BRUI01-001_059r4 20-03-2003 2:58 PM Page 1

To discuss organic compounds, you must be able to name
them and visualize their structures when you read or hear
their names. In Chapter 2, you will learn how to name
five different classes of organic compounds. This will
give you a good understanding of the basic rules followed
in naming compounds. Because the compounds examined in the chapter are either the reactants or the products
of many of the reactions presented in the next 10 chapters, you will have the opportunity to review the nomenclature of these compounds as you proceed through those
chapters. The structures and physical properties of these
compounds will be compared and contrasted, which
makes learning about them a little easier than if each
compound were presented separately. Because organic
chemistry is a study of compounds that contain carbon,
the last part of Chapter 2 discusses the spatial arrangement of the atoms in both chains and rings of carbon
atoms.

ONE

Chapter 1 reviews the topics from general chemistry
that will be important to your study of organic chemistry.
The chapter starts with a description of the structure of
atoms and then proceeds to a description of the structure
of molecules. Molecular orbital theory is introduced.
Acid–base chemistry, which is central to understanding
many organic reactions, is reviewed. You will see how the
structure of a molecule affects its acidity and how the
acidity of a solution affects molecular structure.

An Introduction


Ethene

T
Jöns Jakob Berzelius (1779–1848)
not only coined the terms “organic”
and “inorganic,” but also invented
the system of chemical symbols still
used today. He published the first list
of accurate atomic weights and
proposed the idea that atoms carry
an electric charge. He purified or
discovered the elements cerium,
selenium, silicon, thorium, titanium,
and zirconium.
German chemist Friedrich Wöhler
(1800–1882) began his professional
life as a physician and later became
a professor of chemistry at the University of Göttingen. Wöhler codiscovered the fact that two different
chemicals could have the same molecular formula. He also developed
methods of purifying aluminum—at
the time, the most expensive metal on
Earth—and beryllium.

2

o stay alive, early humans
must have been able to tell the
difference between two kinds of
materials in their world. “You can live


For the first time, an “organic” compound had been obtained from something other
than a living organism and certainly without the aid of any kind of vital force. Clearly,
chemists needed a new definition for “organic compounds.” Organic compounds are
now defined as compounds that contain carbon.
Why is an entire branch of chemistry devoted to the study of carbon-containing
compounds? We study organic chemistry because just about all of the molecules that


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Section 1.1

make life possible—proteins, enzymes, vitamins, lipids, carbohydrates, and nucleic
acids—contain carbon, so the chemical reactions that take place in living systems, including our own bodies, are organic reactions. Most of the compounds found in
nature—those we rely on for food, medicine, clothing (cotton, wool, silk), and energy
(natural gas, petroleum)—are organic as well. Important organic compounds are not,
however, limited to the ones we find in nature. Chemists have learned to synthesize
millions of organic compounds never found in nature, including synthetic fabrics,
plastics, synthetic rubber, medicines, and even things like photographic film and
Super glue. Many of these synthetic compounds prevent shortages of naturally occurring products. For example, it has been estimated that if synthetic materials were not
available for clothing, all of the arable land in the United States would have to be used
for the production of cotton and wool just to provide enough material to clothe us.
Currently, there are about 16 million known organic compounds, and many more are
possible.
What makes carbon so special? Why are there so many carbon-containing compounds? The answer lies in carbon’s position in the periodic table. Carbon is in the
center of the second row of elements. The atoms to the left of carbon have a tendency
to give up electrons, whereas the atoms to the right have a tendency to accept electrons
(Section 1.3).



An atom consists of a tiny dense nucleus surrounded by electrons that are spread
throughout a relatively large volume of space around the nucleus. The nucleus contains positively charged protons and neutral neutrons, so it is positively charged. The
electrons are negatively charged. Because the amount of positive charge on a proton
equals the amount of negative charge on an electron, a neutral atom has an equal number of protons and electrons. Atoms can gain electrons and thereby become negatively
charged, or they can lose electrons and become positively charged. However, the number of protons in an atom does not change.
Protons and neutrons have approximately the same mass and are about 1800 times
more massive than an electron. This means that most of the mass of an atom is in its
nucleus. However, most of the volume of an atom is occupied by its electrons, and that
is where our focus will be because it is the electrons that form chemical bonds.

