Unit 2 Module 2
Looking for Patterns
John Pollard
University of Arizona
Knowing both the atomic composition and connectivity of the atoms in a molecule is
fundamental to determining the identity and properties of a substance. The idea that
molecules are comprised of atoms connected to each other in some way and arranged in
particular geometries in space is very useful in explaining and predicting properties. To
fully describe molecular structure, we must first understand the bonding model used to
explain how atoms connect to each other
A Bonding Model
In molecules, atoms are thought to be bonded together by the
electrostatic interactions between the electrons and protons.
Electrons, being negatively charged are attracted to the protons
residing in the nuclei of the atoms bonded. There is a balance
between attraction and repulsion (between like charges) that
establishes a lowest energy distance between the nuclei called
the bond length. In addition to the electrostatic forces
involved in bonding, electrons (and protons) have an intrinsic
property called “spin”. Spin generates an additional force
between electrons that is magnetic in nature and weaker than the
electrostatic forces involved in bonding. When electrons are
confined to the same region of space, like in between two nuclei, “spin pairing” reduces
the energy of the system. The spin pairing of 2 electrons in a bond is often symbolically
represented by an upward and downward pairing of arrows.
Electrons do not behave as “classical” particles in that we cannot
know their position and velocity simultaneously. Electrons are more
accurately described as particles that occupy regions of probability.
The electron density is a measure of this probability. When a simple
covalent bond is formed between atoms, there is an increase in
electron density between the atoms involved. In addition, the
electrons are delocalized over the bonding region and there is a spin pairing between the
two electrons involved. Therefore, two electrons are involved in each bond. Atoms can
have more than one bond between them but in general, every pair of electrons will be
spin paired.
Chemical bonds are not static. The nuclei and electrons involved are constantly in
motion. The atoms involved in a bond vibrate around their equilibrium position with a
frequency that depends on the bond strength and atomic masses. The vibrational modes
that occur in molecules are also quantized, meaning there are only specific vibrational
modes with specific energies accessible to a molecule. As with the energy level diagrams
used to represent the absorption or emission of electromagnetic radiation by atoms, one
can represent the various vibrational modes of a molecule in the same fashion.
Energy
Higher energy
vibration
Lower energy
vibration
hIR
E
The absorption of infrared (IR) radiation at specific frequencies can be used to detect the
presence of specific bonding motifs. The IR spectrum is a sort of fingerprint for a
molecule and can reveal important information about the presence of certain types of
bonding. Certain structural motifs can be identified by absorption peaks in specific
frequency regions (with units of 1/λ).
Increasing Energy
O-H
C-H
Wavenumber
= 1/(cm-1)
C-C
C-H
Bonding Patterns
It has been found that there are certain bonding patterns that many atoms tend to exhibit.
These patterns are very useful to know as they can help in making predictions about the
possible structures of molecules. In general, molecular compounds result from the
combination of nonmetallic elements and many of these elements exhibit a fixed bonding
capacity (valence). In other words, they tend to form the same number of bonds
regardless of what molecule they are found in. Carbon tends to form 4 bonds, Nitrogen
and Phosphorous form 3, Oxygen and Sulfur form 2 and Hydrogen, Fluorine and
Chlorine tend to form 1. As an example, consider the molecule CH4. One can easily
elucidate the structure by knowing that H forms 1 bond each and C forms 4. Therefore,
the molecule must have a centrally located C with the 4 H’s around it each forming a
bond. Bonds are symbolically represented by lines between atoms with each line
representing 2 electrons in the bond.
Valence
4
3
2
1
0
H
H C H
H
Nonmetallic
elements
Valence is a periodic property
(elements from the same group
behave similarly)
Atoms in periodic 3 (P, S, Cl) are often found to violate these valency rules. We will
explore this more later in the course.
Looking into Atoms
In order to better understand molecular structure and the patterns that arise from the
valence of atoms, we need to describe why different atoms form different numbers of
bonds. As previously mentioned, covalent bonding is the result of interactions between
electrons and protons in bonded atoms. Therefore, exploring and understanding the
structure of single atoms provides important clues to bonding patterns.
Experimental data on the atomic radii and ioniziation energies of atoms are very
revealing about the bonding nature of atoms. The atomic radius of an atom is basically
obtained by doing a series of indirect measurements on a series of elements and
compounds and averaging the “covalent radii” obtained. A common technique used for
this is called X-Ray crystallography. This technique involves exposing crystals of a
sample to EM radiation in the x-ray energy region. This high energy radiation will
deflect off of atoms and generate a diffraction pattern which can then be used to
determine the size of atoms in molecules. There are some interesting and important
trends that arise when the atomic radii of all the elements are compared. When looking at
the periodic table, as you move to the left and down the atomic radii increase in size.
