Physical Chemistry Third Edition

21.4 Molecules with Multiple Bonds 879

Solution

The VSEPR theory predicts C–C–H bond angles of 120◦, approximately equal to the

experimental bond angles of 122◦. We place the molecule in thexyplane with the dou-

ble bond on thexaxis. We rotate the axes for one carbon by 180◦to make the orbital regions

of two of the 2sp^2 hybrids on the two carbons point toward each other and overlap. We

construct a C–C sigma bonding orbital from these two 2sp^2 hybrid orbitals and denote it by

1 σ. We construct a C–H bonding orbital from each of the other 2sp^2 hybrids and a hydrogen

1 sorbital, placing the hydrogen atoms in thexyplane with 120◦bond angles. Denote these

bonding orbitals byσA,σB,σC, andσD. The second C–C bonding orbital is a linear combi-

nation of the two unhybridized 2pzorbitals and is a pi orbital. Denote this orbital by 1π. The

molecule must be planar for the two unhybridized 2pzorbitals to have maximum overlap.

The electron configuration of the molecule in the ground-state is

(1sA)^2 (1sB)^2 (1σ)^2 (1π)^2 (σA)^2 (σB)^2 (σC)^2 (σD)^2

Since the nuclei must be placed on the symmetry axes of the hybrid orbitals to have good

overlap, the C–C–H bond angles equal 120◦, in agreement with the VSEPR prediction. The

double bond consists of a sigma bond and a pi bond.

Exercise 21.6

Describe the bonding in diatomic carbon using hybrid orbitals like those used in ethene. Do you

think this description would be superior to that in Section 20.3?

We now model a carbon–carbon triple bond as a sigma bond and two pi bonds.

EXAMPLE21.5

Describe the bonding in ethyne (acetylene), C 2 H 2 , which has the Lewis dot structure:

H:C:::C:H

The molecule is experimentally found to be linear at each carbon in its equilibrium

conformation.

Solution

Assuming the Born–Oppenheimer approximation and the experimental conformation, we

orient the molecule on thezaxis. Acetylene is isoelectronic with N 2 , which also has a triple

bond. In the simple LCAOMO description of N 2 of Chapter 20 we assigned the first eight

electrons to theσg 1 s,σ∗u 1 s,σg 2 s, andσ∗u 2 sorbitals. Only the LCAOMOs made from the

2 porbitals were involved in the bonding. Two electrons were assigned to theσG 2 pzorbital,

two to theπu 2 pxorbital, and two to theπu 2 pyorbital, making a triple bond that consists of

a sigma bond and two pi bonds.

We cannot make a similar description for acetylene. Since the 2porbitals are all involved

in the C–C bonds, there are no orbitals left to form the C–H bonds. A better description is

obtained by constructing two 2sphybrids on each carbon. The orbital regions of the 2sp

hybrids on the same atom point in opposite directions along thezaxis. We form a carbon–

carbon sigma bonding orbital from the two 2sphybrid orbitals that overlap between the carbon

atoms. We call this the 1σbonding orbital. There is also an antibonding orbital, but we will

not need to occupy it. The carbon–carbon pi bonds are constructed from the unhybridized