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04/10/23 1
Formation of Covalent Bonds
Two different theories which attempt to explain covalent molecular/ionic structure/shape
Localized Electron (LE) Model-electron pairs are still localized around specific atoms, but orbitals around central atom are modified
Molecular Orbital (MO) Model-all electrons in molecule are combined into set of molecular orbitals which describe bonding in entire molecule
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Why hybrid orbitals?Why hybrid orbitals?
VSEPR model does good job at predicting molecular shape, despite fact that it has no obvious relationship to filling and shapes of atomic orbitals
Based on shapes and orientations of 2s/2p orbitals on carbon atom, not obvious why CH4 molecule should have tetrahedral geometry
Used to reconcile covalent bonds formed from overlap of atomic orbitals with molecular geometries from VSEPR model
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Hybridization/Hybrid orbitalsHybridization/Hybrid orbitals
Hybridization (orbitals in covalently bonded atoms) Mixing of 2/more atomic orbitals of similar energies on same atom
to produce new orbitals of equal energies Hybrid orbitals
Valence bond theory creates hybrid orbitals that are linear combinations of s/p orbitals in valence shell (d if necessary) # atomic orbits = # hybrid orbitals Each hybrid orbital equivalent to others but large lobes point in
different directions Atomic orbitals not used to make hybrids unaffected Mixtures of atomic orbitals with intermediate energy
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One 2s electron promoted to empty (2p) orbital
2 occupied orbitals blend to form 2 sp hybrid orbitals/2 remaining p orbitals
unchanged
No unpaired electrons
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sp has 50% s/50% p character 2 sp hybrids point in opposite directions at 180o to each
other Require energy to promote 2s 2p orbital Large lobe of hybrid orbital can be directed at other atoms better than
unhybridized atomic orbital Overlap more strongly/stronger bonds result Energy released by bond formation offsets energy expended to
promote electrons
Each sp hybrid involved in s bond/remaining p orbitals forms 2p bonds (All contain single unpaired electron)
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2s electron promoted to 2p orbital Have 3 unpaired electrons that form 3 sp2 orbitals
Creates 3 identical orbitals of intermediate energy/lengthLeaves one unhybridized p orbital
http://college.hmco.com/chemistry/shared/media/animations/sp2hybridization.html
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Large lobes of orbitals lie in plane at angles of 120o and point toward corners of triangle
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Promotion of 2s electron to 2p orbital results in valence shell with 4 unpaired electrons in four sp3 hybrid orbitals.
4 orbitals form one 2s/three 2p orbitals (s1p3)
te
trah
edra
l
Four sp3 orbitals identical in shape
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http://college.hmco.com/chemistry/shared/media/animations/sp3_hybridization.html
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D-orbital hybridization
Central atoms located in Period 3 and above can use empty d orbitals to receive promoted s electron
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dspdsp33 HybridizationHybridization
5 effective pairs around central atom
Trigonal bipyramidal shape
Lobes have bond angles of 90o & 120O
PCl5 example
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•Each dsp3 orbital also has small lobe not shown in diagram
•Phosphorus uses set of 5 dsp3 orbitals to share electron pairs with sp3 orbitals on 5 chlorine
atoms •Other sp3 orbitals on each
chlorine atom hold lone pairs
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dd22spsp33 HybridizationHybridization
Six effective pairs around central atom Octahedral structure Lobes have angles of 90o
SF6 example
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Atomic Hybridorbital set orbital set_
s/p 2 sp
s/p/p 3 sp2
s/p/p/p 4 sp3
s/p/p/p/d 5 sp3d
s/p/p/p/d/d 6 sp3d2
Examples
BeF2, HgCl2
BF3, SO3
CH4, NH3, H O, NH4+
PF5, SF4, BrF3, SbCl52-
SF6, ClF5, XeF4, PF4-
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•Basic Derived Hybrid Bonding NonbondingStructure structure e- pairs e- pairs•Linear sp 2 0•Trigonal planar sp2 3 0•Trigonal planar Bent sp2 2 1•Tetrahedron sp3 4 0•Tetrahedron Triangular pyramid sp3 3 1•Tetrahedron Bent sp3 2 2•Trigonal bipyramid sp3d 5 0•Trigonal bipyramid Distorted tetrahedron sp3d 4 1•Trigonal bipyramid T-shape sp3d 3 2•Trigonal bipyramid Linear sp3d 2 3•Octahedron sp3d2 6 0•Octahedron Square pyramid sp3d2 5 1•Octahedron Square planar sp3d2 4 2
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Strength of sigma bonds p-p > p-s > s-s p-orbitals allow overlap to greater
extent as compared to p-s which is larger as compared to s-s overlap
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(s/single /δ)
(Head-to-head overlap)
Lobes of bonding orbital point toward each other.
