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Copyright 2011 Pearson Education, Inc.Tro: Chemistry: A Molecular Approach, 2/e
Chapter 10Chemical Bonding II
Roy KennedyMassachusetts Bay Community College
Wellesley Hills, MA
Chemistry: A Molecular Approach, 2nd Ed.Nivaldo Tro
Copyright 2011 Pearson Education, Inc.Tro: Chemistry: A Molecular Approach, 2/e
Taste• The taste of a food depends on the interaction
between the food molecules and taste cells on your tongue
• The main factors that affect this interaction are the shape of the molecule and charge distribution within the molecule
• The food molecule must fit snugly into the active site of specialized proteins on the surface of taste cells
• When this happens, changes in the protein structure cause a nerve signal to transmit
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Copyright 2011 Pearson Education, Inc.Tro: Chemistry: A Molecular Approach, 2/e
Sugar & Artificial Sweeteners• Sugar molecules fit into the active site of taste cell
receptors called Tlr3 receptor proteins
• When the sugar molecule (the key) enters the active site (the lock), the different subunits of the T1r3 protein split apart
• This split causes ion channels in the cell membrane to open, resulting in nerve signal transmission
• Artificial sweeteners also fit into the Tlr3 receptor, sometimes binding to it even stronger than sugarmaking them “sweeter” than sugar
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Structure Determines Properties!
• Properties of molecular substances depend on the structure of the molecule
• The structure includes many factors, such as:the skeletal arrangement of the atomsthe kind of bonding between the atoms
ionic, polar covalent, or covalentthe shape of the molecule
• Bonding theory should allow you to predict the shapes of molecules
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Molecular Geometry• Molecules are 3-dimensional objects
• We often describe the shape of a molecule with terms that relate to geometric figures
• These geometric figures have characteristic “corners” that indicate the positions of the surrounding atoms around a central atom in the center of the geometric figure
• The geometric figures also have characteristic angles that we call bond angles
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Copyright 2011 Pearson Education, Inc.Tro: Chemistry: A Molecular Approach, 2/e
Lewis Theory PredictsElectron Groups
• Lewis theory predicts there are regions of electrons in an atom
• Some regions result from placing shared pairs of valence electrons between bonding nuclei
• Other regions result from placing unshared valence electrons on a single nuclei
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Using Lewis Theory to PredictMolecular Shapes
• Lewis theory says that these regions of electron groups should repel each otherbecause they are regions of negative charge
• This idea can then be extended to predict the shapes of molecules the position of atoms surrounding a central atom will be
determined by where the bonding electron groups are the positions of the electron groups will be determined
by trying to minimize repulsions between them
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VSEPR Theory
• Electron groups around the central atom will be most stable when they are as far apart as possible – we call this valence shell electron pair repulsion theorybecause electrons are negatively charged, they
should be most stable when they are separated as much as possible
• The resulting geometric arrangement will allow us to predict the shapes and bond angles in the molecule
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Copyright 2011 Pearson Education, Inc.Tro: Chemistry: A Molecular Approach, 2/e
Electron Groups• The Lewis structure predicts the number of valence
electron pairs around the central atom(s)
• Each lone pair of electrons constitutes one electron group on a central atom
• Each bond constitutes one electron group on a central atom regardless of whether it is single, double, or triple
O N O ••••
••
••
•••• there are three electron groups on Nthree lone pairone single bondone double bond
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Electron Group Geometry• There are five basic arrangements of electron
groups around a central atombased on a maximum of six bonding electron groups
though there may be more than six on very large atoms, it is very rare
• Each of these five basic arrangements results in five different basic electron geometries in order for the molecular shape and bond angles to be
a “perfect” geometric figure, all the electron groups must be bonds and all the bonds must be equivalent
• For molecules that exhibit resonance, it doesn’t matter which resonance form you use – the electron geometry will be the same
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Linear Electron Geometry• When there are two electron groups around the
central atom, they will occupy positions on opposite sides of the central atom
• This results in the electron groups taking a linear geometry
• The bond angle is 180°
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Linear Geometry
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Trigonal Planar Electron Geometry
• When there are three electron groups around the central atom, they will occupy positions in the shape of a triangle around the central atom
• This results in the electron groups taking a trigonal planar geometry
• The bond angle is 120°
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Trigonal Geometry
