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CH AP TER
1
Introduction
1.1 Nature of Physical Chemistry
Physical chemistry can be described as a set of characteristically quantitative approaches to the study of chemical problems. A physical chemist seeks to predict and/
or explain chemical events using certain models and postulates.
Because the problems encountered in physical chemistry are diversified and often
complex, they require a number of di¤erent approaches. For example, in the study
of thermodynamics and rates of chemical reactions, we employ a phenomenological,
macroscopic approach. But a microscopic, molecular approach is necessary to understand the kinetic behavior of molecules and reaction mechanisms. Ideally, we
study all phenomena at the molecular level, because that is where change occurs. In
fact, our knowledge of atoms and molecules is neither extensive nor thorough enough
to permit this type of investigation in all cases, and we sometimes have to settle for
a good, semiquantitative understanding. It is useful to keep in mind the scope and
limitations of a given approach.
The principles of physical chemistry can be applied to the study of any chemical
system. For example, let us consider how we use these principles to understand the
binding of dioxygen (O2 ) to hemoglobin. This system is one of the most important
biochemical reactions and is probably the most extensively studied. Hemoglobin, a
protein molecule with a molar mass of about 65,000 g, contains four subunits, made
up of two a chains (141 amino acids each) and two b chains (146 amino acids each).
Each chain contains a heme group to which an oxygen molecule can bind. The
main functions of hemoglobin are to carry oxygen in the blood from the lungs to the
tissues, where it transfers the oxygen molecules to myoglobin, and to transport carbon dioxide from the tissues back to the lungs. Myoglobin, which possesses only one
polypeptide chain (153 amino acids) and one heme group, stores oxygen for metabolic processes.
A detailed understanding of the three-dimensional structure of a protein molecule, such as hemoglobin, is perhaps the most crucial key to revealing the secrets of
its functions. Physical chemistry provides us with a number of techniques, including
spectroscopy and X-ray di¤raction, for such structural determination.
Another question for which we use physical chemistry principles concerns the
binding of oxygen to hemoglobin. To understand how oxygen and other molecules,
such as carbon monoxide, bind to the heme group, we need to investigate the coordination chemistry of transition-metal ions in general and complexes of iron in particular. For example, it is important to know which orbitals are involved in the iron–
ligand complex and the reasons the binding constant for CO is some 200 times
stronger than that for O2 . Knowledge of the molecular orbitals involved will also help
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Chapter 1: Introduction
explain hemoglobin’s spectroscopic properties, including the purple color of venous
blood (deoxyhemoglobin) and the red color of arterial blood (oxyhemoglobin).
A very important phenomenon is the cooperative nature of binding of oxygen to
hemoglobin. Scientists noticed many years ago that oxygen molecules did not bind to
the four heme groups independently; rather, the presence of the first molecule facilitates the binding of the second, and so on. Similarly, when the first oxygen molecule
is released from a fully oxygenated hemoglobin, the remaining molecules come o¤
with increasing ease. The biological function of cooperative binding is to increase the
e‰ciency of the transport and release of oxygen. The kinetic and thermodynamic
details of this phenomenon have been successfully accounted for by current theories
based on allosteric interaction, which is the long-range interaction between spatially
distant ligand-binding sites mediated by the structure of a protein molecule.
The function and e‰ciency of most proteins and enzymes depend critically on the
pH. Hemoglobin is no exception. The CO2 aO2 transport process in blood is bu¤ered
by the bicarbonate–carbonic acid system. Being amphoteric, that is, possessing the
ability to act both as an acid and as a base, hemoglobin itself can act as a bu¤er. This
process is an acid–base equilibrium reaction.
