George Mason University

1
George Mason University General Chemistry
211 Chapter 10 The Shapes (Geometry) of
Molecules Acknowledgements Course Text
Chemistry the Molecular Nature of Matter and
Change, 6th edition, 2011, Martin S. Silberberg,
McGraw-Hill The Chemistry 211/212 General
Chemistry courses taught at George Mason are
intended for those students enrolled in a science
/engineering oriented curricula, with particular
emphasis on chemistry, biochemistry, and biology
The material on these slides is taken primarily
from the course text but the instructor has
modified, condensed, or otherwise reorganized
selected material.Additional material from other
sources may also be included. Interpretation of
course material to clarify concepts and solutions
to problems is the sole responsibility of this
instructor.
2
Lewis Electron-Dot Symbols

• A Lewis electron-dot symbol is a symbol in which
  the electrons in the valence shell of an atom or
  ion are represented by dots placed around the
  letter symbol of the element
• Note that the group number indicates the number
  of valence electrons

3s1
3s2
3s23p1
3s23p2
3s23p3
3s23p4
3s23p5
3s23p6
3
Lewis Electron-Dot Formulas

• A Lewis electron-dot formula is an illustration
  used to represent the transfer of electrons
  during the formation of an ionic bond
• The Magnesium has two electrons to give, whereas
  the Fluorines have only one vacancy each
• Consequently, Magnesium can accommodate two
  Fluorine atoms

4
Lewis Structures

• The tendency of atoms in a molecule to have eight
  electrons (ns2np6) in their outer shell (two for
  hydrogen) is called the octet rule
• You can represent the formation of the covalent
  bond in H2 as follows
• This uses the Lewis dot symbols for the hydrogen
  atom and represents the covalent bond by a pair
  of dots

5
The Electron Probability Distribution for the H2
Molecule
6
Lewis Structures

• The shared electrons in H2 spend part of the time
  in the region around each atom
• In this sense, each atom in H2 has a helium (1s2)
  configuration

7
Lewis Structures

• The formation of a bond between H and Cl to give
  an HCl molecule can be represented in a similar
  way
• Thus, hydrogen has two valence electrons about it
  (as in He) and Cl has eight valence electrons
  about it (as in Ar)

8
Lewis Structures

• Formulas such as these are referred to as Lewis
  electron-dot formulas or Lewis structures
• An electron pair is either a
• bonding pair (shared between two atoms)
• lone pair (electron pair that is not shared)
• Hydrogen has no unbonded pairs
• Chlorine has 3 unbonded pairs

9
Lewis Structures

• Rules for obtaining Lewis electron dot formulas
• Calculate the number of valence electrons for the
  molecule from
• group for each atom (1-8)
• add the charge of Anion
• subtract the charge of a Cation
• Put atom with the lowest group number and lowest
  electronegativity as the central atom
• Arrange the other elements (ligands) around the
  central atom

10
Lewis Structures

• Rules for Lewis Dot Formulas
• Distribute electrons to atoms surrounding the
  central atom to satisfy the octet rule for each
  atom
• Distribute the remaining electrons as pairs to
  the central atom
• If the Central atom is deficient in electrons to
  complete the octet move electron pairs from
  surrounding atoms to complete central atom
  valence electron needs, that is form one or more
  double bonds (possibly triple bonds) around the
  central atom

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Practice Problem

• Write a lewis structure for CCl2F2
• Step 1 Arrange Atoms (Carbon is Central
  Atom because is has the lowest group number and
  lowest electronegativity
• Step 2 Determine total number of valence
  electrons
• 1 x C(4) 2 x Cl(7) 2 x
  F(7) 32
• Step 3 Draw single bonds to central atom and
  subtract 2 e- for each single bond
  (4 x 2 8) ? 32 8 24 remaining
• Step 4 Distribute the 24 remaining electrons in
  pairs around surrounding atoms (3 electron
  pairs around each Fluoride atom)

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Writing Lewis Dot Formulas

• The Lewis electron-dot formula of a covalent
  compound is a simple two-dimensional
  representation of the positions of electrons in a
  molecule
• Bonding electron pairs are indicated by either
  two dots or a dash
• In addition, these formulas show the positions of
  lone pairs of electrons

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Writing Lewis Dot Formulas

• The following rules allow you to write
  electron-dot formulas even when the central atom
  does not follow the octet rule
• To illustrate, draw the structure of
• Phosphorus Trichloride

Cont on next slide
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Writing Lewis Dot Formulas

