Question

The phosphorus trihalides \(\left(\mathrm{PX}_{3}\right)\) show the following variation in the bond angle \(\mathrm{X}-\mathrm{P}-\mathrm{X}: \mathrm{PF}_{3,}, 96.3^{\circ} ; \mathrm{PCl}_{3}, 100.3^{\circ}\); \(\mathrm{PBr}_{3}, 101.0^{\circ} ; \mathrm{PI}_{3}, 102.0^{\circ}\). The trend is generally attributed 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 halide electronegativity increases? (c) Using the VSEPR model, explain the observed trend in \(\mathrm{X}-\mathrm{P}-\mathrm{X}\) angle as the electronegativity of \(\mathrm{X}\) changes. (d) Based on your answer to part (c), predict the structure of \(\mathrm{PBrCl}_{4}\).

Short answer

In summary, the VSEPR model predicts a bond angle of 109.5° for the phosphorus trihalides. The bond angle increases as the halide electronegativity decreases, which can be attributed to the decrease in repulsion between the lone pair and bond pairs. Based on the VSEPR model, the structure of \(\mathrm{PBrCl}_{4}\) is seesaw-shaped with two axial chlorine and two equatorial bromine atoms.

Step-by-step solution

(a) Predicting the bond angle using VSEPR model

The VSEPR (Valence Shell Electron Pair Repulsion) model is used to predict the shape of a molecule based on the arrangement of valence electrons and minimizing the repulsion between the electron pairs. Let's consider a phosphorus trihalide, \(\mathrm{PX}_{3}\). Phosphorus has five valence electrons and the halogen atom has seven valence electrons. Since there is one phosphorus atom and three halogen atoms, the central atom is phosphorus. The three valence electrons from three halogen atoms form three single bonds with phosphorus, and the remaining two valence electrons on phosphorus form one lone pair. Now, there are three bond pairs and one lone pair around the phosphorus atom. According to the VSEPR model, such a molecule has a trigonal pyramidal shape. The predicted bond angle \(\mathrm{X}-\mathrm{P}-\mathrm{X}\) between the three bond pairs in a trigonal pyramidal shape is based on the tetrahedral angle: 109.5°.

(b) Trend in the bond angle based on halide electronegativity

The trend observed in the given data set is: \(\mathrm{PF}_{3} < \mathrm{PCl}_{3} < \mathrm{PBr}_{3} < \mathrm{PI}_{3}\) The bond angle increases as we move from \(\mathrm{PF}_{3}\) to \(\mathrm{PI}_{3}\). As we know, electronegativity decreases down a group, so the electronegativity of the halogen atom decreases in the following order: F > Cl > Br > I Thus, based on the given data, the general trend in the \(\mathrm{X}-\mathrm{P}-\mathrm{X}\) angle is that it increases as the halide electronegativity decreases.

(c) Explanation using VSEPR model

The observed trend in the bond angle can be explained using the VSEPR model as follows: For \(\mathrm{PF}_{3}\), the bond angle is less than the predicted angle, because fluorine has the highest electronegativity among all the halogens, and as a result, it attracts the shared electrons in the bond towards itself. This leads to a more significant repulsion between the lone pair and the bond pairs. This repulsion shrinks the angle, making it smaller than the predicted bond angle of 109.5°. As we move from \(\mathrm{PF}_{3}\) to \(\mathrm{PI}_{3}\), the electronegativity of the halogen atom decreases, and so does the lone pair-bonding pair repulsion. Therefore, the bond angle becomes larger, leading to the observed trend.

(d) Predicting the structure of \(\mathrm{PBrCl}_{4}\)

In the \(\mathrm{PBrCl}_{4}\) molecule, the central atom is phosphorus, which forms four single bonds with bromine and chlorine atoms and has a lone pair of electrons. The distribution of electron pairs around phosphorus is: - Four electron pairs from bonding with the four halogen atoms (Bromine and Chlorine) - One lone pair from the remaining two valence electrons of the phosphorus atom According to the VSEPR model, with four bond pairs and one lone pair, the molecule will have a seesaw shape. That is, two chlorine atoms (smaller electronegativity) will be in axial positions and two bromine atoms (larger electronegativity) will be in equatorial positions. Therefore, the structure of \(\mathrm{PBrCl}_{4}\) is predicted to be seesaw-shaped with two axial chlorine and two equatorial bromine atoms.

