Homework Problems
Chapter 8 Homework Problems: 4, 6, 18, 20, 21, 22, 28, 30, 38, 42, 48,
54, 58, 68, 71, 76, 88, 90, 106 a-c, 115
CHAPTER 8
Chemical Bonding I: Basic Concepts
Types of Chemical Bonds
There are three general types of chemical bonds that substances
form, two of which we discuss in this chapter.
Ionic bonding - Electrons are transferred; bonding is due to
electrostatic attraction between cations (positive ions) and anions
(negative ions).
Covalent bonding - Pairs of electrons are shared between atoms.
Metallic bonding - Electrons are pooled (spread out) among
positively charged metal cations.
Lewis Dot Structure
In ionic and covalent bonding it is the valence electrons that are
usually involved in bond formation. One method used to focus on
changes that occur when bonds formed is to represent atoms and ions in
terms of dot structures. The method was developed by the American
chemist G. N. Lewis, and so is often called the Lewis dot structure
method.
In the dot structure method valence electrons are represented as
dots around the symbol for the element. For simple cases a maximum of
8 valence electrons can occur (2 for hydrogen and helium). The
electrons are placed around the atom or ion, in pairs when necessary.
Example: What are the Lewis structures for H, N, and F?
H 1s1
N 1s22s22p3
F 1s22s22p5
Dot Structure For Main Group Elements
The dot structures for atoms of main group elements are given
below.
Dot Structure For Atomic Ions
In addition to dot structures for atoms, we can also write dot
structures for ions formed from atoms by adding or removing the
appropriate number of electrons.
Example: Give the dot structures for O, O2-, and O2+.
O
1s2 2s2 2p4
O2-
1s2 2s2 2p6
O2+
1s2 2s2 2p2
O
O2-
O2+
Octet Rule
The general behavior observed by main group elements in ionic
compounds may be summarized in terms of a general principle called the
octet rule.
Octet rule - Main group elements tend to gain or lose electrons so
that they end up with a noble gas electron configuration. This will either
completely fill or completely empty the valence shell of electrons.
For most atoms, filling the valence shell means having a total of
eight electrons - hence, the name octet rule.
Note that for two elements (Li, Be) the octet rule predicts that
atoms of these elements will lose one (Li) or two (Be) electrons to obtain
the same electron configuration as He. Hydrogen (H) will tend to add
one electron to obtain the same electron configuration as He.
Ionic Bonding
Ionic bonding refers to the bonding that occurs between cations
and anions due to the attractive force that acts between particles of
opposite charge. We may say the following:
1) Ionic bonding usually occurs between a metal cation and a
nonmetal anion (or anion group).
2) The attractive forces in ionic bonding are isotropic (the same
in all directions).
3) Ionic compounds are usually solids at room temperature.
4) Ionic compounds usually have high melting points and high
boiling points relative to those observed for other substances.
5) Ionic solids are usually hard and brittle, and easily cleaved.
Formation of Ionic Compounds
To form a binary ionic compound one or more electrons are
transferred between a metal atom and a nonmetal atom to form ions.
NaCl Na
Cl
MgCl2 Mg
Cl
1s2 2s2 2p6 3s1
Na+
1s2 2s2 2p6
1s2 2s2 2p6 3s2 3p5
Cl-
1s2 2s2 2p6 3s2 3p6
1s2 2s2 2p6 3s2
Mg2+ 1s2 2s2 2p6
1s2 2s2 2p6 3s2 3p5
Cl-
1s2 2s2 2p6 3s2 3p6
The general tendency is for atoms to gain or lose electrons to either
completely fill or completely empty the ns np valence orbitals. This
accounts for the characteristic charges observed for main group ions.
Note that the formation of ions is similar to the processes of
ionization (for formation of cations) and electron affinity (for the
formation of anions).
Ionic Bonding With Dot Structures
Formation of ionic bonds can be pictured in terms of dot structure
as the transfer of electrons from metal atoms to nonmetal atoms.
Example: Na + Cl  NaCl
Note that we place ions within brackets, with the charge of the ion
indicated outside of the bracket.
This dot structure notation is not particularly useful for discussing
ionic bonding, but is extremely useful in discussing covalent bonding.
Lattice Energy
Lattice energy (Hlattice) is defined as the energy required to
convert exactly one mole of an ionic compound into gas phase ions.