• Step 1 Total all valence electrons in the
  molecular formula. That is, total the group
  numbers of all the atoms in the formula
• For a polyatomic anion, add the number of
  negative charges to this total
• For a polyatomic cation, subtract the number of
  positive charges from this total

P 3s23p3 Cl 3s23p5 (23) 3x(25) 521
26 total electrons
Cont on next slide
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Writing Lewis Dot Formulas

• Step 2
• Arrange the atoms radially, with the least
  electronegative atom in the center
• Place one pair of electrons between the central
  atom and each peripheral atom

26 6 20 remaining
Cont on next slide
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Writing Lewis Dot Formulas

• Step 3 Distribute the remaining electrons to the
  peripheral atoms to satisfy the octet rule

Cl
P


Cl

26 (3 x 6 6) 2 remaining
Cont on next slide
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Writing Lewis Dot Formulas

• Step 4 Distribute any remaining electrons (2) to
  the central atom. If the number of electrons on
  the central atom is less than the number of
  electrons required to complete the octet for that
  atom, use one or more electrons pairs from other
  atoms to form double or triple bonds

Phosphorus has an octet of electrons No double
bonds required
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Exceptions to the Octet Rule

• Although many molecules obey the octet rule,
  there are exceptions where the central atom has
  more than eight electrons
• Generally, if a nonmetal is in the third period
  or greater it can accommodate as many as twelve
  electrons, if it is the central atom
• These elements have unfilled d subshells that
  can be used for bonding

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Exceptions to the Octet Rule

• For example, the bonding in phosphorus
  pentafluoride, PF5, shows ten electrons
  surrounding the phosphorus

Total valence electrons 5 x 7 (F) 5 (P)
40 Distribute electrons to F atoms 5 x 6
30 Establish bonding pairs 5 x 2 10 Remaining
electrons 40 30 10 0 Phosphorus has 0
non-bonding pairs
Since Phosphorus is in Period 3, PF5 is a
hypervalent molecule The phosphorus utilizes
electrons from other shells (vacant orbitals) to
create a valence shell with more than 8 electrons
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Exceptions to the Octet Rule

• In Xenon Tetrafluoride, XeF4, the Xenon atom must
  accommodate two extra lone pairs

Total valence electrons 4 x 7 8
36 Distribute electrons to F atoms 4 x 6
24 Establish bonding pairs 4 x 2 8 Remaining
electrons 36 24 8 4 Add 2 non-bonding
pairs to Xe Xe violates octet rule XeF4 is a
hypervalent molecule and utilizes vacant d
orbitals to create a valence shell with more than
8 electrons
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Delocalized Bonding Resonance

• The structure of Ozone, O3, can be represented by
  two different Lewis electron-dot formulas
• Experiments show, however, that both bonds are
  identical

Ozone (O3)
or
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Delocalized Bonding Resonance

• According to Resonance Theory, these two equal
  bonds are represented as one pair of bonding
  electrons spread over the region of all three
  atoms
• This is called delocalized bonding, in which a
  bonding pair of electrons is spread over a number
  of atoms

Ozone (O3)
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Resonance Bond Order

• Recall (Chap 9) Bond Order
• The number of electron pairs being shared by any
  pair of Bonded Atoms or
• The number of electron pairs divided by the
  number of bonded-atom pairs
• Ex. Ozone

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Practice Problem

• In the following compounds, the Carbon atoms form
  a single ring. Draw a Lewis structure for each
  compound, identify cases for which resonance
  exists, and determine the C-C bond order(s).

C3H4
C3H6
25
Practice Problem
C4H6
C4H4
26
Practice Problem
C6H6
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Formal Charge Lewis Structures

• In certain instances, more than one feasible
  Lewis structure can be illustrated for a
  moleculeFor example, H, C and N
• The concept of formal charge can help discern
  which structure is the most likely
• Formal Charge
• An atoms formal charge is
• Total number of valence electrons
• Minus all unshared electrons
• Minus ½ of its shared electrons
• Formal Charges must sum to actual charge of
  species
• Zero Charge for a Molecule
• Ionic Charge for an Ion

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Formal Charge Lewis Structures

• When you can write several Lewis structures,
  choose the one having the least formal charge

