Chemical Energetics and Thermodynamics

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Oct 27, 2013 (3 years and 5 months ago)

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Chemical Energetics and Thermodynamics
A Chem
1
Reference Text
Stephen K.Lower
Simon Fraser University
Contents
1 Potential energy and kinetic energy 3
1.1 Chemical Energy:::::::::::::::::::::::::::::::::::::::::3
2 Energetics of chemical reactions 4
3 The thermodynamic view:system and surroundings 4
3.1 Heat and work::::::::::::::::::::::::::::::::::::::::::5
4 Internal energy 6
4.1 Changes in internal energy::::::::::::::::::::::::::::::::::::7
4.2 The heat capacity::::::::::::::::::::::::::::::::::::::::7
4.3 The First Law of thermodynamics.:::::::::::::::::::::::::::::::8
5 Molecular interpretation of heat capacity 8
5.1 Polyatomic molecules:::::::::::::::::::::::::::::::::::::::9
Heat capacities of metals:::::::::::::::::::::::::::::::::::::10
6 Pressure-volume work 10
6.1 Reversible processes:::::::::::::::::::::::::::::::::::::::12
7 Heat changes at constant pressure:the enthalpy 13
8 Thermochemical equations and standard states 14
9 Enthalpy of formation 15
10 Hess'law and thermochemical calculations 16
11 Calorimetry 17
12 Interpretation of reaction enthalpies 21
12.1 Enthalpy diagrams::::::::::::::::::::::::::::::::::::::::21
12.2 Bond enthalpies and bond energies:::::::::::::::::::::::::::::::21
12.3 Energy content of fuels::::::::::::::::::::::::::::::::::::::22
12.4 Energy content of foods:::::::::::::::::::::::::::::::::::::23