The Structure of an Atom

3


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CHAPTER 1

Electronic Structure and Bonding • Acids and Bases

Louis Victor Pierre Raymond duc
de Broglie (1892–1987) was born in
France and studied history at the
Sorbonne. During World War I, he
was stationed in the Eiffel Tower as a
radio engineer. Intrigued by his exposure to radio communications, he returned to school after the war, earned

1>12 of the mass of 12C, the atomic mass of 12C is 12.0000 amu; the atomic
mass of 13C is 13.0034 amu. Therefore, the atomic weight of carbon is 12.011 amu
10.9889 * 12.0000 + 0.0111 * 13.0034 = 12.0112. The molecular weight is the
sum of the atomic weights of all the atoms in the molecule.
PROBLEM 1 ◆
Oxygen has three isotopes with mass numbers of 16, 17, and 18. The atomic number of
oxygen is eight. How many protons and neutrons does each of the isotopes have?

1.2

Erwin Schrödinger (1887–1961)
was teaching physics at the University of Berlin when Hitler rose to
power. Although not Jewish,
Schrödinger left Germany to return
to his native Austria, only to see it
taken over later by the Nazis. He
moved to the School for Advanced
Studies in Dublin and then to Oxford
University. In 1933, he shared the
Nobel Prize in physics with Paul
Dirac, a professor of physics at Cambridge University, for mathematical
work on quantum mechanics.
An orbital tells us the energy of the
electron and the volume of space
around the nucleus where an electron
is most likely to be found.

The Distribution of Electrons in an Atom

Electrons are moving continuously. Like anything that moves, electrons have kinetic

was nothing left to teach him. Eventually, Einstein was asked to leave the school because of his
disruptive behavior. Popular folklore says he left because of poor grades in Latin and Greek, but
his grades in those subjects were fine.
Einstein was visiting the United States when Hitler came to power, so he accepted a position
at the Institute for Advanced Study in Princeton, becoming a U.S. citizen in 1940. Although a
lifelong pacifist, he wrote a letter to President Roosevelt warning of ominous advances in German nuclear research. This led to the creation of the Manhattan Project, which developed the
atomic bomb and tested it in New Mexico in 1945.

closest to the nucleus. The second shell lies farther from the nucleus, and even farther
out lie the third and higher numbered shells. Each shell contains subshells known as
atomic orbitals. Each atomic orbital has a characteristic shape and energy and occupies a characteristic volume of space, which is predicted by the Schrödinger equation.
An important point to remember is that the closer the atomic orbital is to the nucleus,
the lower is its energy.
The first shell consists of only an s atomic orbital; the second shell consists of s and
p atomic orbitals; the third shell consists of s, p, and d atomic orbitals; and the fourth
and higher shells consist of s, p, d, and f atomic orbitals (Table 1.1).
Each shell contains one s atomic orbital. The second and higher shells—in addition
to their s orbital—each contain three degenerate p atomic orbitals. Degenerate
orbitals are orbitals that have the same energy. The third and higher shells—in
Table 1.1

The closer the orbital is to the nucleus,
the lower is its energy.

Distribution of Electrons in the First Four Shells
That Surround the Nucleus

Atomic orbitals
Number of atomic orbitals
Maximum number of electrons

in 1930. Planck felt that it was his duty to remain in Germany during the Nazi era, but he never
supported the Nazi regime. He unsuccessfully interceded with Hitler on behalf of his Jewish colleagues and, as a consequence, was forced to resign from the presidency of the Kaiser Wilhelm Society in 1937. A second son was accused of taking part in the plot to kill Hitler and was executed.
Planck lost his home to Allied bombings. He was rescued by Allied forces during the final days of
the war.

