A molecule’s properties are deeply connected to its three-dimensional shape, and one of the most important properties affected by geometry is polarity. Whether a trigonal bipyramidal molecule is polar depends entirely on the specific atoms attached to the central atom. While the perfectly symmetrical form is nonpolar, any deviation from this ideal state—such as substituting different atoms or introducing lone pairs of electrons—will result in a polar molecule. Understanding this requires examining how charge distribution works at the molecular level.
Understanding Molecular Polarity
Molecular polarity is determined by the overall distribution of electrical charge across a molecule. This distribution begins with electronegativity, which is an atom’s ability to attract electrons toward itself within a chemical bond. When two atoms with different electronegativities bond, the shared electrons are pulled closer to the more electronegative atom, creating a separation of charge called a bond dipole. The more electronegative atom gains a partial negative charge, and the less electronegative atom gains a partial positive charge.
A bond dipole is a vector quantity, possessing both magnitude and direction. To determine if an entire molecule is polar, all individual bond dipoles must be added together as vectors. The resulting sum is called the net dipole moment, and a molecule is considered polar only if this net dipole moment is non-zero. If the bond dipoles are arranged symmetrically, they cancel each other out, resulting in a nonpolar molecule despite having polar bonds.
Defining Trigonal Bipyramidal Geometry
The trigonal bipyramidal (TBP) geometry is adopted by molecules where a central atom is bonded to five surrounding atoms or groups (AX5). This structure is characterized by two distinct types of positions for the peripheral atoms, which are not equivalent. Three of the surrounding atoms lie in a single plane around the central atom, forming a triangle, and these are known as the equatorial positions. The bond angles between these three equatorial atoms are 120°.
The remaining two atoms occupy the axial positions, lying on an axis perpendicular to the equatorial plane, one above and one below. The bond angle between an axial atom and any equatorial atom is 90°, while the two axial atoms are 180° apart from each other. This difference in spatial arrangement means that the axial positions experience greater repulsion from the equatorial atoms. The two distinct types of positions are fundamental to understanding how symmetry dictates the molecule’s polarity.
The Symmetry That Creates Nonpolar TBP Molecules
A molecule with a perfect trigonal bipyramidal shape is nonpolar if all five peripheral atoms are identical, such as in phosphorus pentachloride (\(\text{PCl}_5\)). In this ideal scenario, the high degree of symmetry ensures that all individual bond dipoles perfectly cancel one another out. This cancellation occurs in two distinct sets of opposing forces.
The three bond dipoles in the equatorial plane, each separated by 120°, sum to a net vector of zero. Simultaneously, the two bond dipoles in the axial positions are exactly opposite one another, pulling in a straight line at a 180° angle. Because the peripheral atoms are identical, these two axial dipoles are equal in magnitude and cancel each other out. The overall result is a net dipole moment of zero, making the molecule nonpolar despite the presence of individual polar bonds.
When TBP Derivatives Become Polar
The nonpolar nature of the ideal TBP geometry is immediately lost when the surrounding atoms are not all the same. If the five peripheral atoms are a mix of two different elements, such as in \(\text{PCl}_3\text{F}_2\), the inherent non-equivalence of the axial and equatorial positions means the molecule will be polar. Substituting one type of atom for another breaks the perfect symmetry, creating an unequal distribution of electron density that results in a net dipole moment.
The presence of one or more lone pairs on the central atom fundamentally changes the molecular shape, even though the electron geometry remains based on the trigonal bipyramid. Because lone pairs of electrons repel more strongly than bonding pairs, they preferentially occupy the equatorial positions to minimize repulsion, further distorting the shape. Molecules like \(\text{SF}_4\) (one lone pair) adopt a “seesaw” shape, while \(\text{ClF}_3\) (two lone pairs) forms a “T-shaped” structure. These distorted geometries are inherently asymmetrical and are therefore polar, as the bond dipoles and the unequal electron distribution from the lone pairs do not cancel out. The only exception is the linear molecular shape derived from TBP with three lone pairs, such as in \(\text{XeF}_2\), where the lone pairs occupy all three equatorial positions, leading to a nonpolar molecule.