EXPERIMENT 8. SPARTAN LAB #1. BOND LENGTHS AND
HYBRIDIZATION
Introduction
is surrounded by four atoms in a roughly tetrahedral geEometry, while each carbonin ethane
in ethylene is surrounded by three atoms in a trigonal-planar
ACH OF THE CARBONS
geometry and each carbon in acetylene by two atoms in a linear geometry. These structures
can be rationalized by suggesting that the valence 2s and 2p orbitals of carbon are able to “combine” either to produce four equivalent “sp3 hybrids” directed toward the four corners of a tetrahedron, or three equivalent “sp2 hybrids” directed toward the corners of an equilateral
triangle, or two equivalent “sp hybrids” directed along a line.
C
four sp3 hybrids
C
three sp2 hybrids
C
two sp hybrids
In the first instance, no atomic orbitals remain, while in the second instance, a 2p atomic orbital, directed perpendicular to the plane made by the three sp2 hybrids, remains and in the
third instance, a pair of 2p atomic orbitals, directed perpendicular to the line of the two sp hybrids and perpendicular to each other, remain. Thus, the “bonding” in ethane is described by
four sp3 hybrids, that in ethylene by three sp2 hybrids and a p orbital and that in acetylene by
two sp hybrids and two p orbitals.
2p atomic orbitals are higher in energy and extend further from carbon than the 2s orbital. The
higher the “fraction of 2p” in the hybrid, the more it will extend. Therefore, sp3 hybrids will
extend further than sp2 hybrids, which in turn will extend further than sp hybrids. As a consequence, bonds made with sp3 hybrids should be longer than those made with sp2 hybrids, which
should in turn be longer than bonds made with sp hybrids. In this activity, you will first test
such an hypothesis and explore its generality. Finally, you will search for a molecule with a very
short carbon-carbon single bond.
Procedure
1.! Build ethane, ethylene, and acetylene and put into a single document. Obtain
HF/3-21G equilibrium geometries for all three molecules. Is the ordering in CH bond
lengths what you expect on the basis of the hybridization arguments presented above?
Using the CH bond length in ethane as a standard, what is the % reduction in CH
bond lengths in ethylene? In acetylene? Is there a rough correlation between % reduction in bond length and % of 2p in the hybrid?
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2.! Obtain the HF/3-21G equilibrium geometry for cyclopropane and measure the CH
bond length. Based on your experience in the previous part, would you say that the
carbons are sp3 hybridized? Elaborate.
3.! Based on the assignments given on page 5, build all molecules in the set and again obtain HF/3-21G equilibrium geometries. When completed, measure the C–C (C–F or
C–Cl) bond lengths.
Is the ordering of bond lengths the same as that observed for the CH bond lengths in
ethane, ethylene and acetylene? Are the % reductions in bond lengths from the appropriate standards (propane, fluoroethane and chloroethane) similar (within 5 percentage points) to those seen for ethylene and acetylene (relative to ethane)?
4.! How short can a carbon-carbon single bond be? Propose one or more “shortest bond”
candidates and perform HF/3-21G calculations. (You might find several of your “candidates” in the database of HF/3-21G calculations supplied with Spartan. Look for the
molecule name at the bottom of the screen.) Is your shortest carbon-carbon single
bond shorter or longer than the typical carbon-carbon double bond?
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Data Sheets and Questions
Part 1.
Molecule
H
H
C
C
H
H
H
H
C
H
C
H
H
HF/3-21G C—H bond length / Å
H
H
C
C
H
Q1.
Is the ordering in CH bond lengths what you would expect on the basis of the hybridization arguments presented in the lab manual? Explain.
Q2.
Calculate the % reduction in bond lengths in ethylene and acetylene compared to ethane.
Molecule
% 2p in hybrid
ethane
ethylene
acetylene
Q3.
% Reduction in C—H
bond length
0
Is there a correlation between % 2p in hybrid and the % reduction in C—H bond length?
Explain.
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Part 2.
Molecule
H
Q1.
C
H
HF/3-21G C—H bond length / Å
Based on your experience in Part 1, would you say that the carbons are sp3 hybridized?
Elaborate.
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Part 3.
Name
Ethan
Jacob
Alex
Jordan
Jon
David
Connor
Set
alkane
fluoroalkane
fluoroalkane
chloroalkane
alkane
fluoroalkane chloroalkane
Sets
Alkane: propane, propene, propyne
Fluoroalkane: fluoroethane, fluoroethylene, fluoroacetylene
Chloroalkane: chloroethane, chloroethylene, chloroacetylene
C—C (alkane)
C—F (fluoroalkane)
C—Cl (chloroalkane)
Molecule
HF/3-21G bond length / Å
Q1.
Is the ordering of bond lengths the same as observed for the C—H bond lengths in
Part 1?
Q2.
Are the % reductions in bond lengths compared to the first molecule in each set similar
(within 5 percentage points) to those seen for ethylene and acetylene (relative to ethane)?
Molecule
% Reduction in bond length
0
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Part 4.
Q1.
How short can a carbon–carbon single bond be? Propose three “shortest bond” candidates and perform HF/3-21G calculations. (Please: do not get too creative with the laws
of chemical valence! No Texas carbons, etc.)
Candidates:
1.
2.
3.
C—C bond length / Å for candidate:
1.
Q2.
2.
3.
Is your shortest carbon-carbon single bond shorter or longer than the typical carbon–
carbon double bond?
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Pre-Lab Questions
Q1.
Read Spartan Essay 2: “Theoretical Models.” Write a short summary of the Hartree-Fock
Molecular Orbital model.
Q2.
In this lab, we will use a 3-21G basis set. Read sections 11-1 through 11-3 of McQuarrie
and Simon’s textbook and give a short explanation of this basis set. What would it mean
if we used a 3-21G* basis set instead?
Q3.
Using the valence-bond and hybrid-orbital approach, explain the bonding in ethane and
ethylene. Your explanation should be at a level consistent with chapter 10 of our General
Chemistry textbook: Raymond Chang, General Chemistry: The Essential Concepts.
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