A dipole moment measures the net polarity of a molecule, resulting from the separation of positive and negative electrical charges within its three-dimensional structure. For phosphorus pentachloride (\(\text{PCl}_5\)), the answer lies in analyzing its bond properties and highly symmetrical shape.
Understanding Molecular Polarity
A dipole moment arises from bond polarity, the unequal sharing of electrons in a covalent bond caused by a difference in electronegativity. In \(\text{PCl}_5\), chlorine is significantly more electronegative than phosphorus, meaning each individual \(\text{P-Cl}\) bond is polar.
Polarity is a vector quantity, and the overall polarity of a molecule is determined by the vector sum of all its individual bond dipoles. If these dipoles are arranged symmetrically, their effects can cancel one another out completely. Consequently, a molecule can have highly polar bonds yet possess a net dipole moment of zero, rendering the entire molecule nonpolar.
Determining the Trigonal Bipyramidal Structure of \(\text{PCl}_5\)
The molecular geometry of \(\text{PCl}_5\) is determined by the Valence Shell Electron Pair Repulsion (VSEPR) theory, which predicts the arrangement of electron pairs around a central atom. The central phosphorus atom uses its five valence electrons to form five single bonds with the five surrounding chlorine atoms, resulting in five bonding pairs and zero lone pairs.
To minimize repulsion, these electron pairs orient themselves into a geometry known as trigonal bipyramidal. Three chlorine atoms occupy the equatorial positions, forming a triangle in a single plane with \(120^\circ\) bond angles.
The remaining two chlorine atoms occupy the axial positions, situated perpendicular to the equatorial plane. The angle between an axial and an equatorial bond is \(90^\circ\), and the two axial bonds are \(180^\circ\) apart. Furthermore, the axial \(\text{P-Cl}\) bonds are slightly longer than the equatorial \(\text{P-Cl}\) bonds.
Why Symmetry Results in Zero Dipole Moment
The highly symmetrical trigonal bipyramidal shape causes \(\text{PCl}_5\) to have a net dipole moment of zero. Although each \(\text{P-Cl}\) bond is polar, the vector sum of these five individual bond dipoles is zero.
The two \(\text{P-Cl}\) bonds in the axial positions are oriented exactly \(180^\circ\) from each other. Because they have the same magnitude and pull in opposite directions, the dipole moment of the upper axial bond is perfectly canceled by the lower axial bond.
The three \(\text{P-Cl}\) bonds in the equatorial plane are arranged symmetrically in a flat triangle with \(120^\circ\) angles between them. This arrangement ensures that the vector sum of the three equal equatorial bond dipoles also results in zero.
Since the axial dipoles cancel each other and the equatorial dipoles cancel each other, the overall net dipole moment of the gaseous or liquid \(\text{PCl}_5\) molecule is zero. \(\text{PCl}_5\) is classified as a nonpolar molecule.
The Unique Case of Solid Phosphorus Pentachloride
The discussion of molecular polarity typically focuses on the isolated molecule, which is the structure found in the gaseous or liquid state. However, when \(\text{PCl}_5\) transitions to the solid state, it undergoes a dramatic structural change. It does not simply condense while maintaining its neutral trigonal bipyramidal molecular structure.
Instead, solid phosphorus pentachloride is an ionic compound that autoionizes into two separate ions: the tetrahedral cation \(\text{PCl}_4^+\) and the octahedral anion \(\text{PCl}_6^-\). This transformation occurs because the formation of an ionic lattice structure is thermodynamically more stable in the solid phase.
The individual ions (\(\text{PCl}_4^+\) and \(\text{PCl}_6^-\)) are also highly symmetrical. Their geometries cause their internal bond dipoles to cancel out, resulting in zero net dipole moment for each ion. The answer to the \(\text{PCl}_5\) molecule’s dipole moment rests on the symmetrical, nonpolar nature of its trigonal bipyramidal form in the gas phase.