are kilojoules (not kJ/mol), because theenthalpy change applies to the reactants and products as written, with the numbers ofmoles of reactants and products given in the equation. The same equation could bewritten as:

�12

� CO(g) + H2(g) → �12

� CH3OH(l) �H � –64.3 kJ

Section 5.3

ExampleWrite a thermochemical equation to represent the dissolving of one mole of silvernitrate in water. The molar enthalpy of solution is + 22.6 kJ/mol.

Solution

AgNO3(s) � 22.6 kJ → Ag�(aq) � NO3

�(aq)

Sulfur dioxide and oxygen react to form sulfur trioxide (Figure 4). The molarenthalpy for the combustion of sulfur dioxide, �Hcomb , in this reaction is �98.9 kJ/mol SO2. What is the enthalpy change for this reaction?

First, write the balanced chemical equation:

2 SO2(g) � O2(g) → 2 SO3(g)

Then obtain the amount of sulfur dioxide, n, from the balanced equation and use

�H � n�Hc

n � 2 mol and �Hc � �98.9 kJ/mol, so

�H � 2 mol� �

� –197.8 kJ

The enthalpy change and the reaction are

2 SO2(g) � O2(g) → 2 SO3(g) �H � �197.8 kJ

ExampleWrite a thermochemical equation, including a �H value, to represent the exothermic reac-tion between xenon gas and fluorine gas to produce solid xenon tetrafluoride, given thatthe reaction produces 251 kJ per mol of Xe reacted.

�98.9 kJ�

1 mol�

Writing Thermochemical Equations with �H Values SAMPLE problem

Figure 4Most sulfuric acid is produced inplants like this by the contactprocess, which includes twoexothermic combustion reactions.Sulfur reacts with oxygen, formingsulfur dioxide; sulfur dioxide, in contact with a catalyst, reacts withoxygen, forming sulfur trioxide.

316 Chapter 5 NEL

As previously described, the enthalpy change ∆H depends on the chemical equationas written. Therefore, if the balanced equation for the reaction is written differently, theenthalpy change should be reported differently. For example,

SO2(g) + �12

� O2(g) → SO3(g) �H � –98.9 kJ

Both this thermochemical equation and the one in the sample problem aboveagree with the empirically determined molar enthalpy for sulfur dioxide in this reaction.

�Hc � ��1

29m7.8

olkJ

�

� �–198

m.9

oklJ

�

� –98.9 kJ/mol SO2

The enthalpy changes for most reactions must be accompanied by a balanced chem-ical equation that includes the state of matter of each substance.

Method 3: Molar Enthalpies of ReactionAs you have seen in the previous section, molar enthalpies are convenient ways ofdescribing the energy changes involved in a variety of physical and chemical changes. Ineach case, one mole of a particular reactant or product is specified. For example, theenthalpy change involved in the dissolving of one mole of solute is called the molarenthalpy of solution and can be symbolized by ∆Hsol. In Table 1, the substance under con-sideration in each reaction is highlighted in red.

A molar enthalpy that is determined when the initial and final conditions of the chem-ical system are at SATP is called a standard molar enthalpy of reaction. The symbol ∆H °

xdistinguishes standard molar enthalpies from molar enthalpies, ∆Hx, which are measuredat other conditions of temperature and pressure. Standard molar enthalpies allow chemiststo create tables to compare enthalpy values, as you will see in the next two sections.

Solution

Xe(g) � 2 F2(g) → XeF4(s) �H � �251 kJ

Table 1 Some Molar Enthalpies of Reaction

Type of molar enthalpy Example of change

solution (�Hsol) NaBr(s) → Na+(aq) � Br–

(aq)

combustion (�Hcomb) CH4(g) + 2 O2(g) → CO2(g) � H2O(l)

vaporization (�Hvap) CH3OH(l) → CH3OH(g)

freezing (�Hfr) H2O(l) → H2O(s)

neutralization (�Hneut)* 2 NaOH(aq) � H2SO4(aq) → 2 Na2SO4(aq) + 2 H2O(l)

neutralization (�Hneut)* NaOH(aq) � 1/2 H2SO4(aq) → 1/2 Na2SO4(aq) � H2O(l)

formation (�Hf)** C(s) + 2 H2(g) + 1/2 O2(g) → CH3OH(l)

* Enthalpy of neutralization can be expressed per mole of either base or acid consumed.

** Molar enthalpy of formation will be discussed in more detail in Section 5.5.

molar enthalpy of reaction, �Hxthe energy change associated withthe reaction of one mole of a sub-stance (also called molar enthalpychange)

For the purposes of this text-book, tabulated values will bestandard values at 25°C, so thatmolar enthalpies will beassumed to be standard molarenthalpies. For example, thevalues for �Hc and �H °

c will beequivalent.

LEARNING TIP

standard molar enthalpy of reaction, �H°x the energy changeassociated with the reaction of onemole of a substance at 100 kPa and a specified temperature (usually 25°C)


For an exothermic reaction, the standard molar enthalpy is measured by taking intoaccount all the energy required to change the reaction system from SATP, in order to ini-tiate the reaction, and all the energy released following the reaction, as the products arecooled to SATP. For example, the standard molar enthalpy of combustion of methanol(Figure 5) is

�H °c � �726 kJ/mol CH3OH

This quantity takes into account the energy input to initiate the reaction, the burningof 1 mol of methanol in oxygen to produce 1 mol CO2(g) and 2 mol H2O(g), then theenergy released as the products are cooled to SATP.

Molar enthalpies can be used to describe reactions other than combustion, as longas the reaction is clearly described. For example, methanol is produced industrially bythe high-pressure reaction of carbon monoxide and hydrogen gases.

CO(g) � 2 H2(g) → CH3OH(l)

Chemists have determined the standard molar enthalpy of reaction for methanol inthis reaction, ∆H °

r, to be –128.6 kJ/mol CH3OH. To describe the reaction fully, we wouldwrite the thermochemical equation

CO(g) � 2 H2(g) → CH3OH(l) �H °r � –128.6 kJ/mol CH3OH

The symbol for the molar enthalpy of reaction uses the subscript “r” to refer to the reac-tion under consideration, with the stated number of moles of reactants and products.Since two moles of hydrogen are consumed as 128.6 kJ of heat are produced, the stan-dard molar enthalpy of reaction in terms of hydrogen could be described as half theabove value, or �64.3 kJ/mol H2.

Section 5.3

Figure 5Methanol burns more completelythan gasoline, producing lowerlevels of some pollutants. The tech-nology of methanol-burning vehicleswas originally developed for racingcars because methanol burns fasterthan gasoline. However, its energycontent is lower so it takes twice asmuch methanol as gasoline to drivea given distance.

The combustion of fuels is alwaysexothermic: heat is released to thesurroundings. Enthalpies of com-bustion are often called heats ofcombustion and given as absolutevalues. For example,�Hcomb(methanol) � 726 kJ/mol.

LEARNING TIP

Write an equation whose energy change is the molar enthalpy of combustion ofpropanol (C3H7OH).

Hydrocarbons such as propanol undergo combustion in air by reacting with oxygen gas toproduce carbon dioxide gas and water. Since SATP is assumed unless further informationis provided, water is produced in liquid form.

Since it is a molar enthalpy, we must write the equation for 1 mol of C3H7OH, whichrequires a fractional coefficient in front of oxygen gas.

The equation is

C3H7OH(g) � �92

� O2(g) → 3 CO2(g) + 4 H2O(l)

ExampleWrite an equation whose enthalpy change is the molar enthalpy of reaction of calciumwith hydrochloric acid to produce hydrogen gas and calcium chloride solution.

Solution

Ca(s) � 2 HCl(aq) → H2(g) � CaCl2(aq)

Describing Molar Enthalpies of Reaction SAMPLE problem

318 Chapter 5 NEL

Method 4: Potential Energy DiagramsChemists sometimes explain observed energy changes in chemical reactions in termsof chemical potential energy. This stored energy is related to the relative positions ofparticles and the strengths of the bonds between them. Potential energy is stored orreleased as the positions of the particles change, just as it is when a spring is stretched andthen released. As bonds break and re-form and the positions of atoms are altered, changesoccur in potential energy. As you have seen before, the potential energy change in thesystem is equivalent to the heat transferred to or from the surroundings.

We can visually communicate this energy transferred by using a potential energydiagram. In this theoretical description, the energy transferred during a change is rep-resented as changes in the chemical potential energy of the particles as bonds are brokenor formed.

The vertical axis on the diagram represents the potential energy of the system. Sincethe reactants are written on the left and the products on the right, the horizontal axis issometimes called a reaction coordinate or reaction progress. In an exothermic change(Figure 6(a)), the products have less potential energy than the reactants: energy is releasedto the surroundings as the products form. In an endothermic change (Figure 6(b)), theproducts have more potential energy than the reactants: energy is absorbed from thesurroundings. Neither of the axes is numbered; only the numerical change in potentialenergy (enthalpy change, ∆H) of the system is shown in the diagrams.

Potential energy diagrams can be used to describe a wide variety of chemical changesas shown in Figure 7.

potential energy diagram agraphical representation of theenergy transferred during a physicalor chemical change

Reaction Progress

Endothermic Reaction

Ep

Reaction Progress

Exothermic Reaction

Ep

products

products reactants

reactants

∆H∆H

(b)(a)

Figure 6(a) During an exothermic reaction,

the enthalpy of the systemdecreases and heat flows intothe surroundings. We observe atemperature increase in thesurroundings.

(b) During an endothermic reac-tion, heat flows from the sur-roundings into the chemicalsystem. We observe a tempera-ture decrease in the surround-ings. This corresponds to anincrease in the enthalpy of thechemical system.

Combustion of Alcohols (p. 349)Do different alcohols produce dif-ferent quantities of heat when theycombust? How do their molarenthalpies compare?

INVESTIGATION 5.3.1

Reaction Progress

Exothermic Chemical Change

Reaction Progress

Endothermic Chemical Change

Mg(s) + O2(g) H2(g) + O2(g)

MgO(s) H2O(l)

∆H ̊f = –601.6 kJ ∆H d̊ecomp = +285.8 kJEp

(kJ)Ep

(kJ)

12

12

(b)(a)

Figure 7(a) The reaction in which one mole

of magnesium oxide is formedfrom its elements is exothermic,so the reactants must have ahigher potential energy thanthe product.

(b) The reaction in which waterdecomposes to form hydrogenand oxygen gases isendothermic, so the reactant(water) must have a lowerpotential energy than the prod-ucts (hydrogen and oxygen).


Section 5.3

4 Potential energy diagram for cellular respiration:

Molar enthalpy for photosynthesis:∆Hphotosynthesis = +2802.7 kJ/mol glucose

6 CO2(g) + 6 H2O(l) + 2802.7 kJ C6H12O6(s) + 6 O2(g)

6 CO2(g) + 6 H2O(l) C6H12O6(s) + 6 O2(g) ∆H = +2802.7 kJ2 C6H12O6(s) + 6 O2(g) 6 CO2(g) + 6 H20(l) ∆H = –2802.7 kJ

1 C6H12O6(s) + 6 O2(g) 6 CO2(g) + 6 H2O(l) + 2802.7 kJ

Potential energy diagram for photosynthesis:

3

4

2

1

3Molar enthalpy for cellular respiration:∆Hrespiration = –2802.7 kJ/mol glucose

Reaction Progress

∆H = –2802.7 kJEp

(kJ)Ep

(kJ)

6CO2(g) + 6H2O(l)

Reaction Progress

∆H = +2802.7 kJ

6CO2(g) + 6H2O(l)

C6H12O6(s) + 6O2(g)C6H12O6(s) + 6O2(g)

Cellular Respiration of Glucose Photosynthesis

Figure 8Energy is transformed in cellularrespiration and in photosynthesis.Cellular respiration, a series ofexothermic reactions, is thebreakdown of foodstuffs, such asglucose, that takes place withincells. Photosynthesis, a series ofendothermic reactions, is theprocess by which green plantsuse light energy to make glucosefrom carbon dioxide and water.


1. Communicate the enthalpy change by using the four methods described in this sec-tion for each of the following chemical reactions. Assume standard conditions (SATP)for the measurements of initial and final states.(a) The formation of acetylene (ethyne, C2H2) fuel from solid carbon and gaseous

hydrogen (�H° � +228 kJ/mol acetylene)(b) The simple decomposition of aluminum oxide powder (�H° � +1676 kJ/mol

aluminum oxide)(c) The complete combustion of pure carbon fuel (�H° � �393.5 kJ/mol CO2)

2. For each of the following balanced chemical equations and enthalpy changes, writethe symbol and calculate the molar enthalpy of combustion for the substance thatreacts with oxygen.