5


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CHAPTER 1

Electronic Structure and Bonding • Acids and Bases

addition to their s and p orbitals—also contain five degenerate d atomic orbitals, and
the fourth and higher shells also contain seven degenerate f atomic orbitals. Because
a maximum of two electrons can coexist in an atomic orbital (see the Pauli exclusion
principle, below), the first shell, with only one atomic orbital, can contain no more
than two electrons. The second shell, with four atomic orbitals—one s and three p—
can have a total of eight electrons. Eighteen electrons can occupy the nine atomic
orbitals—one s, three p, and five d—of the third shell, and 32 electrons can occupy the
16 atomic orbitals of the fourth shell. In studying organic chemistry, we will be concerned primarily with atoms that have electrons only in the first and second shells.
The ground-state electronic configuration of an atom describes the orbitals occupied by the atom’s electrons when they are all in the available orbitals with the lowest energy. If energy is applied to an atom in the ground state, one or more electrons can jump
into a higher energy orbital. The atom then would be in an excited-state electronic
configuration. The ground-state electronic configurations of the 11 smallest atoms are
shown in Table 1.2. (Each arrow—whether pointing up or down—represents one electron.) The following principles are used to determine which orbitals electrons occupy:
1. The aufbau principle (aufbau is German for “building up”) tells us the first
thing we need to know to be able to assign electrons to the various atomic orbitals. According to this principle, an electron always goes into the available orbital with the lowest energy. The relative energies of the atomic orbitals are as

number

H
He
Li
Be
B
C
N
O
F
Ne
Na

Hydrogen
Helium
Lithium
Beryllium
Boron
Carbon
Nitrogen
Oxygen
Fluorine
Neon
Sodium

1
2
3
4

orbital, the third electron of a lithium atom occupies a 2s atomic orbital, the fourth
electron of a beryllium atom fills the 2s atomic orbital, and the fifth electron of a boron
atom occupies one of the 2p atomic orbitals. (The subscripts x, y, and z distinguish the
three 2p atomic orbitals.) Because the three p orbitals are degenerate, the electron can
be put into any one of them. Before we can continue to larger atoms—those containing six or more electrons—we need Hund’s rule:
3. Hund’s rule states that when there are degenerate orbitals—two or more orbitals
with the same energy—an electron will occupy an empty orbital before it will
pair up with another electron. In this way, electron repulsion is minimized. The
sixth electron of a carbon atom, therefore, goes into an empty 2p atomic orbital,
rather than pairing up with the electron already occupying a 2p atomic orbital.
(See Table 1.2.) The seventh electron of a nitrogen atom goes into an empty 2p
atomic orbital, and the eighth electron of an oxygen atom pairs up with an electron occupying a 2p atomic orbital rather than going into a higher energy 3s
orbital.
Using these three rules, the locations of the electrons in the remaining elements can be
assigned.
PROBLEM 2 ◆
Potassium has an atomic number of 19 and one unpaired electron. What orbital does the
unpaired electron occupy?

PROBLEM 3 ◆
Write electronic configurations for chlorine (atomic number 17), bromine (atomic number
35), and iodine (atomic number 53).

1.3

Ionic, Covalent, and Polar Bonds

In trying to explain why atoms form bonds, G. N. Lewis proposed that an atom is most
stable if its outer shell is either filled or contains eight electrons and it has no electrons
of higher energy. According to Lewis’s theory, an atom will give up, accept, or share


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CHAPTER 1

Electronic Structure and Bonding • Acids and Bases

Lithium and sodium each have one valence electron. Elements in the same column
of the periodic table have the same number of valence electrons, and because the number of valence electrons is the major factor determining an element’s chemical properties, elements in the same column of the periodic table have similar chemical
properties. Thus, the chemical behavior of an element depends on its electronic
configuration.
PROBLEM 4
Compare the ground-state electronic configurations of the following atoms, and check the
relative positions of the atoms in Table 1.3 on p. 10.
a. carbon and silicon
b. oxygen and sulfur

c. fluorine and bromine
d. magnesium and calcium

When we draw the electrons around an atom, as in the following equations, core
electrons are not shown; only valence electrons are shown. Each valence electron is
shown as a dot. Notice that when the single valence electron of lithium or sodium is
removed, the resulting atom—now called an ion—carries a positive charge.
Li+ + e−

Li


Sodium chloride lattice

Figure 1.1 N
(a) Crystalline sodium chloride.
(b) The electron-rich chloride ions
are red and the electron-poor
sodium ions are blue. Each chloride
ion is surrounded by six sodium
ions, and each sodium ion is
surrounded by six chloride ions.
Ingore the “bonds” holding the
balls together; they are there only
to keep the model from falling
apart.

