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25.1: Carbon, A Unique Element

Difficulty Level: At Grade Created by: CK-12
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Lesson Objectives

The student will:

  • describe the hybridization states available to carbon.
  • explain how the hybridization of carbon allows for the formation of large number of compounds containing carbon.
  • describe the three primary allotropes of carbon.


  • allotropes
  • delocalized electrons


Carbon plays a unique role among the chemical elements. You may have heard of life on earth being referred to as “carbon-based.” Although the molecules that make up living creatures also contain large amounts of hydrogen, oxygen, nitrogen, phosphorus, and sulfur, these atoms are all generally stitched together by long carbon chains. Due to its four valence electrons, carbon is the smallest element that is able to make covalent bonds to four different atoms in its neutral form. Because of this, large, heavily branched compounds can be made by stringing together carbon and a few other nonmetallic atoms in various arrangements. The almost limitless number of compounds that can be constructed in this way is the focus of organic chemistry.


Recall from the chapter “Covalent Bonds and Formulas” that s and p atomic orbitals can be combined in various ratios to make a set of hybrid orbitals. During hybridization, the number of orbitals combined to make the hybrids is always equal to the number of orbitals created. Thus, carbon will always have a total of four valence orbitals, regardless of how it is hybridized.

When one s and three p orbitals are combined, it produces a set of four sp3 orbitals (see figure below). These orbitals are all identical to one another, and they point outward from the carbon atom toward the corners of a tetrahedron. Recall from VSEPR theory that when a central atom is bonded to four different atoms, they are arranged into the shape of a tetrahedron. The shapes of the hybrid orbitals used to make these bonds help explain why this arrangement is chosen.

When one s and two p orbitals are combined, a set of three identical sp2 orbitals is created (see below). These orbitals have a trigonal planar arrangement, which is what we would expect from VSEPR theory for a central atom bonded to three other atoms, assuming it has no unshared electron pairs. In addition to the three hybrid orbitals created, the carbon atom will still have one leftover p orbital oriented perpendicular to the other three. This orbital is available for side-by-side overlap with other p orbitals, forming a pi bond.

Lastly, sp orbitals are created by combining one s and one p orbital, leaving two unchanged p orbitals available for pi bonding. The two sp orbitals point in opposite directions, which is again what one would expect by looking at VSEPR theory. The number of different hybridization states available to carbon further amplifies the number of organic (carbon-containing) compounds that can be made.

Allotropes of Carbon

Carbon can exist in at least three different forms based on the arrangement of bonds between the atoms. Although these substances are comprised only of carbon atoms, they have quite different properties. When a pure element exists in multiple forms due to different bonding arrangements, these forms are referred to as allotropes. Note that different phases (solid, liquid, gas) of an element are not considered to be allotropes; a family of allotropes must all be in the same phase. The three primary allotropes of carbon are diamond, graphite, and fullerenes.

The structure of diamond consists exclusively of sp3 hybridized carbon atoms. Each one is bound to four other carbon atoms in a tetrahedral array (see Figure below). This is a very stable structure, because each atom is held in place by four strong sigma bonds. Consequently, diamonds are extremely hard, and the diamond form of carbon has the highest melting point (> \begin{align*}3500^\circ\mathrm{C}\end{align*}) of all known elements. Diamond has the rare property that it is a good conductor of heat but a poor conductor of electricity. Electricity is transmitted by the movement of electrons, and since all the valence electrons of diamond are held tightly in localized sigma bonds, very little electric current can flow through the solid.

Diamond lattice structure

Diamond lattice structure.

Graphite, most commonly encountered as pencil lead, is clearly a very different substance. The reason for the differing properties has to do with how the atoms are bonded to one another. The structure of graphite is shown in Figure below.

Graphite structure with multiple layers

Graphite structure with multiple layers.

The carbon atoms are sp2 hybridized, and each carbon makes a strong sigma bond to three other atoms, forming hexagonal sheets. However, this only accounts for three of carbon’s four valence electrons. The remaining electron is located in the leftover p orbital. This orbital can overlap with the leftover p orbital from all the adjacent carbon atoms, forming pi bonds. Unlike sigma bonds, where the electrons are held tightly between the two nuclei, pi bonds can interact with adjacent pi bonds, allowing the electrons in those bonds to delocalize over all the atoms involved.

Within a sheet of graphite, the carbon atoms are held together by strong sigma bonds. The bond between sheets, however, involves a weaker interaction between the delocalized pi systems of two adjacent sheets. Because of the delocalization, a carbon from one sheet is not rigidly attached to any single carbon from an adjacent sheet, which allows the sheets to slide around freely. For this reason, graphite can be used as a lubricant. When you write with a pencil, the marks left on the paper are sheets of graphite that have slipped all the way off the carbon rod.

Unlike diamond and graphite, which are covalent networks that can extend indefinitely, fullerenes often have a fixed size, forming what are essentially individual molecules made only of carbon. The first fullerene to be discovered was buckminsterfullerene, \begin{align*}\mathrm{C}_{60}\end{align*}, often referred to as a buckyball (see Figure below).

Buckyball structure (left) compared to soccer ball (right).

This allotrope of carbon was not even isolated until 1985, although its possible existence had been postulated in the mid-20th century. A great deal of current research in medicinal chemistry and material science is devoted to the study of this relatively new class of compounds. Examples include carbon nanotubes (fullerenes that fold into a tube instead of a sphere) and superconducting metal-fullerene complexes.

Lesson Summary

  • Hybridization is the process of combining atomic orbitals from different subshells to create a new set of orbitals that are all identical to one another. The electrons in these orbitals have equal energy and can all form identical covalent bonds.
  • Electrons located in p orbitals that are not used during hybridization are available for side-by-side (pi) bonding.
  • Allotropes are the different forms that can be taken by a pure element. Each allotrope is a unique substance with its own chemical properties.
  • The differences between allotropes stem from the different bonding arrangements available to those atoms.
  • The three primary allotropes of carbon are diamond, graphite, and fullerenes.

Further Reading / Supplemental Links

The learner.org website allows users to view streaming videos of the Annenberg series of chemistry videos. You are required to register before you can watch the videos but there is no charge. The website has one video that relates to this lesson called “Carbon.”

Review Questions

  1. Carbon is considered to be unique in the periodic table. What property of the carbon atom makes it unique?
  2. What is the difference between \begin{align*}sp\end{align*}, \begin{align*}sp^2\end{align*}, and \begin{align*}sp^3\end{align*} hybridization?
  3. Which of the following are allotropes of carbon?
    1. diamond
    2. buckminsterfullerene
    3. graphite
    4. all of the above
  4. What is the hybridization of the carbon atoms in each of the following molecules:
    1. \begin{align*}sp\end{align*}
    2. \begin{align*}sp^2\end{align*}
    3. \begin{align*}sp^3\end{align*}
    4. \begin{align*}dsp^3\end{align*}

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