lecture notes on physical organic chemistry and how to study physical chemistry| download free pdf
Prof. Ing. Anatol Malijevsk´ y, CSc., et al.
(September 30, 2005)
Institute of Chemical Technology, Prague
Faculty of Chemical Engineering4
Physical Chemistry is generally considered to be a diﬃcult subject. We thought long and
hard about ways to make its study easier, and this text is the result of our endeavors. The
book provides accurate deﬁnitions of terms, deﬁnitions of major quantities, and a number of
relations including speciﬁcation of the conditions under which they are valid. It also contains
a number of schematic ﬁgures and examples that clarify the accompanying text. The reader
will not ﬁnd any derivations in this book, although frequent references are made to the initial
formulas from which the respective relations are obtained.
istry II” as taught at the Institute of Chemical Technology (ICT), Prague up to 2005. However
the extent of this work is a little broader as our objective was to cover all the major ﬁelds of
This publication is not intended to substitute for any textbooks or books of examples. Yet
we believe that it will prove useful during revision lessons leading up to an exam in Physical
Chemistry or prior to the ﬁnal (state) examination, as well as during postgraduate studies.
Even experts in Physical Chemistry and related ﬁelds may ﬁnd this work to be useful as a
Physical Chemistry In Brief has two predecessors, “Breviary of Physical Chemistry I” and
“Breviary of Physical Chemistry II”. Since the ﬁrst issue in 1993, the texts have been revised
and re-published many times, always selling out. Over the course of time we have thus striven
to eliminate both factual and formal errors, as well as to review and rewrite the less accessible
passages pointed out to us by both students and colleagues in the Department of Physical
togrow, wedecidedtogivethemaproventoolwrittenintheEnglishlanguage. Thistextisthe
result of these eﬀorts. A number of changes have been made to the text and the contents have
been partially extended. We will be grateful to any reader able to detect and inform us of any
errors in our work. Finally, the authors would like to express their thanks to Mrs. Flemrov´a
for her substantial investment in translating this text.CHAP. 1: BASIC TERMS CONTENTS 24
A good deﬁnition of basic terms is an essential prerequisite for the study of any
physicochemical processes. Some of these terms may be also used beyond the ﬁeld of
sum up the major basic terms that will be used in the subsequent parts of this book.
1.1 Thermodynamic system
The concept (thermodynamic) system as used in this book refers to that part of the world
whose thermodynamic properties are the subject of our interest, while the termsurroundings
is used for the remaining part of the universe.
Note: Both a certain part of the real space and a certain part of the imaginary (abstract)
space forming a simpliﬁed model system, e.g. an ideal gas, may be chosen as a system.
Systems are classiﬁed as isolated, closed and open, based on their inter-relations with their
1.1.1 Isolated system
A chemical system exchanging neither matter nor energy with its surroundings is an isolated
system.CHAP. 1: BASIC TERMS CONTENTS 25
1.1.2 Closed system
1.1.3 Open system
A chemical system exchanging both energy and matter with its surroundings is an open sys-
Diﬀerences between individual types of chemical systems may be demonstrated using the example
of making coﬀee. The pot on the heater represents a (practically) closed system until the water
is brought to the boil. At the boiling point, when steam is leaking from the pot, it becomes an
open system. The ready-made coﬀee kept in a thermos bottle represents a simple model of an
1.1.4 Phase, homogeneous and heterogeneous systems
The termphase is used for that portion of the investigated system volume in which its proper-
ties areconstantor continuouslychanginginspace. If asystembehaves in this way throughout
all its volume, we call it a homogeneous system. If a system contains more phases, we call
it a heterogeneous system.
Let us imagine a bottle of whisky. How many phases does this system consist of?CHAP. 1: BASIC TERMS CONTENTS 26
If we are, from the thermodynamic point of view, interested solely in the liquid content of the
bottle, the system is homogeneous. It contains one liquid phase (a mixture of water, ethanol and
some additives). If, on the other hand, we are interested in the entire content of the bottle but
not the bottle itself, the system is heterogeneous. In this case it consists of two phases, liquid and
gaseous, with the latter containing air and whisky vapour. If, however, we focus our attention
on both the bottle content and the bottle itself, we have a heterogeneous system again, but this
time it also contains other phases in addition to the gaseous and liquid ones, i.e. the glass of the
bottle, its cap, label, etc.CHAP. 1: BASIC TERMS CONTENTS 27
Obr. 1.1: The volume of a system as an extensive quantity. The volume V is the sum of the volumes
of the individual parts (i.e. sub-systems) I, II and III, i.e. V =V +V +V .
