5.111 Lecture Summary #15
Readings for today: Sections 3.4, 3.5, 3.6 and 3.7 (Sections 3.4, 3.5, 3.6, 3.7, and 3.8 in
3rd ed) – Valence Bond Theory.
Read for Lecture #16: Sections 6.13, 6.15, 6.16, 6.17, 6.18, and 6.20 (Sections 6.14, 6.16,
6.17, 6.18, 6.19, and 6.21 in 3rd ed) – The Enthalpy of Chemical Change.
Assignment: Problem set #5 (due Friday, October 17th at noon)
_______________________________________________________________________________
Topics:
Valence bond theory and hybridization
I. Sigma and pi bonds
II. Hybridization of atomic orbitals
A. sp3 hybridization
B. sp2 hybridization
C. sp hybridization
________________________________________________________________________________
VALENCE BOND THEORY AND HYBRIDIZATION
1s
1s
In valence bond theory, bonds result from the pairing of
unpaired electrons in atomic orbitals.
H
H
I. SIGMA AND PI BONDS
σ (sigma) bond: cylindrically symmetric with ____ nodal plane across the bond axis.
π (pi) bond: a bond with e- density in two lobes, one on each side of the bond axis.
A pi bond has a _______________ nodal plane along the bond axis.
We can describe multiple bonds according to valence-bond theory.
•
single bond: ____________________
•
double bond: one σ-bond plus one ____________________
•
triple bond: one σ-bond plus ___________ π-bonds
1
Applying simple VB theory results in the following prediction for methane bonding:
H
2pz
2pz
2px
2py
2px
+
-
+
H
-
2s
C
C
According to this model, the C is bonded to only two H-atoms with an H-C-H bond
of _______°. This is NOT what is observed for methane!
II. HYBRIDIZATION OF ATOMIC ORBITALS
A. sp3 hybridization
A carbon atom has four unpaired electrons available for bonding once a 2s-electron is
__________________ to an empty 2-p orbital.
E
2pz
2px
2py
e- promotion
2sp3
2sp3
2sp3 2sp3
2s
C
orbitals
(4 valence e-s)
The sp3 hybrid orbitals are equivalent and degenerate. They differ only in their
___________________ in space.
2s
2pz
2px
2py
-
-
-
-
+
-
+
+
-
+
+
-
+
+
+
four sp3 hybrid orbitals
2
In carbon, each sp3 orbital contains a single electron, allowing four bonds.
H
°
sp3
2sp3
C
2sp3 2sp3
2sp3
H
H
H
H
C
What provides the energy for the initial electron promotion?
2sp3 1s
_______________!
σ bond
Each bond is labeled based on the bond type
(σ or π) and atomic orbital composition.
____ (C______, H______)
Consider ethane, C2H6.
109.5°
H
C
C
H
H
H
2sp3
H
2sp3
2sp3 2sp3
2sp3
2sp3
2sp3
H
σ bond
Two bond types in ethane: ____________________ and ____________________ .
Nitrogen: Electron promotion _____________ occur with nitrogen because promotion
would not increase the number of unpaired electrons available for bonding.
E
2pz
sp3
2px
2py
2sp3
2sp3
H
N
(5 valence e-s)
2sp3
2sp3 2sp3
N
2sp3 2sp3
H
2s
2sp3
H
hybrid orbitals
°
N
H
2sp3 1s
σ bond
N-H bond description: ________________
N-atom geometry: ____________________
3
Oxygen: Electron promotion does not occur.
E
sp3
2pz
2px
2py
2sp3
2sp3
2sp3 2sp3
O
2sp3
2sp3 2sp3 2sp3
H
O
H
2s
H
O
hybrid orbitals
(6 valence e-s)
104.5°
H2O geometry: ________________
B. sp2 hybridization
sp2 hybrid orbitals form from the combination of one s-orbital and two p-orbitals.
2pz
2px
2py
-
+
-
-
+
+
-
-
+
+
+
+
2py
+
2s
3 hybrid orbitals
1 p-orbital
Boron: Boron has 3 unpaired electrons available for bonding once a 2s-electron is
promoted to an empty 2-p orbital.
E
2pz
2px
2py
electron promotion
2sp2
2sp2 2sp2
hybrid orbitals
2s
B
(3 valence e-s)
The s-orbital and two of the p-orbitals hybridize to form ______________ sp2 orbitals.
The three sp2-orbitals lie in a ________________ to minimize electron repulsion.
4
H
+
x
2py
2sp2
sp2
2sp2 2sp2
+
+
B
H
σ(
H
z
, H1s)
120°
trigonal planar
Carbon: Carbon can also form sp2 hybrid orbitals.
2s
E
2pz
2px
2py
+
2py
+
2py
2sp2
-
2sp2 2sp2
hybridize
hybrid orbitals
+
2s
C
-
(4 valence e-s)
electron promotion
+
+
+
sp2
-
-
-
2py
2sp2 2sp2
2sp2
x
2py
+
2px
+
+
2pz
-
+
+
2py
trigonal planar
z
120°
Ethylene (C2H4) has a C-C double bond, meaning one _______-bond and 1 _______-bond.
+
+
+ x
z
2py
+
+
+
2py
+
+
z
2py
+
+
looking down the y-axis
σ( _________, __________)
y
looking down the x-axis
π( _________, _________)
5
+
z
+
+ x
H
2py
+
H
+
+
z
H
+
+
H
+
+
H
H
y
In addition to the C-C double bond, there are four C-H bonds: σ( _______, ______)
Note: molecules cannot rotate around a double bond.
Rotation would require breaking the pi bond.
H
H
H
H
Benzene (C6H6)
H
+
C
C
+
+
C
+
C
+
+
+
H
H
___________ σ(C2sp2, C2sp2) bonds
+
H
+
+
+
+
C
+
+
H
+
+
H
+
+
C
C
C
C
+
+
+
+
H
C
+
+
+
+
C
H
+
+
C
H
+
2py
H
+
H
2sp2
+
+
H
___________ π(C2py, C2py) bonds
___________ σ(C2sp2, H1s) bonds
H
H
C
H
C
C
H
H
C
C
C
H
H
H
C
C
C
C
H
C
H
H
C
H
In reality, the 6 pi-electrons are ________________ over all six carbon atoms in the benzene
molecule. Each C-C bond is a ________ bond.
6
C. sp hybridization
sp hybrid orbitals form from the combination of one s-orbital and 1 p-orbital.
E
2pz
2px
2py
2px 2py
2sp 2sp
hybrid orbitals
2s
C
(4 valence e-s)
electron promotion
2pz
2px
2px
2py
+
H
2px
2px
C π(2py) C
H
2px
x
x
z H
+
+
+
+
C
+
C
π(2px)
+
z H
+
H
+
+
+
2py
+
π(2px)
sp
2p
Cy
+
+
-
+
-
-
+
-
+
z H
2py
+
+
-
2s
x
180
σ( ______, _______ )
π( ______, _______ )
π( ______, _______ )
7