Question

Consider a molecule with formula \(\mathrm{AX}_{3}\). Supposing the \(\mathrm{A}-\mathrm{X}\) bond is polar, how would you expect the dipole moment of the \(\mathrm{AX}_{3}\) molecule to change as the \(\mathrm{X}-\mathrm{A}-\mathrm{X}\) bond angle increases from \(100^{\circ}\) to \(120^{\circ} ?\)

Short answer

As the X-A-X bond angle in the AX3 molecule increases from 100 degrees to 120 degrees, we expect the overall dipole moment of the molecule to decrease. This is because, with increasing bond angle, the bond dipoles are more symmetrically distributed, and they better cancel each other out, leading to a reduction in the net dipole moment.

Step-by-step solution

Understanding polar bonds and dipole moments

A bond is considered polar when the difference in electronegativity between the two bonded atoms is significant, leading to a partial charge separation and an electric dipole moment. In the AX3 molecule, it is given that the A-X bond is polar, which means each A-X bond has a dipole moment related to the bond polarity. A molecule's dipole moment is the vector sum of its individual bond dipoles. If the bond dipoles cancel out, then the overall dipole moment is zero, and the molecule is said to be nonpolar. If not, then the molecule has a nonzero dipole moment and is considered polar.

Assessing the AX3 molecule geometry

In the molecule AX3, there are three X atoms bonded to the central A atom. To spatially arrange the reference AX3 molecule in a way that maximizes separation of electron valence pairs while maintaining connectivity, we use the Valence Shell Electron Pair Repulsion (VSEPR) theory. For AX3, the basic geometry is trigonal planar with a 120-degree bond angle.

Analyzing the dipole moment with varying bond angles

First, consider the case where the X-A-X bond angle is equal to 100 degrees. Since the bond dipoles do not perfectly cancel out, the AX3 molecule has a nonzero dipole moment. Next, let's increase the bond angle from 100 to 120 degrees. As the bond angle approaches 120 degrees, which is the ideal trigonal planar bond angle, the bond dipoles become more symmetrically distributed. As a result, the overall dipole moment should decrease because as the angle increases, the bond dipoles tend to cancel each other out more effectively.

Conclusion

As the X-A-X bond angle in the AX3 molecule increases from 100 degrees to 120 degrees, we expect the overall dipole moment of the molecule to decrease. This is because, with increasing bond angle, the bond dipoles are more symmetrically distributed, and they better cancel each other out, leading to a reduction in the net dipole moment.

Key concepts

Molecular Polarity

Understanding molecular polarity is essential when studying the properties of molecules and how they interact with each other. The polarity of a molecule determines if it is a polar or nonpolar entity. A molecule is considered polar if it has a net dipole moment, which is a measure of the separation of positive and negative charges within the molecule. This occurs due to the uneven distribution of electrons between atoms with different electronegativities, leading to partial charges at the ends of the bonds.
For example, water (H₂O) is a polar molecule because oxygen is more electronegative than hydrogen, leading to a partial negative charge near the oxygen atom and a partial positive charge near the hydrogen atoms. In the case of an AX₃-type molecule with polar bonds, if the geometry is such that the bond dipoles do not cancel each other out, the molecule will have a net dipole moment and will be considered polar. However, as bond angles change, so can the overall dipole moment due to changes in the symmetry of the molecule, affecting its polarity.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory provides a straightforward approach to predicting the geometry of molecules. It is based on the principle that electron pairs around a central atom will organize themselves as far apart as possible to minimize repulsion. This theory helps us understand why certain molecules have specific shapes.
According to VSEPR theory, an AX₃ molecule, where 'A' is the central atom and 'X' denotes peripheral atoms, adopts a trigonal planar geometry to keep the electron pairs at the maximum distance from each other. In this basic structure, all the AX bonds are at 120 degrees to each other. This idealized model serves as a useful predictor of bond angles in real-world molecules, allowing us to infer how these angles affect properties like the dipole moment.

Electronegativity

Electronegativity is a fundamental concept describing how strongly atoms attract electrons when forming a bond. Atoms with high electronegativity, such as fluorine and oxygen, tend to pull shared electrons toward themselves more forcefully than atoms with lower electronegativity, like hydrogen or sodium.
This difference in electronegativity between bonded atoms becomes crucial when determining if a bond is polar or nonpolar. A significant difference in electronegativity results in a polar bond, where the electrons are more closely associated with one atom, thus creating a dipole moment. The understanding of electronegativity helps to predict the behavior of molecules in various situations, including their reactivity and interactions with other molecules.

Bond Angles

Bond angles, the angles between two adjacent bonds emanating from the same atom, are critical in determining the shape and thus the overall physical and chemical properties of molecules. In molecules such as AX₃, where A is the central atom, the bond angles determine how far apart the atoms lie from each other and how the bond dipoles are arranged in space.
An increase in the bond angle can cause a decrease in the dipole moment of polar molecules, as observed when the bond angle approaches the ideal geometry. For instance, when the bond angle of an AX₃ molecule increases from 100 to 120 degrees, the dipoles become more symmetrical, leading to a decrease in the net dipole moment. This effect is observed due to the more efficient cancellation of the bond dipoles when they are equidistant from each other, illustrating the importance of bond angles in understanding molecular polarity and dipole moments.