Finally, we may raise the following question: Of the numerous possible structures that a molecule this size can assume, why is only one predominant structure
observed for hemoglobin? We must realize that in addition to the normal chemical
bonds, many other types of molecular interaction, such as electrostatic forces, hydrogen bonding, and van der Waals forces, exist. In principle, a macromolecule can
fold in many di¤erent ways; the native conformation represents the minimum Gibbs
energy structure. The specificity in binding depends precisely on the environment at
and near the active site, an environment that is maintained by the rest of the threedimensional molecule. To appreciate how delicate the balance of these forces can be
in some cases, consider the replacement of a glutamic acid by valine in the b chains of
hemoglobin:
NH3
HOOC
(CH 2 )2
C
H
Glutamic acid
CH 3
COO
CH
CH 3
NH3
C
COO
H
Valine
This seemingly small alteration is su‰cient to produce a significant conformational
change—an increase in the attraction between protein molecules, resulting in polymerization. The insoluble polymers that form distort red blood cells into a sickle
shape, causing the symptoms of the disease sickle-cell anemia.
All these phenomena can be understood, at least in theory, by applying the
principles of physical chemistry. Obviously, very di¤erent approaches are necessary
for a thorough investigation of the chemistry of hemoglobin—or photosynthesis or
atmospheric chemistry, for that matter. The point is that the principles of physical
chemistry provide a foundation for the study of many exciting chemical and biochemical phenomena.
1.2 Units
Before we proceed with the study of physical chemistry, let us review the units
chemists use for quantitative measurements.
For many years, scientists recorded measurements in metric units, which are related decimally, that is, by powers of 10. In 1960, however, the General Conference
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1.2 Units
Table 1.1
SI Base Units
Base Quantity
Length
Mass
Time
Electrical current
Temperature
Amount of substance
Luminous intensity
Name of Unit
Symbol
meter
kilogram
second
ampere
kelvin
mole
candela
m
kg
s
A
K
mol
cd
of Weights and Measures, the international authority on units, proposed a revised
metric system called the International System of Units (abbreviated SI). The advantage of the SI system is that many of its units can be derived from natural constants.
For example, the SI system defines meter (m) as the length equal to 1,650,763.73
wavelengths of radiation corresponding to a particular electronic transition from the
6d to the 5p orbital in krypton. The unit of time, the second, is equivalent to
9,192,631,770 cycles of the radiation associated with a certain electronic transition of
the cesium atom. In contrast, the fundamental unit of mass, the kilogram (kg), is
defined in terms of an artifact, not in terms of a naturally occurring phenomenon.
One kilogram is the mass of a platinum–iridium alloy cylinder kept by the International Bureau of Weights and Measures in Sevres, France.
Table 1.1 gives the seven SI base units. Note that in SI units, temperature is given
as K without the degree symbol, and the unit is plural—for example, 300 kelvins
(300 K). A number of physical quantities can be derived from the list in Table 1.1.
We shall discuss only a few of them here (see the inside front cover of the book).
Force
The unit of force in the SI system is the newton (N) (after the English physicist
Sir Isaac Newton, 1642–1726), defined as the force required to give a mass of 1 kg an
acceleration of 1 m s2 ; that is,
1 N ¼ 1 kg m s2
It is interesting to note that one newton is approximately equal to the gravitational
pull on an apple.
Pressure
Pressure is defined as
pressure ¼
force
area
The SI unit of pressure is the pascal (Pa) (after the French mathematician and physicist Blaise Pascal, 1623–1662), where
1 Pa ¼ 1 N m2
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Chapter 1: Introduction
The following relations are exact:
1 bar ¼ 1 10 5 Pa ¼ 100 kPa
1 atm ¼ 1:01325 10 5 Pa ¼ 101:325 kPa
1 atm ¼ 1:01325 bar
1 atm ¼ 760 torr
76 cm
Atmospheric
pressure
Figure 1.1
A barometer for measuring
atmospheric pressure. Above the
mercury in the tube is a vacuum.
The column of mercury is supported by atmospheric pressure.
The torr is named after the Italian mathematician Evangelista Torricelli (1608–1674).
The standard atmosphere (1 atm) is used to define the normal melting point and
boiling point of substances, and the bar is used to define standard states in physical
chemistry. We shall use all of these units in this text.
Pressure is sometimes expressed in millimeters of mercury (mmHg): 1 mmHg is
the pressure exerted by a column of mercury 1 mm high when its density is 13.5951
g cm3 and the acceleration due to gravity is 980.67 cm s2 . The relation between
mmHg and torr is 1 mmHg ¼ 1 torr.
