Daniel L. Reger Scott R. Goode David W. Ball

http://academic.cengage.com/chemistry/reger

Chapter 10 Molecular Structure and Bonding Theories

VSEPR

Valence-Shell Electron-Pair Repulsion Model

(VSEPR) predicts shape from Lewis Structures.

•

VSEPR Rule 1

: A molecule has a shape that minimizes electrostatic repulsions between valence-shell electron pairs. • Minimum repulsion results when the electron pairs are as far apart as possible.

Steric Number •

Steric number

= (number of lone pairs on central atom) + (number of atoms bonded to central atom) • The steric number is determined from the Lewis structure.

• Steric number determines the

bonded-atom lone-pair arrangement

, the shape that maximizes the distances between the valence-shell electron pairs.

Geometric Arrangements

Geometric Arrangements

Steric Number = 2 • In the Lewis structure of BeCl 2 ,

Cl Be Cl

beryllium has two bonded atoms and no lone pairs, steric number = 2 .

• A linear geometry places the two pairs of electrons on the central beryllium atom as far apart as possible.

• • • Molecules with Multiple Bonds The Lewis structure of HCN (H-C  N:) shows that the carbon atom is bonded to two atoms and has no lone pairs, steric number = 2 .

The bonded-atom lone-pair arrangement is linear . The number of bonded atoms, not the number of bonds, determines the steric number.

Steric Number = 3 • The Lewis structure of BF 3

F B F F

shows the boron atom has a steric number = 3 ; the bonded-atom lone-pair arrangement is trigonal planar .

Steric Number = 4 • The Lewis structure of CH 4

H H C H H

shows the carbon atom has a steric number = 4 tetrahedral .

; the bonded-atom lone pair arrangement is

Steric Number = 5 • The phosphorus atom in PF 5 has a steric number = 5; the bonded atom lone-pair arrangement is trigonal bipyramidal .

Steric Number = 6 • The sulfur atom in SF 6 has a steric number = 6 ; the bonded-atom lone-pair arrangement is octahedral .

Central Atoms with Lone Pairs • The Lewis structure of H 2 O is

H O H

• • Steric number = 4 , 2 bonded atoms and 2 lone pairs.

The bonded-atom lone-pair arrangement is tetrahedral .

Molecular Shape of H 2 O • •

Molecular shape

is the arrangement of the

atoms

in a species.

The bonded-atom lone pair arrangement of H 2 O is tetrahedral (top); the molecular shape is bent or V-shaped (bottom).

Molecular Shape of NH 3 • What is the electron pair geometry and molecular shape of NH 3 ?

• • Electron Pair Repulsions The measured bond angle in H 2 O (104.5

o ) is smaller than the predicted angle (109.5

o ) Explanation: repulsions vary

lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair

Location of Lone Pair in SF 4

Two structures are possible:

• The favored structure for a trigonal bipyramid minimizes 90 o lone pair interactions – the one on the right.

Lone Pairs in Trigonal Bipyramids • Lone pairs always occupy the equatorial positions in a trigonal bipyramid so that lone pair-lone pair repulsions are oriented at 120 o .

Location of Lone Pairs in XeF 4 • The structure on right has no 90 o lone pair-lone pair interactions and is favored.

Test Your Skill

• What is the steric number, the bonded atom lone-pair arrangement, and the molecular shape of ClF 3 ?

Multiple Central Atoms • • The geometry of each central atom is determined separately.

The C H 3 carbon in C H 3 CN has tetrahedral geometry and the other carbon has linear geometry.

Shapes of Molecules • What are the bonded-atom lone-pair arrangements and the shapes about each central atom in NH 2 SH?

• Draw the Lewis structure.

H H N S H

• The bonded-atom lone-pair arrangements of both are tetrahedral, the nitrogen shape is trigonal pyramidal and sulfur is “V” shaped.

Overall Shape of C 2 H 4 • Ethylene, C 2 H 4 , could be planar (left) or nonplanar (right). The VSEPR model does not predict which is preferred.

Polarity of Molecules • The bond dipoles in CO 2 cancel because the linear shape orients the equal magnitude bond dipoles in exactly opposite directions.

• Polarity of Molecules The bond dipoles do not cancel in COSe; they are oriented in the same direction and are of unequal length. They do not cancel in OF 2 because the V-shape of the molecule does not orient them in opposite directions.

• Polarity of Molecules The bond dipoles in BCl 3 and CCl 4 cancel because of the regular shape and equal magnitude.

• Polarity of Molecules The bond dipoles in BCl 2 F and CHCl 3 not cancel because they are not of the do same magnitude.

Test Your Skill

• Are the following molecules polar or nonpolar: H 2 S, SiF 4 , CH 2 Cl 2 ?

Valence Bond Theory • Valence bond theory describes bonds as being formed by overlap of partially filled valence orbitals.

Test Your Skill

• Identify the orbitals that form the bond in HCl.

• Bonding in NH 3 The observed bond angles of 107.5

o in NH 3 90 o are not consistent with the angles of expected if the bonds formed from N 2

p

orbitals.

