Q.Why does NO2 dimerise ?

Step 1 — Electron count in $NO_2$.

$NO_2$ has an odd total number of electrons, so it must have one unpaired electron somewhere in its structure (largely nitrogen-centred), making it a paramagnetic free-radical-like species.

Step 2 — Instability of an odd electron.

An unpaired electron is energetically unfavourable compared to a filled/paired electronic arrangement — the molecule seeks to pair this electron for greater stability.

Step 3 — Dimerisation.

Two $NO_2$ molecules combine, each contributing its unpaired electron to form a new N–N single bond:

$2NO_2 \rightleftharpoons N_2O_4$ …

Check the total electron count of $NO_2$ to spot the unpaired electron, then recognise that radical-type species st …

• Don't say $NO_2$ dimerises "to complete its octet" — nitrogen's octet in $NO_2$ is already effectively satisfied via resonance; the real driver is the unpaired electron. …