Form I
Form II
FC Total Valence e- unshared e- ½
shared e-
FCH 1 - 0 - ½(2) 0 FCC 4 - 0 - ½(8)
0 FCN 5 - 2 - ½(6) 0
FCH 1 - 0 - ½(2) 0 FCC 4 - 2 - ½(6)
-1 FCN 5 - 0 - ½(8) 1
Preferred Form - Form I (Least Formal Charge)
Note HCN is a neutral molecule Sum of
Formal Charges in the preferred form (0) equals
molecular charge (0)
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Formal Charge Lewis Structures
Ozone
FCOA 6 - 4 - ½(4) 0 FCOB 6 - 2 - ½(6)
1 FCOC 6 - 6 - ½(2) -1
FCOA 6 - 6 - ½(2) -1 FCOB 6 - 2 -
½(6) 1 FCOC 6 - 4 - ½(4) 0
Both Resonance forms have the same formal
charge and thus, are identical Note Ozone (O3)
is a neutral molecule Sum of Formal
Charges (0) equals molecular charge (0)
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Formal Charge Lewis Structures
Boron Trifuoride BF3
FC B 3 0 -(1/2 6) 0 Even
though B violates Octet Rule, this is the
preferred form because it has less formal charge
FC B 3 0 -(1/2 8) -1 FC F
7 4 - (1/2 4) 1
Sulfur Dioxide SO2
FC S 6 2 (1/2 8) 0 Preferred Form
(Less Formal Charge)
FC S 6 2 (1/2 6) 1
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Resonance/Formal Charge Nitrate Ion

• Total Valence electrons - 3 x 6 (O) 1 x 5
  (N) 1 (ion charge) 24
• Add 1 pair electrons between central atom and
  each other atom 3 x 2 6
• Add electrons to oxygen atoms to complete octet
• Nitrogen still missing 2 electrons to complete
  octet
• Borrow 2 electrons from one oxygen to form double
  bond
• Formal Charge Nitrogen 5 (0 ½8) 5
  4 1
• Formal Charge Single bonded Oxygen 6 (6
  ½2) 6 7 -1 x 2 -2
• Formal Charge Double bonded Oxygen 6 (4
  ½4) 6 6 0
• Net Charge of ion is 1 (-2) -1

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Resonance/Formal Charge Cyanate Ion
FCN 5 (6 ½2) -2 FCC 4 (0 ½8)
0 FCO 6 (2 ½6) 1
FCN 5 (4 ½4) -1 FCC 4 (0 ½8)
0 FCO 6 (4 ½4) 0
FCN 5 (2 ½6) 0 FCC 4 (0 ½8)
0 FCO 6 (6 ½2) -1
Preferred Form Eliminate I Higher formal
charge on Nitrogen than Carbon Oxygen
Positive formal charge on Oxygen,
which is more
electronegative than Nitrogen Eliminate II
Forms II III have the same magnitude of
formal charges, but form
III has a -1 charge on the more
electronegative Oxygen
atom Forms II III both contribute to the
resonant hybrid of the Cyanate Ion, but form III
is the more important Note Net formal charge in
form III is same as ionic charge (-1)
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Formal Charge vs Oxidation No

• Formal Charge is used to examine resonance
  hybrid structures , whereas Oxidation Number
  is used to monitor REDOX reactions
• Formal Charge - Bonding electrons are assigned
  equally to the atoms as if the bonding were
  Nonpolar covalent, i.e., each atom has half the
  electrons making up the bond
• Formal Charge valence e- (unbonded e- ½
  bonding e-)
• Oxidation Number - Bonding electrons are
  transferred completely to the more
  electronegative atom, as if the bonding were
  Ionic
• Oxidation No. valence e- (unbonded e-
  bonding e-)

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Formal Charge vs Oxidation No
FC (-2) (0) (1) (-1)
(0) (0) (0) (0) (-1)
N 5 (6 ½ (1)) -2 C 4 (0 ½ (8))
0 O 6 (2 ½ (6)) 1
N 5 (4 ½ (4)) -1 C 4 (0 ½ (8))
0 O 6 (4 ½ (4)) 0
N 5 (2 ½ (6)) 0 C 4 (0 ½ (8))
0 O 6 (6 ½ (2)) -1
ON (-3) (4) (-2) (-3) (4)
(-2) (-3) (4) (-2)
N 5 (6 2)) -3 C 4 (0 0)) 4 O 6
(2 6)) -2
N 5 (4 4)) -3 C 4 (0 0)) 4 O 6
(4 4)) -2
N 5 (2 6)) -3 C 4 (0 0)) 4 O 6
(6 2)) -2
Note Both Nitrogen (N) Oxygen (O) are more
electronegative than Carbon (C) thus,
in the computation of Oxidation Number all the
electrons are transferred to the N O
leaving C with no lone pairs and no
bonded pairs
Note Oxidation Nos do not change from one
resonance form to another
(electronegativities remain same)
35
The Valence-Shell Electron Pair Repulsion Model
(VSEPR)