NaCl(s)  Na+(g) + Cl-(g)
Hlattice(NaCl) = 787. kJ/mol
Lattice energy is expected to be positive when defined in this
way, as we must add energy to break apart an ionic solid
Lattice Energy and Coulomb’s Law
We may use Coulomb’s law to predict general trends in lattice
energy.
F ~ Q+ Qd2
Q+ = charge of cation
Q- = charge of anion
d = distance between ion centers
d = r+ + r-
r+ = radius of cation
r- = radius of anion
The larger in magnitude the attractive force between ions the
larger the value for lattice energy.
Trends in Lattice Energy
We may use Coulomb’s law to predict general trends in lattice
energy.
F ~ Q+ Qd2
The following follows from the above relationship.
1) As Q+ increases in magnitude the size of the lattice energy
increases.
2) As Q- increases in magnitude the size of the lattice energy
increases.
3) As the sizes of the ions decreases the size of the lattice energy
increases (since smaller ion size means a smaller value for d).
So the lattice energy increases as the magnitude of the charges of
the ions increases and as the size of the ions decreases.
Examples of Trends (1)
1) Cations in same group forming ionic compounds with the
same anion. Lattice energy decreases in size in moving from top to
bottom within a group.
Ionic compound
Hlattice(kJ/mol)
LiCl
834.
NaCl
787.
KCl
701.
CsCl
657.
Examples of Trends (2)
2) Anions in the same group forming ionic compounds with the
same cation. Lattice energy decreases in size in moving from top to
bottom within a group.
Ionic compound
Hlattice(kJ/mol)
LiF
1017.
LiCl
860.
LiBr
787.
LiI
632.
Examples of Trends (3)
3) As |Q+Q-| increases, the size of the lattice energy increases.
Hlattice= 910. kJ/mol
Hlattice= 3414. kJ/mol
Example
Arrange the following ionic compounds in order from largest to
smallest size of lattice energy.
1) KF, KCl, KBr, KI
2) MgO, CaO, SrO, BaO
3) KF, K2O, K3N
Example: Arrange the following ionic compounds in order from
largest to smallest size for lattice energy.
1) KF, KCl, KBr, KI
KF > KCl > KBr > KI
Cation is the same, anion is larger as we go from F- to I-.
2) MgO, CaO, SrO, BaO
MgO > CaO > SrO > BaO
Anion is the same, cation is larger as we go from Mg2+ to Ba2+.
3) KF, K2O, K3N
K3N > K2O > KF
Cation is the same, anion has a larger charge as we go from Fto N3-.
Determination of the Value for Lattice Energy
We may use our previous discussion of thermodynamics to find
an experimental method for determining a value for lattice energy. We
illustrate the method for the ionic compound sodium chloride
Na(s)  Na(g)
1/
2
Cl2(g)  Cl(g)
Hf(Na(g))
Hf(Cl(g))
Na(g)  Na+(g) + e-
IE1(Na)
Cl(g) + e-  Cl-(g)
EA(Cl)
Na+(g) + Cl-(g)  NaCl(s)
- Hlattice(NaCl)
Na(s) + 1/2 Cl2(g)  NaCl(s)
Hf(NaCl(s))
The above collection of processes is called a Born-Haber cycle.
Finding the Lattice Energy
Na(s)  Na(g)
1/
2
Cl2(g)  Cl(g)
Hf(Na(g))
Hf(Cl(g))
Na(g)  Na+(g) + e-
IE1(Na)
Cl(g) + e-  Cl-(g)
EA(Cl)
Na+(g) + Cl-(g)  NaCl(s)
- Hlattice(NaCl)
Na(s) + 1/2 Cl2(g)  NaCl(s)
Hf(NaCl(s))
Hf(Na(g)) + Hf(Cl(g)) + IE1(Na) + EA(Cl) + (- Hlattice(NaCl))
= Hf(NaCl(s))
Hlattice(NaCl) = [Hf(Na(g)) + Hf(Cl(g)) + IE1(Na) + EA(Cl)]
- Hf(NaCl(s))
“Ionic Bonding” in Nonmetals
Given the success of ionic bonding in explaining substances
composed of metals + nonmetals, it is reasonable to attempt to apply the
model for bonding between nonmetal atoms.