Because sodium gives up an electron easily and chlorine acquires an electron readily,
when sodium metal and chlorine gas are mixed, each sodium atom transfers an electron to a chlorine atom, and crystalline sodium chloride (table salt) is formed as a result. The positively charged sodium ions and negatively charged chloride ions are
independent species held together by the attraction of opposite charges (Figure 1.1). A
bond is an attractive force between two atoms. Attractive forces between opposite
charges are called electrostatic attractions. A bond that is the result of only electrostatic attractions is called an ionic bond. Thus, an ionic bond is formed when there is
a transfer of electrons, causing one atom to become a positively charged ion and the
other to become a negatively charged ion.
a.

b.


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Section 1.3

Cl

−

+

Na
Cl

−

sodium chloride

Sodium chloride is an example of an ionic compound. Ionic compounds are
formed when an element on the left side of the periodic table (an electropositive element) transfers one or more electrons to an element on the right side of the periodic
table (an electronegative element).

Covalent Bonds
Instead of giving up or acquiring electrons, an atom can achieve a filled outer shell by
sharing electrons. For example, two fluorine atoms can each attain a filled shell of
eight electrons by sharing their unpaired valence electrons. A bond formed as a result
of sharing electrons is called a covalent bond.
a covalent bond

F

+

F



a proton

H

e–

+

a hydrogen atom

e–

+

H

−

a hydride ion

Because oxygen has six valence electrons, it needs to form two covalent bonds to
achieve an outer shell of eight electrons. Nitrogen, with five valence electrons, must
form three covalent bonds, and carbon, with four valence electrons, must form four covalent bonds to achieve a filled outer shell. Notice that all the atoms in water, ammonia, and methane have filled outer shells.
2H

+

O


pounds. In his left hand, Einstein
holds the mathematical equations
that represent his three most important contributions to science: the
photoelectric effect, the equivalency
of energy and matter, and the theory
of relativity. At his feet is a map of
the sky.


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CHAPTER 1

Electronic Structure and Bonding • Acids and Bases

Polar Covalent Bonds
In the F ¬ F and H ¬ H covalent bonds shown previously, the atoms that share the
bonding electrons are identical. Therefore, they share the electrons equally; that is,
each electron spends as much time in the vicinity of one atom as in the other. An even
(nonpolar) distribution of charge results. Such a bond is called a nonpolar covalent
bond.
In contrast, the bonding electrons in hydrogen chloride, water, and ammonia are
more attracted to one atom than another because the atoms that share the electrons in
these molecules are different and have different electronegativities. Electronegativity
is the tendency of an atom to pull bonding electrons toward itself. The bonding electrons in hydrogen chloride, water, and ammonia molecules are more attracted to the
atom with the greater electronegativity. This results in a polar distribution of charge. A
polar covalent bond is a covalent bond between atoms of different electronegativities.
The electronegativities of some of the elements are shown in Table 1.3. Notice that
electronegativity increases as you go from left to right across a row of the periodic
table or up any of the columns.


H

H

H

δ+

δ+

The direction of bond polarity can be indicated with an arrow. By convention, the
arrow points in the direction in which the electrons are pulled, so the head of the arrow
is at the negative end of the bond; a short perpendicular line near the tail of the arrow
marks the positive end of the bond.
H

Cl

TABLE 1.3 The Electronegativities of Selected Elementsa
IA

IIA

IB

IIB

IIIA


Cl
3.0
Br
2.8
I
2.5

H
2.1
Li
1.0
Na
0.9
K
0.8

Be
1.5
Mg
1.2
Ca
1.0

increasing electronegativity

increasing electronegativity

10

aElectronegativity values are relative, not absolute. As a result, there are several scales of electronegativities. The

nonpolar
covalent bond
C H, C C

PROBLEM 5 ◆
Which of the following has
a. the most polar bond?
NaI

b. the least polar bond?

