Question

Compare the molecular shapes and hybrid orbitals of \(\mathrm{PF}_{3}\) and \(\mathrm{PF}_{5}\) molecules. Explain why their shapes differ.

Short answer

The molecular shape of PF3 is trigonal pyramidal with sp3 hybrid orbitals, resulting from 4 electron domains including one lone pair. In contrast, PF5 has a trigonal bipyramidal shape with sp3d hybrid orbitals, stemming from 5 electron domains and no lone pairs. The difference in their shapes is due to the different hybridizations and the presence of a lone pair in PF3.

Step-by-step solution

1. Determine electron domain geometries

To find the electron domain geometries, we need to determine the number of electron domains around the central atom (P). In PF3, there are 3 single bonds and one lone pair, while in PF5, there are 5 single bonds. For PF3, 3 bonding domains + 1 lone pair = 4 electron domains. For PF5, 5 bonding domains = 5 electron domains.

2. Determine molecular geometries

With the electron domain geometries found, we can now determine the molecular geometries. For PF3, 4 electron domains result in a tetrahedral electron domain geometry. However, there is one lone pair, which gives a trigonal pyramidal molecular geometry. For PF5, 5 electron domains result in a trigonal bipyramidal electron domain geometry, with no lone pairs. So, the molecular geometry is also trigonal bipyramidal.

3. Identify hybrid orbitals

To identify the hybrid orbitals, we need to look at the electron domains: For PF3, 4 electron domains require hybridization of one 3s, and three 3p orbitals, giving a set of sp3 hybrid orbitals. For PF5, 5 electron domains require hybridization of one 3s, three 3p, and one 3d orbitals, giving a set of sp3d hybrid orbitals.

4. Explain the difference in molecular shapes

The difference in molecular shapes between PF3 and PF5 can be attributed to the difference in their hybridization. PF3 has a sp3 hybridization with one lone pair, resulting in a trigonal pyramidal molecular geometry. Meanwhile, PF5 has a sp3d hybridization with no lone pairs, which makes its molecular geometry trigonal bipyramidal. In conclusion, the molecular shape of PF3 is trigonal pyramidal with sp3 hybrid orbitals while PF5 has a trigonal bipyramidal shape with sp3d hybrid orbitals. The shapes differ due to the different hybridizations and the presence of a lone pair in PF3.

Key concepts

Electron Domain Geometries

Understanding the shapes of molecules starts with electron domain geometries.

This concept is guided by the VESPR (Valence Shell Electron Pair Repulsion) theory, which tells us that electron domains—regions in space where electrons are most likely to be found—will arrange themselves as far apart as possible to minimize repulsion. Electron domains include lone pairs, single, double, triple bonds, or even a single unpaired electron.

The number of electron domains around the central atom thus dictates the geometric arrangement. For instance, four electron domains result in a tetrahedral electron domain geometry, as seen in the molecule PF₃. On the other hand, five electron domains as in PF₅ result in a trigonal bipyramidal electron domain geometry. These geometries form the foundation for predicting the actual shape of the molecule.

Trigonal Pyramidal Molecular Geometry

When a molecule has four electron domains with one of them being a lone pair, as observed in PF₃, it adopts what’s known as a trigonal pyramidal molecular geometry.

Imagine a tetrahedron which has a triangular base; when one vertex is a lone pair, the visible shape forms a pyramid with a triangular base, hence the term 'trigonal pyramidal'. The three corners of the base are the positions where the fluorine atoms are bonded to the phosphorus atom in PF₃. This geometry results in a non-symmetrical shape leading to a dipole moment and polar nature of such molecules.

sp3 and sp3d Hybridization

Hybridization is the process where atomic orbitals of similar energies mix to form new hybrid orbitals that are identical in energy. For a molecule like PF₃, with four electron domains, the central phosphorus atom undergoes sp³ hybridization. This mixing involves one s orbital and three p orbitals, resulting in four sp³ hybridized orbitals.

Contrarily, PF₅, which has five electron domains, undergoes sp³d hybridization because it combines one s, three p, and one d orbital to form five equivalent sp³d hybrid orbitals. These orbitals are essential for housing the bonding and lone pair electrons and are crucial for predicting the resultant molecular geometry.

• PF₃: sp³ hybridization leads to a trigonal pyramidal shape.
• PF₅: sp³d hybridization leads to a trigonal bipyramidal shape.

Thus, the hybrid orbitals provide homes for electron pairs and largely determine the shape and bond angles of the resulting molecules.