Question

If B-Cl bond has a dipole moment, explain why \(\mathrm{BCl}_{3}\) molecule has zero dipole moment.

Short answer

The symmetry of the trigonal planar shape cancels individual bond dipoles, resulting in zero net dipole moment.

Step-by-step solution

Understanding Dipole Moments

The dipole moment is a measure of the separation of positive and negative charges in a bond. A molecule with a net dipole moment means there is an uneven distribution of electron density due to differences in electronegativity between atoms.

Determine the Geometry of \\( ext{BCl}_3\\)

The molecule \( ext{BCl}_3\) is trigonal planar, meaning the B atom is in the center with three Cl atoms symmetrically spaced at 120 degrees apart in a flat plane.

Evaluate the Symmetry

In \( ext{BCl}_3\), the symmetric trigonal planar geometry causes the dipole moments of the B-Cl bonds to point in directions that are 120 degrees apart.

Analyze the Vector Sum

The dipole moment is a vector quantity, which means each B-Cl bond contributes a vector pointing away from the Boron. Due to symmetry, these vectors cancel each other out because they are equally spaced, resulting in no net dipole moment.

Key concepts

Molecular Geometry

Molecular geometry plays a pivotal role in determining a molecule's properties, including its dipole moment. In the case of \( \text{BCl}_3 \), the geometry is trigonal planar. This means the boron atom is at the center with three chlorine atoms symmetrically spaced 120 degrees apart in a flat plane. This symmetry is crucial because it dictates how the individual bond dipoles interact and combine.

In simpler terms, imagine a triangle where the vertices are chlorine atoms, and the center is boron. This flat, symmetrical shape allows for an even distribution of charge across the molecule.
Symmetry in molecular geometry often leads to a cancellation of dipole moments, explaining why some symmetric molecules, despite having polar bonds, exhibit no overall dipole moment. Understanding molecular geometry helps predict the behavior of molecules, specifically noting whether a molecule is polar or nonpolar.

Vector Cancellation

Vector cancellation is essential when evaluating the overall dipole moment of a molecule like \( \text{BCl}_3 \). Each B-Cl bond in \( \text{BCl}_3 \) has its dipole moment vector pointing from the less electronegative boron towards the more electronegative chlorine. These vectors resemble arrows pointing from Boron to each Chlorine.

Due to the molecule's trigonal planar geometry, each of these vector arrows is equidistant and 120 degrees from the others. This equal spacing ensures that for every vector pointing in one direction, there is another that points in the exact opposite direction, thus canceling each other out.

The result of this vector cancellation is that the molecule shows no net dipole moment, explaining its nonpolar nature despite the presence of polar covalent bonds. This concept highlights why molecular symmetry can lead to the cancellation of dipole moments.

Electronegativity Differences

Understanding electronegativity differences is key to comprehending why bond dipoles form in the first place. Electronegativity is a measure of an atom's ability to attract electrons in a bond. In a B-Cl bond, chlorine is more electronegative than boron, causing a dipole moment with the electron density shifting towards chlorine.

While this shift creates a polar bond with a dipole moment, the symmetrical trigonal planar arrangement of \( \text{BCl}_3 \) ensures these individual dipole moments counterbalance each other. The overall electronegativity difference remains significant only within each bond and does not contribute to a net dipole moment across the whole molecule.

Grasping the concept of electronegativity differences alsoprovides insight into why certain molecules are polar or nonpolar. It is the interplay between bond dipoles and molecular geometry that determines the net dipole moment, affecting molecular interactions and properties.