(a) 2H2(g) � O2(g) → 2H2O(g) �H° � �483.6 kJ

(b) 4 NH3(g) � 7O2(g) → 4 NO2(g) � 6 H2O(g) � 1134.4 kJ

(c) 2N2(g) � O2(g) � 163.2 kJ → 2N2O(g)

(d) 3 Fe(s) � 2O2(g) → Fe3O4(s) �H° � �1118.4 kJ

3. The neutralization of a strong acid and a strong base is an exothermic process.

H2SO4(aq) � 2 NaOH(aq) → Na2SO4(aq) � 2 H2O(l) � 114 kJ

(a) What is the enthalpy change for this reaction? (b) Write this thermochemical equation, using the �H°x to produce H2O(g) notation.(c) Calculate the molar enthalpy of neutralization in kJ/mol sulfuric acid.(d) Calculate the molar enthalpy of neutralization in kJ/mol sodium hydroxide.

Figure 8 uses the chemical reactions for photosynthesis and respiration to summarizethe four methods of communicating the molar enthalpy or change in enthalpy of achemical reaction. Each method has advantages and disadvantages. To best communi-cate energy changes in chemical reactions, you should learn all four methods.

Communicating Enthalpy ChangesSUMMARY

Answers

2. (a) �241.8 kJ/mol H2

(b) �283.6 kJ/mol NH3

(c) �81.6 kJ/mol N2

(d) �372.8 kJ/mol Fe

3. (c) �114 kJ/mol H2SO4

(d) �57 kJ/mol NaOH

320 Chapter 5 NEL

4. The standard molar enthalpy of combustion for hydrogen to produce H20(g) is –241.8 kJ/mol.The standard molar enthalpy of decomposition for water vapour is 241.8 kJ/mol.(a) Write both chemical equations as thermochemical equations with a �H° value.(b) How does the enthalpy change for the combustion of hydrogen compare with the

enthalpy change for the simple decomposition of water vapour? Suggest a gen-eralization to include all pairs of chemical equations that are the reverse of oneanother.

5. Classify the reactions in Figure 9 as endothermic or exothermic. Explain your classifi-cation.

Figure 9


1. Draw a potential energy diagram with appropriately labelledaxes to represent(a) the exothermic combustion of octane (�H° � –5.47 MJ)(b) the endothermic formation of diborane (B2H6) from its

elements (�H° � +36 kJ)

2. Translate each of the molar enthalpies given below into abalanced thermochemical equation, including the enthalpychange, �H.(a) The enthalpy change for the reaction in which solid

magnesium hydroxide is formed from its elements atSATP is �925 kJ/mol.

(b) The standard molar enthalpy of combustion for pen-tane, C5H12, is �2018 kJ/mol.

(c) The standard molar enthalpy of simple decomposition,�H °

decomp, for nickel(II) oxide to its elements is 240kJ/mol.

3. For each of the following reactions, write a thermochemicalequation including the energy as a term in the equation.(a) Butane obtained from

natural gas is used as a fuel in lighters (Figure 10). Thestandard molar enthalpy of combustion for butane is�2.86 MJ/mol.

(b) Carbon exists in two different forms, graphite and dia-mond, which have very different crystal forms. The molarenthalpy of transition of graphite to diamond is 2 kJ.

(c) Ethanol, obtained from the fermentation of corn andother plant products, can be added to gasoline to actas a cheaper alternative. The standard molar enthalpyof combustion for ethanol is �1.28 MJ/mol.


4. A calorimeter is used to determine the enthalpy changeinvolved in the combustion of eicosane (C20H42), a solidhydrocarbon found in candle wax. Complete the Analysisand Evaluation sections of the investigation report.

Experimental Design

A candle is placed under a copper can containing water,and a sample of candle wax (eicosane) is burned such thatthe heat from the burning is transferred to the calorimeter.

Figure 10Butane is the fuel used in lighters.

Reaction Progress

Ep

Reaction Progress

Ep∆H ∆H

(a) (b)


Section 5.3

Evidence Analysis(a) Calculate the molar enthalpy of combustion of

eicosane.(b) Was the reaction exothermic or endothermic? Explain.(c) Write two thermochemical equations to represent the

combustion of eicosane: using an energy term in theequation, and using a �H value.

Evaluation(d) If the accepted value for the molar enthalpy of combus-

tion of eicosane is �13.3 MJ, calculate the percentageerror of this procedure.

Table 2 Observations When Burning Candle Wax

Quantity Measurement

mass of water, m 200.0 g

specific heat capacity of 0.385 J/(g•°C)copper, ccopper

mass of copper can, mcopper 50.0 g

initial temperature of calorimeter, T1 21.0°C

final temperature of calorimeter, T2 76.0°C

initial mass of candle wax, mwax,1 8.567 g

final mass of candle wax, mwax,2 7.357 g

322 Chapter 5 NEL

5.45.4 Calorimetry is an accurate technique for determining enthalpychanges, but how do chemists deal with chemical systems thatcannot be analyzed using this technique? For example, the rustingof iron (Figure 1) is extremely slow and, therefore, the resultingtemperature change would be too small to be measured using aconventional calorimeter. Similarly, the reaction to producecarbon monoxide from its elements is impossible to measurewith a calorimeter because the combustion of carbon producesboth carbon dioxide and carbon monoxide simultaneously.

Chemists have devised a number of methods to deal with thisproblem. These methods are based on the principle that net (oroverall) changes in some properties of a system are independentof the way the system changes from the initial state to the finalstate. An analogy for this concept is shown in Figure 2. The netvertical distance that the bricks rise is the same whether they goup in one stage or in two stages. The same principle applies to

enthalpy changes: If a set of reactions occurs in different steps but the initial reactantsand final products are the same, the overall enthalpy change is the same (Figure 3).

Hess’s Law of Additivity of Reaction Enthalpies

Figure 1Some reactions are too slow to bestudied experimentally.

Figure 2In this illustration, bricks on a con-struction site are being moved fromthe ground up to the second floor,but there are two different pathsthat the bricks could follow. In onepath, they could move from theground up to the third floor andthen be carried down to the secondfloor. In the other path, they wouldbe carried up to the second floor ina single step. In both cases, theoverall change in position — onefloor up — is the same.


Predicting �H Using Hess’s LawBased on experimental measurements of enthalpy changes, the Swiss chemist G. H. Hesssuggested that there is a mathematical relationship among a series of reactions leadingfrom a set of reactants to a set of products. This generalization has been tested in manyexperiments and is now accepted as the law of additivity of reaction enthalpies, alsoknown as

Another way to state Hess’s law is: If two or more equations with known enthalpychanges can be added together to form a new “target” equation, then their enthalpychanges may be similarly added together to yield the enthalpy change of the target equa-tion.

Hess’s law can also be written as an equation using the uppercase Greek letter

� (pronounced “sigma”) to mean “the sum of.”

�Htarget � �H1 � �H2 � �H3 � …

or

Hess’s discovery allowed chemists to determine the enthalpy change of a reactionwithout direct calorimetry, using two familiar rules for chemical equations and enthalpychanges:

• If a chemical equation is reversed, then the sign of ∆H changes.

• If the coefficients of a chemical equation are altered by multiplying or dividingby a constant factor, then the ∆H is altered in the same way.

Section 5.4

Reaction Progress

Ep

Potential Energy Diagram Showing Additive Enthalpy Changes

N2 and O2

NO2

NO

+90 kJ

–56 kJ

+34 kJ

Figure 3In this potential energy diagram,nitrogen gas and oxygen gas com-bine to form nitrogen dioxide, butthere are two different paths toreach the products. In one path,nitrogen (N2) and oxygen (O2) gasesreact to form nitrogen monoxide(NO), a reaction for which �H � +90 kJ. Then, nitrogenmonoxide and more oxygen react toform nitrogen dioxide (NO2) gas, areaction for which �H � �56 kJ. Inthe other path, nitrogen (N2) andoxygen (O2) gases react directly toform nitrogen dioxide (NO2) gas. Inboth cases, the overall enthalpychange, �H � � 34 kJ, is the same.

Hess’s LawThe value of the �H for any reaction that can be written insteps equals the sum of the values of �H for each of theindividual steps.

�Htarget � ��Hknown

324 Chapter 5 NEL

1. What is the enthalpy change for the formation of two moles of nitrogenmonoxide from its elements?

N2(g) � O2(g) → 2 NO(g) �H° � ?

This reaction, which may be called the target equation to distinguish it clearly from theother equations, is difficult to study calorimetrically since the combustion of nitrogen pro-duces nitrogen dioxide as well as nitrogen monoxide. However, we can measure theenthalpy of complete combustion in excess oxygen (to nitrogen dioxide) for both nitrogenand nitrogen monoxide by calorimetry. Consider the following two known reference equa-tions:

(1) �12

� N2(g) � O2(g) → NO2(g) �H°1 � +34 kJ

(2) NO(g) � �12

� O2(g) → NO2(g) �H°2 � –56 kJ

If we work with these two equations, which may be called known equations, and thenadd them together, we obtain the chemical equation for the formation of nitrogenmonoxide.

The first term in the target equation for the formation of nitrogen monoxide is one moleof nitrogen gas. We therefore need to double equation (1) so that N2(g) will appear on thereactant side when we add the equations. However, from equation (2) we want 2 mol ofNO(g) to appear as a product, so we must reverse equation (2) and double each of itsterms (including the enthalpy change). Effectively, we have multiplied known equation (1)by +2, and multiplied known equation (2) by –2.

2 � (1): N2(g) � 2 O2(g) → 2 NO2(g) �H° � 2(+34) kJ

–2 � (2): 2 NO2(g) → 2 NO(g) � O2(g) �H° � –2(–56) kJ

Note that the sign of the enthalpy change in equation (2) will change, since the equationhas been reversed.

Now add the reactants, products, and enthalpy changes to obtain a net reaction equa-tion. Note that 2 NO2(g) can be cancelled because it appears on both sides of the netequation. Similarly, O2(g) can be cancelled from each side of the equation, yielding thetarget equation:

N2(g) � 2� O2(g) + 2 NO�2(g) → 2 NO�2(g) � 2 NO(g) + O�2(g)

or N2(g) � O2(g) → 2 NO(g)

Now we can apply Hess’s law: If the known equations can be added together to form thetarget equation, then their enthalpy changes can be added together.

�H° � (2 � 34) kJ + (–2 � (–56)) kJ

� �68 kJ � 112 kJ

�H° � +180 kJ

The enthalpy change for the formation of two moles of nitrogen monoxide from its elements is 180 kJ.

When manipulating the known equations, you should check the target equation andplan ahead to ensure that the substances end up on the correct sides and in the correctamounts.

Using Hess’s Law to Find �HSAMPLE problem

Generally, a subscript on a �Hvalue indicates a molar enthalpyvalue, expressed in kJ/mol. The“known” equations in Hess’s lawproblems are exceptions. The sub-script is used as a convenience indistinguishing equations fromeach other and the units of the�Hn values are kilojoules.

LEARNING TIP


Section 5.4

2. What is the enthalpy change for the formation of one mole of butane ( C4H10 )gas from its elements? The reaction is:

4 C(s) + 5 H2(g) → C4H10(g) �H° � ?

The following known equations, determined by calorimetry, are provided:

(1) C4H10(g) + �123� O2(g) → 4 CO2(g) + 5 H2O(g) �H°1 � �2657.4 kJ

(2) C(s) + O2(g) → CO2(g) �H°2 � �393.5 kJ

(3) 2 H2(g) + O2(g) → 2 H2O(g) �H°3 � �483.6 kJ

Reversing known equation (1), which will require multiplying its �H by �1, will makeC4H10(g) a product; multiplying known equation (2) by 4 will provide the required amountof C(s) reactant; and multiplying known equation (3) by 5/2 will provide the requiredamount of H2(g) reactant. Cancellation when the equations are added will determinewhether the required amount of O2(g) remains.

�1 � (1): 4 CO2(g) + 5 H2O(g) → C4H10(g) � �123� O2(g)

�H° � �1(�657.4) kJ

4 � (2): 4 C(s) � 4 O2(g) → 4 CO2(g) �H° � 4(�393.5) kJ

�52

� � (3): 5 H2(g) � �52

� O2(g) → 5 H2O(g) �H° � �52

�(�483.6) kJ

4 CO�2(g) � 5 H2O�(g) + 4 C(s) � �123� O�2(g) � 5 H2(g) → C4H10(g) � �

123� O�2(g)

+ 4 CO�2(g) � 5 H2O�(g)

or 4 C(s) � 5 H2(g) → C4H10(g)

If the known equations can be added together to form the target equation, then theirenthalpy changes can be added together. In this case,

�H°total � (+2657.4) + (� 1574.0) + (� 1209.0) kJ

�H°total � �125.6 kJ

The enthalpy change for the formation of one mole of butane is �125.6 kJ.

ExampleDetermine the enthalpy change involved in the formation of two moles of liquid propanol.

6 C(s) � 8 H2(g) � O2(g) → 2 C3H7OH(l)

The standard enthalpies of combustion of propanol, carbon, and hydrogen gas at SATPare �2008, �394, and �286 kJ/mol, respectively.