Cl2
Cl [Ne] 3s2 3p5
Cl- [Ne] 3s2 3p6
Cl [Ne] 3s2 3p5
Cl+ [Ne] 3s2 3p4
Problems:
1) While the Cl- anion now satisfies the octet rule, the Cl+ cation
is worse off than before.
2) Experimentally, both Cl atoms in Cl2 are the same.
3) Cl2 exists as molecules and is a gas at room temperature. We
would expect ionic substances to exist as crystalline solids.
Covalent Bonding
We can get around the problems associated with transferring
electrons by sharing one or more pairs of electrons. The shared electrons
can be counted by both atoms in satisfying the octet rule. Bonding by
sharing of one or more electron pairs is called covalent bonding.
Notation
1) Bonding electron pairs are indicated by lines.
2) Nonbonding electrons, called lone pair electrons, are indicated
by dots.
Multiple Bonds
It is possible for atoms to share more than one pair of electrons.
Consider the diatomic molecules F2, O2, and N2.
F 1s2 2s2 2p5
O 1s2 2s2 2p4
N 1s2 2s2 2p3
Bond order = number of pairs of shared electrons.
Polyatomic Molecules and Ions
Covalent bonding can take place in polyatomic molecules or ions.
Lewis structure - Indicates which atoms are bonded together, the
bond orders for these bonds, and the number of lone pairs electrons.
Lewis structures do not directly indicate molecular geometry (the
arrangement of atoms in three dimensions).
As previously noted, we often write molecular formulas in such a
way that they provide information about the arrangement of atoms in a
polyatomic molecule.
There are often several ways in which a Lewis structure may be
drawn for a particular molecule.
Example: CH3COOH (acetic acid)
Although these Lewis structures look different, they are all the same,
and communicate the same information about the bonding in acetic acid.
Average Bond Length
The average bond length is the average length of a particular type
of bond (single, double, triple) between two atoms.
In general, the average bond length decreases as we go from a
single to a double to a triple bond.
bond
N-N
N=N
NN
length (nm)
0.147
0.124
0.110
Average Bond Lengths (Table)
Lewis Structures For Ions
Lewis structures for ions are drawn the same way as for molecules,
except that the ion is placed within brackets, with the charge of the ion
shown outside the brackets.
NO2+
NH4+
Comparison of Ionic and Covalent Compounds
Ionic
Covalent
Bonding by transfer of electrons
Bonding by sharing of electrons
Bonding is isotropic
Bonding is directional
Do not exist as molecules
Exists as molecules
Solids at room temperature
May be solid, liquid, or gas
at room temperature
High melting point
Low melting point
High boiling point
Low boiling point
Strong electrolytes
Usually nonelectrolytes
Bond Polarity
A covalent bond represents the sharing of one or more pairs of
electrons. However, the electron pairs are not necessarily equally shared
between the two bonded atoms. We call a bond where there is an
unequal sharing of electrons a polar covalent bond.
There are three general cases:
1) Equal sharing - Atoms bonded by electrons that are equally shared
2) Unequal sharing - Atoms bonded by electrons that are unequally
shared.
3) Ionic bonding - Ions are formed from the transfer of one or more
electrons to form cations and anions
Bond Polarity - Examples
H-H
H+ - F-
[ Na+] [F-]
Electronegativity
Electronegativity (EN) is a number (between 0 - 4) that is
assigned to an element that represents the tendency of atoms of that
element to attract electrons. The larger the value for electronegativity the
greater the tendency for atoms of that element to attract electrons. Note
that a value for electronegativity is not assigned to most noble gases.
The general trends for electronegativity are as follows:
1) Within a group of elements electronegativity increases from
bottom to top.
2) Within a period electronegativity increases from left to right.
For a polar covalent bond between two atoms, the atom with the
larger value for electronegativity will have a partial negative charge (-)
and the atom with the smaller value for electronegativity will have a
partial positive charge (+).
Electronegativity Chart
Use of Electronegativity
The difference in electronegativity between two atoms can be
used to predict the type of bonding that exists between the atoms.
EN < 0.5
Bond is nonpolar or only slightly polar.
EN 0.5 - 2.0 Bond is polar covalent, more electronegative
atom has a partial negative charge
EN > 2.0
Bond is ionic; more electronegative atom forms
an anion
Above guidelines are approximate.
