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Why does higher pressure favour the formation of dinitrogen tetroxide from nitrogen dioxide?

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Higher pressure favours the formation of dinitrogen tetroxide ( $N_{2} O_{4}$ ) from nitrogen dioxide ( $N O_{2}$ ) because of the way the system responds to external stress, as described by Le Chatelier's principle.

The reversible reaction is represented as:
$2 N O_{2} ⇌ N_{2} O_{4}$

In this system, the dissociation of one molecule of $N_{2} O_{4}$ into two molecules of $N O_{2}$ results in an expansion of the gas, effectively doubling the number of molecules. Because the volume a gas occupies at a given temperature and pressure depends on the number of molecules present, the formation of $N O_{2}$ increases the volume, which is opposed by external pressure.1

When the external pressure is increased, the system acts to relieve that stress by reducing its total volume. It achieves this by combining the $N O_{2}$ monomers to form $N_{2} O_{4}$ dimers, thereby decreasing the total number of gas molecules. Consequently, the chemical equilibrium shifts in favour of the dimer ( $N_{2} O_{4}$ ) under increased pressure.1