Periodic Behavior
R increases
In addition, a close look across rows of the periodic table reveals that there are large
jumps in size when starting a new row.
Atomic Radius
Atomic Radius (pm)
250
K
200
Li
150
Rb
Na
100
Ar
Kr
Ne
50
He
0
0
5
10
15
20
25
30
35
40
Atomic Number
Insight into atomic structure can also be gained by analyzing the energy required to
remove an electron from a gaseous atom. This measured value is called the first
ionization energy and the values also show periodic behavior.
Periodic Behavior
1st IE increases
In general, the ionization energy increases moving up and to the right on the periodic
table. Again, a close inspection of the trends across rows reveals that the ionization
energy peaks when the last group on the right (the noble gases) is reach.
First Ionization Potential
Energy (kJ/mol)
2500
He
2000
Ne
Ar
Kr
1500
1000
500
Li
Na
K
Rb
0
0
5
10
15
20
25
Atomic Number
30
35
40
To explain the periodic trends observed in both atomic radii and ionization energies, we
assume that the electrons are arranged in shells.
Shell Model
Shell  # of en = 1  2 en = 2  8 en = 3  8 en = 4  18 e-
E
H
He
Li
Ne
Na
0
The shell model explains the trend in atomic radii by arranging electrons into discreet
energy levels or shells. Shells are quantized energy states where multiple electrons
reside. They represent the area of probability of finding an electron and define the size of
the atom. In this model, the shells stack on top of each other with increasing size. The
shells have different electron occupancy limits with the first shell holding 2 electrons, the
next two holding 8 each and the subsequent shells holding a maximum of 18 electrons.
On moving across the periodic table, shells become more stable or lower in energy due to
the increase in the number of protons in the nucleus of atoms. This also causes the
electrons that occupy each shell to be, on average, pulled in closer to the nucleus. Shells
also have a maximum occupancy and newly occupied shells are further out from the
nucleus. Therefore, upon moving across a row of the periodic table shells are being filled
and are contracting due to the increase in the number of protons (the effective nuclear
charge). Completion of a row signifies the filling of a shell and the start of a new row
begins the filling of a new shell that is higher in energy and resides further from the
nucleus.
Photoelectron Spectroscopy
KE
The ionization energies of atoms are measured by a
technique called photoelectron spectroscopy (PES). PES
can not only determine the first ionization energy but all
the subsequent ionization energies. In other words, it can
be used to measure the amount of energy required to
remove all the electrons from an atom. The technique
utilizes various energies of EM radiation to eject electrons completely off of atoms. It
can be done selectively such that only the electrons of unfilled shells are ejected
(typically done with UV radiation), or can be done where all the electrons are ejected
h
(with X-Ray radiation). The ionization energy is determined by introducing a known
energy of photons (hν) and measuring the kinetic energy that the ejected electron comes
off with. The weaker the electron is held to the atom, the more kinetic energy it will
come off with when ejected. This means that the incoming light or photon energies must
be of sufficient energy to completely remove the electron and not just excite it to a higher
energy state. Inner shell electrons (referred to as core electrons) are held much more
tightly to the nucleus so it usually takes high energy x-ray photons to eject these
electrons.
Photoelectron Spectroscopy (PES)
•
First ionization energy removes electron from
outermost shell.
•
PES measures the energy to remove one
electron from any shell of a neutral atom.
•
Energy of entering photon (h) is larger than
ionization energy (IE), so the electron leaves
the atom with excess kinetic energy (KE),
which PES measures.
h
= IE + KE
known
measured
KE
determined
IE
n=
h
The data (spectra) from PES plots the ionization energy vs. the number of electrons
removed. The following plots are the full (all electrons removed) photoelectron spectra
of the first 9 elements of the periodic table.
He
H
1.31
Energy (MJ/mol)
Energy (MJ/mol)
2.37
0
2
4
6
8
10
Number of Electrons
12
14
16
0
2
4
6
8
10
Number of Electrons
12
14
16
Li
Be
0.52
0.90
0
2
Energy (MJ/mol)
Energy (MJ/mol)
6.26
4
6
8
10
12
14
11.5
0
16
2
4
6
8
Number of Electrons
0.80
Energy (MJ/mol)
Energy (MJ/mol)
2
4
6
8
10
12
14
16
28.6
0
2
4
Number of Electrons
6
8
10
12
14
16
Number of Electrons
N
O
1.40
1.31
2.45
3.12
Energy (MJ/mol)
Energy (MJ/mol)
16
1.72
19.3
39.6
2
14
1.09
1.36
0
12
C
B
0
10
Number of Electrons
4
6
8
10
Number of Electrons
12
14
16
52.6
0
2
4
6
8
10
Number of Electrons
12
14
16
F
Ne
1.68
2.08
67.2
0
2
4.68
Energy (MJ/mol)
Energy (MJ/mol)
3.88
4
6
8
10
12
14
16
84.0
0
2
Number of Electrons
4
6
8
10
12
14
16
Number of Electrons
Na
Shell
Subshell
# of e-
n=1
1s
2 e-
n=2
2s
2 e-
2p
6 e-
3s
2 e-
3p
6 e-
3d
10 e-
0.50
Energy (MJ/mol)
3.67
6.84
104
0
2
n=3
4
6
8
10
Number of Electrons
12
14
16
The photoelectron spectra for hydrogen and helium correlate well with the shell model.