² CONTENTS
13 Variation of the enthalpy with temperature 24
14 The direction of spontaneous change 1
14.1 A closer look at disorder:::::::::::::::::::::::::::::::::::::2
15 The entropy 5
15.1 The entropy of the world always increases:::::::::::::::::::::::::::6
15.2 Absolute entropies::::::::::::::::::::::::::::::::::::::::7
15.3 Entropies of substances:::::::::::::::::::::::::::::::::::::8
15.4 E®ect of temperature,volume,and concentration on the entropy::::::::::::::9
15.5 The second law of thermodynamics:::::::::::::::::::::::::::::::10
16 The free energy 12
16.1 The standard Gibbs free energy:::::::::::::::::::::::::::::::::12
16.2 Temperature dependence of ¢G
±
::::::::::::::::::::::::::::::::13
16.3 How free energies determine melting and boiling points::::::::::::::::::::14
17 Free energy and concentration 14
17.1 The free energy of a gas:Standard states:::::::::::::::::::::::::::15
17.2 The free energy of a solute::::::::::::::::::::::::::::::::::::15
18 Free energy and the equilibrium constant 16
18.1 The equilibrium constant::::::::::::::::::::::::::::::::::::18
18.2 Equilibrium and temperature::::::::::::::::::::::::::::::::::19
18.3 Equilibrium without mixing:coupled reactions::::::::::::::::::::::::20
19 Coupled reactions 20
19.1 Extraction of metals from their oxides:::::::::::::::::::::::::::::21
20 Bioenergetics 23
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² 1 Potential energy and kinetic energy
Part 1:
Introduction to chemical energetics
All chemical changes are accompanied by the absorption or release of heat.The intimate connection
between matter and energy has been a source of wonder and speculation from the most primitive times;
it is no accident that ¯re was considered one of the four basic elements (along with earth,air,and water)
as early as the ¯fth century bc.In this unit we will review some of the fundamental concepts of energy
and heat and the relation between them.We will begin the study of thermodynamics,which treats the
energetic aspects of change in general,and will ¯nally apply this speci¯cally to chemical change.Our goal
will be to provide you with the tools to predict the energy changes associated with chemical processes.
This will provide the groundwork for a more ambitious goal:to predict the direction and extent of change
itself.
1 Potential energy and kinetic energy
Ultimately,there are only two kinds of energy:kinetic and potential.Kinetic energy is associated with
the motion of an object;a body with a mass m and moving at a velocity v possesses the kinetic energy
1
2
mv
2
.Potential energy is energy a body has by virtue of its location.For example,if an object of mass
m is raised o® the °oor to a height h,its potential energy increased by gmh,where g is a proportionality
constant known as the acceleration of gravity.This tells us something else about potential energy:it is
energy a body has by virtue of its location in a force ¯eld of some kind;a gravitional,electrical,or a
magnetic ¯eld.
An interesting thing about energy is that its values are always relative:there is no\zero"of energy.
You might at ¯rst think that a book sitting on the table has zero kinetic energy since it is not moving.
You forget,however,that the earth itself is moving;it is spinning on its axis,it is orbiting the sun,and
the sun itself is moving away from the other stars in the general expansion of the universe.Since these
motions are normally of no interest to us,we are free to adopt an arbitrary scale in which the velocity
of the book is measured with respect to the table;on this so-called laboratory coordinate system,the
kinetic energy of the book will be considered zero.
We do the same thing with potential energy.If the book is on the table,its potential energy with
respect to the surface of the table will be zero.If we adopt this as our zero of potential energy,and then
push the book o® the table,its potential energy will be negative after it reaches the °oor.
1.1 Chemical Energy
When you buy a litre of gasoline for your car,a cubic metre of natural gas to heat your home,or a small
battery for your °ashlight,you are purchasing energy in a chemical form.In each case,some kind of
a chemical change will have to occur before this energy can be released and utilized:the fuel must be
burned in the presence of oxygen,or the two poles of the battery must be connected through an external
circuit (thereby initiating a chemical reaction inside the battery).And eventually,when each of these
reactions is complete,our source of energy will be exhausted;the fuel will be used up,or the battery will
be\dead".
Chemical substances are made of atoms,or more generally,of positively charged nuclei surrounded
by negatively charged electrons.A molecule such as dihydrogen,H
2
,is held together by electrostatic
attractions mediated by the shared electrons between the two nuclei.The total potential energy of the
molecule is the sum of the repulsions between like charges and the attractions between electrons and
nuclei:
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² 2 Energetics of chemical reactions
PE
total
= PE
electron¡electron
+PE
nucleus¡nucleus
+PE
nuclus¡electron
In other words,the potential energy of the molecule depends on the relative locations of the two
atoms in the force ¯eld of the nuclear charges and the electron cloud.This dependence is expressed
by the familiar potential energy curve which serves as an important description of the chemical bond
between two atoms.
If the H
2
is in the gaseous state,the molecules will be moving freely from one location to another;this
is called translational motion,and the molecules therefore possess translational kinetic energy KE
trans
=
mv
2
=2,in which v stands for the average velocity of the molecules;you may recall from your study of
gases that v,and therefore KE
trans
,depends on the temperature.
In addition to translation,molecules can possess other kinds of motion.Because a chemical bond acts
as a kind of spring,the two nuclei in H
2
will have a natural vibrational frequency.In more complicated
molecules,many di®erent modes of vibration become possible,and these all contribute a vibrational term
KE
vib
to the total kinetic energy.Finally,a molecule can undergo rotational motions which give rise to
a third term KE
rot
.Thus the total kinetic energy of a molecule is the sum
KE
total
= KE
trans
+KE
vib
+KE
rot
The total energy of the molecule is just the sum
E
total
= KE
total
+PE
total
(1)
Although this formula is simple and straightforward,it cannot take us very far in understanding and
predicting the behavior of even one molecule,let alone a large number of them.The reason,of course,is
the chaotic and unpredictable nature of molecular motion.Fortunately,the behavior of a large collection
of molecules,like that of a large population of people,can be described by statistical methods.
2 Energetics of chemical reactions
A chemical reaction is de¯ned by its reactants and products,but there is one other property of a reaction
that is not shown in the balanced chemical equation,but is important to know about:the amount of
heat absorbed or liberated when the reaction takes place.If the chemical reaction is serving as a source
of heat,such as in the combustion of a fuel,for example,then these heat e®ects are of direct and obvious
interest.We will soon see,however,that a study of the energetics of chemical reactions in general can
lead us to a deeper understanding of chemical equilibrium and the basis of chemical change itself.This
more general body of knowledge is known as thermodynamics (from the Greek words referring to the
movement of heat),and this will be the subject of this and the next units of this course.
One of the interesting things about thermodynamics is that although it deals with matter,it makes
no assumptions about the microscopic nature of that matter.Thermodynamics deals with matter in a
macroscopic sense;it would be valid even if the atomic theory of matter were wrong.This is an important
quality,because it means that reasoning based on thermodynamics is unlikely to require alteration as
new facts about atomic structure and atomic interactions come to light.
3 The thermodynamic view:system and surroundings
The thermodynamic view of the world requires that we be very precise about our use of certain words.
The two most important of these are system and surroundings.A thermodynamic system is that part of
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² Heat and work
the world to which we are directing our attention.Everything that is not a part of the system constitutes
the surroundings.The system and surroundings are separated by a boundary.If our system is one mole
of a gas in a container,then the boundary is simply the container itself.The boundary need not be a
physical barrier;for example,if our system is a factory or a forest,then the boundary can be wherever
we wish to de¯ne it.We can even focus our attention on the dissolved ions in an aqueous solution of
a salt,leaving the water molecules as part of the surroundings.The single property that the boundary
must have is that it be clearly de¯ned,so we can unambiguously say whether a given part of the world
is in our system or in the surroundings.
If matter is not able to pass across the boundary,then the system is said to be closed;otherwise,it is
open.A closed system may still exchange energy with the surroundings unless the system is an isolated
one,in which case neither matter nor energy can pass across the boundary.The tea in a closed Thermos
bottle approximates a closed system over a short time interval.
Properties and the state of a system The properties of a system are those quantities such as the
pressure,volume,temperature,and its composition,which are in principle measurable and capable of
assuming de¯nite values.There are of course many properties other than those mentioned above;the
density and thermal conductivity are two examples.However,the values of these latter properties are
determined by the others;thus the density of a gas is determined by its volume and its composition.The
P,V,T (as well as the composition) are known as state properties,because if these have ¯xed values,
then the values of all the other properties are ¯xed,and the system is in a de¯nite state.
In the case of chemical substances,we must also be careful to specify the physical state (liquid,solid,
etc.) of the substance in the system.
Change of state In dealing with thermodynamics,we must be able to unambiguously de¯ne the change
in the state of a system when it undergoes some process.This is done by specifying changes in the values
of the di®erent state properties as illustrated here for a change in the volume:
¢V = V
¯nal
¡V
initial
We can compute similar ¢-values for changes in P,T,n
i
(the number of moles of substance i),and the
other state properties we will meet later.
3.1 Heat and work
Heat and work are both measured in energy units,so they must both represent energy.How do they
di®er from each other,and from just plain\energy"itself?
First,recall that energy can take many forms:mechanical,chemical,electrical,radiation (light),
:::and thermal,or heat.So heat is a form of energy,but it di®ers from all the others in one crucial
way.All other forms of energy are interconvertible:mechanical energy can be completely converted to
electrical energy,and the latter can be completely converted to heat.However,complete conversion of
heat into other forms of energy is impossible.We will defer a discussion of the profound implications of
this fact until later;for the moment,we will simply state that this places heat in a category of its own
and justi¯es its special treatment.
There is another special property of heat that you already know about:heat can be transferred from
one body (i.e.,one system) to another.We often refer to this as a °ow of heat,recalling the 18th-century
notion that heat was an actual substance called\caloric"that could °ow like a liquid.Moreover,you
know that heat can only °ow from a system at a higher temperature to one at a lower temperature.This
special characteristic is often used to distinguish heat from other modes of transferring energy from one
system to another.
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² 4 Internal energy
Next,what about work?Work,like energy,can take various forms:mechanical,electrical,gravita-
tional,etc.All have in common the fact that they depend on two factors.For example,the simplest form
of mechanical work arises when an object moves a certain distance against an opposing force.Electrical
work is done when a body having a certain charge moves through a potential di®erence.Performance
of work involves a transformation of energy;thus when a book drops to the °oor,gravitational work is
done (a mass moving through a gravitational potential di®erence),and the potential energy the book had
before it was dropped is converted into kinetic energy which ultimately appears as heat.
Heat and work are best thought of as processes by which energy is exchanged,rather than as energy
itself.That is,heat\exists"only when it is °owing,work\exists"only when it is being done.
When two bodies are placed in thermal contact and energy °ows fromthe warmer
body to the cooler one,we call the process\heat".A transfer of energy to or
from a system by any means other than heat is called\work".
4 Internal energy
What is internal energy?It is simply the totality of all forms of kinetic and potential energy of the
system.Thermodynamics makes no distinction between these two forms of energy and it does not
assume the existence of atoms and molecules.But since we are studying thermodynamics in the context
of chemistry,we can allow ourselves to depart from\pure"thermodynamics enough to point out that
the internal energy is the sum of the kinetic energy of motion of the molecules,and the potential energy
represented by the chemical bonds between the atoms and any other intermolecular forces that may be
present.The internal energy of a molecule is given by Eq 1;the internal energy of the system is just the
sum of this quantitity over all the molecules comprising the system.
How can we know how much internal energy a system possesses?The answer is that we cannot,at
least not on an absolute basis;all scales of energy are arbitrary.The best we can do is measure changes in
energy.However,we are perfectly free to de¯ne zero energy as the energy of the system in some arbitrary
reference state,and then say that the internal energy of the system in any other state is the di®erence
¢U between the energies of the system in these two di®erent states.
In chemical thermodynamics,we de¯ne the zero of internal energy as the internal energy of the
elements as they exist in their stable forms at 298
±
K and 1 atm pressure.Thus the internal energies U
of Xe
(g)
,O
2
(g)
,Br
2
(l)
,Cu
(s)
and C(diamond) are all zero.When the reaction
H
2
(g)
+ Cl
2
(g)
¡!2 HCl
(g)
takes place,there is a fall in the internal energy,and the di®erence ¢U is also the internal energy of two
moles of gaseous HCl.What this represents physically is that the arrangement of electrons and atoms