SolutionThe known equations are

(1) C3H7OH(l) � �92

� O2(g) → 3 CO2(g) � 4 H2O(l) �H°1 � –2008 kJ

(2) C(s) � O2(g) → CO2(g) �H°2 � –394 kJ

(3) H2(g) + �12

� O2(g) → H2O(l) �H°3 � –286 kJ

326 Chapter 5 NEL

�2 � (1): 6 CO2(g) � 8 H2O(l) → 2 C3H7OH(l) � 9 O2(g) �H° � �2(�2008 kJ)

6 � (2): 6 C(s) � 6 O2(g) → 6 CO2(g) �H° � 6(�394 kJ)

8 � (3): 8 H2(g) � 4 O2(g) → 8 H2O(l) �H° � 8(�286 kJ)

6 C(s) � 8 H2(g) � O2(g) → 2 C3H7OH(l) �H° � –636 kJ

The enthalpy change involved in the formation of propanol is �636 kJ.


1. The enthalpy changes for the formation of aluminum oxide and iron(III) oxide fromtheir elements are:

(1) 2 Al(s) � �32

� O2(g) → Al2O3(s) �H°1 � –1675.7 kJ

(2) 2 Fe(s) � �32

� O2(g) → Fe2O3(s) �H°2 � –824.2 kJ

Calculate the enthalpy change for the following target reaction.

Fe2O3(s) � 2 Al(s) → Al2O3(s) � 2 Fe(s) �H° � ?

2. Coal gasification converts coal into a combustible mixture of carbon monoxide andhydrogen, called coal gas (Figure 4), in a gasifier.

H2O(g) � C(s) → CO(g) � H2(g) �H° � ?

Calculate the standard enthalpy change for this reaction from the following chem-ical equations and enthalpy changes.

(1) 2 C(s) � O2(g) → 2 CO(g) �H°1 � �221.0 kJ

(2) 2 H2(g) � O2(g) → 2 H2O(g) �H°2 � �483.6 kJ

Figure 4Electric power generating stationsthat use coal as a fuel are only30% to 40% efficient. Coal gasifi-cation and combustion of the coalgas provide one alternative toburning coal. Efficiency isimproved by using both a com-bustion turbine and a steam tur-bine to produce electricity.

mineralslag

ash andsulfur

removal

powerout

powerout

steam

gasifier

oxygen

coalslurry

coalgas

boiler water

generator generator

coal gascombustionturbine

heat recoverysteam generator

to exhauststack

mixed withwater

pulverized coal

Answers

1. �851.5 kJ

2. 131.3 kJ

3. �524.8 kJ


Multistep Energy CalculationsIn practice, energy calculations rarely involve only a single-step calculation of heat orenthalpy change. Several energy calculations might be required, involving a combinationof energy change definitions such as

• heat flows, q � mc∆T

• enthalpy changes, ∆H � n∆Hr

• Hess’s law, ∆Htarget � �∆Hknown

In these multi-step problems, ∆H is often found by using standard molar enthalpies orHess’s law and then equated to the transfer of heat, q. As shown in the following sampleproblem, if we know the enthalpy change of a reaction and the quantity of reactant orproduct, we can predict how much energy will be absorbed or released.

Section 5.4

3. The coal gas described in the previous question can be used as a fuel, for example,in a combustion turbine.

CO(g) � H2(g) � O2(g) → CO2(g)� H2O(g) �H° � ?

Predict the change in enthalpy for this combustion reaction from the followinginformation.

(1) 2 C(s) � O2(g) → 2 CO(g) �H°1 � –221.0 kJ

(2) C(s) � O2(g) → CO2(g) �H°2 � –393.5 kJ

(3) 2 H2(g) � O2(g) → 2 H2O(g) �H°3 � –483.6 kJ

Hess’s Law (p. 351)Use calorimetry to determine yourown “known” equations and usethem to calculate the molarenthalpy of combustion ofmagnesium.

INVESTIGATION 5.4.1

In the Solvay process for the production of sodium carbonate (or washing soda),one step is the endothermic decomposition of sodium hydrogen carbonate:

2 NaHCO3(s) � 129.2 kJ → Na2CO3(s) � CO2(g) � H2O(g)

What quantity of chemical energy, �H, is required to decompose 100.0 kg ofsodium hydrogen carbonate?

First, calculate the energy absorbed per mole of NaHCO3, that is, the molar enthalpy ofreaction with respect to sodium hydrogen carbonate.

�H � n�Hr

�Hr � ��

nH�

� �1229m.2oklJ

�

�Hr � 64.6 kJ/mol

This means that 64.6 kJ of energy is required for every mole of NaHCO3 decomposed.Converting 100.0 kg to an amount in moles and multiplying by the molar enthalpy will giveus the required enthalpy change, �H, for the equation.

Solving Multistep Enthalpy Problems SAMPLE problem

328 Chapter 5 NEL

nNaHCO3� 100.0 kg� � �

814.

m01

olg�

�

� 1.190 kmol

�H � n�Hr

� 1.190 kmol� � �614

m.6

okl�J

�

�H � 76.9 MJ

The decomposition of 100 kg of sodium hydrogen carbonate requires 76.9 MJ of energy.

ExampleHow much energy can be obtained from the roasting of 50.0 kg of zinc sulfide ore?

ZnS(s) � �32

� O2(g) → ZnO(s) � SO2(g)

You are given the following thermochemical equations.

(1) ZnO(s) → Zn(s) � �12

� O2(g) �H°1 � 350.5 kJ

(2) S(s) � O2(g) → SO2(g) �H°2 � �296.8 kJ

(3) ZnS(s) → Zn(s) � S(s) �H°3 � 206.0 kJ

Solution

MZnS � 97.44 g/mol

�1 � (1): Zn(s) � �12

� O2(g) → ZnO(s) �H° � �1(350.5 kJ)

1 � (2): S(s) � O2(g) → SO2(g) �H° � 1(�296.8 kJ)

1 � (3): ZnS(s) → Zn(s) � S(s) �H° � 1(206.0 kJ)

_____________________________________________________________________

ZnS(s) � �32

� O2(g) → ZnO(s) � SO2(g) �H° � �441.3 kJ

According to Hess’s law, 441.3 kJ of energy can be obtained from the roasting of 1 mol ofZnS for which reaction �H°r � �441.3 kJ/mol.

nZnS � 50.0 kg� � �917.

m44

olg�

�

� 513 mol

�H° � nZnS�H°r� 513 mol� �

�H° � �2.26 � 105 kJ or �226 MJ

According to Hess’s law, 226 MJ of energy can be obtained from the roasting of 50.0 kgof zinc sulfide ore.

(�441.3 kJ)��

1 mol�


Section 5.4


4. Ethyne gas may be reduced by reaction with hydrogen gas to form ethane gas inthe following reduction reaction:

C2H2(g) � 2 H2(g) → C2H6(g)

Predict the enthalpy change for the reduction of 200 g of ethyne, using the fol-lowing information.

(1) C2H2(g) � �52

� O2(g) → 2 CO2(g) � H2O(l) �H°1 � �1299 kJ

(2) H2 � �12

� O2(g) → H2O(l) �H°2 � �286 kJ

(3) C2H6(g) + �72

� O2(g) → 2 CO2(g) � 3 H2O(l) �H°3 � �1560 kJ

5. As an alternative to combustion of coal gas described earlier in this section, coalgas can undergo a process called methanation.

3 H2(g) � CO(g) → CH4(g) � H2O(g) �H � ?

Determine the enthalpy change involved in the reaction of 300 g of carbonmonoxide in this methanation reaction, using the following reference equationsand enthalpy changes.

(1) 2 H2(g) � O2(g) → 2 H2O(g) �H°1 � �483.6 kJ

(2) 2 C(s) + O2(g) → 2 CO(g) �H°2 � �221.0 kJ

(3) CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g) �H°3 � �802.7 kJ

(4) C(s) + O2(g) → CO2(g) �H°4 � �393.5 kJ

Answers

4. �2.39 MJ

5. �2.20 MJ

330 Chapter 5 NEL


1. (a) Write three balanced thermochemical equations torepresent the combustions of one mole each of octane,hydrogen, and carbon, given that their molar enthalpiesof combustion are, respectively, –5.47 MJ, –285.8 kJ,and –393.5 kJ/mol.

(b) Use Hess’s law to predict the enthalpy change for theformation of octane from its elements.

8 C(s) � 9 H2(g) → C8H18(l) �H � ?

2. Predict the enthalpy change for the reaction

HCl(g) + NaNO2(s) → HNO2 (g) + NaCl(s)

using the following information:

(1) 2 NaCl � H2O → 2 HCl � Na2O �H°1 � 507 kJ

(2) NO � NO2 + Na2O → 2 NaNO2 �H°2 � –427 kJ

(3) NO � NO2 → N2O + O2 �H°3 � –43 kJ

(4) 2 HNO2 → N2O + O2 + H2O �H°4 � 34 kJ

3. Bacteria sour wines and beers by converting ethanol(C2H5OH) into acetic acid (CH3COOH). The reaction is

C2H5OH � O2 → CH3COOH � H2O

The molar enthalpies of combustion of ethanol and aceticacid are, respectively, �1367 kJ/mol and �875 kJ/mol.Write thermochemical equations for the combustions, anduse Hess’s law to determine the enthalpy change for theconversion of ethanol to acetic acid.


4. A series of calorimetric experiments is perfomed to testHess’s law. Complete the Experimental Design, Prediction,and Analysis sections of the investigation report.

Question

Can Hess’s law be verified experimentally by combiningenthalpies of reaction?

Experimental Design

Three calorimetry experiments are performed, with thechoice of chemical systems such that the enthalpy changesof two of the reactions should equal the enthalpy change ofthe third. The three thermochemical reactions are:

(1) HBr(aq) � KOH(aq) → H2O(l) + KBr(aq) �H1 � ? kJ

(2) KOH(s) → KOH(aq) �H2 � ? kJ

(3) KOH(s) � HBr(aq) → H2O(l) � KBr(aq) �H3 � ? kJ

(a) Use Hess’s law to show how two of the thermochem-ical equations can be added together to yield the thirdthermochemical equation.

Evidence

See Table 1.

Analysis(b) Use the experimental values to calculate the enthalpy

change in each system.

Evaluation(c) Calculate a percentage error in the experiment, given

that the �H for one equation should equal exactly thesum of the other two.

Table 1 Observations for Hess’s Law Investigation

Observation Experiment 1 Experiment 2 Experiment 3

quantity of 100.0 mL of 5.61 g KOH(s) 5.61 g KOH(s)reactant 1 1.00 mol/L KOH(aq)

quantity of 100.0 mL of N/A 200.0 mL ofreactant 2 1.00 mol/L HBr(aq) 0.50 mol/L HBr(aq)

initial temperature 20.0°C 20.0°C 20.0°C

final temperature 22.5°C 24.1°C 26.7°C


5.55.5Calorimetry and Hess’s law are two ways of determining enthalpies of reaction. A thirdmethod uses tabulated enthalpy changes (standard enthalpies of formation) for a spe-cial set of reactions called formation reactions, in which compounds are formed fromtheir elements. For example, the formation reaction and standard enthalpy of formationfor carbon dioxide are:

C(s) + O2(g) → CO2(g) �H f̊ � �393.5 kJ/mol

Both the elements on the left side of the equation are in their standard states — theirmost stable form at SATP (25°C and 100 kPa). Note also that the units of standardenthalpies of formation are kJ/mol because they are always stated for that quantity of sub-stance.

Writing Formation EquationsFormation equations are always written for one mole of a particular product, whichmay be in any state or form, but the reactant elements must be in their standard states.For example, the standard states of most metals are monatomic solids (Mg(s), Ca(s), Fe(s),Au(s), Na(s)), some nonmetals are diatomic gases (N2(g), O2(g), H2(g)), and the halogenfamily shows a variety of states (F2(g), Cl2(g), Br2(l), I2(s)). The periodic table at the backof this text identifies the states of elements.

Standard Enthalpies of Formation

Although the name “standardenthalpies of formation” does notinclude the word molar, it is alwaysa quantity of energy per mole.

LEARNING TIP

standard enthalpy of formationthe quantity of energy associatedwith the formation of one mole of asubstance from its elements in theirstandard states

Step 1: Write one mole of product in the state that has been specified.

Step 2: Write the reactant elements in their standard states.

Step 3: Choose equation coefficients for the reactants to give a balanced equa-tion yielding one mole of product.

Writing Formation EquationsSUMMARY

Write the formation equation for liquid ethanol.

Start with one mole of product.

C2H5OH(l)

Write the reactant elements in their standard states.

C(s) � H2(g) � O2(g) → C2H5OH(l)

Balance the equation to yield one mole of product.

2 C(s) � 3 H2(g) � �12

� O2(g) → C2H5OH(l)

Writing Formation Equations SAMPLE problem

The standard state of most ele-ments in the periodic table is solid.There are five common gaseouselements at SATP that form com-pounds readily: H2, O2, N2, F2, andCl2. There are only two liquid ele-ments at SATP: Hg and Br2.