I II III
There are two basic forms of energy exchange between a system and its surroundings, heat
andwork. A positive value is assigned to such energy exchange during which the system gains
energy (work or heat) from its surroundings, i.e. energy is added to the system. A negative
value indicates that the system passes energy (work or heat) to its surroundings, i.e. energy is
subtracted from the system.
and its surroundings (e.g. transfer of kinetic energy of disordered movement of molecules), we
speak about exchanged heat.
U Main unit: J.
Other forms of energy exchange, which are usually driven by some forces acting between the
system and its surroundings, are called work. Based on the type of interaction between the
system and its surroundings, we distinguish volume work see 3.1.2, electrical work, surface
U Main unit: J.CHAP. 1: BASIC TERMS CONTENTS 28
1.3 Thermodynamic quantities
Observation of any system allows us to determine a number of its properties. The proper-
ties in which we are interested from the thermodynamic point of view are called thermody-
namic quantities, or, brieﬂy, quantities. Typical thermodynamic quantities are temperature,
pressure, volume, enthalpy and entropy. Neither heat nor work rank among thermodynamic
Note: Terms such as thermodynamic function, thermodynamic variable, state quantity
are used as synonyms of the term thermodynamic quantity.
1.3.1 Intensive and extensive thermodynamic quantities
betweenextensive andintensive thermodynamic quantities of a system. Intensive quantities
are those whose values do not change when the system is divided into smaller sub-systems.
Extensive quantities are those whose values are proportional to the amount of substance of
the system at a ﬁxed temperature and pressure (see Figure 1.1). Temperature, pressure, and
composition expressed by mole fractions are typical intensive quantities. Volume, mass and the
number of particles are typical extensive quantities.
Note: Some quantities, e.g. the system surface, are neither extensive nor intensive.
Every extensive quantity may be converted into an intensive one if we relate it to a certain
constantmassofthesystem. Wethenobtainspeciﬁcormolarquantities(see3.2.5). Forevery
extensive quantity X and the respective molar and speciﬁc quantities X and x we may
X = nX , (1.1)
X = mx, (1.2)
where n is the amount of substance and m is the mass of the system.
S Symbols: We will use the subscript to denote molar quantities and small letters to denote
speciﬁc quantities.CHAP. 1: BASIC TERMS CONTENTS 29
1.4 The state of a system and its changes
Any system may be in any moment characterized using a certain number of quantities. These
quantities deﬁne the state of a given system. The degree of generality at which we observe
a given system has to be taken into account at the same time. In terms of a microscopic
scale, the state of a system is deﬁned by the position and velocity of all its particles. In terms
of thermodynamics, however, it is enough to know only a few quantities, e.g. temperature,
pressure and composition.
1.4.1 The state of thermodynamic equilibrium
The state of thermodynamic equilibrium (equilibrium state, equilibrium) is a state in which no
macroscopic changes occur in the system and all quantities have constant values in time.
Note: In the state of thermodynamic equilibrium, changes take place at the microscopic
level. For instance, when the liquid and vapour phases are in equilibrium, some molecules
continuously move from the liquid to the vapour phase and others from the vapour to the
liquid phase. However, the temperature and pressure of the system do not change.
The state of thermodynamic equilibrium embraces the following partial equilibria:
• mechanical (pressure) equilibrium—the pressure in all parts of the system is the same ,
• thermal (temperature) equilibrium—the temperature in all parts of the system is equal-
• concentration equilibrium—the concentration of the system components is the same in
all parts of each phase of the system, but the composition of individual phases is usually
are in equilibrium.
The osmotic equilibrium is an exception.CHAP. 1: BASIC TERMS CONTENTS 30
Note: If a system in the state of thermodynamic equilibrium occurs in an external force
ﬁeld, e.g. the gravitational ﬁeld, the pressure is not the same in all parts of the system
but it changes continuously. The concentration of the system components also changes
continuously in each phase, with a discontinual change occurring at the phase boundary.
1.4.2 System’s transition to the state of equilibrium
If a system is not in the state of equilibrium, its properties change in time in such a way that
it tends toward equilibrium. Thermodynamics postulates that every system under invariable
for pressure equalization up to hundreds of years needed for glass transition to the crystalline
If we immerse several crystals of copper(II) sulphate pentahydrate (CuSO· H O) into a closed
4 5 2
vessel containing water, the system thus created will be in a non-equilibrium state at the be-
ginning. There will be neither a phase equilibrium between the crystals and the liquid phase
nor a concentration equilibrium. After some time the crystals will dissolve (phase equilibrium).
If we do not mix the system, the dissolved copper(II) sulphate pentahydrate will slowly diﬀuse
through the solution from the bottom up to the surface, and after many weeks (relaxation time),
concentration in all parts of the system will become equal as well (thermodynamic equilibrium).
