Molecular Geometry
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C HAPTER
Chapter 1. Molecular Geometry
1
Molecular Geometry
Lesson Objectives
• Explain the basis of VSEPR theory.
• Predict the shapes of molecules and polyatomic ions using VSEPR theory.
• Account for variations in bond angles based on the relative repulsive forces exerted by lone pairs and bonding
pairs of electrons.
• Describe the relationship between molecular geometry and electron domain geometry.
Lesson Vocabulary
•
•
•
•
electron domain geometry
molecular geometry
valence shell
valence shell electron pair repulsion (VSEPR)
Check Your Understanding
Recalling Prior Knowledge
• How are Lewis electron dot structures determined?
• What are bonding pairs of electrons and what are lone pairs?
Molecular geometry is the three-dimensional arrangement of atoms in a molecule. The molecular geometry, or
shape, of a molecule is an important factor that affects the physical and chemical properties of a compound. Those
properties include melting and boiling points, solubility, density, and the types of chemical reactions that a compound
undergoes. In this lesson, you will learn a technique to predict molecular geometry based on a molecule’s Lewis
electron dot structure.
VSEPR Theory
The valence shell is the outermost occupied shell of electrons in an atom. This shell holds the valence electrons,
which are the electrons that are involved in bonding and shown in a Lewis structure. The valence-shell electron
pair repulsion model, or VSEPR model, states that a molecule will adjust its shape so that the valence electron
pairs stay as far apart from each other as possible. This makes sense, based on the fact that negatively charged
electrons repel one another. We will systematically classify molecules according to the number of bonding pairs
of electrons and the number of nonbonding or lone pairs around the central atom. For the purposes of the VSEPR
model, a double or triple bond is no different in terms of repulsion than a single bond. We will begin by examining
molecules in which the central atom does not have any lone pairs.
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Central Atom with No Lone Pairs
In order to easily understand the types of molecules possible, we will use a simple system to identify the parts of any
molecule.
A = central atom in a molecule
B = atoms surrounding the central atom
Subscripts after the B will denote the number of B atoms that are bonded to the central A atom. For example, AB4
is a molecule with a central atom surrounded by four covalently bonded atoms. Again, it does not matter if those
bonds are single, double, or triple bonds.
AB2 : Beryllium Hydride (BeH2 )
Beryllium hydride consists of a central beryllium atom with two single bonds to hydrogen atoms. Recall that it
violates the octet rule.
According to the requirement that electron pairs maximize their distance from one another, the two bonding pairs
in the BeH2 molecules will arrange themselves on directly opposite sides of the central Be atom. The resulting
geometry is a linear molecule, shown in a “ball and stick” model below ( Figure 1.1).
FIGURE 1.1
The H-Be-H bond angle is 180° because of its linear geometry.
Carbon dioxide is another example of a molecule which falls under the AB2 category. Its Lewis structure consists of
double bonds between the central carbon atom and each oxygen atom.
The repulsion between the two groups of four electrons (two pairs) is no different than the repulsion between the
two groups of two electrons (one pair) in the BeH2 molecule. Carbon dioxide is also linear.
AB3 : Boron Trifluoride (BF3 )
Boron trifluoride consists of a central boron atom with three single bonds to fluorine atoms. The boron atom also
has an incomplete octet.
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Chapter 1. Molecular Geometry
FIGURE 1.2
The geometry of the BF3 molecule is called trigonal planar. The fluorine atoms are positioned at the vertices of an
equilateral triangle. The F-B-F angle is 120°, and all four atoms lie in the same plane.
FIGURE 1.3
AB4 : Methane (CH4 )
Methane is an organic compound that is the primary component of natural gas. Its structure consists of a central
carbon atom with four single bonds to hydrogen atoms.
In order to maximize their distance from one another, the four groups of bonding electrons do not lie in the same
plane. Instead, each of the hydrogen atoms lies at the corners of a geometrical shape called a tetrahedron. The
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carbon atom is at the center of the tetrahedron. Each face of a tetrahedron is an equilateral triangle.
FIGURE 1.4
(left) Tetrahedron. (right) Ball and stick
model of methane.
The molecular geometry of the methane molecule is referred to as tetrahedral ( Figure 1.4). The H-C-H bond angles
are 109.5°, which is larger than the 90° that they would be if the molecule was planar. When drawing a structural
formula for a molecule such as methane, it is advantageous to be able to indicate the three-dimensional character of
its shape. The structural formula below ( Figure 1.5) is called a perspective drawing. The dotted line bond should
be visualized as receding into the page, while the solid triangle bond should be visualized as coming out of the page.