EN = 2.1
EN = 0.9
EN = 0.0
ionic
polar covalent
nonpolar covalent
Dipole Moment ()
Dipole moment () is a measure of how polar a bond or a
molecule is. By definition, dipole moment is given by the expression
 = Qr
Q = size of separated +/- charge
r = distance of separation of charge
As q increases and r increases  also increases.
Dipole moment is measured in units of Debye
1 Debye = 3.336 x 10-30 Cm
Molecule
EN
|e-| = 1.602 x 10-19 C
 (Debye)
F2
0.0
0.00
HF
1.9
1.82
LiF
3.0
6.33
Percent Ionic Character
The percent ionic character is a measure of the approximate
amount of ionic character in a bond between two atoms. It is defined as
% ionic character =
(observed)
100 %
(assuming discrete charges)
where (observed) = experimentally observed dipole moment
(assuming discrete charges) = dipole moment calculated using
the bond distance and assuming complete electron transfer
Percent Ionic Character - Example
The experimental values for dipole moment and bond distance for
the molecule HCl are
 = 1.08 D
r = 0.127 nm
What is the percent ionic character of the bond?
The experimental values for dipole moment and bond distance for
the molecule HCl are
 = 1.08 D
r = 0.127 nm
What is the percent ionic character of the bond?
(assuming discrete charges) = dipole moment calculated using
the bond distance and assuming complete electron transfer
= (1)(1.602 x 10-19 C)(0.127 x 10-9 m)
= 6.10 D
% ionic character = 1.08 D 100% = 18%
6.10 D
1D
3.336 x 10-30 Cm
Electronegativity and Percent
Ionic Character
Guidelines For Drawing Lewis Structures
The following general guidelines are useful in drawing Lewis
structures for molecules and ions.
1) The central atom is usually the least electronegative atom
(excluding hydrogen, which will never be the central atom).
2) For molecules or ions that obey the octet rule
number of bonds = (# e- needed for octet rule) - (# valence e-)
2
3) There is usually one electron from each atom making a
covalent bond.
4) Common number of covalent bonds formed
H - 1 bond (no exceptions)
O - 2 bonds
F - 1 bond (no exceptions)
N - 3 bonds
Cl, Br, I - 1 bond
C - 4 bonds (almost no exceptions)
Example:
Draw the Lewis structure for the following molecules
a) NOF
b) CH2O
c) CH3CHO
Example:
Draw the Lewis structure for the following molecules
a) NOF
b) CH2O
c) CH3CHO
NOF
N 5 valence e-
central atom = N (least electronegative)
O 6 valence eF 7 valence e-
18 valence e- total
(8 + 8 + 8) = 24 e- needed for octet rule
number of covalent bonds = [ 24 - 18 ]/2 = 6/2 = 3
Examples of Covalent Bonding
NOF
central atom = N
# bonds = ( 24 - 18 ) = 3
2
CH2O central atom = C
# bonds = ( 20 - 12) = 4
2
CH3CHO
# bonds = ( 32 - 18) = 7
2
Organic Molecules
For organic molecules, we can often use the way in which the
formula for the molecule is written as a guide to its Lewis structure.
Example: What is the Lewis structure for diethyl ether, whose
chemical formula is CH3CH2OCH2CH3?
Organic Molecules
For organic molecules, we can often use the way in which the
formula for the molecule is written as a guide to its Lewis structure.
Example: What is the Lewis structure for diethyl ether, whose
chemical formula is CH3CH2OCH2CH3?
Coordinate Covalent Bond
In most covalent bonds each atom contributes the same number
of electrons to the bond. In a coordinate covalent bond, (sometimes
called a dative bond) both electrons come from the same atom. One
example of a coordinate covalent bond is in the ammonium ion (NH4+).
Coordinate covalent bonds can form when there is an atom that
has one or more available lone pairs of electrons. Note that in the
ammonium ion nitrogen is making more bonds than usual, and that all
four of the N-H bonds are identical.
Formal Charge
Formal charge (FC) is a number that represents in an approximate
way the electron density around a particular atom in a molecule or ion.
Note that it does not represent the real charge on the atom - it is a
bookkeeping device to keep track of electron density in the molecule or
ion. It is similar to, but not the same, as oxidation number.