LEARNING TIP

332 Chapter 5 NEL

Using Standard Enthalpies of FormationConsider the equation for the formation of hydrogen gas:

H2(g) → H2(g)

The product and reactant are the same, so there is no change in the enthalpy of thesystem. This observation can be generalized to all elements in their standard states:

Thus, the standard enthalpies of formation of, for example, Fe(s), O2(g), and Br2(l) areall zero.

Standard molar enthalpies of formation give us a means of comparing the stabilitiesof substances. For example, the element carbon exists in two solid forms at SATP: dia-mond, used in jewellery and mining drill bits; and graphite, the black substance used inpencil “leads” and composite plastics. Graphite is the more stable form of carbon atSATP, so

�Hºf(graphite) � 0 kJ/mol

Diamond is slightly less stable at SATP and has a greater potential energy than graphite(Figure 1). For the formation of diamond,

C(graphite) → C(diamond) �H ºf(diamond) � +1.9 kJ/mol

You have seen that Hess’s law may be applied to a set of known equations to find anunknown enthalpy change (Section 5.4). We can apply this problem-solving method topredict the energy changes for many reactions.

ExampleWhat is the formation equation for liquid carbonic acid?

SolutionH2(g) � C(s) � �

32

� O2(g) → H2CO3(l)


1. Write formation equations for the compounds: (a) benzene (C6H6), used as a solvent(b) potassium bromate, used in commercial bread dough(c) glucose (C6H12O6), found in soft drinks(d) magnesium hydroxide, found in antacids

�H f̊ for ElementsThe standard enthalpy of formation of an element already inits standard state is zero.

Reaction Progress

Relative Potential Energies ofGraphite and Diamond

Ep

diamond

graphite

∆H = 1.9 kJ/mol

Figure 1Graphite is the more stable form ofcarbon. The formation of diamondrequires an increase in potentialenergy.


Section 5.5

What is the thermochemical equation for the reaction of lime (calcium oxide) andwater?

We can express the target equation as

CaO(s) � H2O(l) → Ca(OH)2(s) �H � ?

Consider the following set of formation reactions for each compound in the equation, eachwith its corresponding standard enthalpy of formation. (Tables of standard enthalpies offormation are readily available, including a sample reference in Appendix C6 in this text.)Use these with Hess’s law to find the enthalpy change �H for the target equation.

(1) Ca(s) � �12

� O2(g) → CaO(s) �H1 � �634.9 kJ/mol

(2) H2(g) � �12

� O2(g) → H2O(l) �H2 � �285.8 kJ/mol

(3) Ca(s) � H2(g) � O2(g) → Ca(OH)2(s) �H3 � �986.1 kJ/mol

Manipulating and adding the equations according to Hess’s law results in a sum for thethermochemical equation

�1 � (1): Ca(s) � �12

� O2(g) → CaO(s) –1 � �H1

�1 � (2): H2(g) � �12

� O2(g) → H2O(l) –1 � �H2

1 � (3): Ca(s) � H2(g) + O2(g) → Ca(OH)2(s) 1 � �H3

___________________________________________________________________________

CaO(s) � H2O(l) → Ca(OH)2(s) �H � �H3 � (–�H2) � (–�H1)

Notice that the enthalpy change for the target equation equals the enthalpy of formationfor the products (calcium hydroxide) minus the enthalpies of formation of the reactants(calcium oxide and water). This observation can be generalized to any chemical equation:The enthalpy change for any given equation equals the sum of the enthalpies of formationof the products minus the sum of the enthalpies of formation of the reactants, or, symboli-cally

�H � �n�H°f(products) ��n�H°f(reactants)

where n represents the amount (in moles) of each particular product or reactant.Substitute our known molar enthalpies of formation into this equation:

�H � n�H °f(Ca(OH)(s)) � (n�H °f(CaO(s)) � n� H °f(H2O)(l))

� �(1 mol� � �9816m.1okl�J

�) � ((1 mol� � ��6

13m4.

o9l�kJ

�) � (1 mol� � ��2

18m5.

o8l�kJ

�)

�H � �65.4 kJ

The thermochemical equation for the slaking of lime with water is

CaO(s) � H2O(l) → Ca(OH)2(s) �H � �65.4 kJ

Using Enthalpies of Formation to Find �H SAMPLE problem

KEY EQUATION

�H � �n�H °f(products) –�n�H °f(reactants)

334 Chapter 5 NEL

Example 1The main component in natural gas used in home heating or laboratory burners ismethane. What is the molar enthalpy of combustion of methane fuel?

Solution

CH4(g) � 2 O2(g) → CO2(g) � 2 H2O(l)

�H � �n�H °f(products) � �n�H °f(reactants)

� (1 mol�� 3

19m3.

o5l�kJ

�) � 2 mol�� 2

18m5.o8l�kJ

�) � (1 mol��

174

m.4ol�kJ

� � 2 mol�� 10mkoJl�

�)

� �965.1 kJ � (�74.4 kJ)

�H � �890.7 kJ

�Hc � ��

nH� �

� �890.7 kJ/mol CH4

The molar enthalpy of combustion of methane fuel is –890.7 kJ/mol.

A variation on the application of standard enthalpies of formation to thermochemicalequations is a problem in which the enthalpy change of reaction is provided, and you areasked to find one of the �H °f values.

Example 2The standard enthalpy of combustion of benzene (C6H6(l)) to carbon dioxide and liquidwater is –3273 kJ/mol. What is the standard enthalpy of formation of benzene, given thetabulated values for carbon dioxide and liquid water (Appendix C6)?

Solution

C6H6(g) � �125� O2(g) → 6 CO2(g) � 3 H2O(l)

�H � �n�H°f(products) ��n�H°f(reactants)

�3273 kJ � (6 mol� � � 3 mol� � ��

128

m5o.8l�)kJ

�

� �1 mol � �H°f(benzene) + �125� mol� � �

10mkoJl�

��3273 kJ � �3217.5 kJ � 1 mol � �H°f(benzene)

�H°f(benzene) �

�H°f(benzene) � 56 kJ/mol

The standard enthalpy of formation of benzene is +56 kJ/mol.

�3217.5 kJ � 3273 kJ��

1 mol

�393.5 kJ��

1 mol�

�890.7 kJ��1 mol CH4

Enthalpies of combustion ofhydrocarbons generally assumeproduction of CO2(g) and H2O(l),the states of these compoundsat SATP.

LEARNING TIP

Note the importance of usingthe standard enthalpy of forma-tion appropriate to the state of asubstance. The standardenthalpy of formation of H2O(g)(�241.8 kJ/mol) is different fromthat of H2O(i) (�285.8 kJ/mol).

LEARNING TIP


Section 5.5


2. Use standard enthalpies of formation to calculate:(a) the molar enthalpy of combustion for pentane to produce carbon dioxide gas

and liquid water;(b) the enthalpy change that accompanies the reaction between solid iron(III)

oxide and carbon monoxide gas to produce solid iron metal and carbondioxide gas.

3. The standard enthalpy of combustion of liquid cyclohexane to carbon dioxide andliquid water is –3824 kJ/mol. What is the standard enthalpy of formation of cyclo-hexane (C6H12(l))?

4. Methane, the major component of natural gas, is used as a source of hydrogen gasto produce ammonia. Ammonia is used as a fertilizer and a refrigerant, and is usedto manufacture fertilizers, plastics, cleaning agents, and prescription drugs. Thefollowing questions refer to some of the chemical reactions of these processes. Foreach of these equations, use standard enthalpies of formation to calculate �H:(a) The first step in the production of ammonia is the reaction of methane with

steam, using a nickel catalyst.

NiCH4(g) � H2O(g) → CO(g) � 3 H2(g)

(b) The second step of this process is the further reaction of water with carbonmonoxide to produce more hydrogen. Both iron and zinc–copper catalysts areused.

Fe, Zn � Cu

CO(g) � H2O(g) → CO2(g) � H2(g)

(c) After the carbon dioxide gas is removed by dissolving it in water, the hydrogenreacts with nitrogen in the air to form ammonia.

N2(g) + 3 H2(g) → 2 NH3(g)

5. Nitric acid, required in the production of nitrate fertilizers, is produced fromammonia by the Ostwald process. Use standard enthalpies of formation to calcu-late the enthalpy changes in each of the following systems.

(a) 4 NH3(g) � 5 O2(g) → 4 NO(g) � 6 H2O(g)

(b) 2 NO(g) + O2(g) → 2 NO2(g)

(c) 3 NO2(g) � H2O(l) → 2 HNO3(l) + NO(g)

Making Connections

6. Energy is used in the manufacture of fertilizers, to grow crops. We then extractfood energy from these crops.(a) Trace the energy path through the various steps in this process.(b) If more thermal energy is put into the process than food energy is gained from

the process, should we abandon the practice of manufacturing fertilizers?Discuss.

Answers

2. (a) �3509 kJ

(b) �24.8 kJ

3. �252 kJ/mol

4. (a) 249.7 kJ

(b) 2.8 kJ

(c) �91.8 kJ

5. (a) �906.4 kJ

(b) �114.2 kJ

(c) �71.8 kJ

336 Chapter 5 NEL

Multistep Energy Calculations Using Standard Enthalpies of FormationChemical engineers frequently need to do calculations in which they determine the heatsproduced by an internal-combustion engine. Such calculations involve bringing togethermany of the problem-solving skills that you are developing. In Section 3.4 you learnedhow to solve multistep problems where enthalpy changes, heats transferred, and massesof reactants were interrelated. Two key relationships that you applied were

1. enthalpy change in the system � heat transferred to/from the surroundings

�H � q

and

2. �H � n�Hr

The following sample problem illustrates a situation involving both a multistepproblem approach and the technique of referring to standard enthalpies of formationintroduced earlier in this section.

When octane burns in an automobile engine, heat is released to the air and to themetal in the car engine, but a significant portion is absorbed by the liquid in thecooling system—an aqueous solution of ethylene glycol. What mass of octane iscompletely burned to cause the heating of 20.0 kg of aqueous ethylene glycolautomobile coolant from 10°C to 70°C? The specific heat capacity of the aqueousethylene glycol is 3.5 J/(g •°C). Assume water is produced as a gas and that all theheat flows into the coolant.

First, write and balance the combustion equation for octane. To simplify later calculations,write the equation so there is 1 mol of octane:

C8H18(g) � �225� O2(g) → 8 CO2(g) � 9 H2O(g)

Use a reference (such as Appendix C6) to find the standard enthalpies of formation for theproducts and reactants:

�H°f (CO2(g))� �393.5 kJ/mol �H°f (C8H18(g))� �250.1 kJ/mol

�H°f (H2O(g))� �241.8 kJ/mol �H°f (O2(g))� 0.0 kJ/mol

Next, use the coefficients from the combustion equation and the standard molarenthalpies to calculate the molar enthalpy of combustion of octane:

�H � �n�H°f(products) � �n�H °f(reactants)

� (8 mol � �H °f (CO2(g))� 9 mol � �H °f (H2O(g)))

� �2 mol � �H °f (C8H18(g)) � �225� mol � �H °f (O2(g))�

�H � �8 mol� � ��3

19m3.

o5l�kJ

� � 9 mol� � ��2

14m1.8

ol�kJ

�� 1 mol� � �

�215m0.

o1l�kJ

� � �225� mol� � �

10mkoJl�

��H � �5074.1 kJ

Note that if you check tabulated values, you will find a listing of �5471 kJ/mol foroctane, because the standard reaction is for H2O(l), not H2O(g).

Solving Multistep Problems Using Standard Enthalpies of FormationSAMPLE problem


Section 5.5

Next, we assume that the enthalpy change in the reaction in the engine equals the heatflow into the aqueous ethylene glycol coolant, or

�Hoctane � qcoolant

n�Hc � mc�T

Rearrange to solve for the required amount of octane, noctane:

noctane � �m�

cH�

c

T�

Substitute the givens from the problem and the calculated value of �H c:

mcoolant � 20.0 kg

�T � 70°C � (�10°C) � 80°C

ccoolant � 3.5 J/(g•°C)

noctane �

20.0 k�g� � � 80°C�

� 1.1 mol

To find the required mass of octane, convert the amount into mass, using the molar massof octane (114.26 g/mol):

moctane � 1.1 mol� � �1114m.26

ol�g

�

moctane � 0.13 kg

If you are well practised in this technique, you may want to do the final steps in one cal-culation. Since

noctane � �M

mo

o

c

c

t

t

a

a

n

n

e

e�

we can rewrite

noctane � �m�

cH�

c

T�

as

moctane �

�

20.0 kg � � 80°C � �1114m.26

ol�g

�

moctane � 0.13 kg

According to the molar enthalpy of formation method and the law of conservation ofenergy, the mass of octane required is 0.13 kg.

ExampleOne way to heat water in a home or cottage is to burn propane. If 3.20 g of propane burns,what temperature change will be observed if all of the heat from combustion transfersinto 4.0 kg of water?