Overlap of two S orbitals to form sigma
bond (green)
Overlap of two P orbitals to form sigma
bond (green)
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Maximum electron density lies along bond (electron pair shared in area centered on line connecting nuclei)
Line joining 2 nuclei passes through middle of overlap region (between nuclei)
Maximum overlap forms strongest-possible sigma bond
Atoms arrange themselves to give greatest-possible orbital overlap
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(p/)
• Axes parallel to each other but perpendicular to internuclear axis
• Occupies space above/below internuclear axis (imaginary line connecting nuclei of two atoms)
• Electron density zero along bond• Atomic orbitals interact above and below
nuclei
(perpendicular)
• Formed only in addition to sigma bond• Always present in molecules with
double/triple bonds• Occur only w/sp or sp2 hybridization
present on central atom, but not sp3
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•Pi bonds are superimposed on sigma bonds so they simply modify dimensions of molecule.
• Significantly less overlap between component p-orbitals due to parallel orientation
• Weaker than sigma bonds-electrons farther from nucleus, so more reactive
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Multiple BondsMultiple Bonds
Double Bonds Consist of 1 s bond
(overlap of 2 sp orbitals) and 1 p bond (overlap of 2 p orbitals)
s bond where electron pair located directly between atoms
p bond where shared pair occupies space above and below s bond
Triple Bonds Consist of 1 s / 2 p bonds Side-to-side overlap
makes p bond electrons more reactive
Electron density no longer located on internuclear axis (one electron cloud above and one below)
Bond is weaker-p orbitals do not overlap as much in p bond as s bond
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Double bondsDouble bonds Triple bondsTriple bonds
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Consists of sigma (green)/2 pi bonds (red)
http://college.hmco.com/chemistry/shared/media/animations/molecularorbitaldiagram.html
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(a) sp hybridized nitrogen atom
(b) s bond in N2 molecule
(c) 2 p bonds in N2 are formed when electron pairs are shared between two sets of parallel p orbitals
(d) Total bonding picture for N2
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Carbon is uniqueCarbon is unique
sp3 hybrid orbitals = single bonds
sp2 hybrid orbitals = double bonds
sp hybrid orbitals = triple bonds
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Carbon atom of methane (CHCarbon atom of methane (CH44) )
Made up of 4 C-H sigma (σ) bondsEach hybrid sp3 orbitals of carbon undergoes
end-on overlap with s-orbitals of H atomsTetrahedral geometry
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Carbon atoms of ethyne Carbon atoms of ethyne (acetylene - C(acetylene - C22HH22) )
2 C-H σ bonds, 1 C-C σ bond, 2 C-C π bonds Δ bonds (gray) are linear in arrangement Unhybridized p-orbitals (green/purple) interact with
each other laterally, resulting in bond formation
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Carbon atoms of ethene Carbon atoms of ethene (ethylene - C(ethylene - C22HH44))
4 C-H σ bonds, 1 C-C σ bond, 1 C-C π bond Hybrid orbital overlap end-on with s-orbitals of H
atoms (δ bond in gray) Unhybridized p-orbitals (purple) at right angles to
plane of hybrids, overlap laterally (π bond-double)
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Formaldehyde has following Formaldehyde has following Lewis structure: Lewis structure:
Describe it bonding in terms of appropriate hybridized/unhybridized orbitals
VSEPR predicts trigonal planar geometry which suggests sp2 hybrid orbitals on C
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Acetonitrile moleculeAcetonitrile molecule
Predict bond angles around each C Approximately 109° around left C and 180° on
right C
Give hybridization of each C sp3, sp
Determine total number of δ/π bonds 5 δ bonds and 2 π bonds
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orbitals of sp hybridized carbon atom
orbital arrangement for sp2 hybridized oxygen atom
hybrid orbitals in the CO2 molecule
(a) orbitals in carbon dioxide-carbon-oxygen double bonds each consist of one s bond and one p bond. (b) Lewis structure for carbon dioxide
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Determine the total number of sigma and pi bonds in each of the following:Using the simple Lewis structure, also determine
the hybridization for each: CH3Cl 4 δ, 0 Π, sp3
PH3
2 δ, 2 Π, sp H2S 3 δ, 0 Π, sp3
CO32-
4 δ, 0 Π, sp3