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Tetrahedral Electron Geometry
• When there are four electron groups around the central atom, they will occupy positions in the shape of a tetrahedron around the central atom
• This results in the electron groups taking a tetrahedral geometry
• The bond angle is 109.5°
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Tetrahedral Geometry
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Trigonal Bipyramidal Electron Geometry
• When there are five electron groups around the central atom, they will occupy positions in the shape of two tetrahedra that are base-to-base with the central atom in the center of the shared bases
• This results in the electron groups taking a trigonal bipyramidal geometry
• The positions above and below the central atom are called the axial positions
• The positions in the same base plane as the central atom are called the equatorial positions
• The bond angle between equatorial positions is 120°
• The bond angle between axial and equatorial positions is 90°
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Trigonal Bipyramid
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Trigonal Bipyramidal Geometry
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Octahedral Electron Geometry
• When there are six electron groups around the central atom, they will occupy positions in the shape of two square-base pyramids that are base-to-base with the central atom in the center of the shared bases
• This results in the electron groups taking an octahedral geometry it is called octahedral because the geometric figure has
eight sides
• All positions are equivalent
• The bond angle is 90°
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Octahedral Geometry
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Octahedral Geometry
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Molecular Geometry• The actual geometry of the molecule may be
different from the electron geometry
• When the electron groups are attached to atoms of different size, or when the bonding to one atom is different than the bonding to another, this will affect the molecular geometry around the central atom
• Lone pairs also affect the molecular geometrythey occupy space on the central atom, but are not
“seen” as points on the molecular geometry
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Not Quite Perfect Geometry
Because the bonds and atom sizes are not identical in formaldehyde, the observed angles are slightly different from ideal
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The Effect of Lone Pairs
• Lone pair groups “occupy more space” on the central atombecause their electron density is exclusively on the
central atom rather than shared like bonding electron groups
• Relative sizes of repulsive force interactions is
Lone Pair – Lone Pair > Lone Pair – Bonding Pair > Bonding Pair – Bonding Pair
• This affects the bond angles, making the bonding pair – bonding pair angles smaller than expected
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Effect of Lone Pairs
The bonding electrons are shared by two atoms, so some of the negative charge is removed from the central atom
The nonbonding electrons are localized on the central atom, so area of negative charge takes more space
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Bond Angle Distortion from Lone Pairs
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Bond Angle Distortion from Lone Pairs
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Bent Molecular Geometry:Derivative of Trigonal Planar Electron Geometry
• When there are three electron groups around the central atom, and one of them is a lone pair, the resulting shape of the molecule is called a trigonal planar — bent shape
• The bond angle is less than 120°because the lone pair takes up more space
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Pyramidal & Bent Molecular Geometries:Derivatives of Tetrahedral Electron Geometry• When there are four electron groups around the
central atom, and one is a lone pair, the result is called a pyramidal shapebecause it is a triangular-base pyramid with the
central atom at the apex
• When there are four electron groups around the central atom, and two are lone pairs, the result is called a tetrahedral—bent shape it is planar it looks similar to the trigonal planar—bent shape,
except the angles are smaller
• For both shapes, the bond angle is less than 109.5°
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Methane
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Pyramidal Shape
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Pyramidal Shape
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Tetrahedral–Bent Shape
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Tetrahedral–Bent Shape
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Derivatives of theTrigonal Bipyramidal Electron Geometry
• When there are five electron groups around the central atom, and some are lone pairs, they will occupy the equatorial positions because there is more room
• When there are five electron groups around the central atom, and one is a lone pair, the result is called the seesaw shape aka distorted tetrahedron
• When there are five electron groups around the central atom, and two are lone pairs, the result is called the T-shaped
• When there are five electron groups around the central atom, and three are lone pairs, the result is a linear shape
• The bond angles between equatorial positions are less than 120°