One instrument that measures atmospheric pressure is the barometer. A simple
barometer can be constructed by filling a long glass tube, closed at one end, with
mercury, and then carefully inverting the tube in a dish of mercury, making sure that
no air enters the tube. Some mercury will flow down into the dish, creating a vacuum
at the top (Figure 1.1). The weight of the mercury column remaining in the tube is
supported by atmospheric pressure acting on the surface of the mercury in the dish.
The device used to measure the pressure of gases other than the atmosphere
is called a manometer. Its principle of operation is similar to that of a barometer.
There are two types of manometers (Figure 1.2): the closed-tube manometer (Figure
1.2a) is normally used to measure pressures lower than atmospheric pressure, and the
open-tube manometer (Figure 1.2b) is more suited for measuring pressures equal to
or greater than atmospheric pressure.
Vacuum
h
Gas
Pgas
(a)
Ph
h
Gas
Pgas
Ph
Patm
(b)
Figure 1.2
Two types of manometers used to measure gas pressures. (a) Gas pressure is less than
atmospheric pressure. (b) Gas pressure is greater than atmospheric pressure.
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1.3 Atomic Mass, Molecular Mass, and the Chemical Mole
Energy
The SI unit of energy is the joule (J) (after the English physicist James Prescott
Joule, 1818–1889). Because energy is the ability to do work and work is force times
distance, we have
1J¼1Nm
Some chemists have continued to use the non-SI unit of energy, calorie (cal), where
1 cal ¼ 4.184 J.
1.3 Atomic Mass, Molecular Mass, and the Chemical Mole
By international agreement, an atom of the carbon-12 isotope, which has six
protons and six neutrons, has a mass of exactly 12 atomic mass units (amu). One
atomic mass unit is defined as a mass equal to exactly one-twelfth the mass of one
carbon-12 atom. Experiments have shown that a hydrogen atom is only 8.400% as
massive as the standard carbon-12 atom. Thus, the atomic mass of hydrogen must be
0:08400 12 ¼ 1:008 amu. Similar experiments show that the atomic mass of oxygen
is 16.00 amu and that of iron is 55.85 amu.
When you look up the atomic mass of carbon in a table such as the one on
the inside front cover of this book, you will find it listed as 12.01 amu rather than
12.00 amu. The reason for the di¤erence is that most naturally occurring elements
(including carbon) have more than one isotope. This means that when we measure
the atomic mass of an element, we must generally settle for the average mass of the
naturally occurring mixture of isotopes. For example, the natural abundances of
carbon-12 and carbon-13 are 98.90% and 1.10%, respectively. The atomic mass of
carbon-13 has been determined to be 13.00335 amu. Thus, the average atomic mass
of carbon can be calculated as follows:
average atomic mass of carbon ¼ ð0:9890Þð12:0000 amuÞ
þ ð0:0110Þð13:00335 amuÞ
¼ 12:01 amu
Because there are many more carbon-12 isotopes than carbon-13 isotopes, the average atomic mass is much closer to 12 amu than 13 amu. Such an average is called the
weighted average.
If we know the atomic masses of the component atoms, we can calculate the
mass of a molecule. Thus, the molecular mass of H2 O is
2ð1:008 amuÞ þ 16:00 amu ¼ 18:02 amu
A mole (abbreviated mol) is the amount of substance that contains as many
atoms, molecules, ions, or any other entities as there are atoms in exactly 12 g of
carbon-12. It has been determined experimentally that the number of atoms in one
mole of carbon-12 is 6:0221367 10 23 . This number is called Avogadro’s number
(after the Italian physicist and mathematician Amedeo Avogadro, 1776–1856).
Avogadro’s number has no units, but dividing this number by one mole gives us
Avogadro’s constant (NA ), where
NA ¼ 6:0221367 10 23 mol1
One atomic mass unit is also
called the dalton.
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Chapter 1: Introduction
For most purposes, NA can be taken as 6:022 10 23 mol1 . The following examples
indicate the number and kind of particles in one mole of any substance.