1.4.3 Thermodynamic process
we say that a certain thermodynamic process takes place in the system. The term process
relates to a very broad range of most varied processes, from simple physical changes such as,
e.g., heating, various chemical reactions, up to complex multistage processes. Individual kinds
of processes may be classiﬁed according to several criteria.CHAP. 1: BASIC TERMS CONTENTS 31
1.4.4 Reversible and irreversible processes
The course of any process depends on the conditions under which the given system changes.
If we arrange the conditions in such a way that the system is nearly at equilibrium in every
moment, and that, consequently, the direction of the process may be reversed by even a very
slight change of the initial conditions, the process is called reversible or equilibrium. A
reversible process is thus a sequence of (nearly) equilibrium states of a system.
However, processes in the real world are mostly such that the system is out of equilibrium
at least at the beginning. These processes are called irreversible or non-equilibrium (the
direction of the process cannot be reversed by any slight change of external conditions, and
the process is a sequence of non-equilibrium states). An equilibrium process is thus actually a
limiting case of a non-equilibrium process going on at an inﬁnitesimal velocity.
Inﬁnitely slow heating or inﬁnitely slow compression of a system may serve as an example of
equilibrium processes which cannot be carried out in practice. In contrast, water boiling at a
temperature of 100 C and pressure of 101 325 Pa is an example of an equilibrium process which
may take place in practice. If we lower the temperature slightly, the direction of the process will
be reversed and boiling will be replaced by water vapour condensation.
1.4.5 Processes at a constant quantity
during the whole process. These processes are mostly termed using the preﬁx iso- (is-), and
denoted using the symbol X, with X indicating the given constant quantity. The following
processes are encountered most often:CHAP. 1: BASIC TERMS CONTENTS 32
Name of the process Constant quantity Symbol
Isothermal temperature T
Isobaric pressure p
Isochoric volume V
Adiabatic heat ad
Isentropic entropy S
Isenthalpic enthalpy H
Polytropic heat capacity C
In the initial state, a system of a constant volume has a temperature of 300K and a pressure
of 150kPa. A certain process takes place in the system, and in the ﬁnal state the system’s
temperature is 320K and its pressure is 150kPa. Does the process take place under a constant
The initial and the ﬁnal temperatures of the system are diﬀerent. Consequently, the process
cannot be isothermal. Both the initial pressure and the ﬁnal pressure are identical. In this case
it may be, but not necessarily is, an isobaric process. The speciﬁcation does not allow us to ﬁnd
out whether pressure changes in any way in the course of the process. However, the process is
deﬁnitely an isochoric one because the system has a constant (i.e. unchanging) volume.
1.4.6 Cyclic process
A cyclic process is such at which the ﬁnal state of the system is identical with its initial state.
In a cyclic process, changes of thermodynamic quantities are zero.
Note: Heat and work are not thermodynamic quantities and therefore they are not zero
during a cyclic process.CHAP. 1: BASIC TERMS CONTENTS 33
Let our system be a cube of ice with a mass of 1g, and the initial state be a temperature of
−10 C and a pressure of 100kPa. The sequence of processes taking place in the system was as
follows: thecubewasheated to0 C atwhichitmelted. Theliquid waterwas electrolyzed atthis
temperature. The resulting mixture of hydrogen and oxygen was expanded to 200Pa and ignited.
The water vapour resulting from the reaction had a temperature of 500 C at the end of the
reaction. It was then cooled to−10 C and compressed to 100kPa. In the course of compression
desublimation (snowing) occurred, and the system returned to its initial thermodynamic state. A
cyclic process took place.CHAP. 1: BASIC TERMS CONTENTS 34
1.5 Some basic and derived quantities
1.5.1 Mass m
U Main unit: kg.
1.5.2 Amount of substance n
U Mainunit: mol. 1molisN ofparticles(atoms,molecules,ions...),whereN = 6.022025×10
is the Avogadro constant.
1.5.3 Molar mass M
U Main unit: kgmol . Themolarmassisthemassofonemoleofparticles. Therelationbetween
the amount of substance, mass and molar mass is
n =m/M. (1.3)
This relation applies to both a pure substance and a mixture. The molar mass of a mixture
can be calculated using the relation
M = xM , (1.4)
where M is the molar mass of component i, and x is its mole fraction see 1.6.1
1.5.4 Absolute temperature T
U Main unit: K.
Note: Temperature given in C is denoted t (t = T – 273.15)
1.5.5 Pressure p
U Main unit: Pa.
Older units: bar (1bar = 10 Pa), atm (1atm = 101 325Pa), torr (760torr = 101 325Pa).CHAP. 1: BASIC TERMS CONTENTS 35
1.5.6 Volume V
U Main unit: m .