• The bond angles between axial and equatorial positions are less than 90° linear = 180° axial–to–axial
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Replacing Atoms with Lone Pairsin the Trigonal Bipyramid System
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Seesaw Shape
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T–Shape
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T–Shape
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Linear Shape
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Derivatives of theOctahedral Geometry
• When there are six electron groups around the central atom, and some are lone pairs, each even number lone pair will take a position opposite the previous lone pair
• When there are six electron groups around the central atom, and one is a lone pair, the result is called a square pyramid shape the bond angles between axial and equatorial positions is
less than 90°
• When there are six electron groups around the central atom, and two are lone pairs, the result is called a square planar shape the bond angles between equatorial positions is 90°
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Square Pyramidal Shape
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Square Planar Shape
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Predicting the Shapes Around Central Atoms
1. Draw the Lewis structure
2. Determine the number of electron groups around the central atom
3. Classify each electron group as bonding or lone pair, and count each type remember, multiple bonds count as one group
4. Use Table 10.1 to determine the shape and bond angles
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Example 10.2: Predict the geometry and bond angles of PCl3
1. Draw the Lewis structure
a) 26 valence electrons
2. Determine the Number of electron groups around central atom
a) four electron groups around P
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Example 10.2: Predict the geometry and bond angles of PCl3
3. Classify the electron groupsa) three bonding groups
b) one lone pair
4. Use Table 10.1 to determine the shape and bond angles
a) four electron groups around P = tetrahedral electron geometry
b) three bonding + one lone pair = trigonal pyramidal molecular geometry
c) trigonal pyramidal = bond angles less than 109.5°
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Practice – Predict the molecular geometry and bond angles in SiF5
−
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Practice – Predict the molecular geometry and bond angles in SiF5
─
Si = 4e─
F5 = 5(7e─) = 35e─
(─) = 1e─
total = 40e─
5 electron groups on Si
5 bonding groups0 lone pairs
Shape = trigonal bipyramid
Bond anglesFeq–Si–Feq = 120°Feq–Si–Fax = 90°
Si least electronegative
Si is central atom
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Practice – Predict the molecular geometry and bond angles in ClO2F
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Practice – Predict the molecular geometry and bond angles in ClO2F
Cl = 7e─
O2 = 2(6e─) = 12e─
F = 7e─
Total = 26e─
4 electron groups on Cl
3 bonding groups1 lone pair
Shape = trigonal pyramidal
Bond anglesO–Cl–O < 109.5°O–Cl–F < 109.5°
Cl least electronegative
Cl is central atom
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Representing 3-Dimensional Shapes on a 2-Dimensional Surface
• One of the problems with drawing molecules is trying to show their dimensionality
• By convention, the central atom is put in the plane of the paper
• Put as many other atoms as possible in the same plane and indicate with a straight line
• For atoms in front of the plane, use a solid wedge
• For atoms behind the plane, use a hashed wedge
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SF6
S
F
F
F
F F
F
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• •
H O•
•
| || • •
H − C − C − O − H
| • •
H
Multiple Central Atoms• Many molecules have larger structures with many
interior atoms
• We can think of them as having multiple central atoms
• When this occurs, we describe the shape around each central atom in sequence
shape around left C is tetrahedral
shape around center C is trigonal planar
shape around right O is tetrahedral-bent
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Describing the Geometryof Methanol
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Describing the Geometryof Glycine
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Practice – Predict the molecular geometries in H3BO3
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3 electron groups on B
B has3 bonding groups0 pone pairs
4 electron groups on O
O has2 bonding groups2 lone pairs
Practice – Predict the molecular geometries in H3BO3
B = 3e─
O3 = 3(6e─) = 18e─
H3 = 3(1e─) = 3e─
Total = 24e─Shape on B = trigonal planar
B least electronegative
B Is Central Atom
oxyacid, so H attached to O
Shape on O = tetrahedral bent
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Polarity of Molecules
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• For a molecule to be polar it must1. have polar bonds
electronegativity difference - theory bond dipole moments - measured
2. have an unsymmetrical shape vector addition
• Polarity affects the intermolecular forces of attraction therefore boiling points and solubilities
like dissolves like
• Nonbonding pairs affect molecular polarity, strong pull in its direction
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Molecule Polarity
The H─Cl bond is polar. The bonding electrons are pulled toward the Cl end of the molecule. The net result is a polar molecule.