LiBr

KCl

Cl 2

Understanding bond polarity is critical to understanding how organic reactions
occur, because a central rule that governs the reactivity of organic compounds is that
electron-rich atoms or molecules are attracted to electron-deficient atoms or molecules. Electrostatic potential maps (often simply called potential maps) are models
that show how charge is distributed in the molecule under the map. Therefore, these
maps show the kind of electrostatic attraction an atom or molecule has for another
atom or molecule, so you can use them to predict chemical reactions. The potential
maps for LiH, H 2 , and HF are shown below.

LiH

H2

HF

Electronegativity differences
and bond types


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CHAPTER 1

Electronic Structure and Bonding • Acids and Bases

3-D Molecules:
LiH; H2 ; HF

The colors on a potential map can also be used to estimate charge distribution. For
example, the potential map for LiH indicates that the hydrogen atom is more negatively charged than the lithium atom. By comparing the three maps, we can tell that the
hydrogen in LiH is more negatively charged than a hydrogen in H 2 , and the hydrogen
in HF is more positively charged than a hydrogen in H 2 .
A molecule’s size and shape are determined by the number of electrons in the
molecule and by the way they move. Because a potential map roughly marks the
“edge” of the molecule’s electron cloud, the map tells us something about the relative size and shape of the molecule. Notice that a given kind of atom can have different sizes in different molecules. The negatively charged hydrogen in LiH is
bigger than a neutral hydrogen in H 2 , which, in turn, is bigger than the positively
charged hydrogen in HF.
PROBLEM 6 ◆
After examining the potential maps for LiH, HF, and H 2 , answer the following questions:
a. Which compounds are polar?
b. Why does LiH have the largest hydrogen?
c. Which compound has the most positively charged hydrogen?


Bond
H¬C
H¬N
H¬O
H¬F
H ¬ Cl
H ¬ Br
H¬I

The Dipole Moments of Some Commonly Encountered Bonds

Dipole moment (D)

Bond

Dipole moment (D)

0.4
1.3
1.5
1.7
1.1
0.8
0.4

C¬C
C¬N
C¬O
C¬F
C ¬ Cl

would be
14.80 * 10-10 esu211.22 * 10-8 cm2 = 5.86 * 10-18 esu cm = 5.86 D
Knowing that the dipole moment is 2.30 D, we calculate that the partial negative charge on
the oxygen atom is about 0.4:
2.30
= 0.39
5.86

PROBLEM 8
Use the symbols d+ and d- to show the direction of polarity of the indicated bond in each
δ+

of the following compounds (for example, H3C
c. H 3C ¬ NH 2
d. H 3C ¬ Cl

a. HO ¬ H
b. F ¬ Br

1.4

δ−

OH ).

e. HO ¬ Br
f. H 3C ¬ MgBr

g. I ¬ Cl
h. H 2N ¬ OH

electrons.
Once the atoms and the electrons are in place, each atom must be examined to see
whether a charge should be assigned to it. A positive or a negative charge assigned to
an atom is called a formal charge; the oxygen atom in the hydronium ion has a formal
charge of +1, and the oxygen atom in the hydroxide ion has a formal charge of -1. A
formal charge is the difference between the number of valence electrons an atom has
when it is not bonded to any other atoms and the number of electrons it “owns” when
it is bonded. An atom “owns” all of its lone-pair electrons and half of its bonding
(shared) electrons.
formal charge = number of valence electrons −
(number of lone-pair electrons + 1/2 number of bonding electrons)

* The angstrom (Å) is not a Système International unit. Those who opt to adhere strictly to SI units
can convert it into picometers: 1 picometer 1pm2 = 10-12 m; 1 Å = 10-10 m = 100 pm. Because
the angstrom continues to be used by many organic chemists, we will use angstroms in this book.

American chemist Gilbert Newton
Lewis (1875–1946) was born in
Weymouth, Massachusetts, and received a Ph.D. from Harvard in
1899. He was the first person to prepare “heavy water,” which has deuterium atoms in place of the usual
hydrogen atoms (D2O versus H2O).
Because heavy water can be used as
a moderator of neutrons, it became
important in the development of the
atomic bomb. Lewis started his career as a professor at the Massachusetts Institute of Technology and
joined the faculty at the University of
California, Berkeley, in 1912.


