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Chapter 11: Bonding II: Additional Aspects 
465 
more effectively in a sigma bond (end-to-end) than they do in a pi bond (side-to-side). 
Second, molecular geometries are more directly obtained in valence-bond theory than in 
Lewis theory. Although valence-bond theory requires the introduction of hybridization to 
explain these geometries, Lewis theory does not predict geometries at all; it simply 
provides the basis from which VSEPR theory predicts geometries. Third, Lewis theory 
does not explain hindered rotation about double bonds. With valence-bond theory, any 
rotation about a double bond involves cleavage of the -bond, which would require the 
input of considerable energy. 
 
2. (E) The overlap of pure atomic orbitals gives bond angles of 90 or 180 . These bond angles 
are suitable only for 3- and 4-atom compounds in which the central atom is an atom of the 
third (or higher) period of the periodic table. For central atoms from the second period of the 
periodic table, 3- and 4-atom compounds have bond angles closer to 180 , 120 , and 109.5 
than to 90 . These other bond angles can only be explained well through hybridization. 
Second, hybridization clearly distinguishes between the (hybrid) orbitals that form bonds 
and the p orbitals that form bonds. It places those p orbitals in their proper orientation so 
that they can overlap side-to-side to form bonds. Third, the bond angles of 90 and 120 
that result when the octet of the central atom is expanded cannot be produced with pure atomic 
orbitals. Hybrid orbitals are necessary. Finally, the overlap of pure atomic orbitals does not 
usually result in all bonds being equivalent. Overlaps with hybrid orbitals produce 
equivalent bonds. 
 
3. (E) 
 (a) Lewis theory does not describe the shape of the water molecule. It does indicate that 
there is a single bond between each H atom and the O atom, and that there are two 
lone pairs attached to the O atom, but it says nothing about molecular shape. 
 
(b) In valence-bond theory using simple atomic orbitals, each H—O bond results from the 
overlap of a 1s orbital on H with a 2p orbital on O. The angle between 2p orbitals is 90 
so this method initially predicts a 90 bond angle. The observed 104 bond angle is 
explained as arising from repulsion between the two slightly positively charged H atoms. 
(c) In VSEPR theory the H O2 molecule is categorized as being of the AX2E2 type, with 
two atoms and two lone pairs attached to the central oxygen atom. The lone pairs 
repel each other more than do the bond pairs, explaining the smaller than 109.5º 
tetrahedral bond angle. 
 
(d) In valence-bond theory using hybrid orbitals, each H—O bond results from the 
overlap of a 1s orbital on H with an sp3 orbital on O. The angle between sp3 orbitals 
is 109.5º. The observed bond angle of 104º is rationalized based on the greater 
repulsion of lone pair electrons when compared to bonding pair electrons. 
 
4. (E) 
 (a) Lewis theory really does not describe the shape of the molecule. It does indicate that 
there is a single bond between each Cl atom and the C atom, but it says nothing 
about molecular shape. 
 
Chapter 11: Bonding II: Additional Aspects 
466 
(b) In valence-bond theory using simple atomic orbitals, each C Cl bond results from 
the overlap of a 3p orbital on Cl with a 2p orbital on C. Since the angle between 2p 
orbitals is 90º, this method initially predicts a 90º bond angle. The observed 109.5º 
bond angle is explained as resulting from the repulsion between the two slightly 
negative Cl atoms. In addition, the molecule is predicted to have the formula CCl2 , 
since there are just two half-filled orbitals in the ground state of C. 
 
(c) In VSEPR theory, the CCl4 molecule is categorized as being of the AX4 type, with 
four atoms tetrahedrally attached to the central carbon atom. 
 
(d) In valence-bond theory, each C Cl bond results from the overlap of a 3p orbital 
on Cl with an sp3 orbital on C. The angle between the sp3 orbitals is 109.5º. 
 
5. (M) Determining hybridization is made easier if we begin with Lewis structures. Only one 
resonance form is drawn for CO SO3
2
2, , and NO2 . 
 
 
 
The C atom is attached to three ligands and no lone pairs and thus is sp2 hybridized 
in
2
3 CO . The S atom is attached to two ligands and one lone pair and thus is sp
2 
hybridized in SO2 . The C atom is attached to four ligands and no lone pairs and thus is 
sp3 hybridized in CCl4. Both the oxygen and the carbon in Co are sp hybridized. The N 
atom is attached to two ligands and one lone pair in NO2
-
 and thus is sp2 hybridized. 
Thus, the central atom is sp2 hybridized in SO2, CO3
2-, and NO2
-
. 
 
6. (M) (a) HI: H I [Kr] 4 10d 5s 5p 
 The 1s orbital of H overlaps the half-filled 5p orbital of I to produce a linear molecule. 
 
(b) BrCl: Br [Ar] 3 10d Cl [Ne] 
The half-filled 3p orbital of Cl overlaps the half-filled 4 p orbital of Br to produce a 
linear molecule. 
 
(c) 2 H Se : H Se [Ar] 3
10d 
Each half-filled 4 p orbital of Se overlaps with a half-filled 1s orbital of a H atom to 
produce a bent molecule, with a bond angle of approximately90 . 
 
(d) OCl2 : O Cl [Ne] 
Each half-filled 2 p orbital of O overlaps with a half-filled 3p orbital of a Cl atom 
to produce a bent molecule, with a bond angle of approximately 90 . 
 
4s 4p 3s 3p
3s 3p2s 2p1s
4s 4p1s
1s
O C O
O
O S O Cl C Cl
Cl
Cl
C O O N O 
 
2-