in the products corresponds to a lower potential energy than in the reactants.This need not always be
the case,however,and it is quite common for the internal energy of the products to exceed those of the
reactants.
In comparing the internal energies of di®erent substances as we have been doing here,it is important
to compare equal numbers of moles,because internal energy is an extensive property of matter.However,
it is commonly expressed on a molar basis,in which case it may be treated as an intensive property.
The internal energy of a system also depends on its temperature;the higher the temperature,the
greater is the average kinetic energy of the molecules comprising the system,and according to Eq 1 this
will lead to an increase in the internal energy.
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² Changes in internal energy
4.1 Changes in internal energy
We can generalize the foregoing statements that the internal energy of a systemdepends on its composition
and temperature by saying that the internal energy depends only on the state of the system:
¢U = U
¯nal
¡U
initial
The word\only"in the preceding statement is important,because it eliminates any reference to how the
system gets from the initial state to the ¯nal state.In other words,the value of ¢U for a given change
in state is independent of the pathway of the process.A quantity such as internal energy that depends
only on the state of the system is known as a state function.
To help you appreciate the signi¯cance of U being a state function,consider the oxidation of a lump
of sugar to carbon dioxide and water:
C
12
H
22
O
11
+ 6 O
2
(g)
¡!12 CO
2
(g)
+ 11 H
2
O
(l)
This process can be carried out in many ways,for example by burning the sugar in air,or by eating the
sugar and letting your body carry out the oxidation.Although the mechanisms of the transformation
are completely di®erent for these two pathways,the overall change in internal energy of the system (the
atoms of carbon,hydrogen and oxygen that were originally in the sugar) will be identical,and can be
calculated simply by looking up the internal energies of the substances and calculating the di®erence
¢U = U
12 CO
2
+U
11 H
2
O
¡U
C
12
H
22
O
11
4.2 The heat capacity
For systems in which no change in composition (chemical reaction) occurs,things are even simpler:to
a very good approximation,the internal energy depends only on the temperature.This means that the
temperature of such a system can serve as a direct measure of its internal energy.The functional relation
between the internal energy and the temperature is given by the heat capacity:
dU
dT
= C
(or ¢U=¢T if you don't care for calculus!) Heat capacity can be expressed in joules or calories per mole
per degree (molar heat capacity),or in joules or calories per gram per degree;the latter is called the
speci¯c heat capacity or just the speci¯c heat.
If a quantity of heat q crosses the boundaries of a system,the internal energy of the systemwill change
by an identical amount:¢U = q.By convention,the signs of q and of ¢U are positive if heat °ows
into the system and the internal energy increases;the signs are negative if the system loses heat to the
surroundings.
Remember,however,that a °ow of heat into or out of a system is just one way to change the internal
energy.The other way is for the system to do work on the surroundings,or for the surroundings to do
work on the system.The simplest example of work is an expansion of the system against an external
restraining pressure,but there are many other processes that also involve work.If a quantity of work w
is done on the system,its internal energy increases and the sign of w is positive;work done by the system
(and thus on the surroundings) is done at the expense of some internal energy,and its sign is negative.
The distinction between heat and work is quite simple.Heat is the °ow of energy into or out of a
system as the result of a temperature di®erence between the system and surroundings;heat always °ows
from higher to lower temperatures.A process that alters the internal energy of a system by any other
means is,by elimination,work.
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² The First Law of thermodynamics.
4.3 The First Law of thermodynamics.
Since the internal energy of a system is a®ected by both heat and work,we can write
¢U = q +w
(2)
This expression,a simple sum of two quantities,is a statement of one of the most fundamental laws of
the physical world:it is known as the First Law of thermodynamics.The First Law is also known as the
Law of Conservation of Energy,but in the form given in Eq 2 it is stated more explicitly;it says that
there are two kinds of processes,heat and work,that can lead to a change in the internal energy of a
system.Since both heat and work can be measured and quanti¯ed,this is the same as saying that any
change in the energy of a system must result in a corresponding change in the energy of the world outside
the system{ in other words,energy cannot be created or destroyed.
The full signi¯cance of Eq 2 cannot be grasped without understanding that U is a state function.
This means that a given change in internal energy ¢U can follow an in¯nite variety of pathways re°ected
by all the possible combinations of q and w that can add up to a given value of ¢U.
As a simple example of how this principle can simplify our understanding of change,consider two
identical containers of water initially at the same temperature.We place a °ame under one until
its temperature has risen by 1
±
C.The water in the other container is stirred vigorously until its
temperature has increased by the same amount.There is now no physical test by which you could
determine which sample of water was warmed by performing work on it,by allowing heat to °ow
into it,or by some combination of the two processes.In other words,there is no basis for saying that
one sample of water now contains more\work",and the other more\heat".The only thing we can
know for certain is that both samples have undergone identical increases in internal energy,and we
can determine the value of ¢U simply by measuring the increase in the temperature of the water.
5 Molecular interpretation of heat capacity
The heat capacity of a substance is a measure of how sensitively its temperature is a®ected by a change in
heat content;the greater the heat capacity,the less e®ect a given change q will have on the temperature.
You will recall that temperature is a measure of the average kinetic energy due to translational motions
of molecules
1
.Thus the higher the heat capacity of a substance,the smaller will be the fraction of the
heat it absorbs that gets channeled into translational energy.
Where does the heat go that does not produce more vigorous translational motion?It goes into
vibrational and rotational kinetic energy.These two kinds of motion do not a®ect the temperature,but
if they are active and can soak up energy,they compete with translation and reduce the e®ect of a heat
°ow q on the temperature.
Vibrational and rotational motions are not possible for monatomic species such as the noble gas
elements,so these substances have the lowest heat capacities.Moreover,as you can see in the leftmost
column of Table 1,their heat capacities are all the same.This re°ects the fact that translational motions
are the same for all particles;all such motions can be resolved into three directions in space,each
contributing
1
2
R to C
v
(C
p
's of gases are always greater by R owing to the work of expansion that occurs
if the gas is heated at constant pressure).
1
Translation refers to movement of an object as a complete unit.Translational motions of molecules in solids or liquids
are restricted to very short distances,comparable to the dimensions of the molecules themselves,whereas in gases the
molecules travel much greater distances between collisions.
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² Polyatomic molecules
monatomic diatomic triatomic
He 20.5
CO 29.3
H
2
O 33.5
Ne 20.5
N
2
29.3
D
2
O 34.3
Ar 20.5
F
2
31.4
CO
2
37.2
Kr 20.5
Cl
2
33.9
CS
2
45.6
Table 1:Molar heat capacities of some gaseous substances at constant pressure (Jmol
¡1
K
¡1
)
translation
3/2 R
vibration
R
rotation
1/2 R
5.1 Polyatomic molecules
For monatomic molecules such as He or Ar,translation is the only kind of motion allowed.For polyatomic
molecules,two additional kinds of motions become possible.Alinear molecule has an axis that de¯nes two
perpendicular directions in which rotations can occur;each represents an additional degree of freedom,
so the two together contribute a total of R to the heat capacity.For a non-linear molecule,rotations
are possible along all three directions of space,so these molecules have a rotational heat capacity of
3
2
R.
Finally,the individual atoms within a molecule can move relative to each other;this is called vibration.
A molecule consisting of N atoms possesses 3N ¡2 degrees of freedom.For mechanical reasons that we
cannot go into here,each vibrational motion contributes R (rather than
1
2
R to the total heat capacity.
Now we are in a position to understand why more complicated molecules have higher heat capacities.
The total kinetic energy of a molecule is the sum of those due to the various kinds of motions:
KE
total
= KE
trans
+KE
rot
+KE
vib
When a monatomic gas absorbs heat,all of the energy ends up in translational motion,and thus goes
to increase its temperature.In a polyatomic gas,by contrast,the absorbed energy is partitioned among
the other kinds of motions;since only the translational motions contribute to the temperature,the
temperature rise is smaller,and thus the heat capacity is larger.
There is one very signi¯cant complication,however:classical mechanics predicts that the energy
is always partitioned equally between all degrees of freedom.Experiments,however,show that this is
observed only at quite high temperatures.The reason is that these motions are all quantized.This
means that only certain increments of energy are possible for each mode of motion,and unless a certain
minimum amount of energy is availabe,a given mode will not be active at all and will contribute nothing
to the heat capacity.
It turns out that tranlational energy levels are spaced so closely that they these motions are active
almost down to absolute zero,so all gases possess a heat capacity of at least
3
2
R at all temperatures.
Rotational motions do not get started until intermediate temperatures,typically 300-500K,so within this
rnage heat capacities begin to increase with temperature.Finally,at very high temperaures,vibrations
begin to make a signi¯cant contribution to the heat capacity.
The strong intermolecular forces of liquids and many solids allow heat to be channeled into vibrational
motions involving more than a single molecule,further increasing heat capacities.One of the well known
\anomalous"properties of liquid water is its high heat capacity (75 Jmol
¡1
K
¡1
) due to intermolecular
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² 6 Pressure-volume work
10
20
30
Temperature, K
4R
3R
2R
R
50 100 500 1000 5000
H
2
translation
rotation
vibration
C, J K
Ð1
mol
Ð1
Figure 1:Heat capacity as a function of temperature for dihydrogen.
hydrogen bonding,which is directly responsible for the moderating in°uence of large bodies of water on
coastal climates.
Heat capacities of metals
Metallic solids are a rather special case.In metals,the atoms oscillate about their equilibrium positions
in a rather uniform way which is essentially the same for all metals,so they should all have about the
same heat capacity.That this is indeed the case is embodied in the Law of Dulong and Petit.In the 19th
century these workers discovered that the molar heat capacities of all the metallic elements they studied
were around to 25 Jmol
¡1
K
¡1
,which is close to what classical physics predicts for crystalline metals.
This observation played an important role in characterizing new elements,for it provided a means of
estimating their molar masses by a simple heat capacity measurement.
6 Pressure-volume work
Before we can explore the chemical applications of the First Law,we need to examine the nature of work
more closely.Although work can take many forms,they all have in common the feature that they are
the product of two terms:
type of work
intensity term
capacity term
formula
mechanical
force
change in distance
f¢x
gravitational
gravitational potential
mass
mg¢h
electrical
potential di®erence
quantity of charge
Q¢E
The kind of work we are most concerned with in chemistry is connected with changes in the volume
that a system undergoes as the result of some physical or chemical process.This is sometimes called
expansion work or PV-work,and it can most easily be understood by reference to the simplest form of
matter we can deal with,the ideal gas.Fig.2 shows a quantity of gas con¯ned in a cylinder by means
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² 6 Pressure-volume work
￿￿￿￿
￿￿￿￿
force of weights acting on area
a of piston produces external
pressure P = f/a
initial state:
P
1
,V
1
,T
1
final state:
P
2
,V
2
,T
2
￿￿￿￿
P
external
P
external
expansion
Figure 2:Expansion of a gas subjected to an external pressure.
of a moveable piston.Weights placed on top of the piston exert a force f over the cross-section area A,
producing a pressure P = f=A which is exactly countered by the pressure of the gas,so that the piston
remains stationary.Now suppose that we heat the gas slightly;according to Charles'law,this will cause
the gas to expand,so the piston will be forced upward by a distance ¢x.Since this motion is opposed
by the force f,a quantity of work f¢x will be done by the gas on the piston.By convention,work done
by the system (in this case,the gas) on the surroundings is negative,so the work is given by
w = ¡f¢x
When dealing with a gas,it is more convenient to think in terms of the more relevant quantities
pressure and volume rather than force and distance.We can accomplish this by multiplying the second
term by A=A which of course leaves it unchanged:
w = ¡f ¢ (¢x) ¢
A
A
By grouping the terms di®erently,but still not changing anything,we obtain
w = ¡
f
A
¢ (¢x) ¢ A
Since pressure is force per unit area and the product of the length ¢x and the area has the dimensions
of volume,this expression becomes
w = ¡P ¢ ¢V (3)
Eq 3 is a good illustration of how a non-state function like the work depends on the path by which a
given change is carried out.In this case the path is governed by the external pressure P.
Problem Example 1
Find the amount of work done on the surroundings when 1 litre of an ideal gas,initially at a pressure
of 10 atm,is allowed to expand at constant temperature to 10 litres by a) reducing the external
pressure to 1 atm in a single step,b) reducing P ¯rst to 5 atm,and then to 1 atm,c) allowing the
gas to expand into an evacuated space so its total volume is 10 litres.
Solution.First,note that ¢V,which is a state function,is the same for each path:V
2
=
(10=1) £1 L = 10 L,so ¢V = 9 L.
For path (a),w = ¡(1 atm) £9 L = ¡9`-atm.
Chem
1
General Chemistry
11
Chemical Energetics