Formal charge is assigned as follows:
FC = (# valence e- in atom) - [ (# nonbonding e-) + 1/2 (# bonding e-) ]
The sum of the formal charges must add up to the charge of the
molecule or ion.
Example:
FC(N) = 5 - [ 0 + 1/2 (8) ] = +1
FC(H) = 1 - [ 0 + 1/2 (2) ] = 0
Use of Formal Charge
Formal charge can be used to determine which resonance
structure is most important in representing a molecule or ion for cases
where the resonance structures are not equivalent to one another.
The best resonance structure is the one which:
1) Makes the formal charges of all atoms as close to zero as
possible.
2) If there are nonzero formal charges, places negative formal
charges on the more electronegative atoms and positive formal charges
on the less electronegative atoms.
Example: Which of the following structures for N2O is the best
structure?
# bonds = (24 - 16) = 4
2
Example: Which of the following structures for N2O is the best
structure?
# bonds = (24 - 16) = 4
2
0
+1
-1
-1
+1
0
-2
+1
+1
The structure on the right can be ruled out because it has a formal
charge that is more different from zero than the other two structures. Of
the two remaining structures, the one on the left places the negative
formal charge on oxygen, the more electronegative atom, and so is better
than the one in the middle.
Resonance Structures
It is not always possible to represent bonding in a molecule or ion
with a single Lewis structure.
Example: What is the Lewis structure for O3?
# bonds = ( 24 - 18) = 3
2
Experimentally, the two bonds in O3 are the same, and intermediate between a single and a double bond. That suggests the real
structure is some combination of the above two Lewis structures.
Resonance structure - Two or more valid Lewis structures for a
molecule or ion. The actual structure is an “average” of the resonance
structures.
We use an arrow () to indicate the Lewis structures that
contribute to the representation of the molecule or ion.
Resonance structures differ only in the arrangement of electrons,
and not in the arrangement of the atoms making up the molecule or ion.
Example: NO3- (nitrate ion)
# bonds = ( 32 - 24) = 4
N = central atom
2
In this case there are three equivalent Lewis structures that differ only in
the location of the N=O double bond. The N-O bond is equal to 1 1/3 of a
covalent bond.
Formal Charge and Resonance Structures
We can sometimes use formal charge to identify the most
important resonance structure for a molecule or ion. Consider our
previous case of the N2O molecule.
0
+1
-1
-1
+1
0
-2
+1
+1
The average structure will have a larger contribution from the
resonance structure on the left, and a smaller contribution from the
resonance structure on the right, based on the formal charges observed.
Exceptions to the Octet Rule
While the octet rule works well for many substances, there are
several important exceptions to the general rule.
1) Compounds of beryllium (Be) and boron (B). Beryllium
(which often forms covalent compounds) usually makes two covalent
bonds, boron usually makes three covalent bonds.
Be
1s2 2s2
B
1s2 2s2 2p1
2) Molecules or ions with an odd number of electrons. In this
case, it is impossible to pair up the electrons so that every atom satisfies
the octet rule.
In this case, the less electronegative atom generally is the one that
will be one electron short of an octet.
Examples: NO and ClO.
(16-11)/2 = 2.5
(16-13)/2 = 1.5
3.0
3.5
3.0
3.5
Compounds with an odd number of electrons are usually very
reactive, as they would like to acquire an additional electron to satisfy
the octet rule.
3) Elements below the second period of the periodic table. Since
these elements have d orbitals in addition to their s and p orbitals, there is
room in the valence shell for more than 8 electrons. The elements can
form compounds with an expanded octet (more than 8 valence electrons).
N
1s2 2s2 2p3
P
1s2 2s2 2p6 3s2 3p3 3d0
NF3
NF5 -
PF3
does not occur
PF5
We usually consider Lewis structures that contain atoms with more than
an octet of electrons only if no reasonable structure obeying the octet rule
can be found. We also use formal charge to guide us (discussed later).
Example: What are the Lewis structures for SF2, SF4, and SF6?
Example: What are the Lewis structures for SF2, SF4, and SF6?
Formal Charge and the Octet Rule
We sometimes see cases where a resonance structure that is better
based on formal charge is worse based on satisfying the octet rule. In
these cases, how do we decide which resonance structure is more
important?