1. One mole of helium atoms contains 6:022 10 23 He atoms.
2. One mole of water molecules contains 6:022 10 23 H2 O molecules, or
2 ð6:022 10 23 Þ H atoms and 6:022 10 23 O atoms.
3. One mole of NaCl contains 6:022 10 23 NaCl units, or 6:022 10 23 Naþ
ions and 6:022 10 23 Cl ions.
The molar mass of a substance is the mass in grams or kilograms of 1 mole of the
substance. Thus, the molar mass of atomic hydrogen is 1.008 g mol1 , of molecular
hydrogen 2.016 g mol1 , of hemoglobin 65,000 g mol1 . In many calculations, molar
masses are more conveniently expressed as kg mol1 .
Suggestions for Further Reading
The following standard texts are useful references. The
physical and biophysical texts contain many mathematical
derivations of equations and provide experimental details
for a number of topics covered in this book. The biochemistry texts provide the necessary background for the biological examples used in this book.
Physical Chemistry
General
1. Alberty, R. A. and R. J. Silbey, Physical Chemistry, 3rd
ed., John Wiley & Sons, Inc., New York, 2001.
2. Atkins, P. W. Physical Chemistry, 7th ed., W. H.
Freeman and Company, New York, 2002.
3. Chang, R. Physical Chemistry for the Chemical and
Biological Sciences, 3rd ed., University Science Books,
Sausalito, CA, 2000.
4. Laidler, K. J., J. H. Meiser, and B. C. Sanctuary,
Physical Chemistry, 4th ed., Houghton Mi¿in
Company, Boston, 2002.
5. Levine, I. N. Physical Chemistry, 5th ed., McGraw-Hill,
Inc., New York, 2002.
6. McQuarrie, D. A. and J. D. Simon, Physical Chemistry,
University Science Books, Sausalito, CA, 1997.
7. Noggle, J. H. Physical Chemistry, 3rd ed., HarperCollins College Publishers, New York, 1996.
8. Winn, J. S. Physical Chemistry, HarperCollins College
Publishers, New York, 1995.
Historical Development of Physical Chemistry
‘‘One Hundred Years of Physical Chemistry,’’ E. B.
Wilson, Jr., Am. Sci. 74, 70 (1986).
Laidler, K. J. The World of Physical Chemistry, Oxford
University Press, New York, 1993.
Cobb, C. Magic, Mayhem, and Mavericks: The Spirited
History of Physical Chemistry, Prometheus Books,
Amherst, NY, 2002.
Biophysical Chemistry
9. Bergethon, P. R. The Physical Basis of Biochemistry,
Springer-Verlag, New York, 1998.
10. Bergethon, P. R. and E. R. Simons, Biophysical
Chemistry: Molecules to Membranes, Springer-Verlag,
New York, 1990.
11. Cantor, C. R. and P. R. Schimmel, Biophysical
Chemistry, W. H. Freeman and Company, San
Francisco, CA, 1980.
12. Freifelder, D. Physical Biochemistry, 2nd ed., W. H.
Freeman, New York, 1982.
13. van Holde, K. Physical Biochemistry, 2nd ed., Prentice
Hall, Inc., Englewood Cli¤s, NJ, 1984.
14. van Holde, K., W. C. Johnson, and P. S. Ho,
Principles of Physical Biochemistry, Prentice Hall,
Upper Saddle River, NJ, 1998.
Biochemistry
15. Lehninger, A. L., D. C. Nelson, and M. M. Cox,
Principles of Biochemistry, 3rd ed., W. H. Freeman,
New York, 2000.
16. Mathews, C. K. and K. E. van Holde, Biochemistry,
The Benjamin/Cummings Publishing Company, Inc.,
Menlo Park, CA, 1996.
17. Berg, J. M., J. T. Tymoczko, and L. Stryer,
Biochemistry, 5th ed., W. H. Freeman and Company,
New York, 2002.
18. Voet, D. and J. G. Voet, Biochemistry, 3rd ed., John
Wiley & Sons, New York, 2004.