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Why does nitrosonium and nitronium ion

structures of both ions

act as electrophiles when each atom in them have a complete octet of electrons?

Even if we consider that they are electrophile just because of the fact that they have a formal positive charge on O or N then why don't $\ce{H3O+}$, $\ce{Li+}$, $\ce{Ca^2+}$, $\ce{Mg^2+}$, $\ce{NH4+}$, etc. also act as electrophiles they also have a positive centre and a complete octet of electrons?

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TL;DR All the other species you mentioned also act as electrophiles, just not in the way you are thinking of.

Both $\ce{NO^+}$ and $\ce{NO2+}$ have empty $\pi^*$ orbitals, which are low-lying in energy. The reaction, in terms of frontier orbitals, then consists of the addition of the benzene $\pi$ system to the empty $\pi^*$ orbitals of the electrophiles.

The lowest energy unoccupied orbital in $\ce{H3O+}$ would be the $\sigma^*$ orbital. You might ask, why can't it react as an electrophile via the $\sigma^*$? Well, it does. The $\sigma^*$ orbital is largely centred on the hydrogen atom, so that's where the benzene $\pi$ system would attack.

Pushing electrons into the $\ce{O-H}$ $\sigma^*$ orbital would lead to cleavage of the $\ce{O-H}$ bond. How might one draw this with curly arrows?

protonation of benzene by H3O+

Yes, it's an acid-base reaction. (Obviously, this only happens to a tiny extent, but the equilibrium position is not relevant to the discussion.) However, that doesn't stop it from also being a reaction between an electrophile and a nucleophile.

At the end of the day, what's the difference between $\ce{NO2+}$ and $\ce{NH4+}$? It is that the LUMO of $\ce{NO2+}$ is centred on nitrogen, and therefore attack of the benzene ring occurs at nitrogen to form a $\ce{C-N}$ bond. The LUMO of $\ce{NH4+}$ is centred on hydrogen, and therefore attack of the benzene ring would occur at hydrogen to form a $\ce{C-H}$ bond.

Good old valence bond theory is slightly inadequate in explaining this, since there is no notion of an antibonding orbital within VBT. It is still possible to rationalise it by, for example, saying that the $\ce{N-O}$ bond in $\ce{NO+}$ is polarised towards oxygen, and that nitrogen is therefore the electrophilic site within the molecule. [Note that the Lewis structure, which places a formal positive charge on oxygen, is not necessarily representative of the true charge distribution.] The same applies for the $\ce{N-H}$ bonds in $\ce{NH4+}$, which are polarised towards nitrogen, and therefore the electrophilic atoms are the hydrogens.

As for the metal cations you mentioned, why can't they be electrophiles? They jolly well can be electrophiles.

hypothetical reaction of Li+ with OH-

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  • $\begingroup$ So what if N is electrophilic site in $NO_2$ and H in NH_4^+$ $\endgroup$ – Matt Mar 10 '17 at 17:55
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  1. Nitrogen and oxygen are more electronegative atoms. Positive charge on them is much less stable than on Li, Mg and Ca.

  2. Electrophiles must also have a vacant orbital to accept lone pair of electrons from the nucleophile. Oxygen in hydronium ion or nitrogen in ammonium ion has no vacant orbital. They can simply lose a proton and become stable.

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  • $\begingroup$ Neither does n or o in nitrosonium or nitronium have a vacant orbital $\endgroup$ – Matt Mar 10 '17 at 16:23
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    $\begingroup$ @RaghavSingal That is completely not true, read at least about mesomeric structures, or better MOs. $\endgroup$ – Mithoron Mar 10 '17 at 23:42

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