• The Valence-Shell Electron Pair Repulsion (VSEPR)
  model predicts the shapes of molecules and ions
  by assuming that the valence shell electron pairs
  are arranged as far from one another as possible
• Molecular geometry The shape of a molecule is
  determined by the positions of atomic nuclei
  relative to each other, i.e., angular arrangement
• Central Atom
• Place atom with Lower Group Number in center(N
  in NF3 needs more electrons to complete octet)
• If atoms have same group number (SO3 or ClF3),
  place the atom with the Higher Period Number in
  the center (Sulfur Chlorine)

36
VSEPR Model of Molecular Shapes

• The following rules and figures will help discern
  electron pair arrangements
• Select the Central Atom (Least Electronegative
  Atom)
• Draw the Lewis structure
• Determine how many bonding electron pairs are
  around the central atom.
• Determine the number of non-bonding electron
  pairs
• Count a multiple bond as one pair
• Arrange the electron pairs as far apart as
  possible to minimize electron repulsions
• Note the number of bonding and lone pairs

37
VSEPR Model of Molecular Shapes

• To predict the relative positions of atoms around
  a given atom using the VSEPR model, you first
  note the arrangement of the electron pairs around
  that central atom
• Molecular Notation
• A The Central Atom (Least Electronegative
  atom)
• X The Ligands (Bonding Pairs)
• a The Number of Ligands
• E Non-Bonding Electron Pairs
• b The Number of Non-Bonding Electron Pairs
• Double Triple Bonds count as a single
  electron pair
• The Geometric arrangement is determined by
• sum (a b)

AXaEb
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VSEPR Model of Molecular Shapes
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VSEPR Model of Molecular Shapes
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Arrangement of Electron Pairs About an Atom
Basic Shapes
CS2 HCN BeF2 NO2
41
Arrangement of Electron Pairs About an Atom
Basic Shapes
SO3 BF3 NO3- NO2 CO32-
SO2 O3 PbCl2 SnBr2
42
Arrangement of Electron Pairs About an Atom
Basic Shapes
CH4 SiCl4SO42- ClO4-
NH3 PF3 ClO3 H3O
H2O OF2 SCl2
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Arrangement of Electron Pairs About an Atom
Basic Shapes
SF4, XeO2F2, IF4, IO2F2-
PF5 AsF5 SOF4
ClF3 BrF3
XeF2 I3- IF2-
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Arrangement of Electron Pairs About an Atom
Basic Shapes
SF6 IOF5
BrF5 TeF5- XeOF4
XeF4 ICl4-
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Electron Pair Arrangement
46
Electron Pair Arrangement
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Linear Geometry

• Two electron pairs (linear arrangement)
• Double bonds count as a single electron pair
• ? 2 bonding pairs
• 0 non-bonding pairs
• AXaEb a b 2 0 2 (Linear)
• Thus, according to the VSEPR model, the bonds are
  arranged linearly (bond angle 180o)
• Molecular shape of carbon dioxide is linear

Carbon is central atom because it has lower group
number
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Trigonal Planar Geometry

• Three electron pairs on Central atom
• The three groups of electron pairs are arranged
  in a trigonal plane. Thus, the molecular shape of
  COCl2 is trigonal planar. The Bond angle is 120o

Central Atom - Carbon 3 bonding electron pairs
(double bond counts as 1 pair) 0 non-bonding
electron pairs a b 3 0 3 ? Trigonal
Planar
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Trigonal Planar Geometry

• Effect of Double Bonds
• Bond angles deviate from ideal angles when
  surrounding atoms and electron groups are not
  identical
• A double bond has greater electron density and
  repels two single bonds more strongly than they
  repel each other

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Trigonal Planar Geometry

• Effect of Lone Pairs
• The molecular shape is defined only by the
  positions of the nuclei
• When one of the three electron pairs in a
  trigonal planar molecule is a lone (non-bonding)
  pair, it is held by only one nucleus
• It is less confined and exerts a stronger
  repulsive force than a bonding pair
• This results in a decrease in the angle between
  the bonding pairs

The normal Trigonal Planar angle between the
bonding pairs is 120o
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Trigonal Planar Geometry

