Question

In VSEPR theory, which uses the Lewis model to determine molecular geometry, the trend of decreasing bond angles in \(\mathrm{CH}_{4}, \mathrm{NH}_{3},\) and \(\mathrm{H}_{2} \mathrm{O}\) is accounted for by the greater repulsion of lone pair electrons compared to bonding pair electrons. How would this trend be accounted for in valence bond theory?

Short answer

In Valence Bond Theory, the decreasing bond angles from methane to water are accounted for by the repulsion caused by lone pairs, which occupy more space and exert greater force on bonding pairs, thus reducing the bond angles.

Step-by-step solution

Recall the Valence Bond Theory

Valence Bond Theory (VBT) explains the bonding in molecules in terms of the overlap of atomic orbitals. In this model, each atom contributes at least one orbital to the bond formation, and the overlapping orbitals contain the shared electrons that constitute the bond.

Understand Hybridization

Hybridization involves the mixing of atomic orbitals on an atom to generate new hybrid orbitals, which can better align for bonding with other atoms. Molecules like methane (CH4), ammonia (NH3), and water (H2O) involve sp3 hybridized orbitals in the central atom.

Examine the Electron Repulsion in VBT

According to VBT, the geometry of the molecule adjusts in a way to minimize the repulsions between electron pairs in the hybrid orbitals. Lone pairs are located in orbitals that are closer to the nucleus and occupy more space compared to bonding pairs, causing greater repulsion.

Account for the Decreasing Bond Angles

In VBT, the degree of repulsion by lone pairs is taken into account by acknowledging that lone pairs exert a greater force of repulsion on the bonding pairs. Thus, they push the bonding pairs closer together, which decreases the angle between the bonds. Methane (CH4) with no lone pair has the largest bond angles, followed by ammonia (NH3) with one lone pair, and water (H2O) with two lone pairs has the smallest bond angles.

Key concepts

VSEPR theory

Understanding the arrangement of atoms in molecules begins with the Valence Shell Electron Pair Repulsion (VSEPR) theory. This theory posits that electron pairs around a central atom will arrange themselves as far apart as possible to minimize the repulsion between them. The shape of a molecule is thus largely determined by the need to minimize this electron pair repulsion.

Consider atoms like seating guests at a large table; each guest wishes to maximize their personal space. In a similar fashion, electron pairs stay as far away from each other as the room - or in this case, the valence shell - allows. The geometric shapes that arise from these arrangements are crucial for understanding how molecules interact with each other and with their environment.

Molecular geometry

The geometry of a molecule can significantly influence its physical and chemical properties. Molecular geometry is the three-dimensional arrangement of atoms within a molecule. VSEPR theory aids in predicting these arrangements by considering electron pairs as occupying space around the central atom.

For instance, methane (CH4) is tetrahedral, ammonia (NH3) is trigonal pyramidal, and water (H2O) is bent. Each geometric change is a result of the electron pairs, both bonding and non-bonding, arranging themselves to be as far apart as possible. The difference between bonding and non-bonding electron pairs influences the 'tug-of-war' on the central atom, leading to variations in bond angles.

Hybridization

Hybridization is a concept used to describe the blending of atomic orbitals to form new, equivalent orbitals suitable for bonding. It's an integral part of Valence Bond Theory, which suggests that overlapping atomic orbitals form chemical bonds.

The hybridized orbitals, such as the sp3 orbitals in methane, ammonia, and water, are mathematically equivalent but spatially distinct. This equivalence allows for the formation of bonds that have consistent energy and properties, lending a predictability to the molecule's overall structure and reactivity. Understanding hybridization provides a window into why certain molecules have the shapes and bond angles observed.

Electron pair repulsion

The principle of electron pair repulsion is fundamental to both the VSEPR theory and Valence Bond Theory. Electrons, being negatively charged, repel each other due to the like charges. In a molecule, this repulsion between electrons in both bonding and non-bonding pairs influences the overall molecular shape.

Lone pairs of electrons, those not involved in bonding, exert more repulsion because they are held more closely to the nucleus and therefore take up more space relative to bonding pairs. As a result, the presence of lone pairs affects bond angles. For example, in methane there are no lone pairs leading to a perfect tetrahedral geometry. However, in ammonia and water, the presence of lone pairs compresses the bond angles to accommodate the extra repulsive force they generate.