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SO32-
2 δ, 0 Π, sp3
CS2
3 δ, 1 Π, sp2
SiF4
3 δ, 1 Π, sp2
NO3-
4 δ, 0 Π, sp3
PO43-
3 δ, 0 Π, sp2
ClO4-
4 δ, 0 Π, sp3
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VSEPR did not explain why VSEPR did not explain why bonds exist between atomsbonds exist between atoms
Pair of electrons attracted to both atomic nuclei Bond is formed As extent of overlap increases, strength of bond
increases Electronic energy drops as atoms approach each
other Begin to increase again when they become too close Optimum distance (observed bond distance) at which
total energy is at minimum
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Basic s, px, py, and pz orbitals unsatisfactory for two reasons Orbitals not directed in particular direction-tend to
spread out in all directions Geometry of orbitals rarely consistent with
molecular geometry Could not adequately explain fact that some
molecules contain two equivalent bonds with bond order between that of single and double bonds
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Atomic orbitalsAtomic orbitals explain bonding/ explain bonding/ account for molecular geometriesaccount for molecular geometries
Mathematical descriptions of where electrons most likely found Obtained by solving Schrödinger equation
As angular momentum (ml) and energy of electron increases, it tends to reside in differently shaped orbitals
Orbitals corresponding to three lowest energy states (s, p, and d, respectively)
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Localized Electron ModelLocalized Electron Model(Valence Bond Theory)(Valence Bond Theory)
Describes structure of covalent bonds (how bonding occurs)
Atoms in molecule bond together w/shared electrons Lewis structure shows valence electron arrangement Use VSEPR model to predict molecular geometry Atoms use atomic orbitals to share electrons/hold lone
pairs (new set of hybridized orbitals can form) Lone pairsLone pairs: electron pairs localized on atom Bonding pairsBonding pairs: electron pairs in space between atoms
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Combine Lewis’s notion of electron-pair bonds with atomic orbitals Lewis theoryLewis theory: covalent bonding occurs when atoms share
electrons (concentrates electron density between nuclei) Valence-bond theoryValence-bond theory: buildup of electron density between two
nuclei occurs when valence atomic orbital of one atom shares space (overlaps) with that of another atom
Shortcomings of LE Model Electrons not actually localized Does not deal effectively w/molecules containing unpaired electrons Gives no direct information about bond energies
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Direct overlap (electron sharing) of two atomic orbitals Local view of bonding (how adjacent atoms share electrons) How 2 electrons of opposite spin share space between
nuclei/form bond Paired electrons localized in specific internuclear spaces between
bonded atoms or remain unshared (lone pairs) As bond is formed, paired electrons spread out over molecule to
form final electron cloud surrounding nuclei Description confirmed by many chemistry/physics experiments,
including actual Scanning Tunneling Microscope picture of p-orbital
Electronic structure/geometry is best compromise between maximum overlap (electron-nucleus attraction) and repulsion (electron-electron/nucleus-nucleus)
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Bonds (δ-head on/π-sideways) made by overlap of atomic (s,p) or hybridized (sp2) orbitals Formation of bonding
orbital accompanied by formation of antibonding antibonding orbitals (orbitals (δδ*/*/ππ*) *) which remain unoccupied and does not contribute to structure of molecule
δ bonds have cylindrical symmetry Formed between pair of
atoms within molecule Increased electron
density on internuclear axis
Rotation around bond does not change overlap of contributing atomic orbitals
Lower energy than π bonds
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π bonds are not cylindrically symmetric May cover more than 2 nuclei (resonance) Increased electron density above/below internuclear
axis (not on axis itself) Rotation breaks bond
Electrons not always shared equally (EN) Skeletal structures (Lewis structures) correspond
to valence-bond model
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Resonance structures represent molecules not adequately described by single structure, because electrons shared by more than 2 nuclei
Rules for drawing reasonable resonance structures All resonance structures must be valid Lewis structures In all possible resonance structures atomic nuclei must not
