Question

(a) Discuss structural variation among the phosphorus(III) and phosphorus(V) halides, indicating where stereochemical non-rigidity is possible. (b) On what basis is it appropriate to compare the lattice of \(\left[\mathrm{PCl}_{4}\right]\left[\mathrm{PCl}_{6}\right]\) with that of \(\mathrm{CsCl}\) ?

Short answer

Phosphorus(III) halides can be stereochemically non-rigid due to lone pairs, while phosphorus(V) can show fluxionality. \( [\mathrm{PCl}_{4}][\mathrm{PCl}_{6}] \) and \( \mathrm{CsCl} \) are comparable due to their similar cubic lattice structures.

Step-by-step solution

Identify Relevant Phosphorus Halides

There are two primary types of phosphorus halides to consider: phosphorus(III) halides (such as \( \text{PCl}_3 \)) and phosphorus(V) halides (such as \( \text{PCl}_5 \)). These compounds differ in the oxidation state of phosphorus.

Examine Structure for Phosphorus(III) Halides

Phosphorus(III) halides, such as \( \text{PCl}_3 \), typically have a trigonal pyramidal structure. The phosphorus atom is bonded to three chlorine atoms and has a lone pair. The presence of the lone pair offers potential for stereochemical non-rigidity, allowing for possible inversion or rotation.

Examine Structure for Phosphorus(V) Halides

Phosphorus(V) halides, such as \( \text{PCl}_5 \), usually adopt a trigonal bipyramidal structure. They have five chlorine atoms bonded to the phosphorus atom, with no lone pairs. In solution or gas phases, \( \text{PCl}_5 \) can exhibit fluxionality, where the axial and equatorial chlorine atoms interchange, indicating non-rigidity.

Compare the Lattice Structures of Compounds

The lattice structure of \( [\mathrm{PCl}_{4}][\mathrm{PCl}_{6}] \) is similar to that of \( \mathrm{CsCl} \) because both crystallize in similar cubic structures. \( [\mathrm{PCl}_{4}]^+ \) and \( [\mathrm{PCl}_{6}]^- \) ions form a lattice that resembles the simple cubic and closely packed arrangements seen in \( \mathrm{CsCl} \), which consists of alternating cations and anions.

Justify Comparison with \( \mathrm{CsCl} \) Lattice

The comparison between the lattice of \( [\mathrm{PCl}_{4}][\mathrm{PCl}_{6}] \) and \( \mathrm{CsCl} \) is based on their structural similarity. Both compounds can form cubic lattices where each ion is surrounded by others of opposite charge, facilitating a similar packing density and unit cell configuration.

Key concepts

Phosphorus(III) Halides

Phosphorus(III) halides are compounds wherein phosphorus is in the +3 oxidation state, such as in phosphorus trichloride ( \( \text{PCl}_3 \) ). These halides typically adopt a trigonal pyramidal geometry. This geometry arises because the phosphorus atom is bonded to three halogen atoms, in this case, chlorine, and retains a lone pair of electrons.
This lone pair significantly affects the molecule's structure, leading to potential non-rigid behavior. Since the lone pair occupies more space, it can cause the molecule to undergo inversion or rotation, a feature characteristic of stereochemical non-rigidity.

• Phosphorus in the +3 state is sp³ hybridized.
• The presence of a lone pair leads to a trigonal pyramidal shape.
• Possible for stereochemical non-rigidity such as inversion.

Phosphorus(V) Halides

In contrast to phosphorus(III) halides, phosphorus(V) halides like phosphorus pentachloride ( \( \text{PCl}_5 \) ) exhibit a different structural arrangement. These compounds form a trigonal bipyramidal shape because the phosphorus atom makes connections with five chlorine atoms, having no lone pairs left.
Due to the five bonding pairs, fluxional behavior is observable, especially in the gas or solution phases. The axial and equatorial positions can interchange effortlessly, leading to non-rigidity in the structure. Such fluxionality is typical in compounds with this geometry, allowing rapid changes in the positional arrangement of halogen atoms.

• Phosphorus is in the +5 oxidation state.
• Structure is trigonal bipyramidal.
• Exhibits fluxional behavior indicating non-rigidity.

Stereochemical Non-Rigidity

Stereochemical non-rigidity refers to the ability of a molecule to undergo conformational changes, affecting its spatial arrangement. For phosphorus(III) and phosphorus(V) halides, this concept manifests in different forms.
For phosphorus(III) halides, the lone pair allows for potential inversion, modifying how the halogens orient in space. In phosphorus(V) halides, the lack of lone pairs but presence of multiple bonding sites encourages fluxional behavior. This can be seen with the interchange between axial and equatorial positions.
The presence of non-rigidity is crucial in understanding reaction dynamics, as it affects how these molecules interact with other substances or react to environmental changes.

• Inversion: Seen in molecules with lone pairs, like \( \text{PCl}_3 \).
• Fluxionality: Common in geometries with multiple bonds, like \( \text{PCl}_5 \).
• Influences molecular interactions and reactions.

Lattice Structure Comparison

When comparing lattice structures, understanding the similarity in packing and arrangement is essential. The lattice of \( [\mathrm{PCl}_{4}][\mathrm{PCl}_{6}] \) is analogous to that of cesium chloride ( \( \mathrm{CsCl} \) ) due to their cubic structure arrangement.
Both structures involve ions that form a repeating cubic grid, causing each ion to be surrounded efficiently by ions of the opposite charge. This results in similar packing densities and arrangements, making them comparable despite the difference in their individual atomic components.

• \( [\mathrm{PCl}_{4}]^+ \) and \( [\mathrm{PCl}_{6}]^- \) form a cubic lattice.
• Ionic arrangements mimic \( \mathrm{CsCl} \) structure.
• Comparison based on efficient packing and charge placement.