FIGURE 1.5
AB5 : Phosphorus Pentachloride (PCl5 )
The central phosphorus atom in a molecule of phosphorus pentachloride has ten electrons surrounding it, exceeding
the octet rule.
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Chapter 1. Molecular Geometry
Unlike the other basic shapes, the five chlorine atoms in this arrangement are not equivalent with respect to their
geometric relationship to the phosphorus atom. Three of the chlorine atoms lie in a plane, with Cl-P-Cl bond angles
of 120°. This portion of the molecule is essentially the same as a trigonal planar arrangement. These chlorine atoms
are referred to as the equatorial atoms because they are arranged around the center of the molecule. The other two
chlorine atoms are oriented exactly perpendicular to the plane formed by the phosphorus atom and the equatorial
chlorine atoms. These are called the axial chlorine atoms.
FIGURE 1.6
(left) Ball and stick model of phosphorus
pentachloride. (right) Trigonal bipyramidal.
In the figure above ( Figure 1.6), the axial chlorine atoms form a vertical axis with the central phosphorus atom.
There is a 90° angle between P-Claxial bonds and P-Clequitorial bonds. The molecular geometry of PCl5 is called
trigonal bipyramidal. A surface covering the molecule would take the shape of two three-sided pyramids pointing
in opposite directions.
AB6 : Sulfur Hexafluoride (SF6 )
The sulfur atom in sulfur hexafluoride also exceeds the octet rule.
Unlike the trigonal bipyramidal structure, all of the fluorine atoms in SF6 are equivalent. The molecular geometry
is called octahedral ( Figure 1.7) because a surface covering the molecule would have eight sides. All of the F-S-F
angles are 90° in an octahedral molecule, with the exception of the fluorine atoms that are directly opposite one
another.
Central Atom with One or More Lone Pairs
The molecular geometries of molecules change when the central atom has one or more lone pairs of electrons. The
total number of electron pairs, both bonding pairs and lone pairs, leads to what is called the electron domain
geometry. Electron domain geometries are one of the five learned so far: linear, trigonal planar, tetrahedral, trigonal
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FIGURE 1.7
bipyramidal, or octahedral. However, when one or more of the bonding pairs of electrons is replaced with a lone
pair, the molecular geometry, or actual shape of the molecule, is altered. In keeping with the A and B symbols
established in the previous section, we will use E to represent a lone pair on the central atom (A). A subscript will
be used when there is more than one lone pair. Lone pairs on the surrounding atoms (B) do not affect the geometry.
AB2 E: Ozone (O3 )
The Lewis structure for ozone consists of a central oxygen atom that has a double bond to one of the outer oxygen
atoms and a single bond to the other.
This leaves one lone pair on the central atom, and the molecule displays resonance. Since VSEPR does not
distinguish between double and single bonds, the resonance does not affect the geometry. Molecules with three
electron pairs have a domain geometry that is trigonal planar. Here, the lone pair on the central atom repels the
electrons in the two bonds, causing the atom to adopt a bent molecular geometry.
FIGURE 1.8
Ozone, O3 .
One might expect the O-O-O bond angle to be 120°, as in a trigonal planar molecule. However, within the context
of the VSEPR model, lone pairs of electrons can be considered to be slightly more repulsive than bonding pairs of
electrons, due to their closer proximity to the central atom. In other words, lone pairs take up more space. Therefore
the O-O-O angle is slightly less than 120°.
AB3 E: Ammonia (NH3 )
The ammonia molecule contains three single bonds and one lone pair on the central nitrogen atom.
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Chapter 1. Molecular Geometry
The domain geometry for a molecule with four electron pairs is tetrahedral, as was seen with CH4 . In the ammonia
molecule, one of the electron pairs is a lone pair rather than a bonding pair. The molecular geometry of NH3 is called
trigonal pyramidal ( Figure 1.9).
FIGURE 1.9
Ammonia, NH3 .
Recall that the bond angles in the tetrahedral CH4 molecule are all equal to 109.5°. Again, the replacement of one
of the bonded electron pairs with a lone pair compresses these angles slightly. The H-N-H angle is approximately
107°.
AB2 E2 : Water (H2 O)
A water molecule consists of two bonding pairs and two lone pairs.
