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 \(X-P-X\) angle is predicted by the VSEPR model? (b) What is the general trend in the \(X-P-X\) angle as the halide 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 \(\mathrm{PBrCl}_{4}\)

Short answer

In summary, the expected X-P-X bond angle according to VSEPR theory is 120°. The observed trend in bond angles as the electronegativity of the halogen increases is attributed to increased electron density and repulsion, leading to smaller bond angles than predicted. The predicted structure of \(\mathrm{PBrCl}_4\) is a see-saw molecular geometry with the bromide ion and lone pair in equatorial positions and the three chloride ions in one equatorial and two axial positions.

Step-by-step solution

Calculate the expected X-P-X angle using VSEPR model

Using the VSEPR model, we can determine the electron domain geometry of a molecule. In the case of \(\mathrm{PX}_3\), there are three bonding pairs around the central P atom, and no lone pairs. In this trigonal planar geometry, the electron domains will be in the plane of the molecule and will be 120° apart from each other. So, according to VSEPR theory, the expected X-P-X bond angle is 120°.

Identify the electronegativity trend for halogens

Now, let's determine the trend in electronegativity for the given halogens: F, Cl, Br, and I. As we move down a group in the periodic table, the electronegativity of the atom decreases. Therefore, the order of electronegativity is: F > Cl > Br > I

Explain the observed trend in X-P-X angle

As the electronegativity of X increases, the electron density around the X atoms increases, and they tend to repel each other more. This repulsion forces the X-P-X bond angle to compress slightly, resulting in a smaller bond angle than the predicted 120°. This explains the observed trend in X-P-X angles for the phosphorus trihalides as the electronegativity of X changes.

Predict the structure of PBrCl4

Based on the VSEPR theory and the electronegativity trend of halogens, we can predict the structure of \(\mathrm{PBrCl}_4\). The phosphorus atom has a total of five valence electrons. In this ion, the central phosphorus atom is surrounded by four different ligands - one bromide ion and three chloride ions. In addition, phosphorus has one lone pair of electrons. In a molecule with five electron domains (four bonding pairs and one lone pair), the electron domain geometry is trigonal bipyramidal, and the molecular geometry is called see-saw. The lone pair will occupy an equatorial position since it is more repulsive when it is in the axial position. The bromide ion, which has lower electronegativity than the chloride ions, will also occupy an equatorial position since there is more repulsion between bonding electron pairs in equatorial positions. The three chloride ions will occupy the remaining equatorial and two axial positions. So, the predicted structure of \(\mathrm{PBrCl}_4\) is a see-saw molecular geometry with the bromide ion and lone pair in equatorial positions, and the three chloride ions in one equatorial and two axial positions.

Key concepts

Phosphorus Trihalides

Phosphorus trihalides, represented as \( \text{PX}_3 \), are a group of compounds where phosphorus (P) is bonded to three halogen atoms (X). The halogens in these compounds can include fluorine (F), chlorine (Cl), bromine (Br), and iodine (I). These compounds are essential in understanding molecular geometry and bond angles as described by VSEPR theory.

In phosphorus trihalides:

• The central phosphorus atom forms three single covalent bonds with halogen atoms.
• The structure of these compounds is crucial in various chemical reactions, particularly in organic chemistry where they serve as reagents.
• Their variability in bond angles highlights key principles about molecular geometry and electronegativity.

Understanding the properties and behaviors of phosphorus trihalides helps in predicting the structural outcomes of different chemical combinations.

Electronegativity

Electronegativity is a measure of an atom's ability to attract and hold onto electrons in a chemical bond. Halogens, such as fluorine, chlorine, bromine, and iodine, vary in electronegativity. The trend generally decreases as you move down the periodic table group of halogens.

Here is the order of electronegativity for the relevant halogens:

• Fluorine (F) has the highest electronegativity.
• Chlorine (Cl) follows fluorine in electronegativity.
• Bromine (Br) is less electronegative than chlorine.
• Iodine (I) has the lowest electronegativity among these halogens.

Electronegativity affects molecular geometry by influencing the electron density around the atoms. As atoms with higher electronegativity pull electrons closer, this increases electron repulsion, ultimately affecting bond angles. Consequently, the more electronegative the halogen, the smaller the bond angle due to compression from electron repulsion.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It dictates the molecule's shape, determining reactivity, polarity, phase of matter, color, magnetism, biological activity, and more. The VSEPR (Valence Shell Electron Pair Repulsion) theory is pivotal in predicting and understanding molecular geometry.

For \( \text{PX}_3 \) molecules:

• Three bonded pairs and no lone pairs on phosphorus lead to a trigonal planar arrangement of electron domains.
• In a perfect trigonal planar geometry, bond angles are predicted to be 120°.
• However, differences in electronegativity can lead to variations in these angles, as halogens with higher electronegativity create greater electron repulsion, compressing the angle.

By understanding these principles, the geometry and resulting properties of a wide variety of compounds can be predicted, enabling insights into their chemical behaviors.