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Vector Addition
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Molecule Polarity
The O─C bond is polar. The bonding electrons are pulled equally toward both O ends of the molecule. The net result is a nonpolar molecule.
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Molecule Polarity
The H─O bond is polar. Both sets of bonding electrons are pulled toward the O end of the molecule. The net result is a polar molecule.
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Predicting Polarity of Molecules
1. Draw the Lewis structure and determine the molecular geometry
2. Determine whether the bonds in the molecule are polar
a) if there are not polar bonds, the molecule is nonpolar
3. Determine whether the polar bonds add together to give a net dipole moment
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Example 10.5: Predict whether NH3 is a polar molecule
1. Draw the Lewis structure and determine the molecular geometry
a) eight valence electrons
b) three bonding + one lone pair = trigonal pyramidal molecular geometry
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Example 10.5: Predict whether NH3 is a polar molecule
2. Determine if the bonds are polar
a) electronegativity difference
b) if the bonds are not polar, we can stop here and declare the molecule will be nonpolar
ENN = 3.0ENH = 2.13.0 − 2.1 = 0.9therefore the bonds are polar covalent
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Example 10.5: Predict whether NH3 is a polar molecule
3) Determine whether the polar bonds add together to give a net dipole moment
a) vector addition
b) generally, asymmetric shapes result in uncompensated polarities and a net dipole moment
The H─N bond is polar. All the sets of bonding electrons are pulled toward the N end of the molecule. The net result is a polar molecule.
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Practice – Decide whether the following molecules are polar
ENO = 3.5N = 3.0Cl = 3.0S = 2.5
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Practice – Decide whether the following molecules Are polar
polarnonpolar
1. polar bonds, N-O2. asymmetrical shape 1. polar bonds, all S-O
2. symmetrical shape
TrigonalBent Trigonal
Planar2.5
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Molecular Polarity Affects
Solubility in Water
• Polar molecules are attracted to other polar molecules
• Because water is a polar molecule, other polar molecules dissolve well in waterand ionic compounds as well
• Some molecules have both polar and nonpolar parts
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Problems with Lewis Theory• Lewis theory generally predicts trends in properties,
but does not give good numerical predictionse.g. bond strength and bond length
• Lewis theory gives good first approximations of the bond angles in molecules, but usually cannot be used to get the actual angle
• Lewis theory cannot write one correct structure for many molecules where resonance is important
• Lewis theory often does not predict the correct magnetic behavior of moleculese.g. O2 is paramagnetic, though the Lewis structure
predicts it is diamagnetic
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Valence Bond Theory
• Linus Pauling and others applied the principles of quantum mechanics to molecules
• They reasoned that bonds between atoms would occur when the orbitals on those atoms interacted to make a bond
• The kind of interaction depends on whether the orbitals align along the axis between the nuclei, or outside the axis
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Orbital Interaction• As two atoms approached, the half-filled valence
atomic orbitals on each atom would interact to form molecular orbitalsmolecular orbtials are regions of high probability of
finding the shared electrons in the molecule
• The molecular orbitals would be more stable than the separate atomic orbitals because they would contain paired electrons shared by both atomsthe potential energy is lowered when the molecular
orbitals contain a total of two paired electrons compared to separate one electron atomic orbitals
