Explain why does NO2 dimerise

A Dimer is an additive product of two similar species. For example, when two molecules of NO2 combine it would give one molecule of N2O4. The N2O4 formed would be called as a dimer of NO2. Dimerization could be due to the formation of new covalent bonds or due to intermolecular hydrogen bonding.  Here, in case of N2O4, it is due to covalent bonding. 
By carefully looking at the structure and the electronic distribution of NO2, we can see,
1) a dative covalent bond and
2) the presence of a radical electron.
In a dative covalent bond, one atom donates its pair of electrons to another atom. By doing so, the donor atom acquires a positive charge due to its loss and the receiver atom receives a negative charge due to the gain of the electron pair. Such a bond is shown as an arrow (→) with the base of the arrow at the donor and the arrowhead facing the acceptor. In NO2, Nitrogen is the donor and Oxygen is the acceptor. 

NO2 structure

As Nitrogen has five valence electrons in its valence shell (shown enclosed in the purple circle), two of which is given away for dative bond formation, the remaining two is used in forming a double bond with the Oxygen. That leaves one electron as a free radical

NO2 electronic Structure

A free radical is high in energy. This is confirmed by looking at the Molecular Orbital diagram of NO. When the atomic orbitals of Nitrogen and Oxygen mix to form a new set of molecular orbitals, the electrons occupy different energy levels. The lowest energy level is the bonding molecular orbitals, and the high energy levels are the anti-bonding molecular orbitals. The anti-bonding energy levels are shown as an asterisk (*). You can see that after filing all the low energy levels, one electron sits on the highest anti-bonding molecular orbital denoted as pie * (π *).

N and O molecular orbital energy level why NO2 dimerise

The high energy state is unfavorable, so anything that lowers its energy is preferred. When two molecules of NO2 with one electron each combine, a bond formation takes place that lowers the energy of the entire system and is highly favorable
dimerization of NO2 to form N2O4
In addition to the molecular orbital diagrams, the presence of odd electron is confirmed by the paramagnetic (weakly attracted by the magnetic field) nature of NO2. The presence of unpaired electrons is essential for showing the paramagnetic behavior. On pairing up to form N2O4, it loses its paramagnetic activity and becomes diamagnetic (repelled by the magnetic field). The diamagnetic response is shown when all the electrons are paired up. Therefore in N2O4, due to the electron pairing, the octet of Nitrogen is complete, and it acquires a stable, inert gas configuration of Neon with two core electrons and eight valence electrons. 


N2O4 lewis structure dimerization



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