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Why isn’t cyclopropene aromatic?

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Answer
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Hint: To answer the question let us talk about aromatic compounds. Aromatic compounds are the class of unsaturated compounds that are highly stable. The property responsible for their stability is called Aromaticity. Some important examples of aromatic compounds include benzene, toluene, pyridine, thiophene, etc.

Complete answer:
In the question, we are asked why cyclopropene is not aromatic. To answer this let us discuss important conditions of aromatic compounds.
Conditions of aromatic compounds-
(A)The compound must be cyclic
(B)The compound must be planar i.e. has $ s{p^2} $ hybridization.
(C)The compound must be conjugated i.e. shows delocalization of pi-electrons.
(D)Must obey Huckel’s rule i.e. it has $ \left( {4n + 2} \right)\pi $ electrons where $ n $ is an integer whose value can be 0, 1, 2, 3, 4, etc.
A compound must obey all of these conditions to be aromatic.
Let us now talk about the compound cyclopropene and first look at its structure-
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Let us see if this molecule obeys all the conditions of the aromatic compound-
(A)The compound is cyclic so this condition is fulfilled.
(B) 2 of the carbon are $ s{p^2} $ hybridized while 1 of the carbon is $ s{p^3} $ hybridized and hence this condition is not fulfilled.
(C)The compound is not conjugated due to the $ s{p^3} $ hybridized carbon and hence no delocalization of electrons will take place so this condition is also not fulfilled.
(D)The compound has 2 pi-electrons; it means it obeys Huckel’s rule.
 $ (4 \times 0) + 2 = 2 $ Here we have taken the value $ n $ as 0.
So overall we see that the compound does not obey all the rules and is hence not aromatic. This cyclopropene molecule belongs to the category of non-Aromatic compounds.

Additional Information:
Apart from the category of Aromatic compounds, we have a class of compounds called anti-Aromatic compounds in which all conditions are fulfilled except that it does not obey Huckel’s rule and instead follows the $ 4n\pi $ electrons rule. All the compounds except aromatic and antiAromatic belong to the category of non-Aromatic compounds.
So if we look at the cation and anion of cyclopropene we will get the following results-
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This is cyclopropenyl cation. If we look at this compound all the conditions are fulfilled and the molecule is planar as well as conjugated (all the carbons are $ s{p^2} $ hybridized. Hence this compound is Aromatic.
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This is cyclopropenyl anion. If we look at this compound it obeys all conditions except Huckel’s rule and it obeys $ 4n\pi $ electrons and hence it belongs to the category of the anti-Aromatic compound.

Note:
The correct order of the stability of compounds is -Aromatic>non-Aromatic>anti-Aromatic. Cyclopropene is the simplest cycloalkene. It has the general formula of $ {C_3}{H_4} $ . The ring is strained and it is very difficult to be prepared. Since it is not aromatic (non-Aromatic) in nature it is unstable and highly reactive.