Chapter 08

102
1 CHAPTER 8 Molecular Structure & Covalent Bonding Theories

Transcript of Chapter 08

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CHAPTER 8

Molecular Structure & Covalent Bonding Theories

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Chapter Goals1. A Preview of the Chapter2. Valence Shell Electron Pair

Repulsion (VSEPR) Theory3. Polar Molecules:The Influence of

Molecular Geometry4. Valence Bond (VB) Theory Molecular Shapes and BondingMolecular Shapes and Bonding

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Chapter Goals5. Linear Electronic Geometry: AB2 Species6. Trigonal Planar Electronic Geometry: AB3 Species7. Tetrahedral Electronic Geometry: AB4 Species8. Tetrahedral Electronic Geometry: AB3U Species 9. Tetrahedral Electronic Geometry: AB2U2 Species10. Tetrahedral Electronic Geometry – ABU3 Species11. Trigonal Bipyramidal Geometry12. Octahedral Geometry 13. Compounds Containing Double Bonds14. Compounds Containing Triple Bonds15. A Summary of Electronic and Molecular Geometries

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Stereochemistry

Stereochemistry is the study of the three dimensional shapes of molecules.

Some questions to examine in this chapter are:

1. Why are we interested in shapes?2. What role does molecular shape play in life?3. How do we determine molecular shapes?4. How do we predict molecular shapes?

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Two Simple Theories of Covalent Bonding

Valence Shell Electron Pair Repulsion Theory– Commonly designated as VSEPR– Principal originator

• R. J. Gillespie in the 1950’s

Valence Bond Theory– Involves the use of hybridized atomic orbitals– Principal originator

• L. Pauling in the 1930’s & 40’s

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Overview of Chapter• The same basic approach will be used in

every example of molecular structure prediction:

1. Draw the correct Lewis dot structure.• Identify the central atom.• Designate the bonding pairs and lone pairs of

electrons on central atom.2. Count the regions of high electron density on

the central atom.• Include both bonding and lone pairs in the

counting.

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Overview of Chapter

3. Determine the electronicelectronic geometry around the central atom.

• VSEPR is a guide to the geometry.4. Determine the molecular molecular geometry

around the central atom.• Ignore the lone pairs of electrons.

5. Adjust molecular geometry for effect of any lone pairs.

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Overview of Chapter

6. Determine the hybrid orbitals on central atom.

7. Repeat procedure if there is more than one central atom in molecule.

8. Determine molecular polarity from entire molecular geometry using electronegativity differences.

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VSEPR Theory

Regions of high electron density around the central atom are arranged as far apart as possible to minimize repulsions.

There are five basic molecular shapes based on the number of regions of high electron density around the central atom.

Several modifications of these five basic shapes will also be examined.

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VSEPR Theory1 Two regions of high electron density

around the central atom.

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VSEPR Theory2 Three regions of high electron density around the central

atom.

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VSEPR Theory3 Four regions of high electron density around the central

atom.

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VSEPR Theory4 Five regions of high electron density

around the central atom.

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VSEPR Theory5 Six regions of high electron density around the

central atom.

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VSEPR Theory Frequently, we will describe two geometries

for each molecule. 1.1. Electronic geometryElectronic geometry is determined by the

locations of regions of high electron density around the central atom(s).

2.2. Molecular geometryMolecular geometry determined by the arrangement of atoms around the central atom(s).

Electron pairs are not used in the molecular geometry determination just the positions of the atoms in the molecule are used.

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VSEPR Theory An example of a molecule that has the

same electronic and molecular geometries is methane - CH4.

Electronic and molecular geometries are tetrahedral.

H

CHH

H

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VSEPR Theory An example of a molecule that has

different electronic and molecular geometries is water - H2O.

Electronic geometry is tetrahedral. Molecular geometry is bent or angular.

