# How many sigma and pi bonds are in benzene?

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8
Sep 4, 2016

I count:

• $\boldsymbol{6} \times \left(s {p}^{2}\right)$ $\text{C"-"C}$ sigma ($\sigma$) bonds
• $\boldsymbol{6} \times \left(s {p}^{2}\right)$ $\text{C"-"H}$ sigma ($\sigma$) bonds
• $\boldsymbol{3} \times \left(s {p}^{2}\right)$ $\text{C"="C}$ pi ($\pi$) bonds

Benzene is an aromatic compound, one of whose major resonance structures is depicted like so:

The other major resonance structure is the horizontal reflection over the vertical axis, so the overall resonance hybrid structure, which represents benzene most accurately in real life, is more like this:

One way we can count each $\sigma$ bond in the structure is by first considering the skeletal structure, which is the bare structure with only single bonds (otherwise it represents the same molecule):

(all implicit hydrogens are shown. There are no other implicit hydrogens in the full structure.)

From this, recall that one single bond contains one sigma bond. The sigma ($\sigma$) bonds are simply the number of single bonds shown here:

• $6 \times \left(s {p}^{2}\right)$ $\text{C"-"C}$ sigma ($\sigma$) bonds
• $6 \times \left(s {p}^{2}\right)$ $\text{C"-"H}$ sigma ($\sigma$) bonds

Then, when we incorporate the additional electrons that are delocalized throughout the ring, it is easiest to count the pi ($\pi$) bonds when using the major resonance structure, where all the $\pi$ electrons are depicted as localized within pure double bonds:

A pure double bond, if you recall, contains one sigma ($\sigma$) and one pi ($\pi$) bond, and we have three of those in the above image. Since we already counted those $\sigma$ bonds, we only count the $\pi$ bonds here.

We've accounted for all the $\sigma$ and $\pi$ bonds at this point, so in the end we have:

• $\boldsymbol{6} \times \left(s {p}^{2}\right)$ $\text{C"-"C}$ sigma ($\sigma$) bonds
• $\boldsymbol{6} \times \left(s {p}^{2}\right)$ $\text{C"-"H}$ sigma ($\sigma$) bonds
• $\boldsymbol{3} \times \left(s {p}^{2}\right)$ $\text{C"="C}$ pi ($\pi$) bonds
Then teach the underlying concepts
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1
Aug 31, 2016

There are 9 sigma single bonds and three double bonds using pi bonds.

#### Explanation:

Each of the six carbons are bonded to a single hydrogen using the 1s electron of the hydrogen and 1 of the $s {p}^{3}$ orbital of the carbon.

Every other carbon is temporarily joined to another carbon with a single sigma bond involving one of $s {p}^{3}$ orbitals from each carbon.

These bonds shift creating a resonance structure. so that practically there is 1 1/2 bonds between each of the six carbon atoms.

There are three double bonds in the benzene structure. Some text books show these as a sigma bond and a pi bond. More correctly it is a hybrid structure. Two $s {p}^{3}$ orbitals bond not directly (${180}^{o}$) as in a sigma bond and not at ${90}^{o}$ as in a pi bond. but at an angle.

These three double bonds shift with the single bonds creating a resonance structure.

So there are six true sigma bonds. 3 shifting single bonds that could be considered sigma bonds and 3 sets of double bonds that are hybrids between sigma and pi bonds.

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