² Reversible processes
1 step
Ð15 L-atm
2 steps
Ð20 L-atm
3 steps
Ð22 L-atm
￿￿￿￿
￿￿￿￿
￿￿￿￿






Expansion
Compression
Reversible
expansion
Ð31 L-atm
(maximum work)
Reversible
compression
31L-atm
(minimum work)
￿￿￿￿
￿￿￿￿
￿￿￿￿




The shaded areas are proportional to the amount of work that must be done on the gas to compress it,or that
is done on the surroundings when the gas expands.In a cyclic process in which the gas is returned to its initial
state,¢P = ¢V = 0,but the net work is zero only in the unattainable limit of the reversible pathway.All real
cyclic processes are accompanied by a net decrease in the amount of work that can be done in the world.
Figure 3:Work done in reversible and irreversible PV changes.
For path (b),the work is calculated for each stage separately:
w = ¡(5 atm) £(2 ¡1)L ¡(1 atm) £(10 ¡2)L = ¡13`-atm
For path (c) would be carried out by removing all weights from the piston in Fig.2 so that the
gas expands to 10 L against zero external pressure.In this case,w = (0 atm) £9 L = 0;no work is
done.
6.1 Reversible processes
The preceding example shows clearly how the work,a non-state function,depends on the manner in
which a process is carried out.
Evidently the minimum work that can be obtained from the expansion of a gas is zero.What is the
maximum work?To answer this,notice that more work was done when the process was carried out in
two stages than in one stage,and a simple calculation will show that even more work can be obtained by
increasing the number of stages.In order to extract the maximum work from the process,the expansion
would have to be carried out in an in¯nite sequence of in¯nitessimal steps.Each step yields an increment
Chem
1
General Chemistry
12
Chemical Energetics

² 7 Heat changes at constant pressure:the enthalpy
of work P dV which can be expressed as (RT=V ) dV and integrated:
w =
Z
V
2
V
1
RT
V
dV = RT ln
P
2
P
1
Although such a path (which corresponds to what is called a reversible process) cannot be realized in
practice,it can be approximated as closely as desired.
Even though no real process can take place reversibly (it would take an in¯nitely long time!),reversible
processes play an essential role in thermodynamics.The main reason for this is that q
rev
and w
rev
are state functions which are important and are easily calculated.Moreover,many real processes
take place su±ciently gradually that they can be treated as approximately reversible processes for
easier calculation.
7 Heat changes at constant pressure:the enthalpy
Most chemical processes are accompanied by changes in the volume of the system,and therefore involve
both heat and work terms.If the process takes place at a constant pressure,then the work is given by
Eq 3 and the change in internal energy will be
¢U = q ¡P¢V (4)
Since most changes that occur in the laboratory,on the surface of the earth,and in organisms are
subjected to a constant pressure of one atmosphere,Eq 4 is the form of the First Law that is of greatest
interest to most chemists.
Problem Example 2
Hydrogen chloride gas readily dissolves in water,releasing 75.3 kJ/mol of heat in the process.If one
mole of HCl at 298
±
K and 1 atm pressure occupies 24.5 litres,¯nd the ¢U for the system when one
mole of HCl dissolves in water under these conditions.
Solution:In this process the volume of liquid remains practically unchanged,so ¢V = ¡24:5 L.
The work done is
w = ¡P ¢ ¢V = ¡(1 atm)(¡24:5 L) = 24:5`-atm
Using the conversion factor 1 atm= 101:33 Jmol
¡1
and substituting in Eq 4,we obtain
¢U = q +P¢V = ¡75300 J ¡[(101:33 J=`-atm) £¡24:5`-atm] = ¡72:82 kJ
Notice that since the system undergoes a decrease in volume,work is done on the system and this
tends to increase the internal energy of the system.
From a practical standpoint we are usually most interested in the quantity of heat q associated with a
change.This is because q can be easily measured,and its sign determines whether a reaction is classi¯ed
as endothermic or exothermic.Solving Eq 4 for q,we obtain
q = ¢U +P¢V (5)
Notice that the ¢U +P¢V term in this expression is composed entirely of state functions.This means
that U +PV is itself a state function which we refer to as the enthalpy H.In terms of H,the First Law
becomes
q
P
= ¢H (6)
Chem
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General Chemistry
13
Chemical Energetics

² 8 Thermochemical equations and standard states
Remember that q is not a state function,and its value will depend on the particular pathway by which a
process is carried out.The subscript on q in the above expression means that we are referring to the heat
associated with only those pathways in which the pressure remains constant.The equation says that the
heat associated with any process that is carried out at a constant pressure depends only on the di®erence
between the enthalpies of the ¯nal and initial states of the system.
Because of the importance of constant-pressure processes (usually at 1 atm),enthalpies are much
more commonly used than are internal energies.About the only people who widely use ¢U values are
chemical engineers,who typically work with processes that take place in enclosed containers of constant
volume.For the rest of us,the\heat"of a reaction normally means ¢H.
It is worth noting that the di®erence between ¢U and ¢H depends on the change in volume.¢V is
only signi¯cant in processes that involve changes in the number of moles of gas.In fact,if the gases are
assumed to behave ideally,¢V = ¢n
g
RT where n
g
refers to the change in the number of moles of gas.
Thermochemistry The heat that °ows across the boundaries of a system undergoing a change is a
fundamental property that characterizes the change.It is easily measured,and if the process is carried out
at constant pressure,it can also be predicted from the di®erence between the enthalpies of the products
and reactants.The quantitative study and measurement of heat and enthalphy changes is known as
thermochemistry.
8 Thermochemical equations and standard states
In order to de¯ne the thermochemical properties of a process,it is ¯rst necessary to write a thermochemical
equation that de¯nes the system (thus allowing it to be distinghished from the surroundings).This
equation must also de¯ne the initial and ¯nal states of the system in terms of the states of its various
components.
To take a very simple example,here is the complete thermochemical equation for the vaporization of
water at its normal boiling point:
H
2
O(l;373 K;1 atm) ¡!H
2
O(g;373 K;1 atm) ¢H = 40:7 kJmol
¡1
The quantity 40.7 kJmol
¡1
is known as the enthalpy of vaporization (\heat of vaporization") of liquid
water.
For the neutralization of an acid by a strong base in aqueous solution,we must also specify the
concentrations of the various solutes:
H
+
(aq;1 M;298K;1 atm) +OH
¡
(aq;1 M;298K;1 atm)
¡!H
2
O(l;298K;1 atm)
¢H = ¡56:9 kJmol
¡1
Since most thermochemical equations are written for the standard conditions of 298
±
K and 1 atm pres-
sure,we can leave these quantities out if these conditions apply both before and after the reaction.If,
under these same conditions,the substance is in its preferred (most stable) physical state,then the sub-
stance is said to be in its standard state.Thus the standard state of water at 1 atm is the solid below
0
±
C,and the gas above 100
±
C.A thermochemical quantity such as ¢H that refers to reactants and
products in their standard states is denoted by ¢H
±
.
In the case of dissolved substances,the standard state of a solute is that in which the\e®ective
concentration",known as the activity,is unity.This will be close to an actual concentration of 1M for a
non-ionic substance,but for an ionic solute it will be less than 1 M and will depend on the particular ion
and on the other components of the solution.
Chem
1
General Chemistry
14
Chemical Energetics

² 9 Enthalpy of formation
Any thermodynamic quantity such as ¢H or ¢V that is associated with a thermochemical equation
always refers to the number of moles of substances explicitly shown in the equation.Thus for the synthesis
of water we can write
2 H
2
(g)
+ O
2
(g)
¡!2 H
2
O
(l)
¢H
±
= ¡572 kJmol
¡1
or
H
2
(g)
+
1
2
O
2
(g)
¡!
1
2
H
2
O
(l)
¢H
±
= ¡286 kJmol
¡1
When a solute dissolves in a liquid,the resulting heat change is known as the enthalpy of solution.
Since this will depend on the amount of solvent as well as that of the solute,the equation must show
these explicitly:
HCl
(g)
+ 50 H
2
O
(l)
¡!HCl ¢ H
2
O(soln)
9 Enthalpy of formation
The enthalpy change for a chemical reaction is the di®erence
¢H = H
products
¡H
reactants
:::but how can we evaluate the terms on the right side?We take advantage of the fact that energies are
only relative;that is,we can de¯ne the zero of energy arbitrarily.If we arbitrarily set the enthalpy and
internal energy of an element to zero,then the enthalpy of a compound such as H
2
O is de¯ned by the
thermochemical equation
H
2
(g)
+
1
2
O
2
(g)
¡!H
2
O
(l)
When this reaction is carried out at constant pressure,the quantity of heat released is found to be
¡268 kJmol
¡1
,so we can write
q
P
= ¢H = H
±
f
(H
2
O) ¡[H
±
f
(
1
2
O
2
) +H
±
f
(H
2
)] = ¡268 kJmol
¡1
H
±
f
(H
2
O) = ¡268 kJmol
¡1
H
±
f
(H
2
O) is the standard enthalpy of formation of water.
The standard enthalpy of formation of a compound is de¯ned as the heat associ-
ated with the formation of one mole of the compound from its elements in their
standard states.
The following examples illustrate some important aspects of the standard enthalpy of formation of
substances.
² The thermochemical equation de¯nining ¢H
±
must always be written in terms of one mole of the
substance in question:
1
2
N
2
(g)
+
3
2
H
2
(g)
¡!NH
3
(g)
¢H
±
= ¡46:1 kJmol
¡1
² A number of elements,of which sulfur and carbon are well-known examples,can exist in more
then one solid crystalline form.The standard heat of formation of a compound is always taken in
reference to the form that is most stable at 25
±
C and 1 atm pressure.In the case of carbon,this
is the graphite,rather than the diamond form:
C(graphite) + O
2
(g)
¡!CO
2
(g)
¢H
±
= ¡393:5 kJmol
¡1
C(diamond) + O
2
(g)
¡!CO
2
(g)
¢H
±
= ¡395:8 kJmol
¡1
Chem
1
General Chemistry
15
Chemical Energetics