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Orbital Diagram for the Formation of H2S
+
↑
H
1s ↑↓ H─S bond
↑
H
1sS↑ ↑ ↑↓↑↓
3s 3p
↑↓ H─S bond
Predicts bond angle = 90°Actual bond angle = 92°
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Valence Bond Theory – Hybridization• One of the issues that arises is that the number of
partially filled or empty atomic orbitals did not predict the number of bonds or orientation of bonds C = 2s22px
12py12pz
0 would predict two or three bonds that are 90° apart, rather than four bonds that are 109.5° apart
• To adjust for these inconsistencies, it was postulated that the valence atomic orbitals could hybridize before bonding took placeone hybridization of C is to mix all the 2s and 2p orbitals
to get four orbitals that point at the corners of a tetrahedron
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Unhybridized C Orbitals Predict the Wrong Bonding & Geometry
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Valence Bond TheoryMain Concepts
1. The valence electrons of the atoms in a molecule reside in quantum-mechanical atomic orbitals. The orbitals can be the standard s, p, d, and f orbitals, or they may be hybrid combinations of these.
2. A chemical bond results when these atomic orbitals interact and there is a total of two electrons in the new molecular orbitala) the electrons must be spin paired
3. The shape of the molecule is determined by the geometry of the interacting orbitals
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Hybridization
• Some atoms hybridize their orbitals to maximize bonding• more bonds = more full orbitals = more stability
• Hybridizing is mixing different types of orbitals in the valence shell to make a new set of degenerate orbitalssp, sp2, sp3, sp3d, sp3d2
• Same type of atom can have different types of hybridizationC = sp, sp2, sp3
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Hybrid Orbitals• The number of standard atomic orbitals
combined = the number of hybrid orbitals formed combining a 2s with a 2p gives two 2sp hybrid
orbitalsH cannot hybridize!!
its valence shell only has one orbital
• The number and type of standard atomic orbitals combined determines the shape of the hybrid orbitals
• The particular kind of hybridization that occurs is the one that yields the lowest overall energy for the molecule
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Carbon Hybridizations
Unhybridized
2s 2p
sp hybridized
2sp
sp2 hybridized
2p
sp3 hybridized
2p
2sp2
2sp3
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sp3 Hybridization
• Atom with four electron groups around ittetrahedral geometry109.5° angles between hybrid orbitals
• Atom uses hybrid orbitals for all bonds and lone pairs
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Orbital Diagram of the sp3 Hybridization of C
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sp3 Hybridized AtomsOrbital Diagrams
Unhybridized atom
2s 2p
sp3 hybridized atom
2sp3
C
2s 2p
2sp3
N
• Place electrons into hybrid and unhybridized valence orbitals
as if all the orbitals have equal energy• Lone pairs generally occupy hybrid orbitals
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Practice – Draw the orbital diagram for the sp3 hybridization of each atom
Unhybridized atom
3s 3p
Cl
2s 2p
O
sp3 hybridized atom
3sp3
2sp3
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Bonding with Valence Bond Theory
• According to valence bond theory, bonding takes place between atoms when their atomic or hybrid orbitals interact“overlap”
• To interact, the orbitals must either be aligned along the axis between the atoms, or
• The orbitals must be parallel to each other and perpendicular to the interatomic axis
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Methane Formation with sp3 C
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Ammonia Formation with sp3 N
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Types of Bonds
• A sigma () bond results when the interacting atomic orbitals point along the axis connecting the two bonding nucleieither standard atomic orbitals or hybrids
s–to–s, p–to–p, hybrid–to–hybrid, s–to–hybrid, etc.