change their positions All atoms must not change their hybridization Only electron distribution may be changed All resonance structures must have same # unpaired
electrons All atoms involved in resonance (electron sharing)/atoms
directly bonded to them must lie in (or nearly in) same plane
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Homework:
Read 9.1, pp. 413-426
Q pp. 441-443, #12, 14, 16, 21, 22, 27, 28
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Molecular Orbital (MO) Theory (Model)
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Molecular Orbital TheoryMolecular Orbital Theory
Explains distributions (organization of valence electrons) and energy of electrons in molecules Molecule is similar to atom (have distinct energy levels that
electrons can populate) Takes global view of bonding (all electrons in molecule are needed
to describe how bonding occurs) Useful for describing properties of compounds
Bond energies, electron cloud distribution, and magnetic properties
Solution to VB problems by creating new set of orbitals w/intermediate between those of basic orbitals used to construct them
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Basic principles of MO Theory 2 atomic orbitals w/similar energies overlap to form 2 molecular orbitals Electrons from each element participating in bond occupy new molecular
orbitals MOs delocalized over many atoms (don’t directly correspond to specific
bond as in VB theory) No hybridization (all available atomic orbitals mixed into multiple
combination Molecular orbitals have different energies depending on type of
overlap Bonding orbitals (lower energy than corresponding AO) Nonbonding orbitals (same energy as corresponding AO) Antibonding orbitals (higher energy than corresponding AO)
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Molecular orbitals (MOs) made of fractions of atomic orbitals All atoms in molecule provide atomic orbitals to
make MOs, but not all atomic orbitals must participate in all MOs
MO filled by all available electrons (2 per orbital), starting with lowest energy MO orbital
π bonds perpendicular to δ bonds, so can’t mix Reflects orbital geometry of molecule
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Principles for formation of MOsPrinciples for formation of MOs
1. # MOs formed = # atomic orbitals combined
2. Atomic orbitals combine best with other atomic orbitals of similar energy
3. How effectively 2 atomic orbitals combine proportional to their overlap As overlap increases, energy of bonding MO lowered, energy of
antibonding MO raised Lower energy molecular orbitals fill first
4. Each MO accommodates 2 electrons w/opposite spins (Pauli exclusion principle)
5. When MOs of same energy populated, Hund’s rule is followed (equal energy orbitals ½ filled before pairing up)
6. Electron in antibonding orbital “cancels” its corresponding electron in bonding orbital
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In atoms, electrons occupy atomic orbitals,
In molecules they occupy molecular orbitals which surround molecule
Two atomic orbitals combine to form two molecular orbitals, one bonding () and one antibonding (*)
Each line in diagram represents orbital
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Bonding OrbitalBonding Orbital
MOs w/lower energy than its corresponding original atomic orbitals
Promotes formation of stable bond High electron density along internuclear axis
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Antibonding Orbital
MOs w/higher energy than its corresponding atomic orbitals
Destabilizes (negative impact) formation of bond Much lower electron density along internuclear
axis
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When two atomic orbitals overlap in side-by-side fashion, molecular orbitals called π molecular orbitals
Antibonding molecular orbital is designated as π* molecular orbital
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Bond Order (BO)Bond Order (BO)
Describes nature of bond formed by molecular orbitals
Refers to average number of bonds that atom makes in all of its bonds to other atoms
Bond order above 0 considered stable because it has excess of bonding electrons If bond order = 0 (BE = ABE), species does not
exist Larger bond order = Greater bond strength =
Greater bond energy = Shorter bond lengthBO =
# bonding electrons # antibonding electons2
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Pg. 434-444, Sample 9.6
For the species O2, O2+, and O2
-, give the electron configuration and the bond order for each. Which has the strongest bond?