H

CHH

H

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VSEPR Theory

Lone pairs of electrons (unshared pairs) require more volume than shared pairs.– Consequently, there is an ordering of repulsions

of electrons around central atom. Criteria for the ordering of the repulsions:

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VSEPR Theory1 Lone pair to lone pair is the strongest repulsion.2 Lone pair to bonding pair is intermediate

repulsion.3 Bonding pair to bonding pair is weakest

repulsion. Mnemonic for repulsion strengths

lp/lp > lp/bp > bp/bp Lone pair to lone pair repulsion is why bond

angles in water are less than 109.5o.

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Polar Molecules: The Influence of Molecular Geometry

Molecular geometry affects molecular polarity.– Due to the effect of the bond dipoles and

how they either cancel or reinforce each other.

A B A

linear molecule nonpolar

A B A

angular molecule

polar

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Polar Molecules: The Influence of Molecular Geometry

Polar Molecules must meet two requirements:

1. One polar bond or one lone pair of electrons on central atom.

2. Neither bonds nor lone pairs can be symmetrically arranged that their polarities cancel.

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Valence Bond (VB) Theory

Covalent bonds are formed by the overlapoverlap of atomic orbitals.

Atomic orbitals on the central atom can mix and exchange their character with other atoms in a molecule.– Process is called hybridizationhybridization.

Hybrids are common:1. Pink flowers 2. Mules

Hybrid Orbitals have the same shapes as predicted by VSEPR.

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Valence Bond (VB) Theory

Regions of High Electron

Density

Electronic Geometry

Hybridization

2 Linear sp3 Trigonal

planarsp2

4 Tetrahedral sp3

5 Trigonal bipyramidal

sp3d

6 Octahedral sp3d2

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Molecular Shapes and BondingMolecular Shapes and Bonding In the next sections we will use the

following terminology:A = central atomB = bonding pairs around central atomU = lone pairs around central atom

For example:AB3U designates that there are 3 bonding pairs

and 1 lone pair around the central atom.

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Linear Electronic Geometry:AB2

Species (No Lone Pairs of Electrons on A)

Some examples of molecules with this geometry are: BeCl

2, BeBr

2, BeI

2, HgCl

2, CdCl

2

All of these examples are linear, nonpolar molecules.

Important exceptions occur when the two substituents are not the same!BeClBr or BeIBr will be linear and polar!

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Linear Electronic Geometry:AB2

Species (No Lone Pairs of Electrons on A)

Electronic Structures

1s 2s 2pBe

3s 3p

Cl [Ne]

Lewis Formulas

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Linear Electronic Geometry:AB2

Species (No Lone Pairs of Electrons on A)

Dot Formula

180o - linear

BeCl Cl··

····

····

··BeCl Cl

····

····

·· ····

··

Electronic Geometry

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Linear Electronic Geometry:AB2

Species (No Lone Pairs of Electrons on A)

Molecular Geometry

bondspolar very

3.5 51. 3.5 ativitiesElectronegCl - Be- Cl

0.22.0

180o-linear

BeCl Cl····

Polarity

moleculenonpolar symmetric are dipoles bond

Cl---Be---Cl

H

CHH

H

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Linear Electronic Geometry:AB2

Species (No Lone Pairs of Electrons on A)

Valence Bond Theory (Hybridization)1s 2s 2p

Be 1s sp hybrid 2p

3s 3pCl [Ne]

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Linear Electronic Geometry:AB2 Species (No Lone Pairs of

Electrons on A)

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Trigonal Planar Electronic Geometry: AB3 Species (No

Lone Pairs of Electrons on A) Some examples of molecules with this

geometry are: BF3, BCl3

All of these examples are trigonal planar, nonpolar molecules.

Important exceptions occur when the three substituents are not the same!BF2Cl or BCI2Br will be trigonal planar and polar!

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Trigonal Planar Electronic Geometry: AB3 Species (No

Lone Pairs of Electrons on A)Electronic Structures

Lewis Formulas

1s 2s 2pB

3s 3pCl [Ne]

B·· .