5074.1 k�J��

1 mol�

3.5 J��g�•°C

mcoolant ccoolant �TMoctane��Hc(octane)

5074.1 k�J��1 mol

3.5 J��g�•°C�

338 Chapter 5 NEL

Solution

C3H8(g) � 5 O2(g) → 3 CO2(g) � 4 H2O(l)

�H °f (CO2(g) � �393.5 kJ/mol

�H °f (H2O(l)) � �285.8 kJ/mol

�H °f (C3H8(g)) � �104.7 kJ/mol

�H °f (O2(g) � 0.0 kJ/mol

mpropane � 3.20 g

mH2O � 4.0 kg

cH2O � 4.18 J/(g•°C)

The enthalpy of change for the reaction is:

�H � �n�H°f(products) � �n�H °f(reactants)

�H � �3 mol� � � 4 mol� � �� 1 mol� � � 5 mol� � �

�H � �2219 kJ

Therefore, the molar enthalpy of combustion of propane is

�Hc(propane) � 2219 kJ/mol

�Hc(propane) � qwater

n�Hc � mc�T

�T � �n

m

�H

cc

�

��M

m

pr

p

op

ro

a

p

n

a

e

n

me�

w

H

ate

c

rc�

�

�T � 9.6°C

The temperature change of the water is 9.6°C.

3.20 g� � �2121

m9

ok�l�J�

�

��

�414m.11

og�l�� 4.0 k�g� � �

4g�.1•°8CJ�

�

0.0 kJ�1 mol�

�104.7 kJ��

1 mol�

�285.8 kJ��

1 mol��393.5 kJ��

1 mol�

PracticeMaking Connections

7. Ammonium nitrate fertilizer is produced by the reaction of ammonia with nitric acid:

NH3(g) � HNO3(l) → NH4NO3(s)

Ammonium nitrate is one of the most important fertilizers for increasing crop yields(Figure 2).(a) Use standard enthalpies of formation to calculate the standard enthalpy

change of the reaction used to produce ammonium nitrate.

Figure 2The production of canola cropsare dependent on the use of fer-tilizers such as ammonium nitrate.

Specific heat capacities may beexpressed in various units forconvenience. For example, thespecific heat capacity of water is4.18 J/(g•°C) (convenient for astudent lab investigation) or4.18 kJ/(kg•°C) (e.g., in an auto-mobile engine) or4.18 MJ/(Mg•°C) (e.g., in powerplants).

LEARNING TIP


Section 5.5

(b) Sketch a potential energy diagram for the reaction of ammonia and nitric acid.(c) Calculate the heat that would be produced or absorbed in the production of

50 T of ammonium nitrate.

8. Coal is a major energy source for electricity, of which industry is the largest user(Figure 3). Anthracite coal is a high-molar-mass carbon compound with a compo-sition of about 95% carbon by mass. A typical simplest-ratio formula for anthracitecoal is C52H16O(s). The standard enthalpy of formation of anthracite can be esti-mated at �396.4 kJ/mol. What is the quantity of energy available from burning100.0 kg of anthracite coal in a thermal electric power plant, according to the fol-lowing equation?

2 C52H16O(s) � 111 O2(g) → 104 CO2(g) � 16 H2O(g)

9. Alternative transportation fuels include methanol and hydrogen.(a) Use standard enthalpies of formation to calculate the energy produced per

mole of methanol burned.(b) Use standard enthalpies of formation to calculate the energy produced per

mole of hydrogen burned.(c) In terms of energy content, how do these two alternative fuels compare with

gasoline, which is mostly octane? The molar enthalpy of combustion of octaneis �5.07 MJ/mol.

(d) What factors other than energy content are important when comparing different automobile fuels? Include several perspectives.

Making Connections

10. In a typical household, about one-quarter of the energy consumed is used to heatwater.(a) What mass of methane undergoing complete combustion is required to heat

100.0 kg of water from 5.0°C to 70.0°C in a gas water heater? (b) How might we heat water more efficiently?(c) What alternative energy resources are available for heating water?

Figure 3Coal is an important currentsource of electrical energy inOntario but its use has seriousenvironmental consequences.

Answers

7. (a) �145.6 kJ

(c) �9.10 � 104 MJ

8. 3.34 � 103 MJ

9. (a) 22.7 MJ/mol

(b) 142 MJ/mol

10. (a) .48 kg


1. Write balanced equations for the formation of the following: (a) acetylene gas (C2H2), used in welding(b) creatine (C4H9N3O2), used as a food supplement(c) potassium iodide (KI), used as a salt substitute(d) iron(II) sulfate (FeSO4), used as a diet supplement

2. Use standard enthalpies of formation to calculate theenthalpy changes in each of the following equations:(a) Magnesium carbonate decomposes when strongly

heated.(b) Ethene burns in air.(c) Sucrose (C12H22O11(s)) decomposes to carbon and

water vapour when concentrated sulfuric acid ispoured onto it (Figure 4).

3. When octane is strongly heated with hydrogen gas in thepresence of a suitable catalyst, it “cracks,” forming a mix-ture of hydrocarbons. A typical cracking reaction yields 1 mol of methane, 2 mol of ethane, and 1 mol of propanefrom each mole of octane.

(a) Write the balanced equation for this reaction.(b) Use standard enthalpies of formation to calculate the

enthalpy change associated with the cracking of onemole of octane.

Figure 4The decomposition of sucrose produces black carbon and water.

340 Chapter 5 NEL


4. A sample of acetone (C3H6O) is burned in an insulatedcalorimeter to produce carbon dioxide gas and liquid water.

Question

What is the molar enthalpy of combustion of acetone?

Experimental Design

A sample of liquid acetone is burned such that the heatfrom the burning is transferred into an aluminumcalorimeter and its water contents.

Prediction(a) Use tabulated standard enthalpies of formation to cal-

culate a theoretical value for the molar enthalpy ofcombustion of acetone.

Evidence

Analysis(b) Calculate the molar enthalpy of combustion of acetone,

using the experimental evidence.

Evaluation(c) Calculate the percentage error by comparing the pre-

dicted and experimental values.

(d) Does the evidence support the law of conservation ofenergy?

(e) If heat is lost to the surroundings instead of beingtransferred only into the aluminum can and water, willthe experimental molar enthalpy be higher or lower?Explain.

Extension

5. Remote controlled model boats are powered by burningmethanol or a racing mixture of 80% methanol and 20%nitromethane by mass (Figure 5). The standard enthalpies offormation of liquid methanol and nitromethane are, respec-tively, –238.6 kJ/mol and –74.78 kJ/mol.(a) Draw structural diagrams for all reactants and products.(b) Calculate the percentage change in energy output

achieved by using a racing mixture.(c) Considering the various desirable characteristics of a

fuel, why do you suppose such a racing mixture isused?

Table 1 Observations on the Combustion of Acetone


mass of water 100.0 g

specific heat capacity of aluminum 0.91 J/(g • °C)

mass of aluminum can 50.0 g

initial temperature of calorimeter 20.0°C

final temperature of calorimeter 25.0°C

mass of acetone burned 0.092 g

Figure 5


5.65.6Energy is central to our way of life. Everything we do during the dayinvolves energy changes. Earlier in this chapter, we talked about threetypes of changes in matter (physical, chemical, and nuclear) and theenergy changes (net gain or net loss) that accompany them. Our con-sumption of energy also involves these types of changes, but to varyingdegrees. Freon gas vaporizes in the refrigerator coil inside a freezer, thephysical change absorbs energy. When methane burns in a natural gasoven, energy is released to the surroundings. A smoke detector on theceiling emits tiny quantities of energetic radioactive particles. Most ofthese changes involve conversion of potential energy into some formof kinetic energy.

Our household and industrial energy needs are, by and large, met bytwo energy sources: electricity, and the burning of fossil fuels such as gasoline and nat-ural gas. The majority of our household technologies, from the microwave oven in thekitchen to the alarm clock in the bedroom to the television in the living room, use electricity.The production of electricity for consumer use is a multi-billion-dollar industry and, inOntario, this electricity comes mainly from three sources: hydroelectric power, nuclearpower, and the burning of fossil fuels. All of these sources involve some system falling fromhigher potential energy to lower potential energy (Figure 1), releasing a form of kinetic energyin the process.

The major energy sources that we use in Ontario are all in some sense finite: There arelimited numbers of geographical regions where one can harness the flow of water, andboth fossil fuels and nuclear fuel are “used up” as they generate energy. Each of theseresources also has significant advantages and disadvantages. Hydroelectric projects ofteninvolve diversion of rivers, displacement of wildlife and other environmental effects,and huge initial capital expenses, but the result is “clean” energy powered by the Sun (asthe Sun provides the energy to allow water to evaporate) and producing comparativelylittle pollution. Fossil fuels are relatively cheap and available, but they are a finite resourcethat cannot last and their use damages the environment, contributing to acid rain andthe greenhouse effect. Nuclear power can generate huge amounts of energy from a tinyamount of fuel, but reactors are very expensive and there are concerns about the safetyand disposal of nuclear waste products. As you will see in the following pages, the hugepotential benefits and risks involved in the use of nuclear power make it a central issuein the ongoing energy debate.

Power from Nuclear FissionNuclear power stations have much in common with conventional power stations firedby fossil fuels (Figure 2). In both, heat is used to boil water and the resulting steamdrives a turbine. The spinning turbines, in turn, drive generators that produce elec-tricity. In a conventional power station, combustion of natural gas, oil, or coal suppliesthe necessary heat; in a nuclear power station, nuclear fission provides the heat.

The most widely used nuclear reaction is the fission or splitting of uranium into twosmaller nuclei. Nuclear fission reactions such as those shown below for uranium providethe energy for nuclear power generating stations; the enthalpy changes for the reactionsare in the order of 1010 kJ/mol of uranium. Nuclear reactors use the energy that is

The Energy Debate

Figure 1Water falling at Niagara and nuclearfission in a reactor are both exam-ples of systems in which the amountof stored potential energy decreasesand is converted into kinetic energy.

Reaction Progress

Ep

Radiodecay of Uranium

56Ba + 36Kr + 30n

92U + 0n235

141 92 1

1

∆H = 1.9 x 1010 kJ/mol

342 Chapter 5 NEL

released when uranium-235 undergoes nuclear fission to produce any of several pos-sible radioisotopes. One of the nuclear reactions that occurs is

92235 U � 0

1 n → 3692 Kr � 56

141 Ba � 3 01 n � energy �H � 1.9 � 1010 kJ/mol

This process is initiated by relatively slow-moving neutrons hitting a uranium nucleus(Figure 3), releasing large amounts of energy. Moreover, more neutrons are generated,which are able to collide with yet more uranium nuclei to generate even more heatenergy. If there is only a small amount of uranium, most of the neutrons produced justfly out of the fuel without causing further fission. However, if enough uranium nucleiare available—a situation known as critical mass—the neutrons collide with more ura-nium nuclei before they leave the fissionable material. The result is an explosive chainreaction with the sudden release of massive amounts of energy. The complete chainreaction and loss of energy can take place in less than one microsecond (1 � 10�6 s).

Uranium is a very concentrated energy source. For example, when placed in a CANDUreactor, a fuel bundle 50 cm long and 10 cm in diameter, with a mass of 22 kg, can pro-duce as much energy as 400 t of coal or 2000 barrels of oil. At present, approximately 16%of the world’s electricity is generated by nuclear power stations like the ones shown inFigures 1 and 4.

Canadian nuclear reactors (known as CANDU reactors) use natural uranium con-taining about 0.7% uranium-235 and 99.3% uranium-238. The energy is produced bythe fission of uranium-235 inside the reactor. Because of the vast quantities of energyreleased in fission, it has great potential as a commercial power source.

There are strong arguments both for and against nuclear power. Advocates of nuclearenergy point out that nuclear power

• has low uranium fuel costs, including transportation;

• causes very little air pollution, such as greenhouse and acid gases; and

• reduces our dependence on fossil fuels for electricity generation, allowing thosematerials to be used for other purposes.

boiler toconvertwater to

steam

dam to collect water

pressurized steamto drive turbine

flowing water todrive turbine

OR

(a)

(b)

turbine drives generator,producing electricity

Figure 2Many energy sources can generateelectricity.(a) In a hydroelectric power sta-

tion, water collected behind adam is released through a pipeto the turbine.

(b) Water in a boiler is heated inone of several ways:• chemical energy from the

combustion of fossil fuels ina thermal electric powerplant;

• nuclear energy from the fis-sion of uranium in a nuclearpower plant;

• direct radiant solar energyreflected from many mirrorsonto the boiler in a solarpower plant; and

• geothermal energy from theinterior of the Earth in ageothermal power plant.

krypton nucleus

barium nucleus

neutron

uranium-235 nucleus

Figure 3In the fission of U-235, one neutronis absorbed, the nucleus splits, andthree more neutrons are produced.