² 10 Hess'law and thermochemical calculations
² In contrast,the product can be in any physical state,even if it is not the most stable one at 25
±
C
and 1 atm pressure:
H
2
(g)
+
1
2
O
2
(g)
¡!H
2
O
(l)
¢H
±
= ¡285:8 kJmol
¡1
H
2
(g)
+
1
2
O
2
(g)
¡!H
2
O
(g)
¢H
±
= ¡241:8 kJmol
¡1
Notice that the di®erence between these two ¢H
±
values is just the heat of vaporization of water.
² Although the formation of most molecules from their elements is an exothermic process,positive
heats of formation are possible:
1
2
N
2
(g)
+ O
2
(g)
¡!NO
2
(g)
¢H
±
= +33:2 kJmol
¡1
A positive heat of formation usually means that the molecule will be unstable (tend to decompose
into its elements) at room temperature.In many cases,however,the rate of this decomposition
is essentially zero,so it is still possible for the substance to exist.In this connection,it is worth
noting that all molecules will become unstable at higher temperatures.
² The thermochemical reactions that de¯ne the heats of formation of most compounds cannot actually
take place;for example,the direct synthesis of methane from its elements
C(graphite) + 2 H
2
(g)
¡!CH
4
(g)
cannot be carried out in the laboratory.All this means is that the ¢H
±
for such a reaction must be
found indirectly from other H
±
f
data,using Hess's law as explained in the next section.
² The standard enthalpy of formation of gaseous atoms from the element is known as the heat of
atomization.Heats of atomization are always positive,and are important in the calculation of bond
energies.
Fe
(s)
¡!Fe
(g)
¢H
±
= 417 kJmol
¡1
² The standard heat of formation of a dissolved ion such as Cl
¡
(aq)
cannot be determined with
respect to the element,since it is impossible to have a solution containing a single kind of ion.For
this reason,ionic enthalpies are expressed on a separate scale on which H
±
f
of the hydrogen ion at
unit activity (1M e®ective concentration) is de¯ned as zero.Thus for Ca
2+
,H
±
f
= ¡248 kJmol
¡1
;
this means that the reaction
Ca
(s)
¡!Ca
2+
(aq)
+ 2 e
¡
(aq)
would release 248 kJmol
¡1
more heat than the reaction
1
2
H
2
(g)
¡!H
+
(aq)
+ e
¡
(aq)
The standard enthalpy of formation the hydrogen ion is de¯ned as zero.
10 Hess'law and thermochemical calculations
You probably know that two or more chemical equations can be combined algebraically to give a new
equation.Even before the science of thermodynamics developed in the late nineteenth century,it was
observed by Germaine Hess (1802-1850) that the heats associated with chemical reactions can be combined
in the same way to yield the heat of another reaction.For example,the standard enthalpy changes for
Chem
1
General Chemistry
16
Chemical Energetics

² 11 Calorimetry
the oxidation of graphite and diamond can be combined to obtain ¢H
±
for the transformation between
these two forms of solid carbon{ a reaction that cannot be studied experimentally.
C(graphite) + O
2
(g)
¡!CO
2
(g)
¢H
±
= ¡393:51 kJmol
¡1
C(diamond) + O
2
(g)
¡!CO
2
(g)
¢H
±
= ¡395:40 kJmol
¡1
Subtraction of the second reaction from the ¯rst (i.e.,writing the second equation in reverse and adding
it to the ¯rst one) yields
C(graphite) ¡!C(diamond) ¢H
±
= 1:89 kJmol
¡1
(7)
This principle,known as Hess'law of independent heat summation is a direct consequence of the
enthalpy being a state function.¢H
±
for Eq 7 is determined only by the properties of graphite and
diamond,and is independent of the pathway by which the transformation is carried out.Hess'law
is one of the most powerful tools of chemistry,for it allows the change in the enthalpy (and in other
thermodynamic functions) of huge numbers of chemical reactions to be predicted from a relatively small
base of experimental data.
Of the various kinds of information in the world's thermochemical database,the most important are
the standard heats of formation,for these lead directly to the ¢H
±
values for the chemical transformation
of one substance to another.You will ¯nd tables of thermochemical data near the back of most Chemistry
textbooks.
As important as these quantities are,heats of formation are rarely measured directly.The reason is
that most substances cannot be prepared directly from their elements.Instead,Hess'law is employed
to calculate enthalpies of formation from more accessible data.The most important of these are the
standard enthalpies of combustion.Most elements and compounds combine with oxygen,and many of
these oxidations are highly exothermic,making the measurement of their heats relatively easy.
For example,by combining the heats of combustion of carbon,hydrogen,and methane,we obtain the
standard enthalpy of formation of methane,which as we noted above,cannot be determined directly:
C(graphite) + O
2
(g)
¡!CO
2
(g)
¡393:7 kJ
2 H
2
(g)
+ O
2
(g)
¡!2 H
2
O
(l)
¡571:5 kJ
CO
2
(g)
+ 2 H
2
O
(l)
¡!CH
4
(g)
+ O
2
(g)
+784.3 kJ
C(graphite) + 2H
2
(g)
¡!CH
4
(g)
{74.4 kJ
Tables of heats of formation,atomization,and combustion can be found in most textbooks.
11 Calorimetry
How are enthalpy changes determined experimentally?First,you must understand that the only thermal
quantity that can be observed directly is the heat q that °ows into or out of a reaction vessel,and that
q is numerically equal to ¢H only under the special conditions of constant pressure.Moreover,q is
equal to the standard enthalpy change ¢H
±
only when the reactants and products are both at the same
temperature,normally 25
±
C.
The measurement of q is generally known as calorimetry.A very simple calorimetric determination
of the standard enthalpy of the reaction
H
+
(aq)
+ OH
¡
(aq)
¡!H
2
O
(l)
could be carried out by combining equal volumes of 0.1M solutions of HCl and of NaOH initially at
25
±
C.Since this reaction is exothermic,a quantity of heat q will be released.If the reaction is carried out
Chem
1
General Chemistry
17
Chemical Energetics

² 11 Calorimetry
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿￿￿
￿￿￿￿￿￿
￿￿￿￿￿￿
￿￿￿￿￿￿
￿￿￿￿￿￿
￿￿￿￿￿￿
￿￿￿￿￿￿
￿￿￿￿￿￿
￿￿￿￿￿￿
ignition wires
stirrer
thermometer
bomb
sample holder
water in inner container
insulation
Figure 4:Bomb calorimeter for measurement of heat of combustion.
in an insulated vessel such as a Thermos container,this heat will be absorbed by the solution,raising its
temperature.What we actually measure is this temperature rise;if we multiply ¢T by the speci¯c heat
capacity of the solution,which will be close to that of pure water (4.184 J/g-K),we obtain the number
of joules of heat released into each gram of the solution,and q can then be calculated from the mass of
the solution.Since the entire process is carried out at constant pressure,we have ¢H
±
= q.
For reactions that cannot be carried out in dilute aqueous solution,the reaction vessel is commonly
placed within a larger insulated container of water.During the reaction,heat passes between the inner
and outer containers until their temperatures become identical.Again,the temperature change of the
water is observed,but in this case the value of q cannot be found just from the mass and the speci¯c
heat capacity of the water,for we now have to allow for the absorption of some of the heat by the walls
of the inner vessel.Instead,the calorimeter is\calibrated"by measuring the temperature change that
results from the introduction of a known quantity of heat.The resulting calorimeter constant,expressed
in JK
¡1
,can be regarded as the\heat capacity of the calorimeter".The known source of heat is usually
produced by passing an electric current through a resistor within the calorimeter.
Probably the most frequent kind of calorimetric measurement is the determination of heats of com-
bustion.Such measurements present special problems owing to the gaseous nature of O
2
and CO
2
,and
the necessity of igniting the mixture in order to start the reaction.Since the gases must be con¯ned,heat
of combustion determinations are carried out under constant volume,rather than constant pressure con-
ditions,so what is actually measured in the internal energy change.From the formula of the compound
the change ¢n
g
in the number of moles of gas is calculated,and this is used to ¯nd ¢H:
¢H = ¢U +P¢V = q
V
+¢n
g
RT (8)
Since the process takes place at constant volume,the reaction vessel must be constructed to withstand the
high pressure resulting from the combustion process,which amounts to a con¯ned explosion.The vessel
is usually called a\bomb",and the technique is known as bomb calorimetry.In order to ensure complete
combustion,the bomb is initially charged with pure oxygen above atmospheric pressure.The reaction
is initiated by discharging a capacitor through a thin wire which ignites the mixture.The product of
the capacitance and the voltage gives the quantity of charge,and thus the energy introduced into the
Chem
1
General Chemistry
18
Chemical Energetics

