How do you count pi electrons in aromatic compounds?
- Since any one chemical bond (meaning only one line in bond line notation) contains at most two electrons, you can count two
#pi# electrons per double bond, and ignore the#sigma# electrons. - If you see lone pairs, consider the molecular geometry, and only the
#pi# electrons that are in the ring count towards aromaticity.Here are some examples of rings that may or may not be aromatic:
Note that the only
#pi# electrons I've counted are in the ring. The others are either outside of the ring or#sigma# electrons.Counting from top to bottom, column-wise:
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Aromatic, because
#4n + 2 = 6# #pi# electrons in the ring (with#n = 1# ), planar, fully conjugated all around, and cyclic. -
Aromatic, because
#4n + 2 = 6# #pi# electrons in the ring (with#n = 1# ), planar, fully conjugated all around, and cyclic. The#pi# electrons in the double bond outside of the ring do not count towards the#pi# electrons one considers for aromaticity. -
Nonaromatic, because
#4n + 2 ne 4# #pi# electrons, where#n# must be an integer. It's also not conjugated all around, so it's not antiaromatic. The#pi# electrons in the double bond outside of the ring do not count towards the#pi# electrons one considers for aromaticity. -
Aromatic, because
#4n + 2 = 6# #pi# electrons in the ring (with#n = 1# ), planar, fully conjugated all around, and cyclic. The lone pair is actually in a pure#2p# orbital perpendicular to the ring. Don't be fooled, as the alkyl carbon has an implicit hydrogen. -
Aromatic, because
#4n + 2 = 6# #pi# electrons in the ring (with#n = 1# ), planar, fully conjugated all around, and cyclic. The lone pair is actually in a pure#2p# orbital perpendicular to the ring, which means they count as#pi# electrons. -
Aromatic, because
#4n + 2 = 6# #pi# electrons in the ring (with#n = 1# ), planar, fully conjugated all around, and cyclic. Only one of the lone pairs is actually in a pure#2p# orbital perpendicular to the ring, which means those count as#pi# electrons. The other lone pair is actually in a#sigma# (actually,#sp^2# ) orbital, so it doesn't count. Thus furan is not antiaromatic.
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Count the number of π electrons in aromatic compounds by examining the conjugated π system, including double bonds and lone pairs within the cyclic structure. Each double bond or lone pair contributes two π electrons.
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To count pi electrons in aromatic compounds, you typically follow Hückel's rule, which states that aromaticity occurs when a compound has a conjugated ring system with ( 4n + 2 ) pi electrons, where ( n ) is an integer (including zero). Here's how you count the pi electrons:
- Identify the aromatic ring system in the compound.
- Count the number of pi bonds (double bonds, triple bonds, or delocalized pi electrons) within the ring system.
- Determine the total number of pi electrons by multiplying the number of pi bonds by 2.
For example:
- Benzene (( C_6H_6 )) has a conjugated ring system with 3 pi bonds (alternating double bonds). Using Hückel's rule, ( 4n + 2 = 6 ), which is satisfied when ( n = 1 ). So, benzene has 6 pi electrons.
- Pyridine (( C_5H_5N )) has a conjugated ring system with 2 pi bonds (one double bond in the ring). Using Hückel's rule, ( 4n + 2 = 6 ), which is also satisfied when ( n = 1 ). So, pyridine also has 6 pi electrons.
By following Hückel's rule, you can accurately count the pi electrons in aromatic compounds to determine their aromaticity.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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