As for methane and ammonia, the domain geometry for a molecule with four electron pairs is tetrahedral. In the
water molecule, two of the electron pairs are lone pairs rather than bonding pairs. The molecular geometry of the
water molecule is referred to as bent ( Figure 1.10). The H-O-H bond angle is 104.5°, which is smaller than the
bond angle in NH3 .
FIGURE 1.10
Water, H2 O.
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AB4 E: Sulfur Tetrafluoride (SF4 )
The Lewis structure for SF4 contains four single bonds and a lone pair on the sulfur atom.
The sulfur atom ( Figure 1.11) has five electron groups around it, which corresponds to the trigonal bipyramidal
domain geometry, as in PCl5 . Recall that the trigonal bipyramidal geometry has three equatorial atoms and two axial
atoms attached to the central atom. Because of the greater repulsion of a lone pair, it is one of the equatorial atoms
that is replaced by a lone pair. The geometry of the molecule is called a distorted tetrahedron or seesaw.
FIGURE 1.11
Sulfur tetrafluoride, SF4 .
AB3 E2 : Chlorine Trifluoride (ClF3 )
The Lewis structure of ClF3 consists of three Cl-F single bonds and two lone pairs on the central chlorine atom.
As in the case of SF4 , the central atom has five electron groups and a trigonal bipyramidal domain geometry. In ClF3 ,
both of the bonded pairs that have been replaced with lone pairs are equatorial. The resulting molecular geometry is
called T-shaped.
FIGURE 1.12
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Chapter 1. Molecular Geometry
AB2 E3 : Triiodide Ion (I3 − )
The triiodide ion ( Figure 1.13) consists of three iodine atoms linked together by covalent bonds. Its overall charge
of 1- gives this structure 22 total valence electrons, resulting in a Lewis structure with three lone pairs on the central
iodine atom.
The five electron groups around the central atom give it a trigonal bipyramidal domain geometry, and all three
equatorial atoms have been replaced by lone pairs. The result is a linear ion—the central atom and the two axial
atoms.
FIGURE 1.13
Triiodide ion, I3 − .
AB5 E: Bromine Pentafluoride (BrF5 )
The bromine pentafluoride molecule ( Figure 1.14) has a central bromine atom, five single bonds to fluorine atoms,
and one lone pair.
The six groups of electrons around the central atom give it an octahedral domain geometry. Since all of the peripheral
atoms in an octahedral molecule are equivalent, any one of them could equally be replaced by the lone pair. The
resulting geometry is called square pyramidal. A surface covering a square pyramidal molecule is a four sided
pyramid on a flat base.
AB4 E2 : Xenon Tetrafluoride (XeF4 )
Xenon tetrafluoride ( Figure 1.15) has a Lewis structure consisting of four single bonds and two lone pairs on the
central xenon atom.
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FIGURE 1.14
Bromine pentafluoride, BrF5 .
The six groups of electrons give it an octahedral domain geometry, but two of the atoms are replaced by two lone
pairs. In order to maximize the space available to each of the lone pairs, they occupy positions that are directly
opposite each other. As a result, the four remaining fluorine atoms are in the same plane as the xenon atom, and all
F-Xe-F angles are equal to 90°. This molecular geometry is called square planar.
FIGURE 1.15
Xenon tetrafluoride, XeF4 .
Summary of VSEPR
The VSEPR model can be applied to predict the molecular geometry of a given molecular compound. The steps to
follow can be summarized as follows:
• Draw the Lewis electron dot structure for the molecule.
• Count the total number of electron pairs around the central atom. This is referred to as the electron domain
geometry.
• If there are no lone pairs around the central atom, refer to the table below ( Table 1.1), to determine the
molecular geometry, which is the same as the electron domain geometry.
• If there are one or more lone pairs on the central atom, the molecular geometry (the actual shape of the
molecule) will not be the same as the electron domain geometry. Refer to the table below ( Table 1.2).
• In predicting bond angles, remember that a lone pair takes up more space than a bonding pair or pairs of
electrons.