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b.
c.
d.

Which atom bears the formal negative charge in the hydroxide ion?
Which atom is the most negative in the hydroxide ion?
Which atom bears the formal positive charge in the hydronium ion?
Which atom is the most positive in the hydronium ion?

Knowing that nitrogen has five valence electrons (Table 1.2), convince yourself that
the appropriate formal charges have been assigned to the nitrogen atoms in the following Lewis structures:
HNH
H

H+
HNH
H

ammonia

ammonium ion

HN
H

−

HNNH
HH



methyl anion
a carbanion

methyl radical

ethane

A species containing a positively charged carbon atom is called a carbocation, and a
species containing a negatively charged carbon atom is called a carbanion. (Recall
that a cation is a positively charged ion and an anion is a negatively charged ion.) Carbocations were formerly called carbonium ions, so you will see this term in older
chemical literature. A species containing an atom with a single unpaired electron is
called a radical (often called a free radical). Hydrogen has one valence electron, and
each halogen (F, Cl, Br, I) has seven valence electrons, so the following species have
the indicated formal charges:


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Section 1.4

H+

H−

H

Br

hydrogen

lone pairs; oxygen, with two bonds, has two lone pairs; and nitrogen, with three bonds,
has one lone pair. Atoms that have more bonds or fewer bonds than the number required for a neutral atom will have either a formal charge or an unpaired electron.
These numbers are very important to remember when you are first drawing structures
of organic compounds because they provide a quick way to recognize when you have
made a mistake.
H
one bond

F

Cl

I

Br

O

one bond

two bonds

N

C

three bonds

four bonds


H

C

O
O

H

H

O N
+

O
O

−

H

C

O
−

H

O



O

18 electrons have been assigned

double bond

H

O N

O

by using one of oxygen’s lone pairs
to form a double bond, N gets a
complete octet

Representation of Structure

15


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CHAPTER 1

Electronic Structure and Bonding • Acids and Bases


H

C

H
H

H

H

C

N

H

H

H

Condensed Structures
Frequently, structures are simplified by omitting some (or all) of the covalent bonds
and listing atoms bonded to a particular carbon (or nitrogen or oxygen) next to it with
a subscript to indicate the number of such atoms. These kinds of structures are called
condensed structures. Compare the preceding structures with the following ones:
HCO2H

HCN


H

H

C

C

C

C

C

C

H Br H

H

Cl H

H

CH3CHBrCH2CH2CHClCH3

or

CH3CHCH2CH2CHCH3
Br


H

H H

H

H

H

H

CH3CH2CH2CH2CH2CH3

or

CH3(CH2)4CH3

Groups bonded to a carbon can be shown (in parentheses) to the right of the carbon, or hanging from the carbon.

H

H

H

H

H


OH

Groups bonded to the far-right carbon are not put in parentheses.

H

H

H

CH3 H

H

C

C

C

C

H

H CH3 H

C

OH


H

H

C

N

C

C

C

H H

C

H H

H

H

H

(CH3)2NCH2CH2CH3

or

C

H H

H

H

H

(CH3)2CHCH2CH2CH3

or

CH3CHCH2CH2CH3
CH3

H
An oxygen doubly bonded to a carbon can be shown hanging off the carbon or to the right of the carbon.
O
or

CH3CH2CCH3

or

CH3CH2COCH3

CH3CH2C( O)CH3



CH3CH2CO2CH3

or

CH3CH2COOCH3

SOLVED

Draw the Lewis structure for each of the following:
a. NO3 b. NO2 +
c. NO2 -

g. CH 3NH 3 +
h. +C2H 5
i. -CH 3

d. CO2
e. HCO3 f. N2

j. NaOH
k. NH 4Cl
l. Na2CO3

SOLUTION TO 10a

The only way we can arrange one N and three O’s and avoid
O ¬ O single bonds is to place the three O’s around the N. The total number of valence
electrons is 23 (5 for N, and 6 for each of the three O’s). Because the species has one negative charge, we must add 1 to the number of valence electrons, for a total of 24. We then
use the 24 electrons to form bonds and fill octets with lone-pair electrons.