• A pi () bond results when the bonding atomic orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nucleibetween unhybridized parallel p orbitals
• The interaction between parallel orbitals is not as strong as between orbitals that point at each other; therefore bonds are stronger than bonds
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Orbital Diagrams of Bonding
• “Overlap” between a hybrid orbital on one atom with a hybrid or nonhybridized orbital on another atom results in a bond
• “Overlap” between unhybridized p orbitals on bonded atoms results in a bond
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CH3NH2 Orbital Diagram
sp3 C sp3 N
1s H
1s H 1s H 1s H 1s H
H C
H
H
N H
H
··
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Formaldehyde, CH2O Orbital Diagram
sp2 C
sp2 O
1s H
1s H
p C p O
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sp2
• Atom with three electron groups around it trigonal planar system
C = trigonal planar N = trigonal bent O = “linear”
120° bond angles flat
• Atom uses hybrid orbitals for bonds and lone pairs, uses nonhybridized p orbital for bond
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sp2 Hybridized AtomsOrbital Diagrams
Unhybridized atom
2s 2p
sp2 hybridized atom
2sp2
2p
C3 1
2s 2p
2sp2
2p
N2 1
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Practice – Draw the orbital diagram for the sp2 hybridization of each atom. How many
and bonds would you expect each to form?
Unhybridized atom
2s 2p
B
3 0
2s 2p
O
1 1
sp2 hybridized atom
2sp2
2p
2sp2
2p
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Hybrid orbitals overlap to form a bond.Unhybridized p orbitals overlap to form a bond.
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CH2NH Orbital Diagram
sp2 C
sp2 N
1s H
1s H 1s H
p C p N
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C N
H
H H
・・
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Bond Rotation
• Because the orbitals that form the bond point along the internuclear axis, rotation around that bond does not require breaking the interaction between the orbitals
• But the orbitals that form the bond interact above and below the internuclear axis, so rotation around the axis requires the breaking of the interaction between the orbitals
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sp• Atom with two electron groups
linear shape180° bond angle
• Atom uses hybrid orbitals for bonds or lone pairs, uses nonhybridized p orbitals for bonds
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sp Hybridized AtomsOrbital Diagrams
Unhybridized atom
2s 2p
sp hybridized atom
2sp
2p
C22
2s 2p
2sp
2p
N12
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HCN Orbital Diagram
sp C
sp N
1s H
s
p C p N2
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sp3d• Atom with five electron groups
around ittrigonal bipyramid electron
geometrySeesaw, T–Shape, Linear120° & 90° bond angles
• Use empty d orbitals from valence shell
• d orbitals can be used to make bonds
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sp3d Hybridized AtomsOrbital Diagrams
Unhybridized atom
3s 3p
sp3d hybridized atom
3sp3d
S
3s 3p
3sp3d
P
3d
3d
(non-hybridizing d orbitals not shown)
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SOF4 Orbital Diagram
sp3d S
sp2 O
2p F
d S p O
2p F
2p F
2p F
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sp3d2
• Atom with six electron groups around itoctahedral electron geometrySquare Pyramid, Square Planar90° bond angles
• Use empty d orbitals from valence shell to form hybrid
• d orbitals can be used to make bonds
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sp3d2 Hybridized AtomsOrbital Diagrams
Unhybridized atom sp3d2 hybridized atom
S
3s 3p 3sp3d2
↑↓
3d
↑↓ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑
I
5s 5p
↑↓
5d
↑↓ ↑↓ ↑
5sp3d2
↑↓ ↑ ↑ ↑ ↑ ↑
(non-hybridizing d orbitals not shown)
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Predicting Hybridization and Bonding Scheme
1. Start by drawing the Lewis structure
2. Use VSEPR Theory to predict the electron group geometry around each central atom
3. Use Table 10.3 to select the hybridization scheme that matches the electron group geometry
4. Sketch the atomic and hybrid orbitals on the atoms in the molecule, showing overlap of the appropriate orbitals
5. Label the bonds as or
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Example 10.7: Predict the hybridization and bonding scheme for CH3CHO
123
Draw the Lewis structure