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Trigonal Planar Electronic Geometry: AB3 Species (No

Lone Pairs of Electrons on A)Dot Formula

··

B

Cl

Cl Cl··

····

··

···· ··

····

·· ··

B··

··

··

120-trigonal planar

Electronic Geometry

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Trigonal Planar Electronic Geometry: AB3 Species (No

Lone Pairs of Electrons on A)Molecular Geometry

B ClCl

Cl120o-trigonal planar

bondspolar ery v

3.0 1.5 ativitiesElectronegCl - B

1.5

Polarity

B ClCl

Cl

bond dipoles are symmetric nonpolar molecule

H

CHH

H

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Trigonal Planar Electronic Geometry: AB3 Species (No

Lone Pairs of Electrons on A)Valence Bond Theory (Hybridization)

1s 2s 2pB

1s sp2 hybrid

3s 3pCl [Ne]

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Trigonal Planar Electronic Geometry: AB3 Species (No Lone

Pairs of Electrons on A)

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Trigonal Planar Electronic Geometry: AB3 Species (No Lone

Pairs of Electrons on A)

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Tetrahedral Electronic Geometry: AB

4 Species (No Lone Pairs of

Electrons on A) Some examples of molecules with this

geometry are: CH

4, CF

4, CCl

4,

SiH

4,

SiF

4

All of these examples are tetrahedral, nonpolar molecules.

Important exceptions occur when the four substituents are not the same!CF3Cl or CH2CI2 will be tetrahedral and polar!

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Tetrahedral Electronic Geometry: AB

4 Species (No Lone Pairs of

Electrons on A)Electronic Structures

C..

. .

H .

2s 2pC [He]

1s H

Lewis Formulas

C..

. .

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Tetrahedral Electronic Geometry: AB

4 Species (No Lone Pairs of

Electrons on A)Dot Formula

C

H

H

H H.... ..

.. C

....

..

..

tetrahedral109.5o bond angles

Electronic Geometry

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Tetrahedral Electronic Geometry: AB

4 Species (No Lone Pairs of

Electrons on A)Molecular Geometry

CH H

H

H

tetrahedralbondspolar slightly

2.1 2.5 ativitiesElectroneg H- C

0.4

Polarity

symmetric dipolesnonpolar molecule

CH H

H

H

H

CHH

H

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Tetrahedral Electronic Geometry: AB

4 Species (No Lone Pairs of

Electrons on A)Valence Bond Theory (Hybridization) 2s 2p

C [He] four sp3 hybrid orbitals

C [He]

1s H

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Tetrahedral Electronic Geometry: AB

4 Species (No Lone Pairs of

Electrons on A)

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Tetrahedral Electronic Geometry: AB

4 Species (No Lone Pairs of

Electrons on A)

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Example of Molecules with More Than One Central Atom

Alkanes CnH2n+2

Alkanes are hydrocarbons with the general formula CnH2n+2. 1. CH4 - methane2. C2H6 or (H3C-CH3) - ethane3. C3H8 or (H3C-CH2-CH3) - propane

The C atoms are located at the center of a tetrahedron. Each alkane is a chain of interlocking tetrahedra. Sufficient H atoms to form a total of four bonds for

each C.

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Example of Molecules with More Than One Central Atom

Alkanes CnH2n+2

C HHH

H

C C

H

HH

H

HH

CH4

C2H6

CC

CH

HH

H HH

HH

C3H8

H

CHH

H

H

CHH

H

H

CHH

H

H

CHH

H

H

CHH

H

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Tetrahedral Electronic Geometry: AB3U Species (One Lone Pair of

Electrons on A) Some examples of molecules with this geometry

are: NH3, NF3, PH3, PCl3, AsH3

These molecules are our first examples of central atoms with lone pairs of electrons.Thus, the electronic and molecular geometries are

different.All three substituents are the same but molecule is polarpolar.

NH3 and NF3 are trigonal pyramidal, polar molecules.

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Tetrahedral Electronic Geometry: AB3U Species (One Lone Pair of

Electrons on A)Electronic Structures

N..

..

.

F....

.. .

H .

Lewis Formulas

2s 2pN [He]

2s 2pF [He]

1s H

N..

..

.

F....

.. .

N..

..

.

