Question

The phosphorus trihalides \(\left(\mathrm{PX}_{3}\right)\) show the following variation in the bond angle \(\mathrm{X}-\mathrm{P}-\mathrm{X}: \mathrm{PF}_{3}, 96.3^{\mathrm{a}} ; \mathrm{PCl}_{3}\) \(100.3^{\circ} ; \mathrm{PBr}_{3}, 101.0^{\circ} ; \mathrm{Pl}_{3}, 102.0^{\circ} .\) The trend is generally at- tributed to the change in the electronegativity of the halogen. (a) Assuming that all electron domains are the same size, what value of the \(\mathrm{X}-\mathrm{P}-\mathrm{X}\) angle is predicted by the VSEPR model? (b) What is the general trend in the \(\mathrm{X}-\mathrm{P}-\mathrm{X}\) angle as the electronegativity increases? (c) Using the VSEPR model, explain the observed trend in \(X-P-X\) angle as the electronegativity of \(X\) changes. (d) Based on your answer to part (c), predict the structure of \(\mathrm{PBrCI}_{4}\)

Short answer

The X-P-X bond angle is predicted to be slightly less than 109.5° using the VSEPR model. The general trend is that the bond angle increases as the electronegativity of the halogen X decreases. The observed trend in bond angles can be explained by the changing repulsion experienced between the bonding groups as the electronegativity of the substituent X changes. For PBrCl4, the molecular geometry is trigonal bipyramidal with one Br atom at an equatorial position and four Cl atoms at the remaining positions.

Step-by-step solution

Predict the X-P-X bond angle using the VSEPR model

First, let's analyze the structure of the phosphorus trihalides (PX3) using the VSEPR model. In all the molecules, phosphorus is bonded to three halogens (X). In addition, there is a lone pair on phosphorus. The electron pair domain geometry around phosphorus adheres to the tetrahedral structure, which means that there are four electron domains on the central atom (P). With three bonding domains and a lone pair, the molecular geometry should be trigonal pyramidal. From the VSEPR model, we know that the bond angle for a regular tetrahedral geometry is 109.5°. But due to the presence of a lone pair occupying a larger volume of space, the bond angle X-P-X is predicted to be slightly less than 109.5°.

Identify the general trend in the bond angle as the electronegativity increases

Based on the given bond angles for each phosphorus trihalide compound: - PF3: 96.3° - PCl3: 100.3° - PBr3: 101.0° - PI3: 102.0° We can observe that the bond angle X-P-X generally increases as the electronegativity of the halogen X decreases (from F to I). The electronegativity of the halogens is in the following order: F > Cl > Br > I.

Explain the observed trend using the VSEPR model

The observed trend in the bond angles can be explained by the fact that as the electronegativity of the substituent X decreases, the repulsion experienced between the bonding groups decreases. As the halogen becomes more electronegative, it attracts the electrons in the P-X bonding orbital towards itself, making that electron density effectively "smaller." This leads to less repulsion between the lone pair on phosphorus and the bonding pairs, resulting in smaller bond angles in more electronegative substituents. Conversely, as the electronegativity of the substituent X decreases, the electrons in the P-X bonding orbital are less attracted to X and the electron density remains "larger." The larger electron density would cause more repulsion between the lone pair and bonding pairs, leading to larger X-P-X bond angles.

Predict the structure of PBrCl4

To predict the structure of PBrCl4, let's first analyze the molecule's electron domain geometry. Phosphorus has five valence electrons. In PBrCl4, P is bonded to one Br atom and four Cl atoms, which accounts for all five valence electrons. Therefore, there will be no lone pair on phosphorus. With five electron domains around the central atom (P), the electron pair domain geometry will be trigonal bipyramidal, and the molecular geometry will be the same since there is no lone pair on phosphorus. In a trigonal bipyramid, there are two types of bond angles: 90° between equatorial and axial ligands, and 120° between equatorial ligands. Since Br is less electronegative than Cl, the Br atom will occupy an equatorial position to minimize the electron-electron repulsion in the molecule. Consequently, the PBrCl4 molecule will have one Br atom at an equatorial position, and four Cl atoms at the remaining equatorial and axial positions.

Key concepts

Understanding Phosphorus Trihalides

Phosphorus trihalides, such as PF₃, PCl₃, PBr₃, and PI₃, are molecules where a single phosphorus atom (P) is bonded to three halogen atoms, denoted as X. What's intriguing about these compounds is how the bond angle X-P-X changes across the series, illuminating key principles in molecular geometry and bonding.

These molecules have one thing in common: a lone pair of electrons on the central phosphorus atom that significantly influences the molecular structure. Although one might assume that all bond angles would be equal, the lone pair's presence and the different electronegativities of the halogens contribute to the variation in bond angles observed.

When interpreting the bond angles using the Valence Shell Electron Pair Repulsion (VSEPR) model, one can deduce that the perfect tetrahedral angle (109.5°) is not achieved due to the repulsion caused by the lone pair. This exemplifies how the VSEPR theory can provide first-order predictions about molecular shapes and angles, a foundational concept in understanding molecular geometry.

Electron Domain Geometry and the VSEPR Model

The VSEPR (Valence Shell Electron Pair Repulsion) model is integral to predicting the three-dimensional structure of molecules like phosphorus trihalides. According to the VSEPR model, electron domains around a central atom will arrange themselves as far apart as possible to minimize repulsion between negatively charged electron clouds.

In the case of the phosphorus trihalides, there are four electron domains around the central phosphorus atom: three from the P-X bonds and one from the lone pair. This results in a tetrahedral electron domain geometry, but the actual molecular shape is trigonal pyramidal due to the lone pair's presence, which distorts the bond angles slightly. These subtle nuances in electron domain geometry versus molecular shape are critical for students to understand when analyzing and predicting the structure of molecules.

Electronegativity Trend and Bond Angles

Electronegativity is a measure of how strongly an atom can attract electrons towards itself. In phosphorus trihalides, as the electronegativity of the halogen (X) decreases from fluorine (F) to iodine (I), the bond angle X-P-X increases. This counterintuitive trend can be comprehended by examining electron repulsion dynamics.

Higher electronegative atoms pull bonding electrons closer to themselves, effectively reducing the electron cloud size around the bond. Subsequently, this reduces the repulsion between the bond pair and the lone pair on phosphorus, leading to smaller bond angles. Conversely, less electronegative atoms exert weaker pull on bonding electrons, resulting in larger electron clouds that push away the lone pair more forcefully, thus increasing bond angles.

This trend underscores the importance of understanding how electronegativity affects molecular structure, which is a significant factor in a range of chemical phenomena from reactivity to physical properties.