• Three electron pairs (Effect of Lone pairs)
• (trigonal planar arrangement)
• Ozone has two bonding electron pairs about the
  central oxygen (double bond counts as 1 pair)
• There is one non-bonding lone pair
• These groups have a
• Trigonal Planar arrangement
• AXaEb (a b) 2 1 3
• Since one of the groups is a lone pair, the
  molecular geometry is described as bent or angular

SO3 BF3 NO3- CO32-
lt120o
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Tetrahedral Geometry

• Four electron pairs
• (Tetrahedral Arrangement)
• Four electron pairs about the central atom lead
  to three different molecular geometries
• a b 4 0 a b 3 1
  a b 2 2
• 4 4
  4

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Tetrahedral Geometry

• Molecular Geometries produced by variable
  non-bonding electron pairs

Note impact of non-bonding electron pairs on bond
angle
107o
105o
107o
CH4, SiCl4, SO42-, ClO4-
PF3, ClO3-, H3O
OF2, SCl2
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Trigonal Bipyramidal

• Five electron pairs
• (trigonal bipyramidal arrangement)
• This structure results in both 90o and 120o bond
  angles

90o axial 120o equatorial
ASF5 SOF4
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Trigonal Bipyramidal

• Other molecular geometries are possible when one
  or more of the electron pairs is a lone pair

lt90o (ax) lt120o (eq)
180o
lt90o (ax)
XeO2F2 IF4 IOF2-
XeF2 I3- IF2-
ClF3 BrF3
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Octahedral Geometry

• Six electron pairs
• (Octahedral arrangement)
• This octahedral arrangement results in
• 90o bond angles

90o
SF6 IOF5
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Other Geometries

• Six electron pairs
• (octahedral arrangement)

Noble gases not always inert Xenon forms 6
electron domains
Iodine violates octet rule Iodine is sp3d2
hybridized Iodine uses d orbitals
square pyramidal
square planar
lt90o
90o
BrF5 TeF5- XeOF4
XeF4 ICl4-
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Practice Problem

• In the ICl4 ion, the electron pairs are arranged
  around the central iodine atom in the shape of
• a. a tetrahedron
• b. a trigonal bipyramid
• c. a square plane
• d. an octahedron
• e. a trigonal pyramid
• Ans a

AX4
AXaEb a b 4 0 4 (AX4
Tetrahedral)
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Dipole Moment andMolecular Geometry

• The dipole moment is a measure of the degree of
  charge separation in a molecule
• The polarity of individual bonds within a
  molecule can be viewed as vector quantities
• Thus, molecules that are perfectly symmetric have
  a zero dipole moment. These molecules are
  considered nonpolar

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Dipole Moment andMolecular Geometry

• However, molecules that exhibit any asymmetry in
  the arrangement of electron pairs would have a
  nonzero dipole moment. These molecules are
  considered polar

NH3 PF3 ClO3 H3O
61
Dipole Moment andMolecular Geometry
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Practice Problem

• The Nitrogen atom would be expected to have the
  positive end of the dipole in the species
• a. NH4
• b. Ca3N2
• c. HCN
• d. AlN
• e. NO
• Ans e

N is more Electronegative than H
N is more EN than Ca
N is more EN than C
N is more EN than Al
O is more EN than Nitrogen
63
Practice Problem

• Which of the following molecules is polar?
• a. BF3 b. CBr4 c. CO2
• d. NO2 e. SF6
• Ans d

The Lewis structures for BF3, CBr4, CO2, and SF6
do not have any non-bonding electrons on the
central atom The Lewis structure for NO2 shows
one double bond and a lone non-bonding electron
on the Nitrogen The VSEPR Molecular Geometry for
NO2 is AX2E1 (a b 2 1 3) -
Trigonal Planar Formal Charge on N is 5 1 ½
(6) 1 NO2 molecule is polar
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Practice Problem

• Which of the following compounds is nonpolar?
• a. XeF2 b. HCl c. SO2
• d. H2S e. N20
• Ans a
• HCL is ionic and very polar
• SO2 has AX2E1 Trigonal Planar Bent geometry with
  a dipole moment (polar)
• H2S has AX2E2 Tetrahedral Bent geometry and with
  a dipole moment (polar)
• N2O has AX2E0 linear with asymmetric
  geometry.Since oxygen is more EN than N, the
  molecule is polar
• XeF2 has AX2E3 Trigonal Bypyramidal Geometry, but
  linear molecular geometry (nonpolar)

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Equation Summary
VSEPR Model - AXaEb Geometric Configuration
Determined by the sum (a b)