TABLE 1.1: Geometries of Molecules and Ions in Which the Central Atom Has No Lone Pairs
Number of Electron Pairs
Around Central Atom
2
3
10
Electron Domain Geometry
linear
trigonal planar
Molecular Geometry
Examples
linear
trigonal planar
BeCl2 , CO2
BF3 , CO3 2−
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Chapter 1. Molecular Geometry
TABLE 1.1: (continued)
Number of Electron Pairs
Around Central Atom
4
5
6
Electron Domain Geometry
tetrahedral
trigonal bipyramidal
octahedral
Molecular Geometry
Examples
tetrahedral
trigonal bipyramidal
octahedral
CH4 , NH4 +
PCl5
SF6
TABLE 1.2: Geometries of Molecules and Ions in Which the Central Atom Has One or More Lone Pairs
Total Number of
Electron Pairs
Number
of
Bonding Pairs
Number of Lone
Pairs
Electron
Domain
Geometry
trigonal planar
tetrahedral
3
4
2
3
1
1
4
5
2
4
2
1
tetrahedral
trigonal bipyramidal
5
3
2
5
2
3
6
5
1
trigonal bipyramidal
trigonal bipyramidal
octahedral
6
4
2
octahedral
Molecular
Geometry
Examples
bent
trigonal pyramidal
bent
distorted
tetrahedron
(seesaw)
T-shaped
O3
NH3
linear
I3 −
square pyramidal
square planar
BrF5
H2 O
SF4
ClF3
XeF4
Practice with basic molecule shapes at http://phet.colorado.edu/en/simulation/molecule-shapes-basics .
Practice building molecules at http://phet.colorado.edu/en/simulation/build-a-molecule .
Build 3D molecules at http://phet.colorado.edu/en/simulation/molecule-shapes .
Lesson Summary
• Valence shell electron pair repulsion (VSEPR) theory is a technique for predicting the molecular geometry of
a molecule. A molecule’s shape provides important information that can be used to understand its chemical
and physical properties.
• According to VSEPR, electron pairs distribute themselves around a central atom in such a way as to maximize
their distance from each other.
• Electron domain geometries are based on the total number of electron pairs, while molecular geometries
describe the arrangement of atoms and bonding pairs in a molecule.
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Lesson Review Questions
Reviewing Concepts
1. Why is it important to know the geometry or shape of a molecule?
2. What is the difference between electron domain geometry and molecular geometry? Use an example.
3. In terms of its effect on molecular geometry, how does the repulsion from a lone pair of electrons compare to
the repulsion from a bonding pair of electrons?
4. How many atoms are directly bonded to the central atom in molecules that have the following molecular
geometries?
a.
b.
c.
d.
e.
f.
trigonal bipyramidal
tetrahedral
octahedral
bent
trigonal pyramidal
square planar
5. Explain why the bond angle in an H2 O molecule is smaller than the bond angle in an NH3 molecule.
6. SF4 and CH4 have similar molecular formulas. Why does the SF4 molecule adopt a seesaw geometry, while
the CH4 molecule is tetrahedral?
Problems
7. Using the VSEPR method, predict the molecular geometries of the following molecules:
a.
b.
c.
d.
e.
SF2
PBr3
AlCl3
TeCl4
HCN
8. Predict the molecular geometries of the following ions:
a.
b.
c.
d.
e.
NO3 −
ICl2 −
ClO3 −
PO4 3−
SeCl3 −
9. Predict the H-As-H bond angle in AsH3 . Predict the H-B-H bond angle in BH3 . Explain the difference.
10. What are the molecular geometry and the bond angle for XeF2 ?
11. In the XeOF4 molecule, the central xenon atom has a double bond to the oxygen atom and single bonds to the
four fluorine atoms. Predict the geometry of this molecule.
Further Reading / Supplemental Links
• Jeremy K. Burdett, Molecular Shapes: Theoretical Models of Inorganic Stereochemistry, John Wiley Sons,
Inc., 1980.
• Chemistry, Structures & 3D Molecules (http://www.3dchem.com/# )
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Chapter 1. Molecular Geometry
• Valence Shell Electron Pair Repulsion VSEPR (http://www.meta-synthesis.com/webbook/45_vsepr/VSEPR
.html )
• Valence Shell Electron Pair Repulsion (VSEPR): An Interactive Tutorial and Quiz (http://www.chem.ox.ac.uk
/vrchemistry/vsepr/intro/vsepr_splash.html )
Points to Consider
The electronegativity of an atom describes its ability to attract shared electrons. Nonmetal atoms generally have high
electronegativities, while metals generally have low electronegativities.
• How can electronegativity be used to predict whether a bond between two atoms will be ionic or covalent?
• Is the sharing of electrons in a covalent bond always equal, or can the sharing be dominated by one of the
atoms? How would this affect the properties of the molecule?
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