CHAPTER 1

Electronic Structure and Bonding • Acids and Bases
SOLUTION TO 10b The total number of valence electrons is 17 (5 for N and 6 for each
of the two O’s). Because the species has one positive charge, we must subtract 1 from the
number of valence electrons, for a total of 16. The 16 electrons are used to form bonds and
fill octets with lone-pair electrons.

O N O
Two double bonds are necessary to complete N’s octet. The N has a formal charge of +1.
+

O N O

PROBLEM 11
a. Draw two Lewis structures for C2H 6O.

b. Draw three Lewis structures for C3H 8O.

(Hint: The two Lewis structures in part a are constitutional isomers; they have the same
atoms, but differ in the way the atoms are connected. The three Lewis structures in part b
are also constitutional isomers.)

PROBLEM 12
Expand the following condensed structures to show the covalent bonds and lone-pair
electrons:
a. CH 3NHCH 2CH 3
b. (CH 3)2CHCl

1.5

z

x

1s atomic orbital

x

x

2s atomic orbital
node not shown

2s atomic orbital
node shown

An electron in a 1s atomic orbital can be anywhere within the 1s sphere, but a 2s atomic orbital has a region where the probability of finding an electron falls to zero. This is
called a node, or, more precisely—since the absence of electron density is at one set distance from nucleus—a radial node. So a 2s electron can be found anywhere within the
2s sphere—including the region of space defined by the 1s sphere—except in the node.


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Section 1.5

Atomic Orbitals

To understand why nodes occur, you need to remember that electrons have both
particlelike and wavelike properties. A node is a consequence of the wavelike properties of an electron. Consider the following two types of waves: traveling waves and
standing waves. Traveling waves move through space; light is an example of a traveling wave. A standing wave, in contrast, is confined to a limited space. A vibrating


nodal plane

+
or

−
2p atomic orbital

2p atomic orbital

computer-generated
2p atomic orbital

In Section 1.2, you saw that there are three degenerate p atomic orbitals. The px orbital is symmetrical about the x-axis, the py orbital is symmetrical about the y-axis,
and the pz orbital is symmetrical about the z-axis. This means that each p orbital is perpendicular to the other two p orbitals. The energy of a 2p atomic orbital is slightly
greater than that of a 2s atomic orbital because the average location of an electron in a
2p atomic orbital is farther away from the nucleus.
y

y
z

z

z
x

2px orbital


How do atoms form covalent bonds in order to form molecules? The Lewis model,
which describes how atoms attain a complete octet by sharing electrons, tells us only
part of the story. A drawback of the model is that it treats electrons like particles and
does not take into account their wavelike properties.
Molecular orbital (MO) theory combines the tendency of atoms to fill their octets
by sharing electrons (the Lewis model) with their wavelike properties—assigning
electrons to a volume of space called an orbital. According to MO theory, covalent
bonds result from the combination of atomic orbitals to form molecular orbitals—
orbitals that belong to the whole molecule rather than to a single atom. Like an atomic
orbital that describes the volume of space around the nucleus of an atom where an
electron is likely to be found, a molecular orbital describes the volume of space around
a molecule where an electron is likely to be found. Like atomic orbitals, molecular orbitals have specific sizes, shapes, and energies.
Let’s look first at the bonding in a hydrogen molecule (H 2). As the 1s atomic orbital
of one hydrogen atom approaches the 1s atomic orbital of a second hydrogen atom,
they begin to overlap. As the atomic orbitals move closer together, the amount of overlap increases until the orbitals combine to form a molecular orbital. The covalent bond
that is formed when the two s atomic orbitals overlap is called a sigma 1S2 bond. A s
bond is cylindrically symmetrical—the electrons in the bond are symmetrically distributed about an imaginary line connecting the centers of the two atoms joined by the
bond. (The term s comes from the fact that cylindrically symmetrical molecular orbitals possess s symmetry.)
=

