Question

The \(\mathrm{PF}_{3}\) molecule has a dipole moment of \(1.03 \mathrm{D}\), but \(\mathrm{BF}_{3}\) has a dipole moment of zero. How can you explain the difference?

Short answer

Although both \(\mathrm{PF}_{3}\) and \(\mathrm{BF}_{3}\) have a trigonal planar molecular geometry, the difference in dipole moments arises from the electronegativity differences and the bond dipoles' arrangement. The P-F bond dipoles in \(\mathrm{PF}_{3}\) do not cancel each other out, leading to a nonzero dipole moment of \(1.03\,\mathrm{D}\). In contrast, the symmetrically distributed B-F bond dipoles in \(\mathrm{BF}_{3}\) cancel each other out, resulting in a dipole moment of zero.

Step-by-step solution

Determine the molecular geometries of both molecules

To describe the geometries of the molecules, we’ll use the principles of VSEPR (Valence Shell Electron Pair Repulsion) theory. Both \(\mathrm{PF}_{3}\) and \(\mathrm{BF}_{3}\) have a central atom with three bonding pairs and no lone pairs around it, so they both have a trigonal planar molecular geometry.

Analyze the electronegativity differences between the atoms involved

The dipole moment arises due to the difference in electronegativity between the central atom and the surrounding atoms in a polar covalent bond. The electronegativity values for the elements involved are approximately: - Phosphorus (P): 2.19 - Boron (B): 2.04 - Fluorine (F): 3.98 In both molecules, the electronegativity difference exists between the central atom and fluorine atoms. In \(\mathrm{PF}_{3}\), the electronegativity difference between P and F is 1.79, which indicates polar covalent bonds. However, in \(\mathrm{BF}_{3}\), the electronegativity difference between B and F is 1.94, which also leads to polar covalent bonds.

Consider molecular geometry and symmetry to understand the overall dipole moment

In a trigonal planar geometry, the bond dipoles can be arranged in such a way that they either cancel out each other, resulting in a net dipole moment of zero, or they don't, resulting in a nonzero net dipole moment. In the case of \(\mathrm{PF}_{3}\), the three P-F polar bonds do not completely cancel each other out because of the difference in electronegativity between P and F, thus leading to an overall nonzero dipole moment of \(1.03\,\mathrm{D}\). On the other hand, in the case of \(\mathrm{BF}_{3}\), though there are three B-F polar bonds due to electronegativity difference, they are symmetrically distributed around the central boron atom. Hence, the bond dipoles are evenly distributed and cancel each other out, resulting in an overall dipole moment of zero.

Conclusion

The difference in dipole moments between \(\mathrm{PF}_{3}\) and \(\mathrm{BF}_{3}\) arises from the combination of the molecular geometry (trigonal planar) and the electronegativity differences between the atoms involved. In \(\mathrm{PF}_{3}\), the bond dipoles do not cancel each other, giving it a nonzero dipole moment, while in \(\mathrm{BF}_{3}\), the bond dipoles cancel each other out resulting in a dipole moment of zero.

Key concepts

VSEPR Theory

Imagine tiny, invisible balloons wrapping around atoms. That's kind of what VSEPR Theory is like. VSEPR stands for "Valence Shell Electron Pair Repulsion." This theory helps us predict the shapes of molecules based on the repulsion between electron pairs in the valence shell of atoms. These are essentially the outermost electrons that decide how atoms interact with each other.

The main idea is that electron pairs will arrange themselves as far apart as possible to minimize repulsion. For example, in both \(\mathrm{PF}_{3}\) and \(\mathrm{BF}_{3}\), you'll find that the central atom is surrounded by three bonding pairs of electrons. This means:

• The shape will tend to spread out as evenly as possible to counteract the repulsion, resulting in a trigonal planar shape.
• This specific geometric arrangement affects how molecules interact with electric fields, thus influencing their dipole moments.

Understanding VSEPR theory gives us the tools to predict and rationalize the 3D structures molecules might adopt, shedding light on various chemical properties.

Electronegativity

Electronegativity sounds like a big word, but it's actually a simple concept—it's all about how much an atom "wants" electrons. Think of it as a measure of an atom's "greediness" for electrons. In a molecule, the difference in electronegativity between two atoms bonded together can tell us if that bond is polar or nonpolar.

In the molecules \(\mathrm{PF}_{3}\) and \(\mathrm{BF}_{3}\), here's what's happening:

• Fluorine (F) is incredibly electronegative, making it hog the shared electrons in any bond.
• Although both phosphorus (P) and boron (B) are less electronegative, the overall electronegativity difference between these central atoms and fluorine is significant enough to create polar covalent bonds.

Phosphorus and boron have different electronegativities (2.19 for P and 2.04 for B), but fluorine remains much more electronegative at 3.98. The key is how these differences manifest in the context of molecular geometry, impacting the overall molecular dipole moment.

Molecular Geometry

Molecular Geometry is a bit like a molecule's personality, shaped by its electron pair arrangement. It defines how molecules look in 3D space, which is crucial for determining molecular properties and behavior. For instance, in \(\mathrm{PF}_{3}\) and \(\mathrm{BF}_{3}\), we see:

• The arrangement and angles between bonds influence whether dipoles within the molecule cancel out or not.
• \(\mathrm{PF}_{3}\) adopts a trigonal planar shape, but due to the lone pair present, it is slightly distorted, resulting in a nonzero dipole moment.
• On the other hand, \(\mathrm{BF}_{3}\), with a perfect trigonal planar shape and equal electronegativity distribution, has its bond dipoles cancel out, leading to a zero dipole moment.

In genuine trigonal planar geometry, bond angles are typically 120 degrees, and it’s symmetric. However, any deviation can affect whether dipoles reinforce or oppose each other, contributing to whether a molecule has a net dipole moment or not.