The spectra for the period 2 elements reveal a new subtlety of the shell model. Instead of
all 8 electrons existing at the same energy (thus being seen under one ionization peak),
they exist in two subshells. One subshell contains 2 electrons and the second contains 6
electrons. This is first revealed in the spectrum of boron (B) as two peaks close in
energy are observed. One corresponds to 2 electrons and the other to 1 electron. This
second subshell of the n=2 shell is then filled upon moving to neon (Ne) and holds 6
electrons. The pattern then repeats itself in period 3 elements with the addition of a 3rd
subshell that holds 10 electrons. As a result, the shell model is modified to account for
the presence of subshells. Subshells are labeled as either s (holds 2 e¯ ), p (holds 6 e¯ ),
d (holds 10 e¯ ) or f (holds 14 e¯ ).
When an atom is in its ground state, the lower energy levels are occupied first and filled
in order of increasing energy. This state is called the ground state electron configuration
of an atom.
The energy ordering of the shells and subshells are represented and how they relate to the
periodic table is shown in the diagram below.
As an example, the electron configuration of carbon is 1s22s22p2 where the shells and
subshells are listed in order of increasing energy and the superscripts represent the
number of electrons in each shell or subshell. For Germanium (Ge) which has 32 total
electrons, the ground state configuration is 1s22s22p23s23p64s23d104p2. This can be
tedious to write and is often abbreviated by representing all the electrons in filled shells
by the nearest noble gas symbol. For Ge, this short-hand notation would be
[Ar] 4s23d104p2.
s1 s2
d1 d2 d3 d4 d5 d6 d7 d8 d9 d10
Ge  [Ar] 4s2 3d10 4p2
p1 p2 p3 p4 p5 p6
Valence electrons and the octet rule
Now that we have a better picture of the structure of the atom, we can look into why, in
general, atoms have certain bonding capacities. An atoms bonding capacity or valence
can be explained based on their ground state electron configurations. First off, we can
divide the electrons in an atom into two groups. The core electrons exist in filled shells
and are at very low energies. They are stable and not particularly accessible for bonding.
On the other hand, the valence electrons exist in unfilled shells, are high in energy,
farther from the nucleus and exposed to interactions with other atoms. It is the valence
electrons that are primarily responsible for the bonding between atoms. For example,
carbon has 4 valence electrons and is 4 electrons short of completing the n = 2 shell.
Therefore, carbon can obtain a filled n = 2 shell by sharing 4 electrons thus forming 4
bonds. The completion of the shell provides the most stable bonding configuration for
carbon which is why it is almost always found in this configuration when in compounds.
The number of electrons required to complete its unfilled shell (valency) is what dictates
the number of bonds formed in compounds. In general, the number of covalent bonds
that each atom forms is determined by the number of valence electrons that the atom just
share to have a full shell. For the atoms of period 2 (2nd row), this is referred to as the
octet rule and essentially says that the most stable structures occur when each atom
achieves eight valence electrons through bonding. The atoms of period 3 typically obey
the octet rule but not as stringently as periodic 2 elements. Because hydrogen only needs
1 electron to complete the n = 1 shell, it is found only forming one bond in almost all
molecules.
Let’s look at 2 cases where the octet rule guides us in predicting the stable bonding
modalities of the atoms involved.
Case 1- F2
One way to symbolically represent an F atom and its valence electrons is with a Lewis
dot symbol. The Lewis symbol for F is:
The 7 dots around the F represent each of the valence electrons. In the molecule F2 the
fluorine atoms form a single covalent bond which allows each F to achieve an octet. The
shared electrons of the bond are represented as a line in the Lewis structure of F2.
8 e+
8 eF
F
Case 2- N2
Nitrogen has 5 valence electrons and a valency of 3. Therefore, it needs to form 3 bonds
or share 3 electrons with other atoms to complete its octet. If there are just 2 N’s, then
each must form 3 bonds making a triple bond between to two atoms.