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Tetrahedral Electronic Geometry: AB3U Species (One Lone Pair of

Electrons on A)Dot Formulas

NH H

H..

.... ..

.. ....NF F

F..

..

..

....

....

......

tetrahedral

N

..

....

..

Electronic Geometry

NH H

H..

.... ..

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Tetrahedral Electronic Geometry: AB3U Species (One Lone Pair of

Electrons on A)Molecular Geometry

1 lone pair

pyramidal

NF F

F

..

1 lone pair

pyramidal

NH H

H

..

bondspolar ry ve

4.0 3.0 ativitiesElectroneg F-N

bondspolar y ver

2.1 3.0 ativitiesElectroneg H-N

1.0

0.9

Polarity1 lone pair

pyramidal

NH H

H

..

bondspolar y ver

2.1 3.0 ativitiesElectroneg H-N

0.9

NH H

H

..

asymmetrical dipoles polar molecule=1.5 D

bond dipolesreinforce effect of lone pair

NF F

F

..bond dipolesoppose effect of lone pair

asymmetrical dipoles polar molecule=0.2 D

NH H

H

..

asymmetrical dipoles polar molecule=1.5 D

bond dipolesreinforce effect of lone pair

H

CHH

H

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Tetrahedral Electronic Geometry: AB3U Species (One Lone Pair of

Electrons on A)Valence Bond Theory (Hybridization)

2s 2pN [He]

four sp3 hybrids

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Tetrahedral Electronic Geometry: AB2U2 Species (Two Lone Pairs of

Electrons on A) Some examples of molecules with this geometry

are: H2O, OF2, H2S

These molecules are our first examples of central atoms with two lone pairs of electrons.Thus, the electronic and molecular geometries are

different.Both substituents are the same but molecule is polarpolar.

Molecules are angular, bent, or V-shaped and polar.

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Tetrahedral Electronic Geometry: AB2U2 Species (Two Lone Pairs of

Electrons on A)Electronic Structures

O··

··.

.

H .

Lewis Formulas

2s 2pO [He]

1s H

O··

··.

.

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Tetrahedral Electronic Geometry: AB2U2 Species (Two Lone Pairs

of Electrons on A)Molecular Geometry

OH

H

··

··

2 lone pairs

bent, angularor V-shaped

bondspolar y ver

2.1 3.5 ativitiesElectroneg H- O

1.4

Polarity

OH

H

··

··

bond dipolesreinforce lonepairs

asymetric dipolesvery polar molecule1.7 D

H

CHH

H

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Tetrahedral Electronic Geometry: AB2U2 Species (Two Lone Pairs

of Electrons on A)Valence Bond Theory (Hybridization)

2s 2pO [He]

four sp3 hybrids

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Tetrahedral Electronic Geometry: ABU3 Species (Three Lone Pairs

of Electrons on A) Some examples of molecules with this

geometry are: HF, HCl, HBr, HI, FCl, IBr

These molecules are examples of central atoms with three lone pairs of electrons.Again, the electronic and molecular geometries are

different. Molecules are linear and polar when the two

atoms are different.Cl2, Br2, I2 are nonpolarnonpolar.

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Tetrahedral Electronic Geometry: ABU3 Species (Three Lone Pairs

of Electrons on A)Dot Formula

H F··

····

··

tetrahedral

FH

··

····

Electronic Geometry

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Tetrahedral Electronic Geometry: ABU3 Species (Three Lone Pairs

of Electrons on A)Molecular Geometry

linear

FH

··

····

3 lone pairs

PolarityHF is a polar molecule.

H

CHH

H

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Tetrahedral Electronic Geometry: ABU3 Species (Three Lone Pairs

of Electrons on A)Valence Bond Theory (Hybridization)

2s 2pF [He]

four sp3 hybrids

tetrahedral

FH

··

····

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3 Some examples of molecules with this geometry

are: PF5, AsF5, PCl5, etc.

These molecules are examples of central atoms with five bonding pairs of electrons.The electronic and molecular geometries are the same.