Older units: litre (1l = 1dm ).CHAP. 1: BASIC TERMS CONTENTS 36
1.6 Pure substance and mixture
We speak about a pure substance (chemical individual) when only one kind of molecules is
present in a system. When a system contains more kinds of molecules, we speak about a
mixture. The substances of which a mixture is composed are its components. According
to the number of components we distinguish binary mixtures consisting of only two compo-
components, etc. In addition to thermodynamic quantities used to describe pure substances
(temperature, pressure, volume), the description of a mixtures also requires knowledge of the
composition of all its phases, which may be expressed using one of the quantities listed below.
1.6.1 Mole fraction of the i component x
x = , (1.5)
where n is the amount of substance of component i, n is the total amount of substance of all
n = n , (1.6)
and k is the number of components in the mixture.
U Main unit: dimensionless quantity.
It follows from the deﬁnition (1.5) that the sum of mole fractions equals one
x = 1. (1.7)
Note: Instead of mole fractions, the expression mole percent is often used, meaning 100-
times the mole fractions.CHAP. 1: BASIC TERMS CONTENTS 37
A binary mixture contains 4moles of substance A and 6moles of substance B. Express the
composition of the mixture using mole fraction and mole percent.
According to (1.6), the amount of substance in the mixture is n = 4+6 = 10 mol. From (1.5)
we get x = 4/10 = 0.4, x = 6/10 = 0.6. The mixture contains 40mole percent of substance
A, and 60mole percent of substance B.
A mixture in which mole fractions of all components have the same value is called an
Calculate the mole fractions of an equimolar mixture of hydrogen and oxygen, and the mole
fractions of an equimolar mixture of nitrogen, oxygen and argon.
It follows from the deﬁnition of an equimolar mixture that
x =x =
x =x =x = .
N O Ar
1.6.2 Mass fraction w
w = , (1.8)
where m is the mass of component i, and m = m is the mass of the mixture.
U Main unit: dimensionless quantity.CHAP. 1: BASIC TERMS CONTENTS 38
The sum of mass fractions of all components equals one
w = 1. (1.9)
We convert mole and mass fractions using the relations:
i i i i
x = , w = . (1.10)
w /M x M
j j j j
Amixturecontains5gofsubstanceAwithamolarmassM =25 gmol , and15gofsubstance
B with a molar mass M = 75 gmol . Calculate the mass fractions and the mole fractions.
Substituting into (1.8) gives
w = = 0.25, w = = 0.75.
We calculate the mole fractions using the ﬁrst of equations (1.10)
x = = 0.5, x = = 0.5.
1.6.3 Volume fraction φ
φ = = , (1.11)
V x V
j=1 j=1CHAP. 1: BASIC TERMS CONTENTS 39
where V and V are the volume and the molar volume of a pure substance i in the same
state of matter as the mixture.
U Main unit: dimensionless quantity.
S Symbols: ThesymbolX willbeusedtodenotethermodynamicquantityX ofapuresubstance
j at the temperature and pressure of the mixture, with the pure substance being in the same
of a pure liquid substance). If the mixture is in the solid state, the symbol will denote a pure
substance in the same crystalline form as the mixture.
The sum of the volume fractions of all components equals one.
φ = 1. (1.12)
Note: For a mixture of ideal gases, the volume fraction equals the mole fraction
φ =x .
Calculate the volume fractions in a solution prepared by mixing 40 cm of ethanol and 160 cm
of water. Is it possible to calculate the volume of the solution based on this data?
From (1.11) we obtain
φ = = 0.8, φ = = 0.2.
The volume of a solution cannot be calculated using the volumes of pure substances, but it has
to be measured. In the considered mixture of ethanol and water it will be smaller than 160 + 40
= 200 cm .CHAP. 1: BASIC TERMS CONTENTS 40
1.6.4 Amount-of-substance concentration c
c =n/V , (1.13)
where V is the total volume of the mixture.
U Main unit: molm . In a pure component this quantity is identical with the amount-of-
concentration or substance concentration. The same applies to the expression amount-
of-substance density. When there is no risk of ambiguity, the word concentration may
be used alone. In older literature, the term molarity may be found indicating the same
quantity (using the unit moldm ).
A mixture of substances with a volume of 5dm contains 56g of nitrogen. Calculate its concen-
The amount of substance of nitrogen is
n = = 2mol.
From equation (1.13) we obtain
c = = 0.4moldm .
1.6.5 Molality m
m =n/m (1.14)
iCHAP. 1: BASIC TERMS CONTENTS 41
U Main unit: molkg . This quantity is used mainly in connection with aqueous solutions of
A total of 58.5g of NaCl has been mixed with 500g of water. Calculate the molality of sodium
chloride given that you know its molar mass to be M = 58.5gmol .
By substituting into (1.14) we obtain
m = = 2molkg .
The molality of the obtained solution is 2molkg .