H

H

1s atomic
orbital

1s atomic
orbital



+

0

−
−104 kcal/mol

bond length
0.74 Å
Internuclear distance

104 kcal/mol
bond
dissociation
energy


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Section 1.6

An Introduction to Molecular Orbital Theory

until the atoms approach each other so closely that their positively charged nuclei start
to repel each other. This repulsion causes a large increase in energy. We see that maximum stability (i.e., minimum energy) is achieved when the nuclei are a certain distance apart. This distance is the bond length of the new covalent bond. The length of
the H ¬ H bond is 0.74 Å.
As Figure 1.2 shows, energy is released when a covalent bond forms. When the
H ¬ H bond forms, 104 kcal>mol (or 435 kJ> mol)* of energy is released. Breaking the
bond requires precisely the same amount of energy. Thus, the bond strength—also

+

phase of the orbital

destructive combination
waves cancel
each other, and
no bond forms

+

−

Maximum stability corresponds to minimum energy.

> Figure 1.3

constructive combination
waves reinforce
each other, resulting
in bonding

21

node
+
−

phase of the orbital


empty.
Energy

σ∗ antibonding molecular orbital

1s atomic
orbital

1s atomic
orbital

σ bonding molecular orbital

When two atomic orbitals overlap, two
molecular orbitals are formed—one
lower in energy and one higher in energy than the atomic orbitals.

In-phase overlap forms a bonding MO;
out-of-phase overlap forms an antibonding MO.

The MO diagram shows that the bonding molecular orbital is more stable—is lower
in energy—than the individual atomic orbitals. This is because the more nuclei an
electron “feels,” the more stable it is. The antibonding molecular orbital, with less
electron density between the nuclei, is less stable—is of higher energy—than the
atomic orbitals.
After the MO diagram is constructed, the electrons are assigned to the molecular
orbitals. The aufbau principle and the Pauli exclusion principle, which apply to electrons in atomic orbitals, also apply to electrons in molecular orbitals: Electrons always
occupy available orbitals with the lowest energy, and no more than two electrons can
occupy a molecular orbital. Thus, the two electrons of the H—H bond occupy the
lower energy bonding molecular orbital (Figure 1.4), where they are attracted to both

nodes

End-on overlap of two p orbitals to
form a s bonding molecular orbital
and a s* antibonding molecular
orbital.

σ∗ antibonding molecular orbital

Energy

23

2p atomic
orbital

2p atomic
orbital
node

node

σ bonding molecular orbital

formed. The s* antibonding molecular orbital has three nodes. (Notice that after each
node, the phase of the molecular orbital changes.)
Unlike the s bond formed as a result of end-on overlap, side-to-side overlap of two
p atomic orbitals forms a pi 1P2 bond (Figure 1.6). Side-to-side overlap of two inphase p atomic orbitals forms a p bonding molecular orbital, whereas side-to-side
overlap of two out-of-phase p orbitals forms a p* antibonding molecular orbital. The
p bonding molecular orbital has one node—a nodal plane that passes through both nuclei. The p* antibonding molecular orbital has two nodal planes. Notice that s bonds

2p atomic
orbital
nodal plane

π bonding molecular orbital


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24

CHAPTER 1

Electronic Structure and Bonding • Acids and Bases

Figure 1.7 N
σ∗
π∗

Enegry

p Orbitals can overlap end-on to
form s bonding and s*
antibonding molecular orbitals, or
can overlap side-to-side to form p
bonding and p* antibonding
molecular orbitals. The relative
energies of the molecular orbitals
are s 6 p 6 p* 6 s*.


repulsion (VSEPR) model combines the Lewis concept of shared electron pairs and
lone-pair electrons with the concept of atomic orbitals and adds a third principle: the
minimization of electron repulsion. In this model, atoms share electrons by overlapping
Figure 1.8 N
Side-to-side overlap of a p orbital of
carbon with a p orbital of oxygen
to form a p bonding molecular
orbital and a p* antibonding
molecular orbital.

Energy

π∗ antibonding molecular orbital

p atomic orbital
of carbon

p atomic orbital
of oxygen

π bonding molecular orbital