Problem 88 - Chemistry The Central Science

Question

Consider the molecule \(\mathrm{PF}_{4} \mathrm{Cl}\) (a) Draw a Lewis structure for the molecule, and predict its electron-domain geometry. (b) Which would you expect to take up more space, a \(\mathrm{P}-\mathrm{F}\) bond or a \(\mathrm{P}-\mathrm{Cl}\) bond? Explain. (c) Predict the molecular geometry of \(\mathrm{PF}_{4} \mathrm{Cl} .\) How did your answer for part (b) influence your answer here in part \((\mathrm{c}) ?(\mathbf{d})\) Would you expect the molecule to distort from its ideal electron-domain geometry? If so, how would it distort?

Step-by-Step Solution

Answer

The Lewis structure of \(\mathrm{PF}_4\mathrm{Cl}\) has P as the central atom, connected with single bonds to 4 F atoms and one Cl atom. The electron-domain geometry is trigonal bipyramidal, with the longer \(\mathrm{P}-\mathrm{Cl}\) bond occupying an axial position to minimize repulsion. The molecular geometry will thus be a distorted trigonal bipyramidal with Cl in the axial position and 4 F atoms in equatorial positions. The distortion from the ideal geometry is due to the difference in bond lengths between the \(\mathrm{P}-\mathrm{F}\) and \(\mathrm{P}-\mathrm{Cl}\) bonds, leading to slightly smaller angles between equatorial and axial bonds.

Step 1: Draw Lewis Structure

To draw the Lewis structure for \(\mathrm{PF}_4\mathrm{Cl}\), we follow these rules: 1. Calculate the total number of valence electrons: Phosphorus(P) has 5, each Fluorine(F) has 7, and Chlorine(Cl) has 7. Total valence electrons = 5 + 4(7) + 7 = 40 valence electrons. 2. Choose the central atom. Since P is the only atom that can form more than one bond, it will be the central atom. 3. Connect the surrounding atoms with single bonds to the central atom. In this case, 4 F atoms and 1 Cl atom are connected to P by single bonds. This uses 10 valence electrons (2 for each bond). 4. Complete the octets of all surrounding atoms. Fill in lone pairs of electrons around F and Cl atoms, making sure that each atom (except P) has 8 electrons. This uses the remaining 30 valence electrons. The resultant Lewis structure will have P in the center, connected with single bonds to 4 F atoms and one Cl atom. All the surrounding atoms have complete octets.

Step 2: Predict Electron-Domain Geometry

The electron-domain geometry is determined by the number of electron pairs (both bonding and nonbonding) around the central atom. In this case, P has 5 bonding electron pairs and no nonbonding pairs, so it has a total of 5 electron pairs. According to VSEPR theory, this gives rise to a trigonal bipyramidal electron-domain geometry.

Step 3: Compare P-F and P-Cl Bond Lengths

Generally, larger atomic size leads to longer bond lengths. Comparing the atomic radii of F and Cl, we find that Cl (0.99 Å) is larger than F (0.64 Å). As a result, we can expect the \(\mathrm{P}-\mathrm{Cl}\) bond to be longer and take up more space than the \(\mathrm{P}-\mathrm{F}\) bond.

Step 4: Predict Molecular Geometry and Influence of Bond Lengths

The molecular geometry is determined by the arrangement of the 5 atoms around the central P atom. To minimize repulsion, the longer \(\mathrm{P}-\mathrm{Cl}\) bond should occupy one of the axial positions in the trigonal bipyramidal structure. The geometry will thus be a distorted trigonal bipyramidal geometry with the Cl atom in the axial position and the 4 F atoms in the equatorial positions. The longer \(\mathrm{P}-\mathrm{Cl}\) bond influenced our choice for the molecular geometry by occupying the axial position to minimize repulsion with the other atoms.

Step 5: Discuss Distortion from Ideal Electron-Domain Geometry

The distortion of the molecule from the ideal electron-domain geometry (trigonal bipyramidal) is due to the difference in bond lengths between the \(\mathrm{P}-\mathrm{F}\) and \(\mathrm{P}-\mathrm{Cl}\) bonds. Since the \(\mathrm{P}-\mathrm{Cl}\) bond takes more space, the molecule will distort to accommodate this difference. The axial \(\mathrm{P}-\mathrm{Cl}\) bond will likely be elongated, and the angles between the equatorial \(\mathrm{P}-\mathrm{F}\) bonds and the axial \(\mathrm{P}-\mathrm{Cl}\) bond will be slightly less than the ideal 90 degrees.

Key Concepts

Electron-Domain Geometry

Understanding the electron-domain geometry is critical when predicting the shape of molecules. It's based on the number of electron pairs around the central atom. Whether bonding or lone pairs, each pair occupies space and repels the others, influencing the overall structure. In the case of \textbf{PF\(_4\)Cl}, there are five bonding pairs around the phosphorus atom, resulting in a trigonal bipyramidal electron-domain geometry, which is one of the basic shapes predicted by the VSEPR theory.

Molecular Geometry

While the electron-domain geometry takes into account all electron pairs, molecular geometry focuses on the arrangement of atoms alone. It's crucial for understanding how molecules interact with each other and react during chemical processes. For the molecule \textbf{PF\(_4\)Cl}, the molecular geometry deviates from the perfect trigonal bipyramidal shape because of different bond lengths. By determining which bonds might be longer, we can infer the molecular geometry—a slightly distorted trigonal bipyramidal structure with the longer \textbf{P-Cl} bond placed in an axial position to minimize repulsion.

VSEPR Theory

The VSEPR (Valence Shell Electron Pair Repulsion) theory provides a systematic approach to predict the arrangement of atoms in a molecule. According to this theory, groups of electrons around a central atom will arrange themselves as far apart as possible to minimize repulsion. For \textbf{PF\(_4\)Cl}, VSEPR theory guides us to the trigonal bipyramidal shape due to the presence of five bonded electron pairs and no lone pairs on the phosphorus atom, which is a classic example of the theory in practice.

Bond Length Comparison

Bond length comparison involves examining the size of the atoms involved in a bond. Atoms with larger radii tend to form longer bonds. \textbf{PF\(_4\)Cl} presents an interesting comparison—the \textbf{P-F} bonds are shorter due to the smaller size of fluorine, while the \textbf{P-Cl} bond is longer, as chlorine atoms are larger. This difference directly affects the molecular structure, with the \textbf{P-Cl} bond stretching out to occupy more space.

Distortion from Ideal Geometry

Ideally, a molecule with a trigonal bipyramidal electron-domain geometry would have equal angles between bonds. However, the real-world molecule \textbf{PF\(_4\)Cl} exhibits distortion. The presence of different atoms in the structure leads to bonds with different lengths, namely the longer \textbf{P-Cl} bond, which alters the perfect geometry to reduce strain. The molecule adapts by elongating this bond, which in turn affects the bond angles, resulting in a geometry that is a distorted version of the ideal.