Sigma and Pi Bonds
Ck12 Science
Say Thanks to the Authors
Click http://www.ck12.org/saythanks
(No sign in required)
To access a customizable version of this book, as well as other
interactive content, visit www.ck12.org
CK-12 Foundation is a non-profit organization with a mission to
reduce the cost of textbook materials for the K-12 market both
in the U.S. and worldwide. Using an open-content, web-based
collaborative model termed the FlexBook®, CK-12 intends to
pioneer the generation and distribution of high-quality educational
content that will serve both as core text as well as provide an
adaptive environment for learning, powered through the FlexBook
Platform®.
Copyright © 2013 CK-12 Foundation, www.ck12.org
The names “CK-12” and “CK12” and associated logos and the
terms “FlexBook®” and “FlexBook Platform®” (collectively
“CK-12 Marks”) are trademarks and service marks of CK-12
Foundation and are protected by federal, state, and international
laws.
Any form of reproduction of this book in any format or medium,
in whole or in sections must include the referral attribution link
http://www.ck12.org/saythanks (placed in a visible location) in
addition to the following terms.
Except as otherwise noted, all CK-12 Content (including CK-12
Curriculum Material) is made available to Users in accordance
with the Creative Commons Attribution-Non-Commercial 3.0
Unported (CC BY-NC 3.0) License (http://creativecommons.org/
licenses/by-nc/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporated
herein by this reference.
Complete terms can be found at http://www.ck12.org/terms.
Printed: November 13, 2013
AUTHOR
Ck12 Science
www.ck12.org
C ONCEPT
Concept 1. Sigma and Pi Bonds
1
Sigma and Pi Bonds
• Define sigma and pi bonds.
• Describe hybridization of electrons in sigma and pi bonds.
How many people do you think are squeezed on this street?
Our minds can handle two electrons interacting with one another in a sphere of space. But then we start putting in
double bonds and triple bonds. The way we draw these bonds on paper suggests we are squeezing more electrons
into the same space, and that doesn’t work. Electrons don’t like to be pushed together (especially since they all have
negative charges that repel one another). So we need a more complex picture that works for all these electrons.
Sigma and Pi Bonds
The hybridization model helps explain molecules with double or triple bonds. Ethene (C2 H4 ) contains a double covalent bond between the two carbon atoms and single bonds between the carbon atoms and the hydrogen atoms. The
entire molecule is planar.
As can be seen in the diagram above, the electron domain geometry around each carbon independently is trigonal
planar. This corresponds to sp2 hybridization. Previously, we saw carbon undergo sp3 hybridization in a CH4
molecule, so the electron promotion is the same for ethene, but the hybridization occurs only between the single s
orbital and two of the three p orbitals. Thus generates a set of three sp2 hybrids along with an unhybridized 2pz
orbital. Each contains one electron and so is capable of forming a covalent bond.
The three sp2 hybrid orbitals lie in one plane, while the unhybridized 2pz orbital is oriented perpendicular to that
plane. The bonding in C2 H4 is explained as follows. One of the three sp2 hybrids forms a bond by overlapping
with the identical hybrid orbital on the other carbon atom. The remaining two hybrid orbitals form bonds by
1
www.ck12.org
FIGURE 1.1
Geometry of ethene molecule.
FIGURE 1.2
Hybridization in ethene.
overlapping with the 1s orbital of a hydrogen atom. Finally, the 2pz orbitals on each carbon atom form another bond
by overlapping with one another sideways.
It is necessary to distinguish between the two types of covalent bonds in a C2 H4 molecule. A sigma bond (σ
bond) is a bond formed by the overlap of orbitals in an end-to-end fashion, with the electron density concentrated
between the nuclei of the bonding atoms. A pi bond (π bond) is a bond formed by the overlap of orbitals in a
side-by-side fashion with the electron density concentrated above and below the plane of the nuclei of the bonding
atoms. The Figure 1.3 shows the two types of bonding in C2 H4 . The sp2 hybrid orbitals are purple and the pz
orbital is blue. Three sigma bonds are formed from each carbon atom for a total of six sigma bonds total in the
molecule. The pi bond is the “second” bond of the double bonds between the carbon atoms and is shown as an
elongated green lobe that extends both above and below the plane of the molecule. This plane contains the six
atoms and all of the sigma bonds.