Key concepts

Phosphorus Trihalides

Phosphorus trihalides are a group of chemical compounds made up of one phosphorus atom and three halogen atoms, represented by the chemical formula \( \text{PX}_3 \), where \( \text{X} \) denotes the halogen (such as fluorine, chlorine, bromine, or iodine). These compounds offer a unique way to study molecular geometry because they exhibit different properties based on the substituting halide.
The central phosphorus atom in these trihalides utilizes its five valence electrons to form bonds with the halogen atoms. Generally, phosphorus bonds with three halogen atoms and has a pair of non-bonding electrons (lone pair), which makes them a classic example for applying the Valence Shell Electron Pair Repulsion (VSEPR) model to predict their geometric structure.
When considering phosphorus trihalides, molecular geometry often depends on the size, electronegativity, and number of atoms surrounding the central phosphorus, influencing the chemical and physical properties of these compounds.

Electronegativity

Electronegativity is a crucial concept in understanding molecular geometry and the properties of chemical compounds. It describes the ability of an atom to attract electrons when forming a covalent bond. The difference in electronegativity between atoms can quite dramatically influence not only the bonding type but also the properties of the resulting molecules.
In the context of phosphorus trihalides, electronegativity plays a key role in determining bond angles and molecular shape. Generally, as one moves down the halide group in the periodic table from fluorine to iodine, electronegativity decreases.
This decrease in electronegativity affects the electron distribution in phosphorus trihalides:

• Fluorine, being the most electronegative, pulls electron density towards itself more effectively, which increases lone pair-bond pair repulsion, resulting in a smaller bond angle.
• Conversely, iodine is less electronegative, leading to decreased repulsion and a larger bond angle.

This relationship between electronegativity and bond angle is key to both explaining and predicting trends among phosphorus trihalides.

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule and is pivotal for understanding the chemical behavior and interaction of substances. The VSEPR model is essential for predicting the shapes of molecules, such as phosphorus trihalides.
For compounds like \( \text{PX}_3 \), the molecular geometry is influenced by the number of atoms bonded to a central atom (in this case, phosphorus) and the presence of lone pairs of electrons.
In phosphorus trihalides, phosphorus forms three bonds with halogens and holds one lone pair of electrons. According to VSEPR theory, this configuration results in a trigonal pyramidal shape:

• The lone pair on phosphorus pushes the bonded atoms away, minimizing bond pair repulsions.
• This arrangement leads to a distortion from the ideal tetrahedral angle (109.5°) to a slightly smaller bond angle.

This geometry is critical in determining how phosphorus trihalides will interact with other compounds, influencing both reactivity and polarity.

Bond Angle

Bond angles are the angles formed between the neighboring bonds in a molecule. They are crucial for defining the shape and properties of the molecule, such as how it will interact with other substances. In the case of phosphorus trihalides, the bond angle can inform us about the spatial arrangement of atoms and the effect of different substituents on the molecule's overall geometry.
The VSEPR model helps predict bond angles in molecules based on the idea of electron pair repulsion, stating that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion.
For \( \text{PX}_3 \) molecules, the bond angle is influenced by:

• Lone pair-bond pair repulsion, which generally decreases the angle below the ideal tetrahedral value.
• Changes in halogen electronegativity, where higher electronegativity leads to tighter bond angle due to increased repulsion involving the lone pair.

Specifically, in phosphorus trihalides, the bond angle increases as the electronegativity of the halogen decreases, which is explained by reducing repulsion between bond pairs. Understanding these angles is fundamental for applying VSEPR theory and predicting molecule behavior.