Phosphorus trifluoride (\(\text{PF}_3\)) is a colorless gas composed of one phosphorus atom and three fluorine atoms. The three-dimensional arrangement of these atoms, known as molecular geometry, is a fundamental concept in chemistry. This shape dictates the molecule’s physical properties, such as its boiling point, solubility, and chemical behavior.
Counting the Components
The first step in determining a molecule’s shape is identifying the valence electrons available for bonding. Phosphorus (P) contributes five valence electrons. Each of the three fluorine (F) atoms contributes seven valence electrons, totaling 21 electrons from fluorine. Thus, \(\text{PF}_3\) has a total of 26 valence electrons.
In the Lewis structure, phosphorus acts as the central atom, forming single bonds with the three surrounding fluorine atoms. These three P-F bonds use six valence electrons. The remaining 20 electrons are distributed as non-bonding pairs: each fluorine atom receives three lone pairs to satisfy the octet rule, and the final two electrons are placed on the central phosphorus atom as a single lone pair.
The VSEPR Model: Electron Domains
The Valence Shell Electron Pair Repulsion (VSEPR) theory predicts molecular geometry. This model proposes that electron domains around a central atom arrange themselves to maximize the distance between them, minimizing repulsion. An electron domain is any region of high electron density, such as a single bond, a double bond, a triple bond, or a lone pair of electrons.
The central phosphorus atom in \(\text{PF}_3\) has four distinct electron domains. These domains consist of the three bonding pairs (P-F bonds) and one non-bonding lone pair on the phosphorus atom. To minimize repulsion, these four domains occupy positions at the corners of a tetrahedron. This arrangement defines the electron-domain geometry of \(\text{PF}_3\) as tetrahedral.
Translating Arrangement to Shape
The molecular shape is determined only by the positions of the atoms, not by the lone pairs. Since \(\text{PF}_3\) has three bonded atoms and one lone pair, its molecular shape deviates from the tetrahedral electron-domain geometry.
The single lone pair on the phosphorus atom distorts the shape from a perfect tetrahedron. Lone pairs occupy more space than bonding pairs and exert a stronger repulsive force on the adjacent bonding pairs. This repulsion pushes the three fluorine atoms closer together, resulting in a trigonal pyramidal molecular geometry.
In this shape, the three fluorine atoms form the base of the pyramid, and the phosphorus atom sits at the apex. This lone pair repulsion compresses the F-P-F bond angle significantly from the ideal tetrahedral angle of \(109.5^\circ\). The actual F-P-F bond angle is approximately \(96^\circ\) to \(97.8^\circ\).
How Shape Influences Polarity
The trigonal pyramidal shape of phosphorus trifluoride affects the molecule’s overall polarity. Polarity is determined by the presence of polar bonds and the molecule’s symmetry. Fluorine is highly electronegative, attracting the shared electrons in the P-F bonds more strongly than phosphorus does.
This unequal sharing creates individual bond dipole moments, resulting in a partial negative charge on each fluorine atom and a partial positive charge on the phosphorus atom. In a symmetrical shape, these dipoles would cancel out, resulting in a non-polar molecule. However, the trigonal pyramidal shape of \(\text{PF}_3\) is asymmetrical.
Because the molecule is shaped like a pyramid, the net effect of the three P-F bond dipoles is a vector sum pointing toward the base. The asymmetrical arrangement and the polar bonds result in a permanent net dipole moment for the molecule. With a measured net dipole moment of \(1.03\) Debye, \(\text{PF}_3\) is classified as a polar molecule.