Molecules are trigonal bipyramidal and nonpolar when all five substituents are the same.If the five substituents are not the same polarpolar

molecules can result, AsF4Cl is an example.

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3Electronic Structures

As··

...

F···· .··

Lewis Formulas

4s 4pAs [Ar] 3d10

2s 2p F [He]

As··

...

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3Dot Formula

··

As

F

F

FF

F

··

··

····

····

···· ····

····

··

··

··

··

··

·· ··trigonal bipyramidal

As

··

··

······

Electronic Geometry

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3Molecular Geometry

trigonal bipyramid

AsF

F

F

F

F

··

··

··

···· ··

··

··

····

··

····

···· bondspolar ry ve

4.0 2.1 ativitiesElectroneg F- As

1.9

Polarity

symmetric dipoles cancel nonpolar molecule

AsF

F

F

F

F

··

··

··

···· ··

··

··

····

··

····

····

H

CHH

H

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3Valence Bond Theory (Hybridization)

4s 4p 4dAs [Ar] 3d10

five sp3 d hybrids 4d

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3 If lone pairs are incorporated into the trigonal

bipyramidal structure, there are three possible new shapes.

1. One lone pair - Seesaw shape2. Two lone pairs - T-shape3. Three lone pairs – linear

The lone pairs occupy equatorial positions because they are 120o from two bonding pairs and 90o from the other two bonding pairs.

– Results in decreased repulsions compared to lone pair in axial position.

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3 AB4U molecules have:

1. trigonal bipyramid electronic geometry 2. seesaw shaped molecular geometry 3. and are polar

One example of an AB4U molecule is

SF4

Hybridization of S atom is sp3d.

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3Molecular Geometry

H

CHH

H

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3 AB3U2 molecules have:

1. trigonal bipyramid electronic geometry 2. T-shaped molecular geometry 3. and are polar

One example of an AB3U2 molecule is IF3

Hybridization of I atom is sp3d.

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3Molecular Geometry

H

CHH

H

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3 AB2U3 molecules have:

1.trigonal bipyramid electronic geometry 2.linear molecular geometry 3.and are nonpolar

One example of an AB3U2 molecule is XeF2

Hybridization of Xe atom is sp3d.

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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,

and AB2U3Molecular Geometry

H

CHH

H

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

Some examples of molecules with this geometry are: SF6, SeF6, SCl6, etc.

These molecules are examples of central atoms with six bonding pairs of electrons.

Molecules are octahedraloctahedral and nonpolar nonpolar when all six substituents are the same.If the six substituents are not the same polarpolar

molecules can result, SF5Cl is an example.

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

Electronic Structures

··F·· .··

·· Se·· ..

Lewis Formulas

4s 4pSe [Ar] 3d10

2s 2p F [He]

·· Se·· ..

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

Molecular Geometry

octahedral

SeF

F

FF

FF

bondspolar ery v

4.0 2.4 ativitiesElectronegF - Se

1.6

Polarity

symmetric dipoles cancel nonpolar molecule

SeF

FF

F

FF

H

CHH

HH

CHH

H

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

Valence Bond Theory (Hybridization)

4s 4p 4dSe [Ar] 3d10

six sp3 d2 hybrids 4d

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

If lone pairs are incorporated into the octahedral structure, there are two possible new shapes.

1. One lone pair - square pyramidal2. Two lone pairs - square planar

The lone pairs occupy axial positions because they are 90o from four bonding pairs.

– Results in decreased repulsions compared to lone pairs in equatorial positions.

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

AB5U molecules have:1.octahedral electronic geometry 2.Square pyramidal molecular geometry 3.and are polar.

One example of an AB4U molecule is IF5

Hybridization of I atom is sp3d2.

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

Molecular Geometry

H

CHH

H

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

AB4U2 molecules have:1.octahedral electronic geometry 2.square planar molecular geometry 3.and are nonpolar.

One example of an AB4U2 molecule is XeF4

Hybridization of Xe atom is sp3d2.

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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2

Molecular Geometry Polarity

H

CHH

H

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Compounds Containing Double Bonds

Ethene or ethylene, C2H4, is the simplest organic compound containing a double bond.