N
+
N
N N
Combining Analysis
Combining the results of IR and MS can provide direct
structural information about the molecules that make up
substances. Your task is to use experimental data to
determine the molecular structures of the following 4
unknowns.
a) Unknown A is a pleasant smelling liquid with a boiling point of 101ºC. Elemental
analysis results show that it has an empirical formual of C3H6O. Use this and the IR-MS
data to determine the structure of this compound.
b) Unknown B is an oily liquid with boiling point of 101ºC and a melting point of -13
ºC. Elemental analysis results show that it has an empirical formula of C7H5N. Use
this and the IR-MS data to determine the structure of this compound.
c) Unknown C is a colorless solid with a melting point of 103 ºC. Elemental analysis
results show that it has an empirical formula of C5H11NO. Use this and the IR-MS
data to determine the structure of this compound.
d) Unknown D is a colorless gas that condenses at -26 ºC. Elemental analysis results
show that it has an empirical formula of C3F6O. Use this and the IR-MS data to
determine the structure of this compound.
Photoelectron Spectra from Space
Imagine that we were able to communicate with aliens from a parallel universe. Among the
information that we manage to exchange and translate into our scientific language, there is a table
and some graphs containing data for some atomic properties in their universe. You have been
assigned to collaborate in the analysis of the available data and develop a chemical model of the
atom in this parallel universe.
Symbol
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Z
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Atomic
Radius
(pm)
37
32
29
134
90
82
77
75
73
71
69
65
154
130
118
111
First Ionization
Energy (kJ/mol)
Symbol
1312
2372.3
3200
520.2
700.5
800.6
1086.5
1202.3
1413.9
1682
2080.7
2500
495.8
520.7
577.5
786.5
W
X
Y
Z
AA
BB
CC
DD
EE
FF
GG
HH
II
JJ
KK
LL
Z
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
Atomic
Radius (pm)
174
144
136
127
125
124
123
122
121
119
118
117
116
115
115
114
First Ionization
Energy (kJ/mol)
589.8
633.1
658.8
659.9
663.9
717.3
745.5
760.4
777.1
845.5
906.4
925.8
935
1050
1100
1239.9
Q
R
S
T
U
V
17
18
19
20
21
22
870.8
999.6
1251.2
1520.6
1750
418.8
106
102
99
97
95
196
MM
NN
OO
PP
QQ
RR
39
40
41
42
43
44
110
109
108
107
211
1350.8
1399
1451
1502
403
First Ionization Potential
Atomic Radius
Atomic Radius (pm)
250
3500
Energy (kJ/mol)
200
150
100
50
0
3000
2500
2000
1500
1000
500
0
0
5
10
15
20
25
30
Atomic Number
35
40
45
0
5
10 15 20 25 30 35 40 45
Atomic Number
Photoelectron Spectra
Z=1
Z=2
Z=3
1
E
E
E
2
3
# e-
# e-
Z= 4
E
# e-
Z=5
Z=6
1
E
E
Large Energy Gap
E
2
3
Large Energy Gap
3
3
# e-
3
# e-
Z=7
# e-
Z=12
Z=13
1
1
6
E
3
3
3
3
3
3
# e-
Z= 33
# e-
3
E
6
3
3
# e-
5
9
6
3
# e-
Z= 41
Large Energy Gap
1
E
Large Energy Gap
E
Z=22
Large Energy Gap
6
Large Energy Gap
E
Large Energy Gap
Large Energy Gap
ggGap
6
3
E
3
6
3
3
# e-
12
3
Large Energy Gap
ggGap
6
6
3
3
# e-
Emission Spectra
The emission spectrum for element RR indicates that all light emitted by its atoms has a
wavelength smaller than 654 nm.
 = 654 nm
I.
Based on all of the information provided, build a model of the atom in this parallel universe
that allows you to explain the experimental data. Consider things such as:
a) Do you have to assume that the energy of the electrons is quantized? Why?
b) Would a shell model allow you to explain the data? How many shells would help you
explain the data? How would electrons be distributed in the different shells?
c) Would you need to introduce the idea of sub-shells to better explain the data? Why? How
many sub-shells do you have to assume in each major shell? How many electrons occupy
each sub-shell?
d) How many electrons in the valence shell would you expect to lead to a stable electron
configuration? What would be the equivalent to the “octet rule” in our universe?
e) How many electrons would you suspect are shared during the formation of a single
covalent bond between two atoms in this Universe?
f) Compare and contrast your model with our own atomic model for atoms in our universe.
II. According to your model:
a) What would be the electron configuration of element RR? (Create your own notation.
Explain it clearly).
b) Estimate the atomic radius and the 1st ionization energy of this element. Justify your
answer.
c) What would be the minimum energy, in kJ/mol, absorbed by this type of atom when
interacting with electromagnetic radiation?
d) What would be the electron configuration of element K?
e) What would you expect the valence of element K to be?
f) Would you expect element K to exist as single atoms or as diatomic molecules?