FIGURE 1.3
Sigma and pi bonds.
In a conventional Lewis electron-dot structure, a double bond is shown as a double dash between the atoms as in
2
www.ck12.org
Concept 1. Sigma and Pi Bonds
C=C. It is important to realize, however, that the two bonds are different: one is a sigma bond, while the other is a
pi bond.
Ethyne (C2 H2 ) is a linear molecule with a triple bond between the two carbon atoms. The hybridization is therefore
sp.
FIGURE 1.4
Ethyne structure.
The promotion of an electron in the carbon atom occurs in the same way. However, the hybridization now involves
only the 2s orbital and the 2px orbital, leaving the 2py and the 2pz orbitals unhybridized.
FIGURE 1.5
Hybridization in ethyne.
The sp hybrid orbitals form a sigma bond between each other as well as sigma bonds to the hydrogen atoms. Both
the py and the pz orbitals on each carbon atom form pi bonds between each other. As with ethene, these side-toside overlaps are above and below the plane of the molecule. The orientation of the two pi bonds is that they are
perpendicular to one another (see Figure 1.6). One pi bond is above and below the line of the molecule as shown,
while the other is in front of and behind the page.
FIGURE 1.6
The C2 H2 molecule contains a triple bond
between the two carbon atoms, one of
which is a sigma bond, and two of which
are pi bonds.
In general, single bonds between atoms are always sigma bonds. Double bonds are comprised of one sigma and one
pi bond. Triple bonds are comprised of one sigma bond and two pi bonds.
Summary
• Sigma bonds form between two atoms.
• Pi bonds form from p orbital overlap.
Practice
Use the link below to answer the following questions:
3
www.ck12.org
https://sites.google.com/site/ed350201003/Task
1.
2.
3.
4.
What kind of overlap makes a sigma bond?
What kind of overlap makes a pi bond?
Can a sigma bond be formed by overlapping an s and a p orbital?
In methane, which carbon electrons are not involved in bonding?
Review
1.
2.
3.
4.
What is the hybridization around each carbon in ethene?
What are the two bonds in C=C?
What is the shape of the ethene molecule?
How are the ethyne pi bonds oriented in relation to each other?
• pi bond (π bond): A bond formed by the overlap of orbitals in a side-by-side fashion with the electron density
concentrated above and below the plane of the nuclei of the bonding atoms.
• sigma bond (σ bond): A bond formed by the overlap of orbitals in an end-to-end fashion, with the electron
density concentrated between the nuclei of the bonding atoms.
References
1. Courtesy of the Brown Brothers, NY Times. http://commons.wikimedia.org/wiki/File:Crowd_gathers_for_updates_to_1920_World_Series.JPG. Public Domain
2. Ben Mills (Wikimedia: Benjah-bmm27). http://commons.wikimedia.org/wiki/File:Ethylene-CRC-MW-dimen
sions-2D.png. Public Domain
3. CK-12 Foundation - Joy Sheng. . CC-BY-NC-SA 3.0
4. CK-12 Foundation - Zachary Wilson. . CC-BY-NC-SA 3.0
5. CK-12 Foundation - Joy Sheng. . CC-BY-NC-SA 3.0
6. CK-12 Foundation - Joy Sheng. . CC-BY-NC-SA 3.0
7. CK-12 Foundation - Zachary Wilson, using 3D molecular structure by Ben Mills (Wikimedia: Benjahbmm27). 3D model: http://commons.wikimedia.org/wiki/File:Acetylene-CRC-IR-3D-vdW.png. CC-BYNC-SA 3.0 (3D molecule available under the public domain)
4