Question

In the series \(\mathrm{SiF}_{4}, \mathrm{PF}_{3},\) and \(\mathrm{SF}_{2},\) estimate the \(\mathrm{F}-\mathrm{X}-\mathrm{F}\) bond angle in each case and explain your rationale. [Section 9.2\(]\)

Short answer

The F-X-F bond angles in the molecules SiF4, PF3, and SF2 are approximately as follows: In SiF4, the F-Si-F bond angle is around 109.5° due to the tetrahedral electron domain geometry and no lone pairs on the central atom Si. In PF3, the F-P-F bond angle is slightly less than 109.5° because of the presence of a lone pair on the central atom P, causing greater repulsion and reduction in the bond angle. In SF2, the F-S-F bond angle is significantly less than 109.5° due to two lone pairs on the central atom S, leading to even greater repulsion and further reduction in the bond angle. The rationale is based on VSEPR (Valence Shell Electron Pair Repulsion) theory, which states that electron pairs will arrange themselves to minimize repulsion.

Step-by-step solution

Identify the Central Atoms and Lewis Structures

First, we need to identify the central atom (X) of each molecule and draw the Lewis structure. SiF4 has Si as the central atom, PF3 has P, and SF2 has S. For SiF4, the Lewis structure is tetrahedral with Si in the center bonded to four F atoms, and no lone pair of electrons on Si since it has 4 valence electrons, all of them are used in the bond with F. For PF3, the Lewis structure has P in the center bonded to three F atoms and with one lone pair of electrons on P, as P has 5 valence electrons, 3 of which are used in bonding with F. For SF2, the Lewis structure consists of S in the center bonded to two F atoms and with two lone pairs of electrons on S. Sulfur has 6 valence electrons, 2 of which are used in bonding with F.

Determine Electron Domain Geometry

Using VSEPR (Valence Shell Electron Pair Repulsion) theory, we can classify the electron domain geometry for each molecule. For SiF4, the electron domain geometry is tetrahedral, as the central atom Si has 4 electron domains: 4 bonds with F. For PF3, the electron domain geometry is also tetrahedral, as the central atom P has 4 electron domains: 3 bonds with F and 1 lone pair. For SF2, the electron domain geometry is tetrahedral too, as the central atom S has 4 electron domains: 2 bonds with F and 2 lone pairs.

Estimate F-X-F Bond Angles

Now let's estimate the F-X-F bond angles for each molecule based on VSEPR theory. In SiF4, the F-Si-F bond angle should be around 109.5 degrees, as all 4 electron domains are bonding pairs with the same repulsion in a tetrahedral geometry. In PF3, the F-P-F bond angle will be a bit less than 109.5 degrees, as the lone pair on P has greater repulsion than bonding pairs, which will reduce the bond angle between bonding pairs. In SF2, the F-S-F bond angle will be even less than the bond angle in PF3 due to the presence of two lone pairs on S, which cause greater repulsion and further reduction in the bond angle between bonding pairs. So, the predicted F-X-F bond angles are approximately: F-Si-F = 109.5°, F-P-F <109.5°, and F-S-F<< 109.5°.

Explain the Rationale

The rationale behind our estimations of bond angles is the repulsion between electron domains around the central atom. In all three cases, the electron domain geometry is tetrahedral. According to VSEPR theory, electron pairs will arrange themselves in a manner to minimize repulsion. In SiF4, all electron domains are bonding pairs, leading to equal repulsion and an F-Si-F bond angle close to 109.5°. In PF3, the presence of a lone pair on the central atom P causes greater repulsion, pushing the bonding pairs closer to each other, resulting in a bond angle smaller than 109.5° for F-P-F. In SF2, the presence of two lone pairs on the central atom S causes even greater repulsion than in PF3, pushing the bonding pairs even closer to each other, resulting in a bond angle much smaller than 109.5° for F-S-F.

Key concepts

Electron Domain Geometry

Understanding the spatial arrangement of atoms within a molecule is vital for predicting its properties, such as shape and reactivity. This arrangement, known as electron domain geometry, is guided by the Valence Shell Electron Pair Repulsion (VSEPR) theory. According to VSEPR, electron domains (bonding or lone pairs of electrons) around a central atom will arrange themselves as far apart as possible to minimize repulsion. For example, in a molecule with four electron domains like SiF4, PF3, and SF2, the electron domains are arranged in a tetrahedral geometry.

However, lone pairs occupy more space than bonding pairs because they are solely under the influence of one nucleus, rather than being shared between two. This difference influences the shape and angles within a molecule. In SiF4, all electron domains are bonding pairs, resulting in a perfect tetrahedral shape. In PF3 and SF2, the presence of lone pairs alters the electron domain geometry, causing it to deviate from the ideal angles found in a perfect tetrahedral structure.

F-X-F Bond Angle Estimation

The F-X-F bond angle estimation is a practical application of the VSEPR theory. To predict the F-X-F bond angles in molecules like SiF4, PF3, and SF2, one must consider both the electron domain geometry and the type of electron domains present. The bond angle in a perfect tetrahedral structure is 109.5 degrees. However, the presence of lone pairs results in smaller bond angles due to their greater repulsion compared to bonding pairs.

Therefore, in SiF4, the bond angle remains close to the ideal 109.5° because there are no lone pairs. In PF3, the bond angle is slightly less due to one lone pair exerting extra repulsion. In SF2, where there are two lone pairs, the angle is even smaller. The estimation progresses logically from understanding the impact of electron domain types to predicting measurable structural features of the molecules.

Lewis Structures of Molecules

The foundation of understanding a molecule's shape and predicting bond angles begins with drawing the Lewis structures of molecules. A Lewis structure is a diagram that represents the valence electron configuration of an atom in a molecule, including any lone pairs. It also shows the bonding between atoms. Understanding how to draw Lewis structures is crucial for determining the geometry and properties of a molecule.

When we step through Lewis structures for molecules like SiF4, PF3, and SF2, we account for the valence electrons of the central atom (Si, P, or S, respectively) and how they’re distributed in bonds or as lone pairs. This exercise helps in visualizing the electron domain geometry, which directly correlates to the F-X-F bond angles. It is through these structures that the impact of lone pairs and the differences they make to molecular shapes become apparent.