² 11 Calorimetry
calorimeter by the spark;this value is subtracted fromthat calculated fromthe observed temperature rise
of the calorimeter to yield the heat of the combustion reaction.A more common practice is to determine
the temperature rise produced by combustion,under identical conditions,of a substance whose heat of
combustion is accurately known.This yields a calorimeter constant that is usually expressed in Joules
per degree.
Problem Example 3
A sample of biphenyl (C
6
H
5
)
2
weighing 0.526 g was ignited in a bomb calorimeter initially at 25
±
C,
producing a temperature rise of 1.91 K.In a separate calibration experiment,a sample of benzoic acid,
C
6
H
5
COOH,weighing 0.825 g was ignited under identical conditions and produced a temperature
rise of 1.94 K.For benzoic acid,¢U
±
comb
is known to be ¡3226 kJmol
¡1
.Use this information to
determine the standard enthalpy of combusion of biphenyl.
Solution.The calorimeter constant is given by
(3226 kJmol
¡1
)(:825 g)
(1:94 K)(123 g=mol)
= 11:1 kJ=K
The heat released by the combustion of the biphenyl is then
q
V
=
(11:1 kJ=K)(1:91 K)(154 g=mol)
:526 g
= ¡6240 kJmol
¡1
(The negative sign indicates that heat is released in this process.) From the reaction equation
(C
6
H
5
)
2
(s) +
19
2
O
2
(g) ¡!12CO
2
(g) + 5H
2
O(l)
we have ¢n
g
= 12 ¡
19
2
= ¡
5
2
.Substituting into Eq 8,we have
¢H
±
= q
p
= ¢U
±
¡
5
2
(:008314 J mol
¡1
K
¡1
)(298K) = ¡6246 kJmol
¡1
This is the amount of heat that must be lost by the systemif reaction takes place at constant pressure
and the temperature is restored to its initial value.
Although calorimetry is simple in principle,its practice is a highly exacting art,especially when
applied to processes which take place slowly or involve very small heat changes.
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Chemical Energetics

² 11 Calorimetry
￿￿￿￿
￿￿￿￿
￿￿￿￿
￿￿￿￿
￿￿￿￿
￿￿￿￿
￿￿￿￿
sample tube
ice-water mixture
sample
mercury
weighing container
water
￿
￿￿
￿￿
￿
￿￿
￿￿
￿￿
￿￿
￿￿
￿￿
￿￿
￿￿
￿￿
￿￿
The ice calorimeter is an important tool for measuring the heat capacities of liquids and solids,as well as the
heats of certain reactions.This simple yet ingenious apparatus is essentially a device for measuring the change
in volume due to melting of ice.To measure a heat capacity,a warm sample is placed in the inner compartment,
which is surrounded by a mixture of ice and water.The heat withdrawn from the sample as it cools causes some
of this ice to melt.Since ice is less dense than water,the volume of water in the insulated chamber decreases.
This causes an equivalent volume of mercury to be sucked into the inner reservoir from the outside container.
The loss in weight of this container gives the decrease in volume of the water,and thus the mass of ice melted.
This,combined with the heat of fusion of ice,gives the quantity of heat lost by the sample as it cools to 0
±
C.
Figure 5:The ice calorimeter
Chem
1
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20
Chemical Energetics

² 12 Interpretation of reaction enthalpies
kJ mol
Ð1
0
Ð100
Ð200
Ð300
Ð400
C + O
2
(g)
CO(g)
CO
2
(g)
110 kJ
284 kJ
394kJ
reference level
Figure 6:Enthalpy diagram for the carbon-oxygen system
12 Interpretation of reaction enthalpies
12.1 Enthalpy diagrams
Comparison and interpretation of enthalpy changes is materially aided by a graphical construction in
which the relative enthalpies of various substances are represented by horizontal lines on a vertical energy
scale.The zero of the scale can be placed anywere,since energies are always arbitrary anyway.An
enthalpy diagram for carbon and oxygen and its two stable oxides is shown in Fig.6.In this diagram,
we follow the convention of assigning zero enthalpy to graphite,the most stable state of the elements at
298
±
K and 1 atm pressure.The labeled arrows show the changes in enthalpy associated with the various
reactions this system can undergo.Notice how Hess'law is implicit in this diagram;we can calculate the
enthalpy change for the combustion of carbon monoxide to carbon dioxide,for example,by subtraction
of the appropriate arrow lengths without writing out the thermochemical equations in a formal way.
Enthalpy diagrams are especially useful for comparing groups of substances having some common
feature.In Fig.7,the molar enthalpies of species relating to two hydrogen halides are shown with
respect to those of the elements.From this diagram we can see at a glance that the formation of HF
from the elements is considerably more exothermic than the corresponding formation of HCl.The upper
part of this diagram shows the gaseous atoms at positive enthalpies with respect to the elements.The
endothermic processes in which the H
2
and the dihalogen are dissociated into atoms can be imagined as
taking place in two stages,also shown.From the enthalpy change associated with the dissociation of H
2
(218 kJmol
¡1
),the dissociation enthalpies of F
2
and Cl
2
can be calculated and placed on the diagram.
12.2 Bond enthalpies and bond energies
The energy change associated with the reaction
HI
(g)
¡!H
(g)
+ I
(g)
is the heat of dissociation of the HI molecule;it is also the bond energy of the hydrogen-iodine bond in
this molecule.Under the usual standard conditions,it would be expressed as H
±
HI(298)
or U
±
HI(298)
;in
this case they di®er from each other by ¢PV = RT.Since this reaction cannot be observed under these
conditions,the H{I bond enthalpy is calculated from the appropriate standard enthalpies of formation:
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21
Chemical Energetics

² Energy content of fuels
Ð100
Ð200
Ð300
0
100
200
300
F(g) + H(g)
+79
+218
Ð269
+121
H(g)
Ð431
Ð92
Ð564
kJ mol
Ð1
HF(g)
HCl(g)
H
2,
Cl
2
, F
2
Cl(g) + H(g)
Figure 7:Enthalpy diagram comparing HF and HCl
1
2
H
2
(g)
¡!H
(g)
+218 kJ
1
2
I
2
(g)
¡!I
(g)
+107 kJ
1
2
H
2
(g)
+
1
2
I
2
(g)
¡!HI
(g)
+26 kJ
HI
(g)
¡!H
(g)
+ I
(g)
299 kJ
Bond energies and enthalpies are important properties of chemical bonds,and it is very important
to be able to estimate their values from other thermochemical data.The total bond enthalpy of a more
complex molecule such as ethane can be found from
C
2
H
6
(g)
¡!2 C(graphite) + 3 H
2
(g)
84.7 kJ
3 H
2
(g)
¡!6 H
(g)
1308 kJ
2 C(graphite) ¡!2 C
(g)
1430 kJ
C
2
H
6
(g)
¡!2 C
(g)
+ 6 H
(g)
2823 kJ
The total bond energy of a molecule can be thought of as the sum of the energies of the individual
bonds.This principle,known as Pauling's Rule,is only an approximation,because the energy of a given
type of bond is not really a constant,but depends somewhat on the particular chemical environment of
the two atoms.In other words,all we can really talk about is the average C{Cl bond energy,for example,
the average being taken over a representative sample of compounds containing this type of bond.
Despite the lack of strict additivity of bond energies,Pauling's Rule is extremely useful because it
allows one to estimate the heats of formation of compounds that have not been studied,or have not even
been prepared.Thus in the foregoing example,if we know the enthalpies of the C{C and C{H bonds
from other data,we could estimate the total bond enthalpy of ethane,and then work back to get some
other quantity of interest,such as ethane's enthalpy of formation.
12.3 Energy content of fuels
The enthalpy of combustion is obviously an important criterion for a substance's suitability as a fuel,
but it is not the only one;a useful fuel must also be easily ignited,and in the case of a fuel intended
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Chemical Energetics