Opponents of nuclear power are concerned about

• the possible release of radioactive materials in a reactor malfunction;

• the difficulty of disposing of the highly toxic radioactive wastes;

• the large capital costs of building nuclear reactors and then decommissioningthem at the end of their relatively short lifetime;

• unknown health effects of long-term low-level exposure to radiation; and

• thermal pollution from cooling water.

In the 1950s, people had high expectations of endless, inexpensive nuclear energy.Few would have predicted that concerns about reactor safety and radioactive wasteswould severely dampen the enthusiasm for nuclear energy. But public attitudes, alreadychanging as the public concentrated on the risks of nuclear generation, changed decisivelyafter the nuclear accident at Chernobyl in Ukraine (Figure 5), where a serious accident

Section 5.6

electrical outputsteamturbine

27˚C

pump

pump

steam

reactor

pump

38˚C

steam generator

containmentshell

coolant

condenser (steam from turbineis condensed)

large watersource

control rods

Figure 4In nuclear reactors, the energyreleased in nuclear fission isabsorbed by a primary coolant,which then transfers the energy to asecondary coolant. The energy fromthe secondary coolant is used in aturbine or engine to generate elec-trical energy. A typical reactor con-sists of five components: fuel,moderator, coolant, control rods,and shielding. All of these becomeradioactive, to some degree, andpose a disposal challenge.

Figure 5The most serious nuclear accident inhistory happened at Chernobyl,Ukraine.(a) Radioactive material, carried by

the wind, spread for thousandsof kilometres.

(b) The element iodine reaches amaximum concentration in thethyroid gland. To reduce theeffects of radioactive iodinefrom fallout, children in severalcountries were given tabletscontaining non-radioactiveiodine. This iodine would con-centrate in the thyroid, so anyingested radioiodine would notstay in the body but be excreted.

Arctic Ocean

PacificOcean

PacificOcean

Atlantic Ocean

Chernobyl

EUROPE

ASIA

AFRICA

NORTHAMERICA

radioactive cloud • 27 April • by 6 May1986 1986(a)

(b)

344 Chapter 5 NEL

in a nuclear reactor on April 28, 1986, spewed a deadly, steam-driven cloud of radioac-tive plutonium, cesium, and uranium dioxide into the atmosphere. A nuclear reactordoes not explode like a nuclear bomb; rather, the steam pressure can build up, resultingin an explosion more like a dynamite explosion.

In 1979, a reactor malfunctioned at Three Mile Island in Pennsylvania, but the con-tainment structure worked well. There have been no major nuclear accidents in Canada,but no new nuclear generators have been built here or in the United States since 1986.

Less dramatic than a reactor malfunction, but also serious, is the continuing problemof radioactive waste disposal (Figure 6). Scientists and engineers are working to devisea safe and economically feasible method of disposing of radioactive waste, but the publicremains skeptical. Burial in arid regions or in granite layers in mine shafts—to avoidcontaminating ground water—are two possibilities, although both of these “stable” sit-uations could change over geological time. Chemists have been developing suitablematerials for encasing radioactive substances to prevent their escape into the environ-ment. Lead–iron–phosphate glass is a promising material, since the nuclear waste can bechemically incorporated into a stable glass and then buried in the safest possible place.

Figure 6Large tanks of water provide safeshort-term storage of nuclear waste.


1. (a) What are the original sources of energy for most of Ontario’s electricity?

(b) Outline the similarities and differences of power generation from these varioussources.

2. Nuclear reactors in the United States and Europe use different systems than theCANDU system. Research and make a chart to summarize the similarities and differ-ences among these systems.


Potential EnergyWhen a kilogram of water (1 L) flowsover Niagara Falls, it loses roughly1 kJ of gravitational potential energy,some fraction of which may be con-verted into hydroelectricity. When akilogram of gasoline burns, itreleases about 4 � 104 kJ of energy.When a kilogram of uranium in anuclear reactor undergoes fission, itreleases about 1 � 1011 kJ of energy.

DID YOU KNOW ??


Section 5.6

Take a Stand: Energy OptionsEnergy use is an unavoidable part of our everyday life. As citi-zens, we have to make decisions about the sources of energywe use. Our choices affect the future of our country and theworld. Some of the options include:

• hydroelectric power

• conventional fossil fuel power

• nuclear power

• alternative energy generation (non-traditional fuels; wind,geothermal, and solar power)

• “soft energy paths” (conservation, alternatives to electricityuse, changes in lifestyle to use less energy rather thanfinding ways to generate more power)

What are the advantages and disadvantages of each of theabove options? What direction should we go in the future?There are many aspects of power generation to consider, suchas:

• efficiency, in terms of energy output per dollar spent

• efficiency, in terms of energy output per gram of fuel used

• capital cost of technology

• environmental impact

(a) Separate into small groups and choose one of the abovepower options for study.

(b) As a group, research the advantages and disadvantagesof the option that you have chosen, considering as manydifferent aspects of your power source as possible, suchas technological innovations that exist or are proposedto make the option more attractive; the practicality of thisoption, including efficiency, initial capital, and ongoingoperation costs; public attitudes and effects on habits;environmental impact; and comparisons of Canada tothe rest of the world with respect to this option.

(c) Summarize your research, including explanations ofterminology as required to make major points understandable.

(d) Present your research to the class. Compare your pointswith those of other groups. Be prepared to assess yourefforts as well as those of your classmates.

(e) Within your original group, write a consensus statementthat summarizes how your group feels about eachenergy option.

(f) Write a report, intended to influence governmentleaders, expressing the direction that your group feelsthe provincial or federal government should take onenergy policy.

Define the Issue Identify Alternatives ResearchAnalyze the Issue Defend the Position Evaluate

Decision-Making SkillsEXPLORE an issue

Nuclear FusionThe nuclear reactions that occur in the Sun are impor-tant to us because they supply the energy that sustainslife on Earth. There are many different nuclear reac-tions taking place in the Sun, as in other stars. In oneof the main reactions, four hydrogen atoms fuse toproduce one helium atom.

4 11H � 2 �10e → 4

2He

Scientists and engineers think that using a similarreaction, the fusion of two isotopes of hydrogen, is apromising possibility for the development of com-mercial nuclear fusion reactors on Earth (Figure 7).In this reaction, a helium atom (4

2He), a neutron (10n),

and a large quantity of energy are produced.

21H � 3

1H → 42He � 1

0n �H = �1.70 � 109 kJ

This means that 1.7 � 109 kJ of energy is released for every mole of helium produced.The large energies involved in fusion reactions make them a promising area for researchon power generation, but the technology for controlling the process is less well developed than that for fission reactions.

Figure 7This tokomak, an experimentalfusion reactor, is in use at PrincetonUniversity in the United States.

346 Chapter 5 NEL


3. (a) Canadian (CANDU) nuclear reactors produce energy by nuclear fission ofuranium-235:

23592 U � 1

0n → 14156Ba � 92

36Kr � 3 10n

If the molar enthalpy of fission for uranium-235 is 1.9 � 1010 kJ/mol, how muchenergy can be obtained from the fission of 1.00 kg (4.26 mol) of pure uranium-235?

(b) In the Sun, hydrogen atoms undergo nuclear fusion to produce He and 1.7 � 109 kJ/mol He. How much energy can be obtained from 1.00 kg of helium?

(c) Explain why, although the molar enthalpies of reaction of U-235 (fission) and He(fusion) are similar, their energy outputs per kilogram are so different.

Making Connections

4. Current nuclear power generation uses nuclear fission reactions. Why are fissionreactions used instead of fusion reactions? Report on what progress has been madein making nuclear fusion practical as an energy source.



1. Compare, with examples, the energy produced fromnuclear fusion and nuclear fission reactions.

Making Connections

2. Research and report on atomic energy in Ontario. Includedescriptions of:(a) locations of nuclear facilities;(b) amount of power generated; and(c) advantages and disadvantages of this energy source.

3. Coal is often described as the “dirtiest” fossil fuel used forpower generation. Name other fossil fuels that can beburned to generate power and write a short report dis-cussing their advantages and disadvantages, or list theadvantages and disadvantages in a table.

4. Both geothermal and solar energy have been suggested asclean and efficient alternatives to fossil fuels and atomicenergy. Research and write a brief report on the practicalityof one of these energy sources.

5. Hydrogen power is described by some as the ideal alterna-tive to fossil fuel combustion because the only product iswater. Others argue that “dirty” energy sources are used toproduce hydrogen fuel, so that the pollution is just pro-duced somewhere else. Find out how hydrogen fuel isobtained and report on the advantages and disadvantagesof this alternative energy source.

6. Every year several groups in Ontario organize for Canadianfamilies to host children from the Chernobyl area of Ukraine.Research and report on the effects of the Chernobyl nucleardisaster, and how these Ontario communities are trying toimprove life for a few survivors of the Chernobyl disaster.






Answers

3. (a) 8.1 � 1010 kJ

(b) 4.3 � 1011 kJ

Chapter 5 LAB ACTIVITIES Unit 3

Medical Cold Packs

We can study physical changes that involve liquids andaqueous solutions, using a polystyrene calorimeter like theone shown in Figure 1. Such materials can be applied to prac-tical thermochemical systems. For example, when athletesare injured, they may immediately hold an “instant cold pack”against the injury. The medical cold pack operates on theprinciple that certain salts dissolve endothermically in water.The amount of heat per unit mass involved in the dissolvingof a compound is a characteristic property of that substance.It is called the enthalpy of solution. Table 1 lists some com-pounds that might be possible candidates for a cold packbecause they absorb energy when they dissolve.

Table 1 Enthalpies of Solution for Compounds in a Medical Cold Pack

Salt Enthalpy of solution

ammonium chloride, NH4Cl 0.277 kJ/g

potassium nitrate, KNO3 0.345 kJ/g

ammonium nitrate, NH4NO3 0.321 kJ/g

sodium acetate trihydrate, 0.144 kJ/gNaC2H3O2•3 H2O

potassium chloride, KCl 0.231 kJ/g

PurposeThe purpose of this investigation is to use calorimetry todetermine the enthalpy of solution of an unknown salt, andthen to use that value to identify the salt in a medical coldpack.

QuestionWhat is the identity of the unknown salt?

Experimental DesignYou will be given a solid sample of about 10 g of a salt typi-cally used in medical cold packs and listed in Table 1.

(a) Design an experiment to determine the heat trans-ferred when a measured mass of the salt is dissolvedin water.

You will then apply calorimetric calculations to discover theidentity of the salt.

(b) Write a detailed description of the calculations thatyou will use to determine the identity of the salt.Show all formulas and units that you will use. Youwill find it convenient to assign symbols (e.g., m1, m2,T1, etc.) to the measurements that you expect to makeso that your calculations are clear.

Materialslab aproneye protectioncentigram or analytical balance8–10 g of an unknown salt (from the list in Table 1)waterthermometer3 Styrofoam cups100-mL graduated cylinder

Procedure(c) Write your Procedure as a series of numbered steps,

clearly identifying the masses, volumes, and specificequipment to be used (see Materials list), necessarysafety and disposal considerations, and a table inwhich to record your observations.

1. Have your Experimental Design, calculations, andProcedure approved by your teacher before per-forming your experiment.

Questioning Planning AnalyzingHypothesizing Conducting EvaluatingPredicting Recording Communicating

INVESTIGATION 5.1.1 Inquiry Skills

Figure 1A simple laboratorycalorimeter consists of aninsulated container made ofthree nested polystyrenecups, a measured quantity ofwater, and a thermometer.The chemical system isplaced in or dissolved in thewater of the calorimeter.Energy transfers betweenthe chemical system and thesurrounding water are moni-tored by measuring changesin the temperature of thewater.


Analysis(d) Determine, by calculation, the identity of the

unknown salt.

Evaluation(e) Calculate a percentage difference between your exper-

imental value and the accepted value for enthalpy ofsolution of the identified salt.

(f) How confident are you in your identification? Suggestthree sources of experimental error in this experi-ment.

(g) If some heat were transferred to the air or Styrofoamcups, would your calculated enthalpy of solution ofthe unknown salt be too high or too low? Explain.

(h) If some salt were accidentally spilled as it was trans-ferred from the balance to the Styrofoam cup, wouldyour calculated enthalpy of the unknown salt be toohigh or too low? Explain.



Molar Enthalpy of a Chemical Change

When aqueous solutions of acids and bases react in acalorimeter, the solutions may act as both system and sur-roundings. The acid and base form the system as they react toform water and a dissolved salt. For example, sodium hydroxideand sulfuric acid react to form sodium sulfate and water:

NaOH(aq) � �12

� H2SO4 (aq) → H2O(l) � �12

� Na2SO4(aq) � heat

The reactant solutions are mostly water containing dissolvedand dispersed acid and base particles. Thus, a solution of anacid or a base may be regarded for calorimetric purposes tohave the same specific heat capacity as water, at least to thedegree of experimental accuracy that applies to simplecalorimeters. For example, when 100 mL of a dilute acid solu-tion reacts exothermically with 150 mL of a solution of adilute base, the acid and base may be thought to react andrelease heat to a total of 250 mL of water. Assuming that thesolutions have the same density as water (1.00 g/mL) alsomakes calculations simpler.