Lewis dot formulaN = 2(8) + 4(2) = 24A = 2(4) + 4(1) = 12 S = 12

Compound must have a double bond to obey octet rule.

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Compounds Containing Double Bonds

Lewis Dot Formula

CCH

HH

HC C

H

H

H

H····

·· ·· ··

··orC C

H

H

H

H····

·· ·· ··

··

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Compounds Containing Double Bonds

VSEPR Theory suggests that the C atoms are at center of trigonal planes.

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Compounds Containing Double Bonds

VSEPR Theory suggests that the C atoms are at center of trigonal planes.

C C

H

HH

H

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Compounds Containing Double Bonds

Valence Bond Theory (Hybridization)C atom has four electrons.

Three electrons from each C atom are in sp2 hybrids.One electron in each C atom remains in an unhybridized p orbital

2s 2p three sp2 hybrids 2pC

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Compounds Containing Double Bonds

An sp2 hybridized C atom has this shape.Remember there will be one electron in each of the

three lobes.

Top view of an sp2 hybrid

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Compounds Containing Double Bonds

The single 2p orbital is perpendicular to the trigonal planar sp2 lobes.The fourth electron is in the p orbital.

Side view of sp2 hybrid with p orbital included.

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Compounds Containing Double Bonds

Two sp2 hybridized C atoms plus p orbitals in proper orientation to form C=C double bond.

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Compounds Containing Double Bonds

The portion of the double bond formed from the head-on overlap of the sp2 hybrids is designated as a bond.

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Compounds Containing Double Bonds

The other portion of the double bond, resulting from the side-on overlap of the p orbitals, is designated as a bond.

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Compounds Containing Double Bonds

Thus a C=C bond looks like this and is made of two parts, one and one bond.

H

CHH

H

H

CHH

H

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Compounds Containing Triple Bonds

Ethyne or acetylene, C2H2, is the simplest triple bond containing organic compound.

Lewis Dot FormulaN = 2(8) + 2(2) = 20A = 2(4) + 2(1) =10S = 10

Compound must have a triple bond to obey octet rule.

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Compounds Containing Triple Bonds

Lewis Dot Formula

C C HHCH HC·· ·· ···· ·· orCH HC·· ·· ···· ··

VSEPR Theory suggests regions of high electron density are 180o apart.

H C C H

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Compounds Containing Triple Bonds

Valence Bond Theory (Hybridization)Carbon has 4 electrons.Two of the electrons are in sp hybrids.Two electrons remain in unhybridized p

orbitals.2s 2p two sp hybrids 2p

C [He]

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Compounds Containing Triple Bonds

A bond results from the head-on overlap of two sp hybrid orbitals.

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Compounds Containing Triple Bonds

The unhybridized p orbitals form two bonds. Note that a triple bond consists of one and

two bonds.

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Compounds Containing Triple Bonds

The final result is a bond that looks like this.

H

CHH

H

H

CHH

H

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Summary of Electronic & Molecular Geometries

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Synthesis Question The basic shapes that we have discussed in Chapter

8 are present in essentially all molecules. Shown below is the chemical structure of vitamin B6 phosphate. What is the shape and hybridization of each of the indicated atoms in vitamin B6 phosphate?

N+

H

CH3

OH

COH

CH2

OP

O

O

O

12

4

5

3

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Synthesis Questiontrigonal planar sp2

bent or angular sp3

tetrahedral sp3

trigonal planar sp2

trigonal planar sp2

N+

H

CH3

OH

COH

CH2

OP

O

O

O

1

2

4

5

3

Page 101: Chapter 08

101

Group Question Shown below is the structure of penicillin-G.

What is the shape and hybridization of each of the indicated atoms in penicillin-G?

CHC N

CH S

CHC

CH3

CH3

OHO

O

NHO

CH2CCC

CC C

HH

H

HH

1

23 4

5 6

7

8910

Page 102: Chapter 08

102

End of Chapter 8 This is a difficult

chapter. Essential to your

understanding of chemistry!