² Energy content of foods
for self-powered vehicles,its energy density (kJ/m
3
) must be reasonably large.Thus substances such as
methane and propane which are gases at 1 atm must be stored as pressurized liquids for transportation
and portable applications.
Owing to its low molar mass and high heat of combustion,dihydrogen possesses an extraordinarily
high energy density,and would be an ideal fuel if its critical temperature (33
±
K,the temperature above
which it cannot exist as a liquid) were not so low.The potential bene¯ts of using hydrogen as a fuel
have motivated a great deal of research into other methods of getting a large amount of H
2
into a small
volume of space.Simply compressing the gas to a very high pressure is not practical because the weight
of the heavy-walled steel vessel required to withstand the pressure would increase the e®ective weight of
the fuel to an unacceptably large value.One scheme that has shown some promise exploits the ability
of H
2
to\dissolve"in certain transition metals.The hydrogen can be recovered from the resulting solid
solution (actually a loosely-bound compound) by heating.
12.4 Energy content of foods
What,exactly,is meant by the statement that a particular food\contains 1200 calories"per serving?
This simply refers to the standard enthalpy of combustion of the foodstu®,as measured in a bomb
calorimeter.Note,however,that in nutritional usage,the calorie is really a kilocalorie (sometimes called
\large calories"),that is,4184 J.Although this unit is still employed in the popular literature,the SI
unit is now commonly used in the scienti¯c and clinical literature,in which energy contents of foods are
usually quoted in megaJoules (MJ) or kJ per 1-,100-,or 1000 grams.
Although the mechanisms of oxidation of a carbohydrate such as glucose to carbon dioxide and water
in a bomb calorimeter and in the body are complex and completely di®erent,the net reaction involves the
same initial and ¯nal states,and ¢H,being a state function,must be the same for any possible pathway.
C
6
H
12
O
6
+ 6 O
2
¡!6 CO
2
+ 6 H
2
O ¢H
±
= 20:8 kJmol
¡1
(9)
Glucose is a sugar,a breakdown product of starch,and is the most important energy source at the cellular
level;fats,proteins,and other sugars are readily converted to glucose.By writing balanced equations for
the combustion of sugars,fats,and proteins,a comparison of their relative energy contents can be made.
The stoichiometry of each reaction gives the amounts of oxygen taken up and CO
2
released when a given
amount of each kind of food is oxidized;these gas volumes are often taken as indirect measures of energy
consumption and metabolic activity.
For some components of food,oxidation may not always be complete in the body,so the energy that
is actually available will be smaller than that given by the heat of combustion.Mammals,for example,
are unable to break down cellulose (a polymer of sugar) at all;animals that derive a major part of their
nutrition fromgrass and leaves must rely on the action of symbiotic bacteria which colonize their digestive
tracts.The amount of energy available from a food can be found by measuring the heat of combustion of
the waste products excreted by an organism that has been restricted to a controlled diet,and subtracting
this from the heat of combustion of the food.
The amount of energy a person requires depends on the age,sex,surface area of the body,and of
course on the amount of physical activity.The rate at which energy is expended is expressed in watts:
1 W= 1 J=s.For humans,this value varies fromabout 200{800 W.This translates into daily food intakes
having energy equivalents of about 10{15 MJ for most working adults.In order to just maintain weight
in the absence of any physical activity,about 6 MJ per day is required.
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Chemical Energetics

² 13 Variation of the enthalpy with temperature
type of food ¢H
comb
,kJ/g percent availability
Protein
meat 22.4 92
egg 23.4
Fat
butter 38.2
animal fat 39.2 95
Carbohydrate
starch 17.2
glucose 15.5 99
ethanol 29.7 100
Table 2:Energy content and availability of the major food components
13 Variation of the enthalpy with temperature
The enthalpy of a system increases with the temperature.This is mainly due to the similar dependence
of the internal energy on the temperature.The de¯ning relation
¢H = ¢U +P¢V
tells us that the enthalpy is dominated by the internal energy,subject to a slight correction for pressure-
volume work.Heating a substance causes it to expand,making ¢V positive and causing the enthalpy to
increase slightly more than the internal energy.Physically,what this means is that if the temperature
is increased while holding the pressure constant,some extra energy must be expended to push back the
external atmosphere while the system expands.The di®erence between the dependence of U and H on
temperature is only really signi¯cant for gases,since the coe±cients of thermal expansion of liquids and
solids are very small.
You will recall that the proportionality constant that relates the internal energy to the temperature
is called the heat capacity.Since U and H increase with temperature by slightly di®erent amounts,we
can de¯ne two heat capacities,one for processes which take place at constant volume
C
v
=
¢U
¢T
(10)
and one for processes at constant pressure
C
p
=
¢H
¢T
(11)
A plot of the enthalpy of a system as a function of its temperature is called an enthalpy diagram.The
slope of the line is given by C
p
.The enthalpy diagram of a pure substance such as water shows that this
plot is not uniform,but is interrupted by sharp breaks at which the value of C
p
is apparently in¯nite,
meaning that the substance can absorb or lose heat without undergoing any change in temperature at
all.This,of course,is exactly what happens when a substance undergoes a phase change;you already
know that the temperature the water boiling in a kettle can never exceed 100
±
C until all the liquid has
evaporated,at which point the temperature of the steam will rise as more heat °ows into the system.
Fusion and boiling are not the only kinds of phase changes that matter can undergo.Most solids can
exist in di®erent structural modi¯cations at di®erent temperatures,and the resulting solid-solid phase
changes produce similar discontinuities in the heat capacity.Enthalpy diagrams are easily determined
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24
Chemical Energetics

² 13 Variation of the enthalpy with temperature
by following the temperature of a sample as heat °ows into our out of the substance at a constant rate.
The resulting diagrams are widely used in materials science and forensic investigations to characterize
complex and unknown substances.
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25
Chemical Energetics


² 13 Variation of the enthalpy with temperature
20
40
60
80
H, kJ mol
Ð1
100
400300200100
H
vaporization
H
fusion
H
phase transition
CCl
4
T, ¡K
Figure 8:Enthalpy of carbon tetrachloride as a function of temperature at 1 atm
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Chemical Energetics

² 14 The direction of spontaneous change
Part 2:The approach to equilibrium
The greater part of what we call chemistry is concerned with the di®erent kinds of reactions that
substances can undergo.The statement that\hydrogen °uoride is a stable molecule"is really a way of
saying that the reaction HF ¡!
1
2
H
2
+
1
2
F
2
has an overwhelming tendency to occur in the reverse
direction,and a negligible tendency to occur in the forward direction.More generally,we can predict
how the composition of an arbitrary mixture of H
2
,F
2
,and HF will tend to change by comparing the
values of the equilibrium constant K and the equilibrium quotient Q;your study of equilibrium,you will
recall that if Q=K > 1 the reaction will proceed to the left,whereas if Q=K < 1 it will proceed to the
right.In either case,the system will undergo a change in composition until it reaches the equilibrium
state where Q = K.
Clearly,the value of K is the crucial quantity that characterizes a chemical reaction,but what factors
a®ect its value?In particular,is there any way that we can predict the value of the equilibriumconstant of
a reaction solely from information about the products and reactants themselves,without any knowledge
at all about the mechanism or other details of the reaction?The answer is yes,and this turns out to be
the central purpose of chemical thermodynamics:
The purpose of thermodynamics is to predict the equilibrium state
of a system from the properties of its components.
Don't let the signi¯cance of this pass you by;it means that we can say with complete certainty whether
or not a given change is possible,and if it is possible,to what extent it will occur,without the need to
study the particular reaction in question.To a large extent,this is what makes chemistry a science,rather
than a mere cataloging of facts.
14 The direction of spontaneous change
Drop a teabag into a pot of hot water,and you will see the tea di®use into the water until it is uniformly
distributed throughout the water.What you will never see is the reverse of this process,in which the tea
would be re-absorbed by the teabag.The making of tea,like all changes that take place in the world,
possesses a\natural"direction.Here are a few other examples:
² A stack of one hundred coins is thrown onto the °oor,and the numbers that land\heads up"and
\tails up"are noted.
² One mole of gas,initially at 300
±
K and 2 atm pressure,is allowed to expand to double its volume,
keeping the temperature constant.
² A raindrop,supercooled to ¡1
±
C at 1 atm,changes into ice (\freezing rain") as it strikes the
windshield of your car.
² One mole of N
2
O
4
gas is placed in a container and allowed to come to equilibrium with NO
2
.
All of these changes take place spontaneously,meaning that once they are started,they will proceed
to the ¯nish without any outside intervention.It would be inconceiveable that any of these changes could
occur in the reverse direction (that is,be undone) without changing the conditions or actively disturbing
the system in some way.
What determines the direction in which spontaneous change will occur?Your ¯rst thought might be
that the direction of change will be the one that leads to a lower energy,but this is not generally correct.
As a matter of fact,in all of the examples cited above,the energy of the system in its ¯nal state is either
the same or greater that that of the initial state.
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Chemical Energetics