PurposeThe purpose of this investigation is to use calorimetry toobtain an empirical value for the molar enthalpy of neutral-ization of sodium hydroxide by sulfuric acid.

QuestionWhat is the molar enthalpy of neutralization (∆Hneut) ofsodium hydroxide with sulfuric acid?

Experimental DesignA measured volume of sodium hydroxide solution of knownconcentration will be combined with excess sulfuric acid solu-

tion of known concentration. (The sodium hydroxide willbe the limiting reagent.) Calorimetric measurements will bemade to determine the heat produced by the reaction.

(a) Demonstrate by calculation that the quantity of acididentified in the Procedure will be enough to com-pletely consume the base, and that the base will there-fore be the limiting reagent for calculation purposes.

Materialslab aproneye protection1.0 mol/L sodium hydroxide solution1.0 mol/L sulfuric acid solutionthermometerpolystyrene calorimetertwo 100-mL graduated cylinders

CAUTION: 1.0 mol/L sodium hydroxide solution iscorrosive, and 1.0 mol/L sulfuric acid solution is anirritant. Wear eye protection and a lab apron. Cleanup any spills immediately. At these dilutions, thechemicals may be disposed of down the drain withlots of water.

Procedure

1. Add 50 mL of 1.0 mol/L sodium hydroxide solutionto a polystyrene calorimeter. Measure and record itstemperature.

INVESTIGATION 5.1.1 continued

348 Chapter 5 NEL

Unit 3

2. Measure and record the temperature of a 30-mLsample of 1.0 mol/L sulfuric acid solution in a gradu-ated cylinder.

3. Carefully add the acid to the base, stirring slowly withthe thermometer. Measure and record the maximumtemperature obtained.

Analysis(b) Calculate

(i) the masses of acid and base solutions;

(ii) the temperature changes in the acid and base solutions;

(iii) the total heat absorbed by the calorimetric liq-uids (acid and base);

(iv) the amount of base (in moles) that reacted; and

(v) the molar enthalpy of neutralization of thesodium hydroxide.

Evaluation(c) Calculate a percentage difference by comparing your

experimental values and the accepted values forenthalpy of neutralization with respect to sodiumhydroxide (�56 kJ/mol).

(d) Suggest any sources of experimental error in thisinvestigation. Evaluate the experimental design, andyour skill in carrying it out.

Synthesis(e) What would have been the effect on the calculated

enthalpy of reaction if you had used

(i) 100 mL of sulfuric acid solution? Explain.

(ii) 20 mL of sulfuric acid solution? Explain.



Combustion of Alcohols

When alcohols burn they produce heat. Do different alco-hols produce different quantities of heat—do their molarenthalpies of combustion differ? In this investigation, youwill link your study of thermochemistry to your knowledgeof the molecular structure of alcohols to investigate energyrelationships.

PurposeThe purpose of this investigation is to use calorimetry todetermine the molar enthalpy change in the combustion ofeach of a series of alcohols.

QuestionHow do the enthalpies of combustion change as the alcoholmolecules become larger (i.e., ethanol to butanol)?

Prediction(a) Predict what should happen to the enthalpies of com-

bustion per mole of alcohol as the alcohol moleculesbecome larger.

Experimental DesignYou will burn measured masses of a series of alcohols, andcalculate the amount of each alcohol burned. Assume thatthe energy produced is transferred to a measured volume ofwater, the temperature change of which is calculated. Theenthalpy change involved in the combustion of one mole ofeach alcohol can then be calculated and compared.

Materialslab aproneye protectioncentigram or analytical balancealcohol burners containing ethanol, propanol, and butanolthermometersmall tin can, open at one end, and cut under the rim on

opposite sidesstirring rodring stand with iron ringlarge tin can, open at both ends, with vent openings cut

around the rim at the base100-mL graduated cylinder



350 Chapter 5 NEL

Procedure

1. Obtain an alcohol burner containing one of the alco-hols.

2. Put on your eye protection.

3. Place 100 mL of cold water in a small can suspended overan alcohol burner surrounded by a larger can (Figure 2).

4. Measure the mass of the alcohol burner and the tem-perature of the water.

5. Burn the alcohol such that the heat from the reactionis transferred as efficiently as possible into the water.

6. Cease heating when the temperature has risen about20°C.

7. Re-weigh the alcohol burner and remaining alcohol.

8. Repeat steps 3 to 7 for the remaining alcohols.

Analysis(b) Assume that 100 mL of water has a mass of 100 g. For

each of the alcohols, calculate and tabulate:

(i) the heat absorbed by the water in the calorimeter,which equals the heat produced by alcoholburning;

(ii) the heat produced per gram of alcohol;

(iii) the amount (in moles) of alcohol burned;

(iv) the heat produced per mole of alcohol.

(c) Write a thermochemical equation to represent theburning of 1 mol of each of the alcohols, includingyour experimental value for ∆Hcomb.

(d) Use the four methods described in Section 3.3 to rep-resent the experimentally determined enthalpychange for the burning of 2 mol of ethanol.

(e) Use your representations to answer the Question.

Evaluation(f) What are the sources of experimental error in this

experiment?

(g) Accepted values for combustion of the three alcoholsare: 1369 kJ/mol, 2008 kJ/mol, and 3318 kJ/mol.Calculate a percentage difference between your exper-imental value and the accepted values. Based on thiscalculation, was the Experimental Design an accept-able method to answer the Question?

Synthesis(h) If you were in the business of buying, transporting,

and storing alcohols for use as home-heating fuels,which of these alcohols would you choose to workwith? Explain.

Figure 2Apparatus for burning alcohols


Alcohols are highly flammable. Do not attempt torefuel the burners. If refuelling is necessary, askyour teacher to do so.

Do not move the burners after they are lit.

Unit 3

Hess’s Law

The combustion of magnesium is very rapid and exothermic(Figure 3), and is represented by the equation

Mg(s) � �12

� O2(g) → MgO(s)

It is possible to observe and measure a series of reactions thatenable us, with the use of Hess’s law, to determine the enthalpychange for this reaction.

(1) Magnesium reacts in acid to form hydrogen gas and a salt:

Mg(s) � 2 HCl(aq) → H2(g) � MgCl2(aq) �H1 � ? kJ

(2) Magnesium oxide reacts in acid to form water and a salt:

MgO(s) � 2 HCl(aq) → H2O(l) � MgCl2(aq) �H2 � ? kJ

The values ∆H1 and ∆H2 can be determined empiricallyusing a simple calorimeter. The enthalpy of reaction for athird reaction can be found in a reference table.

(3) Hydrogen and oxygen gases react to form water:

H2(g) � �12

� O2(g) → H2O(l) �H3 � �285.8 kJ

PurposeThe purpose of this investigation is to use Hess’s law to deter-mine the molar enthalpy of combustion of magnesium, usingcalorimetry.

QuestionWhat is the molar enthalpy of combustion, ∆Hc, of magnesium?

Experimental DesignMeasured masses of magnesium and magnesium oxide willbe added to measured volumes of hydrochloric acid solutionof known concentration. The temperature changes will bedetermined. Calculated enthalpies of reaction will be com-bined, using Hess’s law, to determine the enthalpy of com-bustion of magnesium.

Prediction(a) Show how the three known equations and their

enthalpies of reaction may be combined, using Hess’slaw, to yield the target equation and its enthalpy ofcombustion.

Materialslab aproneye protectionsteel woolcentigram or milligram balancethermometerpolystyrene calorimeter100-mL graduated cylinderscoopula10- to 15-cm strip of magnesium ribbonmagnesium oxide powder1.00 mol/L hydrochloric acid

Hydrochloric acid is corrosive. Eye protection and alab apron should be worn. All spills should becleaned up quickly and any skin that has come intocontact with acid should be immediately and thor-oughly rinsed with cold water.

Magnesium ribbon is highly flammable and shouldbe kept far from any source of ignition.

Procedure

1. Measure 100.0 mL of 1.00 mol/L hydrochloric acidinto a polystyrene cup. Measure the initial tempera-ture of the acid solution to the nearest 0.2˚C.

2. Polish a length of magnesium ribbon with steel wool.Determine the mass (to �0.01 g) of approximately0.5 g of magnesium metal. Add the solid to the solu-tion, stir it, and record the maximum temperaturethat the solution attains.



Figure 3The reaction of magnesium in air is very exothermic.


3. Dispose of the products as directed by your teacher,and rinse and dry the equipment.

4. Repeat the first three steps, using approximately 1 g ofmagnesium oxide powder measured to �0.01 g.

Analysis(b) Were the changes exothermic or endothermic? Explain.

(c) For the first reaction, calculate the enthalpy changeper mole of magnesium.

(d) Write a thermochemical equation for the reaction ofmagnesium in acid, including your experimental value.

(e) Repeat steps (c) and (d) for magnesium oxide.

(f) Using Hess’s law, the values you have found experimen-tally, and the given value for the enthalpy change for theformation of water from its elements, determine themolar enthalpy of combustion of magnesium.

(g) Which of the measured values limited the precisionof your value? Explain.

Evaluation(h) Explain why (and how) your calculated enthalpies of

reaction would be inaccurate if

(i) some heat were transferred to the air or Styrofoamcup;

(ii) the surface of the magnesium ribbon had a coatingof MgO.

(i) Suggest some other possible sources of experimentalerror in this investigation.

(j) The accepted value for the molar enthalpy of com-bustion of magnesium is –601.6 kJ/mol. Calculate apercentage difference by comparing your experi-mental values and the accepted values. Comment onyour confidence in the evidence.

(k) Based on your evaluation of the Experimental Designand the evidence, is Hess’s law an acceptable methodto calculate enthalpies of reaction?

Synthesis(l) Suggest an experimental technique that could be used

to determine the enthalpy of combustion of magne-sium directly.


LAB EXERCISE 5.5.1 Inquiry Skills

Testing Enthalpies of Formation

Calorimetry is the basic experimental tool used to determineenthalpies of reaction. When carefully obtained calorimetricresults are used to find an enthalpy of reaction, the calcula-tions should be consistent with results obtained using stan-dard enthalpies of formation.

QuestionWhat is the molar enthalpy of combustion of methanol?

Prediction(a) Use the given values for standard enthalpy of forma-

tion to calculate the molar enthalpy of combustion ofmethanol. (Assume that the products of the reactionare gaseous carbon dioxide and liquid water only.)

Experimental DesignA known mass of methanol is burned in a calibrated bombcalorimeter. The enthalpy of combustion is also calculatedusing standard enthalpies of formation. The two values arecompared to test the standard enthalpies.

Materialsmethanolbomb calorimeterthermometer

352 Chapter 5 NEL



Unit 3

Analysis(b) Use the experimental values to calculate, to the

appropriate number of significant figures, the molarenthalpy of combustion of methanol.

Evaluation(c) Calculate the percentage difference between the

experimental and predicted values. Does this experi-ment support the standard enthalpies?

EvidenceTable 2 Observations for Burning Methanol


mass of methanol reacted 4.38 g

heat capacity of bomb calorimeter 10.9 kJ/C°

initial temperature of calorimeter 20.4°C

final temperature of calorimeter 27.9°C

Chapter 5 SUMMARY

354 Chapter 5 NEL

Key Expectations• Determine enthalpy of reaction using a calorimeter,

and use the evidence obtained to calculate theenthalpy change for a reaction. (5.1, 5.2, 5.3, 5.4)

• Compare the energy changes resulting from physicalchange, chemical reactions, and nuclear reactions (fis-sion and fusion). (5.1, 5.6)

• Describe examples of technologies that depend onexothermic or endothermic changes. (5.1, 5.6)

• Analyze simple potential energy diagrams of chemicalreactions. (5.3)

• Write thermochemical equations, expressing theenergy change as a ∆H value or as a heat term in theequation. (5.3)

• Explain Hess’s law, using examples. (5.4)

• Apply Hess’s law to solve problems, including prob-lems that involve evidence obtained through experi-mentation. (5.4, 5.5)

• Calculate enthalpies of reaction, using tabulated stan-dard enthalpies of formation. (5.5)

• Compare conventional and alternative sources ofenergy with respect to efficiency and environmentalimpact. (5.6)

• Use appropriate scientific vocabulary to communicateideas related to the energetics of chemical reactions.(all sections)

Key Termscalorimetry

chemical change

chemical system

endothermic

enthalpy

enthalpy change

exothermic

heat

Hess’s law

isolated system

law of additivity ofreaction enthalpies

molar enthalpy

molar enthalpy of reac-tion

nuclear change

open system

physical change

potential energy dia-gram

specific heat capacity

standard enthalpy offormation

standard molarenthalpy of reaction

surroundings

temperature

thermal energy

thermochemistry

Key Symbols and Equations• q � mc∆T

• ∆Hsystem � � qsurroundings

• ∆H � n∆Hr

• ∆Htarget � �∆Hknown (Hess’s law)

• ∆H °f

• ∆H ° � �n∆H °f(products) –�n∆H °f(reactants)

Problems You Can Solve• How much heat is transferred to a known mass of

matter, for a given temperature change? (5.1)

• What is the enthalpy change for a change in state,given the mass and molar enthalpy? (5.2)

• What is the molar enthalpy of a change taking place ina calorimeter, given the mass of the system and thesolution, and the temperature change? (5.2)

• What is the thermochemical equation (including theenergy term) for a given reaction? (5.3)

• What is the thermochemical equation (including theenthalpy change, ∆H) for a given reaction? (5.3)

• What is the equation for a molar enthalpy of reaction?(5.3)

• What is the enthalpy change for a target reaction,given enthalpy changes for other known reactions andusing Hess’s law? (5.4)

• What is the enthalpy change for the reaction of a givenquantity of a substance, given either the energyinvolved for the reaction of a different amount of thatsubstance or the energy involved in a series of relatedknown reactions? (5.4)

• What is the formation equation for a substance? (5.5)

• What is the enthalpy change of a target reaction, giventhe enthalpies of formation of various known reac-tions? (5.5)

• What mass of a substance is involved in a reaction, orwhat temperature change results from a reaction,given the enthalpies of formation of various knownreactions? (5.5)

MAKE a summary

Make a concept map to summarize what you have learnedin this chapter. Start with the phrase “Energy Changes” inthe centre, and try to include as many as possible of the KeyTerms and Key Symbols and Equations listed above.

