Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: The structure of ${\text{PCl}}_5$ in the solid state is

Phosphorus pentachloride (${\text{PCl}}_5$) is a fascinating molecule that leads a double life. If you observe it in the gaseous or liquid state, it behaves exactly as VSEPR theory predicts for a molecule with five bond pairs: it exists as discrete, covalent molecules with a trigonal bipyramidal geometry.

However, when the temperature drops and ${\text{PCl}}_5$ freezes into a solid, a remarkable structural transformation occurs. The molecules pack closely together, and to maximize their thermodynamic stability, they undergo a process known as auto-ionization.

Why does a perfectly happy covalent molecule suddenly decide to become ionic? The answer lies in lattice energy. In the solid state, forming an ionic crystal lattice releases a massive amount of energy, making the ionic arrangement far more stable than a simple molecular solid.

To achieve this, two ${\text{PCl}}_5$ molecules interact and exchange a chloride ion (${\text{Cl}}^{-}$). One molecule acts as a donor, and the other acts as an acceptor:

This elegant disproportionation creates a cation and an anion, which then arrange themselves into a highly stable ionic lattice.

Let's break down the geometry of the newly formed cation. The central phosphorus atom normally has $5$ valence electrons. By losing one electron to form the positive charge, it is left with $4$ valence electrons.

It uses these $4$ electrons to form four single $\sigma$-bonds with four chlorine atoms. - Bond Pairs: $4$ - Lone Pairs: $0$ - Steric Number: $4$

A steric number of $4$ corresponds to $s{p}^3$ hybridization. Therefore, the $[{\text{PCl}}_4{]}^{+}$ cation adopts a perfect tetrahedral geometry.

Now, let's look at the acceptor molecule. The central phosphorus atom gains an electron, giving it $6$ valence electrons. Because phosphorus is in the third period, it has empty d-orbitals and can comfortably expand its octet.

It uses these $6$ electrons to form six single $\sigma$-bonds with six chlorine atoms. - Bond Pairs: $6$ - Lone Pairs: $0$ - Steric Number: $6$

A steric number of $6$ corresponds to $s{p}^3{d}^2$ hybridization. This results in a highly symmetric octahedral geometry.

By piecing this together, we can definitively say that solid ${\text{PCl}}_5$ is an ionic solid composed of tetrahedral $[{\text{PCl}}_4{]}^{+}$ and octahedral $[{\text{PCl}}_6{]}^{-}$ ions.

This phenomenon is a recurring theme in p-block chemistry. For instance, solid ${\text{PBr}}_5$ auto-ionizes into $[{\text{PBr}}_4{]}^{+}$ and ${\text{Br}}^{-}$ (because six bulky bromine atoms cannot fit around a single phosphorus atom due to steric hindrance). Similarly, solid ${\text{N}}_2{\text{O}}_5$ exists as nitronium (${\text{NO}}_2^{+}$) and nitrate (${\text{NO}}_3^{-}$) ions. Recognizing these solid-state structural shifts is a crucial skill for mastering advanced inorganic chemistry!