Hybrid Orbitals •

Hybrid orbitals

are orbitals obtained by mixing two or more atomic orbitals on the same central atom.

• Appropriate hybrid orbitals formed by mixing one

s

and x

p

atomic orbitals make bonds at either 180 o (x = 1), 120 o (x = 2), or 109.5

o (x = 3).

Analogy for Hybrid Orbitals

sp

Hybrid Orbitals

Shape of Hybrid Orbitals • For clarity, hybrid orbitals are pictured as elongated with the small lobe omitted.

Bonding in BeCl 2 • The bonds in BeCl 2 overlap of two

sp

arise from the hybrid orbitals on the beryllium atom with the 3

p

orbitals on the two chlorine atoms.

sp

2 Hybrid Orbitals

Bonding in BF 3 • The bonds in BF 3 of three

sp

2 arise from the overlap hybrid orbitals on the boron atom with 2

p

orbitals on the three fluorine atoms.

sp

3 Hybrid Orbitals

• Bonding in CH 4 The bonds in CH 4 of four

sp

3 arise from the overlap hybrid orbitals on the carbon atom with 1

s

orbitals on the four hydrogen atoms.

Lone Pairs and Hybrid Orbitals • Hybrid orbitals can hold lone pairs as well as make bonds.

Hybridization with

d

Orbitals • Hybrid orbitals of central atoms with steric numbers of 5 or 6 involve

d

orbitals.

Hybrid Orbitals

Steric Number

2 3 4 5 6

Electron pair geometry

linear trigonal planar tetrahedral trigonal bipyramid octahedral

Hybridization

sp sp sp sp sp

3 3 2 3

d d

2

Test Your Skill

• Identify the hybrid orbitals on the central atoms in SiH 4 and HCN.

Types of Bonds: Sigma Bonds • Sigma bonds shared pair of ( s ): the electrons is symmetric about the line joining the two nuclei of the bonded atoms.

• • Bonding in C 2 H 4 The C-C sigma bond in C 2 H 4 arises from overlap of

sp 2

hybrid orbitals and the four C-H sigma bonds from overlap

sp 2

hybrid orbitals on C with 1

s

orbitals on H.

The second C-C bond forms from sideways overlap of

p

orbitals.

Types of Bonds: Pi Bonds •

Pi bonds (

p

)

places electron density above and below the line joining the bonded atoms – they form by sideways overlap of

p

orbitals.

Bonding in C 2 H 4 • The double bond in C 2 H 4 is one sigma bond and one pi bond – each bond is of similar strength.

Proof of Pi Bonds: Shape of C 2 H 4 • C 2 H 4 is planar (

A

) because pi overlap is at a maximum. Rotation of one end by 90 o (

B

) reduces pi overlap to zero.

Triple Bonds • The triple bond in C 2 H 2 is one sigma bond and two pi bonds between the

sp

hybridized carbon atoms.

Sigma Bonds in Benzene • Each carbon atom in benzene, C 6 H 6 , forms three sigma bonds with

sp

2 hybrid orbitals.

Pi Bonds in Benzene • The remaining

p

orbital on each carbon atom (top) overlap to form three pi bonds.

Test Your Skill

• Describe the bonds made by the carbon atom in HCN.

Molecular Orbital Theory • •

Molecular orbital theory

is a model that combines atomic orbitals to form new

molecular orbitals

that are shared over the entire molecule.

• A

bonding molecular orbital

concentrates electron density between atoms in a molecule.

An

antibonding molecular orbital

electron density between atoms in a molecule.

reduces

Hydrogen Molecule • Addition of the 1

s

orbitals of two H atoms forms a sigma bonding molecular orbital and subtraction forms a sigma antibonding molecular orbital, indicated with a * symbol.

Molecular Orbital Diagram: H 2 • Bonding molecular orbitals are more stable and antibonding molecular orbitals are less stable than the atomic orbital that are combined.

Bond Order •

Bond order

= 1/2 [number of electrons in bonding orbital - number of electrons in antibonding orbitals] • Bond order in H 2 = 1/2 [2 - 0] = 1

Molecular Orbital Diagram: He 2 • Bond order in He 2 = 1/2 [2 - 2] = 0; the molecule does not form.

Sigma Molecular Orbitals from

p

Pi Molecular Orbitals from

p

MO Diagram Second-Period Diatomics

Molecular Orbital Diagram: N 2 • The electron configuration is ( s 2

s

) 2 ( s * 2

s

) 2 ( p 2

p

) 4 ( s 2

p

) 2 .

• • The bond order in N 2 is three and there are no unpaired electrons. Lewis theory (:N  N:) predicts the same result.

Molecular Orbital Diagram: Be 2 • The electron configuration is ( s 2

s

) 2 ( s * 2

s

) 2 . • Bond order in Be 2 is zero and the molecule does not exist.

Molecular Orbital Diagram for O 2 • Draw the molecular orbital diagram of O 2 . What is the electron configuration, the bond order and how many unpaired electrons are present?

Test Your Skill

• Draw the molecular orbital diagram of B 2 . What is the electron configuration, the bond order and number of unpaired electrons?