Predict the electron group geometry around inside atoms
C1 = 4 electron areas
C1= tetrahedral
C2 = 3 electron areas
C2 = trigonal planar
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Example 10.7: Predict the hybridization and bonding scheme for CH3CHO
124
Determine the hybridization of the interior atoms
C1 = tetrahedral
C1 = sp3
C2 = trigonal planar
C2 = sp2
Sketch the molecule and orbitals
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Label the bonds
Example 10.7: Predict the hybridization and bonding scheme for CH3CHO
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Practice – Predict the hybridization of all the atoms in H3BO3
H = can’t hybridizeB = 3 electron groups = sp2
O = 4 electron groups = sp3
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Practice – Predict the hybridization and bonding scheme of all the atoms in NClO
N = 3 electron groups = sp2
O = 3 electron groups = sp2
Cl = 4 electron groups = sp3
••O N Cl ••••
••••••
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Cl
O NNsp2─Clp
Cl
O N
Osp2─Nsp2
Op─Np
↑↓
↑↓↑↓
↑↓
↑↓
↑↓
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Problems with Valence Bond Theory• VB theory predicts many properties better than Lewis
theorybonding schemes, bond strengths, bond lengths, bond
rigidity
• However, there are still many properties of molecules it doesn’t predict perfectlymagnetic behavior of O2
• In addition, VB theory presumes the electrons are localized in orbitals on the atoms in the molecule – it doesn’t account for delocalization
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Molecular Orbital Theory• In MO theory, we apply Schrödinger’s wave
equation to the molecule to calculate a set of molecular orbitals in practice, the equation solution is estimated we start with good guesses from our experience as to
what the orbital should look like then test and tweak the estimate until the energy of the
orbital is minimized
• In this treatment, the electrons belong to the whole molecule – so the orbitals belong to the whole moleculedelocalization
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LCAO
• The simplest guess starts with the atomic orbitals of the atoms adding together to make molecular orbitals – this is called the Linear Combination of Atomic Orbitals methodweighted sum
• Because the orbitals are wave functions, the waves can combine either constructively or destructively
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Molecular Orbitals• When the wave functions combine constructively,
the resulting molecular orbital has less energy than the original atomic orbitals – it is called a Bonding Molecular Orbital, most of the electron density between the nuclei
• When the wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbitals – it is called an Antibonding Molecular Orbital*, *most of the electron density outside the nuclei nodes between nuclei
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Interaction of 1s Orbitals
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Molecular Orbital Theory
• Electrons in bonding MOs are stabilizinglower energy than the atomic orbitals
• Electrons in antibonding MOs are destabilizinghigher in energy than atomic orbitalselectron density located outside the
internuclear axiselectrons in antibonding orbitals cancel
stability gained by electrons in bonding orbitals
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Energy Comparisons of Atomic Orbitals to Molecular Orbitals
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MO and Properties• Bond Order = difference between number of
electrons in bonding and antibonding orbitalsonly need to consider valence electronsmay be a fractionhigher bond order = stronger and shorter bonds if bond order = 0, then bond is unstable compared to
individual atoms and no bond will form
• A substance will be paramagnetic if its MO diagram has unpaired electrons if all electrons paired it is diamagnetic
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1s 1s
*
Hydrogen AtomicOrbital
Hydrogen AtomicOrbital
Dihydrogen, H2 MolecularOrbitals
Because more electrons are in bonding orbitals than are in antibonding orbitals,
net bonding interaction
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H2
* Antibonding MOLUMO
bonding MOHOMO
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1s 1s
*
Helium AtomicOrbital
Helium AtomicOrbital
Dihelium, He2 MolecularOrbitals
Because there are as many electrons in antibonding orbitals as in bonding orbitals,
