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Can all the positively charged species be called electrophiles?

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Perhaps in some sense, but there is a fundamental difference between $\ce{H3C+}$ and $\ce{H4N+}$, for example. The carbocation has an empty (p-) orbital and will form a covalent bond with a nucleophile, like any typical electrophile would. Ammonium on the other hand has a full octet, so the nitrogen cannot accept a new bond and an electron donor would instead bond to a hydrogen, deprotonating the cation. Cations with incomplete octets can be conventional electrophiles (Lewis acids), whereas cations with full octets and hydrogen are better considered Brønsted-Lowry acids (a special case of electrophile).

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According to me basically those species of atoms and molecules which can gain a pair of electron and are positively charged or are neutral are called electrophiles. So only those positive species which can gain a pair of electron can be called electrophiles.

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