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Magnetism can be induced in some Magnetism can be induced in some nonmagnetic materials when in nonmagnetic materials when in presence of magnetic fieldpresence of magnetic field
Paramagnetism: (oxygen-2 unpaired e’s) Unpaired electrons Attracted to induced magnetic field Much stronger than diamagnetism
Diamagnetism Paired electrons Repelled from induced magnetic field Much weaker than paramagnetism
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NONO++ ion has total of 7 + 8 -1 = 14 ion has total of 7 + 8 -1 = 14 electrons to place in molecular electrons to place in molecular orbitals as followsorbitals as follows
Calculate bond order of NO+ ion ½(10 - 4) = 3
Is the NO+ ion diamagnetic or paramagnetic? 0 unpaired electrons
so ion is diamagnetic
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Hydrogen Atom (H)Hydrogen Atom (H)
1 bonding electron/0 antibonding electrons
Stable (lower energy, greater stability)
Bond order of ½ One unpaired electron-
paramagnetic
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2 bonding electrons in δ1s
molecular orbital /0 antibonding electrons
Stable Bond order of 1 Electrons in line w/2 nuclei,
so are s molecular orbitals No unpaired electrons-
diamagnetic
Hydrogen Molecule (HHydrogen Molecule (H22))
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Does HeDoes He22 exist? exist?
He2 has four
electrons, two in s1s orbital and two
in s*1s orbital
Bond order of 0, so He2 does not
exist
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Bonding in Homonuclear Diatomic Bonding in Homonuclear Diatomic Molecules (composed of two identical Molecules (composed of two identical atoms)atoms)
In order to participate in molecular orbitals, atomic orbitals must overlap in space
Larger bond order is favored When molecular orbitals are formed from p orbitals, s
orbitals are favored over p orbitals (stronger) Electrons are closer to nucleus = lower energy
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Molecular orbital energy-level diagrams, bond orders, bond energies, and bond lengths for diatomic molecules
Note that for O2 and F2, 2p orbital lower in energy than the π2p orbitals
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Bonding in Heteronuclear Diatomic Bonding in Heteronuclear Diatomic Molecules (different atoms)Molecules (different atoms)
For atoms adjacent to each other in periodic table Use molecular orbital diagrams for homonuclear
molecules
Significantly different atoms Each molecule must be examined individually Use only electrons that are going to be involved in
bonding
No universally accepted molecular orbital energy order
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N2 NO bond order = 3 bond order = 2.5
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Outcomes of MO ModelOutcomes of MO Model
Strengths Correctly predicts relative bond strength and
magnetism of simple diatomic molecules Accounts for bond polarity Correctly portrays electrons as being delocalized
in polyatomic molecules Disadvantages
Difficult to apply quantitatively to polyatomic molecules
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Combining Localized Electron Combining Localized Electron and Molecular Orbital Modeland Molecular Orbital Model
Resonance Attempt to draw localized electrons in structure in
which electrons not localized s (δ) bonds can be described using localized electron
model p (π) bonds (delocalized) must be described using
molecular orbital model
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BenzeneBenzene
s bonds (C - H and C - C) are sp2 hybridized
Localized model p bonds result of
remaining p orbitals above/ below plane of benzene ring
Delocalizing gives stability
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Homework:
Read 9.2-9.5, pp. 426-441Q pp. 443-444, #32, 33, 38, 40, 46Do 1 additional exercise and 1 challenge problemSubmit quizzes by email to me:http://www.cengage.com/chemistry/book_content/
0547125321_zumdahl/ace/launch_ace.html?folder_path=/chemistry/book_content/0547125321_zumdahl/ace&layer=act&src=ch09_ace1.xml
http://www.cengage.com/chemistry/book_content/0547125321_zumdahl/ace/launch_ace.html?folder_path=/chemistry/book_content/0547125321_zumdahl/ace&layer=act&src=ch09_ace2.xml
http://www.cengage.com/chemistry/book_content/0547125321_zumdahl/ace/launch_ace.html?folder_path=/chemistry/book_content/0547125321_zumdahl/ace&layer=act&src=ch09_ace3.xml