there is no net bonding interaction
BO = ½(2-2) = 0
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1s 1s
Lithium AtomicOrbitals
Lithium AtomicOrbitals
Dilithium, Li2 MolecularOrbitals
Because more electrons are in bonding orbitals than are in antibonding orbitals, there is a
net bonding interaction
2s 2s
Any fill energy level will generate filled bonding and antibonding MO’s;therefore only need to consider valence shell
BO = ½(4-2) = 1
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bonding MOHOMO
* Antibonding MOLUMO
Li2
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Interaction of p Orbitals
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Interaction of p Orbitals
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O2
• Dioxygen is paramagnetic• Paramagnetic material has unpaired electrons• Neither Lewis theory nor valence bond theory
predict this result
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O2 as Described by Lewis and VB Theory
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OxygenAtomicOrbitals
OxygenAtomicOrbitals
2s 2s
2p 2p
Because more electrons are in bonding orbitals than are in antibonding orbitals, there is a net bonding interaction
Because there are unpaired electrons in the
antibonding orbitals, O2 is predicted to be
paramagnetic
O2 MO’s
BO = ½(8 be – 4 abe)BO = 2
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N has 5 valence electrons
2 N = 10e−
(−) = 1e−
total = 11e−
Example 10.10: Draw a molecular orbital diagram of N2
− ion and predict its bond order and magnetic properties
147
Write a MO diagram for N2
− using N2 as a base
Count the number of valence electrons and assign these to the MOs following the aufbau principle, Pauli principle & Hund’s rule ↑↓ 2s
2s
2p
2p
2p
2p
↑↓
↑ ↑↓ ↓
↑↓
↑
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Example 10.10: Draw a molecular orbital diagram of N2
− ion and predict its bond order and magnetic properties
148
Calculate the bond order by taking the number of bonding electrons and subtracting the number of antibonding electrons, then dividing by 2
Determine whether the ion is paramagnetic or diamagnetic
↑↓ 2s
2s
2p
2p
2p
2p
↑↓
↑ ↑↓ ↓
↑↓
↑
BO = ½(8 be – 3 abe)BO = 2.5
Because this is lower than the bond order
in N2, the bond should be weaker
Because there are unpaired electrons, this ion is paramagnetic
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Practice – Draw a molecular orbital diagram of C2+
and predict its bond order and magnetic properties
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↑↓ 2s
2s
2p
2p
2p
2p
↑↓
↑ ↑↓
BO = ½(5 be – 2 abe)BO = 1.5
Because there are unpaired electrons, this ion is paramagnetic
Practice – Draw a molecular orbital diagram of C2+
and predict its bond order and magnetic properties
C has 4 valence electrons
2 C = 8e−
(+) = −1e−
total = 7e−
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Heteronuclear Diatomic Molecules & Ions
• When the combining atomic orbitals are identical and equal energy, the contribution of each atomic orbital to the molecular orbital is equal
• When the combining atomic orbitals are different types and energies, the atomic orbital closest in energy to the molecular orbital contributes more to the molecular orbital
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Heteronuclear Diatomic Molecules & Ions
• The more electronegative an atom is, the lower in energy are its orbitals
• Lower energy atomic orbitals contribute more to the bonding MOs
• Higher energy atomic orbitals contribute more to the antibonding MOs
• Nonbonding MOs remain localized on the atom donating its atomic orbitals
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NO
a free radical
2s Bonding MOshows more
electron density near O because it is mostly O’s
2s atomic orbital153
BO = ½(6 be – 1 abe)BO = 2.5
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HF
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Polyatomic Molecules
• When many atoms are combined together, the atomic orbitals of all the atoms are combined to make a set of molecular orbitals, which are delocalized over the entire molecule
• Gives results that better match real molecule properties than either Lewis or valence bond theories
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Ozone, O3
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MO Theory: Delocalized bonding orbital of O3
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