² A closer look at disorder
This might seem strange to you;after all,you know that a simple mechanical system will always
change in a way that leads to a lower potential energy,so why should a more complex system made
up of many molecules not do the same?When you drop a book onto the °oor there is no question
about what will happen,because the initial potential energy of the book is entirely converted into
kinetic energy of random thermal motion (heat) at the moment of impact,and this has no e®ect on
the book other than to warm it up a bit.
Now imagine that instead of a heavy book,we observe a single molecule as it collides with a
surface.Because its mass is very small,its kinetic energy is also small and comparable to that of
the molecules making up the surface;on colliding with the surface it could just as easily gain kinetic
energy as lose it.The average gas molecule in a container will simply bounce o® the wall with about
the same kinetic energy as it has before the collision,but some will acquire more,and others will
su®er a net loss.
The short (and admittedly incomplete) answer to the above question is that in an exothermic
change,energy is never lost,but simply exchanged between system and surroundings,and when the
packets of energy are of su±ciently small magnitude (as in a collection of molecules that are free to
act individually),this exchange can operate in both directions.
After any of the processes listed on the preceding page is completed,the system may have gained or
lost energy,but the total energy of the systemand the surroundings (and thus,of the world) is unchanged.
However,there is something about the world that has changed,and this is its degree of randomness,or
disorder.
This can be seen most easily in the case of the coins.The process
100 heads ¡!50 heads + 50 tails
which expresses the state of maximum disorder of 100 coins is a far more likely outcome of random tosses
than
50 heads + 50 tails ¡!100 heads
which,if not impossible,is so unlikely that we would have grave doubts about the fairness of the coins if
we were to witness such an outcome.
Similarly,the molecules of a gas can occupy a larger number of possible positions in space if the
volume is larger,so the expansion of a gas is similarly accompanied by an increase in randomness,or
disorder.And looking at the dissociation reaction of dinitrogen tetroxide
N
2
O
4
(g)
¡!2 NO
2
(g)
¢H
±
= +13:9 kJ
it is apparent that the number of molecules increases,and this also leads to an increase in disorder.
But what about the freezing of water?It might appear that this process leads to a decrease in disorder,
since ice is certainly a more ordered state of matter than is liquid water.Furthermore,if you think about
it,a sample of pure gaseous NO
2
will tend to undergo the reverse of the above dissociation reaction,
since the equilibrium composition must be independent of the direction in which it is approached.And
if we increase the pressure on a gas,it will spontaneously contract,leading to a decrease rather than
an increase in disorder of the gas.Clearly,the relation of randomness to similar processes and to most
chemical reactions,requires some further re¯nement of our thinking.
14.1 A closer look at disorder
First,how can we express disorder quantitatively?From the example of the coins,you can probably see
that simple statistics plays a role:the probability of obtaining three heads and seven tails after tossing
ten coins is just the ratio of the number of ways that ten di®erent coins can be arranged in this way,to
the number of all possible arrangements of ten coins.
Chem
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Chemical Energetics

² A closer look at disorder
macrostate ways probability microscopic states
0 heads 1 1/16####
1 head 4 4=16 = 1=4"####"####"####"
2 heads 6 6=16 = 3=8""##"#"#"##"#""###""#"#"
3 heads 4 4=16 = 1=4"""#"#""""#"#"""
4 heads 1 1/16""""
The probability of a given macrostate is proportional to the number of ways of realizing that state,
and thus to the number of microstates that correspond to the macrostate.For the general case of n
coins being in a macrostate with h heads-up,this number (in the second column of the table) is given
by n!=(h!)
2
.The probability of a given macrostate is just the ratio of the number of corresponding
microstates to the total number of microstates.This assumes,of course,that all microstates are
equally probable.
Table 3:Macroscopic and microscopic states of a set of four coins
Using the language of molecular statistics,we say that a collection of coins in which 30% of its
members are heads-up constitutes a macroscopic state of the system.Since we don't care which coins are
heads-up,there are clearly various con¯gurations of coins which can result in this\macrostate".Each of
these con¯gurations speci¯es a microscopic state of the system.
The greater the number of microstates that correspond to a given macrostate,the greater the proba-
bility of that macrostate.To see what this means,study Table 3,which shows the possible outcomes of
a toss of four coins.
In applying these same ideas to molecules,we need to distinguish between two kinds of randomness,
or disorder.The examples we have just given illustrate what might be called positional disorder.We can
quantify positional randomness in a monatomic gas by dividing a container up into imaginary compart-
ments,and counting the number of di®erent ways that the gas molecules could be distributed amongst
these di®erent compartments.The greater the volume occupied by the gas,the more con¯gurations
(microstates) that are consistent with this volume.If the number of molecules is large,the number of
microstates in which the gas occupies the entire volume of the container is much,much greater than the
number that would correspond to a crowding of the molecules into a volume that is smaller by even a tiny
amount;any of the macrostates corresponding to smaller volumes are so improbable statistically that we
can call them\impossible".
Energy disorder.There is another kind of randomness that is generally more important than
positional randomness.This relates to the number of ways in which energy can be distributed in a
collection of molecules.At the atomic and molecular level,all energy is quantized;each particle possesses
discrete states of kinetic energy and is able to accept thermal energy only in packets whose values
correspond to the energies of one or more of these states.
Suppose that we have three molecules and enough kinetic energy to excite three energy states (Fig.9).
We can give all the kinetic energy to one molecule,leaving the others with nothing,we can give two units
to one molecule and one unit to another,or we share out the energy equally and give one unit to each
molecule.All told,there are ten possible ways of distributing three units of energy among three identical
molecules.
However,if the allowed energy levels of the molecule are closer together so that the same amount of
energy can be accepted in smaller packets,then the number of possible distributions is greatly increased,
and so is the\energy randomness"of the system.The spacing of these energy states becomes closer as
the mass and number of bonds in the molecule increases,so we can generally say that the more complex
the molecule,the greater the amount of energy-disorder it has.
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Chemical Energetics

² A closer look at disorder
0
2
1
3
5
4
The quantity of energy indicated by the vertical
arrow can be distributed in three ways in a collection
of molecules whose allowed energy levels are
spaced as shown here.
0
1
2
3
available
energy
In molecules with more widely-
spaced energy levels, there are
fewer ways of distributing the same
total energy.
a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c
0
1
2
3
quantized
energy state
microstat
e
1 2 3 4 5 6 7 8 9
10
molecul
e
( denotes
excited)

If the allowed energy levels are very close (more likely in molecules having stronger bonds and heavier
atoms), then the available energy can be distributed equally among them, greatlly increasing the
energy randomness and thus the probability of the system. This example shows how one macroscopic
state (3 units of energy distributed amongst three molecules) can be realized in ten different ways
(different microscopic states).
Figure 9:Energy randomness at the molecular level
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Chemical Energetics

² 15 The entropy
Three kinds of states associated with kinetic energy are possible.A monatomic molecule such as
helium can absorb energy only by moving faster;the resulting energy is known as translational
kinetic energy.You will recall from the kinetic theory of gases that the average translational kinetic
energy of a gas is related to its temperature.In polyatomic molecules,energy can also be taken up
in the form of vibrational and rotational motions;the number of such motions,and hence the degree
of randomness in which energy can be distributed in a collection of molecules,increases rapidly as
the molecules become more complicated in structure.Because only a portion of the energy absorbed
by such molecules goes into increasing the translational motion (and thus the temperature),larger
molecules have larger heat capacities;that is,their temperatures are less a®ected by absorption or
loss of a given quantity of heat.
15 The entropy
How can we relate disorder to measurable thermodynamic quantities?It turns out that the quantity
of importance is the ratio q=T.If you stop to think about the meaning of this ratio,it makes sense.
Absorption of a quantity of heat q will always lead to in increase in disorder by providing more packets of
energy that can be distributed over the various modes of motion characteristic of the particular molecule.
To understand why we have to divide the quantity of heat by the temperature,consider the e®ect of very
large and very small values of T in the denominator.If a substance is initially at a very low temperature,
it possesses relatively little kinetic energy and what there is cannot be divided up in very many ways.If it
now absorbs a quantity of heat,there will be a relatively large increase in energy randomness.If,however,
the temperature is initially large,there will already be a great amount of disorder and absorption of the
same increase in energy as before will have relatively little e®ect on the randomness of the system.
The only problem with using q=T as a measure of the change in randomness is that q is not a
thermodynamic state function;that is,its value is dependent on the pathway,or manner,by which a
process is carried out.This means,of course,that the quotient q=T cannot be a state function either,so
we are unable to use it to get di®erences between reactants and products as we do with the other state
functions.The way around this is to restrict our consideration to a special class of pathways that are
designated reversible.A change is said to occur reversibly when it can be undone without any exchange
of heat or work with the surroundings.In e®ect,this means that the process is carried out in a series
of in¯nitesimal steps.Of course,such a process would take in¯nitely long to occur,so thermodynamic
reversibility is an idealization that is never achieved in real processes,except when the system is already
at equilibrium,in which case no change will occur anyway!
Why is the concept of a reversible process so important?The answer can be seen by recalling that
the change in the internal energy that characterizes any process can be distributed in an in¯nity of ways
between heat °ow across the boundaries of the system and work done on or by the system,as expressed
by the First Law ¢U = q +w.Each combination of q and w represents a di®erent pathway between the
initial and ¯nal states.It can be shown that as a process,such as the expansion of a gas,is carried out
in successively longer series of smaller steps,the absolute value of q approaches a minimum,and that of
w approaches a maximum that is characteristic of the particular process.Thus when a process is carried
out reversibly,the w-term in the First Law expression has its greatest possible value,and the q-term is
at its smallest.These special quantities w
max
and q
min
(which we denote as q
rev
or\q reversible") have
unique values 12 for any given process and are therefore state functions.
Since q
rev
is a state function,so is q
rev
=T.This quotient is one of the most important quantities
in thermodynamics,because it is expresses the change in disorder that accompanies a process.Note
carefully that the change in disorder is always related to the limiting value q
rev
=T even when the process
is carried out irreversibly and the actual value of q=T is di®erent.
Being a state function,q
rev
=T deserves a name and symbol of its own;it is called the entropy,
Chem
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General Chemistry
5
Chemical Energetics

² The entropy of the world always increases
designated by S.Since q
rev
=T describes a change in state,we write the de¯nition
¢S = q
rev
=T
(12)
15.1 The entropy of the world always increases
All natural processes that involve more than a few particles
2
occur in a direction that leads to a more
random distribution of matter and energy;that is,they lead to an increase in the entropy of the world.