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We know that all Lewis acids are electrophiles but I have a confusion whether the reverse is also true. Electrophiles are molecules that are in search of electrons while Lewis acids are short of electrons. So can't all electrophiles act as Lewis acids?

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The definition of Lewis acids states:

A molecular entity (and the corresponding chemical species ) that is an electron-pair acceptor and therefore able to react with a Lewis base to form a Lewis adduct, by sharing the electron pair furnished by the Lewis base. For example:
example lewis adduct
(source: iupac.org)

In principle, since all electrophiles can be electron acceptors, they can usually act as Lewis bases, too. However, sometimes sterically demanding moieties stabilise the electrophile, so that it is impossible to form a Lewis adduct. These compound are then one part of a frustrated Lewis pair.

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Lewis acids are electron acceptors, the slight asymmetry in the definition arises because accepting means you have to move electrons into a Lewis acid, i.e. H+ and AlCl3. On the other hand the carbonyl carbon is electrophilic, but when it accepts two electrons, it rejects two others. Hence, it is not a Lewis acid.

Electrophilic - desires electrons Lews Acidis - desires and is able to take on additional electrons

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