Chapter 5 SELF-QUIZ


Identify each of the following statements as true, false, orincomplete. If the statement is false or incomplete, rewriteit as a true statement.

1. Nuclear changes generally absorb more energy thanchemical changes.

2. In exothermic reactions, the reactants have morekinetic energy than the products.

3. On a potential energy diagram, the horizontal axismay be called reaction progress.

4. In endothermic reactions, the heat term is written onthe right side of the equation.

5. In an isolated system, neither matter nor energy mayenter or leave the system.

6. In calorimetry, the assumption is made that theenthalpy change of the system equals the heat trans-ferred to the surroundings.

7. The burning of gasoline is an example of anendothermic physical change.

8. A formation reaction has elements in their standardstates as reactants.

9. Specific heat capacity is the amount of heat requiredto change a given mass through 1°C.

10. The ∆H value for an exothermic reaction is negative.

Identify the letter that corresponds to the best answer toeach of the five following questions.

11. Which of the following would involve the largest pro-duction of heat per mole?(a) the burning of gasoline(b) the evaporation of water(c) the fission of uranium(d) the freezing of water(e) the rusting of iron

12. Which of the following would involve the greatestabsorption of heat per mole?(a) the burning of gasoline(b) the evaporation of water(c) the fission of uranium(d) the freezing of water(e) the rusting of iron

13. The evaporation of methanol (molar mass 32.0 g/mol) involves absorption of 1.18 kJ/g. What isthe molar enthalpy of vaporization of methanol?(a) 0.0369 kJ/mol (d) 32.0 kJ/mol(b) 1.18 kJ/mol (e) 37.8 kJ/mol(c) 3.78 kJ/mol

Unit 3

14. When solid ammonium chloride is added to water,the solution feels cold to the hand. Which statementbest describes the observation?(a) NH4Cl(s) → NH4Cl(aq) � 34 kJ(b) The reaction is exothermic.(c) NH4Cl(s) → NH4Cl(aq) ∆H � 34 kJ(d) The system releases heat, so it feels colder.(e) The boiling point is increased, so it feels colder.

15. Which of the following statements is not true?(a) ∆H is the difference in enthalpy between reac-

tants and products.(b) ∆H may be written as part of the equation.(c) ∆H is negative for an endothermic reaction.(d) A reaction consumes heat if ∆H is positive.(e) ∆H equals the heat transferred to or from the

surroundings.

16. Referring to the reaction below, how much heat isreleased if 120 g of potassium metal reacts?

2 K(s) � 2 H2O(l) → 160 kJ � H2(g) � 2 KOH(aq)

(a) 0.0 kJ since no temperature change is indicated(b) 52.1 kJ (d) 491 kJ(c) 246 kJ (e) 280 KJ

17. The standard heat of formation of solid ammoniumnitrate, NH4NO3, is �330 kJ/mol . The equation thatrepresents this process is:(a) N2(g) � 4 H2(g) + 3 O2(g) → NH4NO3(s) �

330 kJ(b) 2 N(g) � 4 H(g) � 3 O(g) → NH4NO3(s) �

330 kJ(c) NH4

+(g) � NO3

�(g) → NH4NO3(s) � 330 kJ

(d) �12

� N2(g) � 2 H2(g) � �32

� O2(g) → NH4NO3(s) +330 kJ

(e) N2(g) � 2 H2(g) � �32

� O2(g) → NH4NO3(s) +330 KJ

18. Consider the following two thermochemical equations:

N2(g) + �52

� O2(g) → N2O5(s) ∆H = x kJ

N2(g) + �52

� O2(g) → N2O5(g) ∆H = y kJ

The enthalpy change, in kJ, for the sublimation of onemole of N2O5 solid to gas would be represented bythe quantity(a) x � y (d) �x � y(b) x � y (e) xy(c) y � x

An interactive version of the quiz is available online.GO www.science.nelson.com

356 Chapter 5 NEL

Understanding Concepts1. Make a chart to summarize the energy changes

involved in physical, chemical, and nuclear changes.For each type of change(a) describe the change in matter;(b) give a range of energies in kJ/mol; and(c) give two examples. (5.1)

2. Bricks in a fireplace will absorb heat and release itlong after the fire has gone out. A student conductedan experiment to determine the specific heat capacityof a brick. Based on the evidence obtained in thisexperiment, 16 kJ of energy was transferred to a 938-g brick as the temperature of the brick changedfrom 19.5°C to 35.0°C. Calculate the specific heatcapacity of the brick. (5.1)

3. What basic assumptions are made in calorimetryexperiments that involve reacting solutions? (5.2)

4. A 2.0-kg copper kettle (specific heat capacity 0.385 J/g•°C) contains 0.500 kg of water at 20.0°C.How much heat is needed to raise the temperature ofthe kettle and its contents to 80.0°C? (5.2)

5. Propane gas is used to heat a tank of water. If the tankcontains 200.0 L of water, what mass of propane willbe required to raise its temperature from 20.0°C to65.0°C? (∆Hcomb for propane � –2220 kJ/mol) (5.2)

6. Draw a labelled potential energy diagram to representthe exothermic combustion of nonane (C9H20) inoxygen. (5.3)

7. (a) Describe four ways in which enthalpy changes fora reaction may be represented.

(b) Use the four methods to represent the dissolvingof ammonium chloride (∆Hsol � �14 kJ/mol).

(5.3)

8. If one mole of water absorbs 44 kJ of heat as it changesstate from liquid to gas, write thermochemical equa-tions, with appropriate energy terms, to represent (a) the evaporation of one mole of water;(b) the condensation of one mole of water vapour;

and(c) the evaporation of two moles of water. (5.3)

9. (a) Write the equation for the formation of liquidacetone (C3H6O).

(b) Write thermochemical equations for the combus-tion of one mole each of hydrogen, carbon, andacetone, given that their molar enthalpies ofcombustion are �285.8 kJ/mol, �393.5 kJ/mol,and �1784 kJ/mol, respectively.

Chapter 5 REVIEW

356 Chapter 5 NEL

(c) Use Hess’s law and the three combustion reactionsto calculate the enthalpy of formation of acetone.

(5.4)

10. When glucose is allowed to ferment, ethanol andcarbon dioxide are produced. Given that theenthalpies of combustion of glucose and ethanol are�2813 kJ/mol and �1369 kJ/mol respectively, useHess’s law to calculate the enthalpy change when0.500 kg of glucose is allowed to ferment. (5.4)

11. The molar enthalpy of combustion of natural gas is�802 kJ/mol. Assuming 100% efficiency andassuming that natural gas consists only of methane,what is the minimum mass of natural gas that mustbe burned in a laboratory burner at SATP to heat 3.77L of water from 16.8°C to 98.6°C? (5.4)

12. Pyruvic acid is a molecule involved as an intermediatein metabolic reactions such as cellular respiration.Pyruvic acid (CH3COCOOH) is converted into aceticacid and carbon monoxide in the reaction

CH3COCOOH → CH3COOH + CO

If the molar enthalpies of combustion of these sub-stances are, respectively, �1275 kJ/mol, �875.3kJ/mol, and �282.7 kJ/mol, use Hess’s law to calcu-late the enthalpy change for the given reaction. (5.4)

13. Ammonia forms the basis of a large fertilizerindustry. Laboratory research has shown thatnitrogen from the air reacts with water, using sunlightand a catalyst to produce ammonia and oxygen. Thisresearch, if technologically feasible on a large scale,may lower the cost of producing ammonia fertilizer.(a) Determine the enthalpy change of the reaction,

using a chemical equation balanced with whole-number coefficients.

(b) Calculate the quantity of solar energy needed toproduce 1.00 kg of ammonia.

(c) If 3.60 MJ of solar energy is available per squaremetre each day, what area of solar collectorswould provide the energy to produce 1.00 kg ofammonia in one day?

(d) What assumption is implied in the previous cal-culation? (5.4)

14. When sodium bicarbonate (NaHCO3) is heated, itdecomposes into sodium carbonate (Na2CO3), watervapour, and carbon dioxide. If the standard enthalpiesof formation of sodium bicarbonate and sodium car-bonate are �947.7 kJ/mol and �1131 kJ/mol respec-tively, calculate the enthalpy change for the reaction.

(5.5)


15. When benzoic acid is burned, the enthalpy of com-bustion is �3223.6 kJ/mol. Use this information andtabulated values of the standard enthalpies of forma-tion of liquid water and carbon dioxide to calculatethe standard enthalpy of formation of benzoic acid.

(5.5)

Applying Inquiry Skills16. A series of calorimetric experiments is performed to

test Hess’s law. Enthalpy changes for two known reac-tions are determined experimentally:

(1) CaCO3(s) + 2 HCl(aq) → CO2(g) + H2O(l) + CaCl2(aq)

�H1 � ? kJ

(2) CaO(s) + 2 HCl(aq) → H2O(l) + CaCl2(aq)

�H2 = ? kJ

The target equation is

CaCO3(s) → CO2(g) + CaO(s) �H = ? kJ

Experimental DesignTwo calorimetry experiments are performed, with thechoice of chemical systems such that the enthalpychanges of these two known reactions are equal to theenthalpy change of the unknown target equation.(a) Use Hess’s law to show how the two known equa-

tions may be added together to yield the targetequation.

Procedure(b) Describe the series of procedural steps that you

would follow to produce the following observa-tions.

Evidence

Analysis(c) Use the evidence to calculate the enthalpy change

in each system. (Assume that the specific heatcapacity of the acid solution is 4.18 J/g•°C).

Unit 3

(d) Calculate the enthalpy change for the targetequation.

(e) Explain the effect that you would expect on thecalculated ∆H for reaction (1) if:(i) some of the calcium carbonate remained on

the weighing paper as it was added to the acid;

(ii)some heat was lost to the air. (5.4)

17. (a) A pure liquid is suspected to be ethanol. Usingthe energy concepts from this chapter, list asmany experimental designs as possible to con-firm or refute the suspected identity of the liquid.

(b) Describe some other experimental designs thatcould be used to determine if the unknownliquid is ethanol. (5.5)

Making Connections18. (a) Calculate the enthalpy change for

• the condensing of 1.00 mol of steam to waterat 100°C.

• the formation of 1.00 mol of water from its elements.

• the formation of 1.00 mol of helium-4 in ahydrogen fusion reaction.

(b) If the preceding enthalpy changes were repre-sented on a graph with a scale of 1 cm per 100 kJ,calculate the distance for each enthalpy change inparts (a), (b), and (c).

(c) Develop an analogy for the relative amounts ofenergy released in part (a). (5.5)

19. Canadians use more energy per capita than almostany other country in the world.(a) List some factors that contribute to this level of

consumption.(b) Compare Canada’s energy consumption with

that of another country. At the same time,compare the factors listed in (a).

(c) Choose one source of energy used in Canada,and research the efficiency and environmentalimpact of our use of this type of energy.

(d) Write a short opinion piece on whether it ismorally appropriate for Canada to have thepresent level of energy consumption. (5.6)

Table 1 Observations for Calorimetry Investigation

Observation Experiment 1 Experiment 2

mass of reactant 1 4.2 g CaCO3(s) 4.7 g CaO

mass of cup 3.0 g 3.1 g

mass of cup and acid 173.2 g 158.6 g

initial temperature of acid 29.0°C 29.0°C

final temperature of mixture 31.0°C 36.0°C GO www.science.nelson.com

chapter5-thermochemistry

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