All the atoms in the structure at left satisfy the octet rule. Sulfur
violates the octet rule in the structure at right, but the formal charges are
all equal to zero. So both are likely to be important.
Note that there are a number of other equivalent resonance
structures for the structure at right.
Bond Dissociation Energy
We define the bond dissociation energy (D) as the amount of
energy required to break (dissociate) one mole of a specific bond in a
specific molecule in the gas phase.
ethane D = 376. kJ/mol
CH3CH3(g)  CH3(g) + CH3(g)
propane D = 356. kJ/mol
CH3CH2CH3(g)  CH3CH2(g) + CH3(g)
butane D = 352. kJ/mol
CH3CH2CH2CH3(g)  CH3CH2CH2(g) + CH3(g)
Average Bond Energy
If we look at the amount of energy required to break a particular
type of bond in different molecules we observe that the values don’t
change much from molecule to molecule. That suggests that we define
an average bond energy that represent the “average” amount of energy
required to break one mole of a particular type of bond.
1) Since these are average values, the actual amount of energy
required to break a specific bond in a particular molecule may differ
from the average.
2) The larger the value for bond energy the stronger the bond.
3) Average bond energies depend on both the identity of the two
atoms bonded together and the bond order.
C-C
347. kJ/mol
C=C
620. kJ/mol
CC
812. kJ/mol
Table of Average Bond Enthalpies
Example: How much energy would it take to break apart one
mole of formaldehyde (CH2O) molecules into atoms in the gas phase?
Example: How much energy would it take to break apart one
mole of formaldehyde (CH2O) molecules into atoms in the gas phase?
CH2O(g)  C(g) + 2 H(g) + O(g)
energy = D(C=O) + 2 D(C-H) = (745 kJ/mol) + 2 (414 kJ/mol)
 1573. kJ/mol
experimental value = 1511. kJ/mol
Estimating Hrxn From Bond Energies
Consider a chemical reaction taking place with gas phase
reactants and products. We can represent the reaction in two ways
reactants  products
reactants  atoms
Hrxn
 products
In the second pathway we break all of the chemical bonds in the reactant
molecules to form atoms, and then make the new chemical bonds
required to form our final products.
Since enthalpy is a state function, the change in enthalpy for both
of the above processes must be the same. Therefore, we may say
Hrxn  ( bond energies for reactants) –
( bond energies for products)
The approximation is due to the fact that the values for bond
energies are average values and so approximate.
Example
Chloroethane may be formed by the following process
C2H4(g) + HCl(g)  CH3CH2Cl(g)
Estimate the value for Hrxn for the above process.
Chloroethane may be formed by the following process
C2H4(g) + HCl(g)  CH3CH2Cl(g)
Estimate the value for Hrxn for the above process.
Bonds broken = 4 (C-H) + (H-Cl) + (C=C)
= 4 (414) + (432) + (620) = 2708 kJ/mol
Bonds formed = 5 (C-H) + (C-Cl) + (C-C)
= 5 (414) + (339) + (347) = 2756 kJ/mol
Hrxn  (2708 kJ/mol) - (2756 kJ/mol) = - 48 kJ/mol
Bonding in Metals
Metals have a general tendency to give up electrons to form
cations. This indicates that the valence electrons in a metallic element
are only loosely attracted to the nucleus of the metal.
A simple model for bonding in metals is to treat the valence
electrons as forming a “sea” of electrons which can easily move about in
the metal. Because of this, this suggests that it should be easy to move
electrons through the volume of the metal. In fact, metals are good
conductors of electricity because these loosely bound electrons can easily
move through the metal.
The above also accounts for the malleability and ductility of
metals. Because there are usually no strong localized bonds in metals, it
becomes easy to alter their shape (hammer them into thin sheets or draw
them into wires).
End of Chapter 8
“The underlying physical laws necessary for the mathematical
theory of a large part of physics and the whole of chemistry are thus
completely known, and the difficulty is only that the application of these
laws leads to equations much too complicated to be soluble.”
- P. A. M. Dirac
“The great importance in Lewis’ theory is that it provided
chemists with a valuable way of visualizing the electronic structures of
atoms and molecules, and for practical purposes his ideas are still used
today.” - Keith J. Laidler
“My name is Bond - Covalent Bond.” - anonymous