Problem 88 - Chemistry: The Central Science in SI Units, Global Edition

Question

Consider the molecule \(\mathrm{PF}_{4}\) 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 (c)? (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 \(\mathrm{PF}_{4}\mathrm{Cl}\) places \(\mathrm{P}\) as the central atom surrounded by \(\mathrm{F}\) and \(\mathrm{Cl}\) atoms, and its electron-domain geometry is trigonal bipyramidal. The \(\mathrm{P}-\mathrm{Cl}\) bond takes up more space than the \(\mathrm{P}-\mathrm{F}\) bond, so \(\mathrm{Cl}\) occupies one of the three equatorial positions. The molecular geometry of \(\mathrm{PF}_{4}\mathrm{Cl}\) is a trigonal bipyramid, with three \(\mathrm{F}\) atoms and one \(\mathrm{Cl}\) atom in the equatorial plane and two more \(\mathrm{F}\) atoms at axial positions. There might be some slight distortion due to the size difference between \(\mathrm{P}-\mathrm{F}\) and \(\mathrm{P}-\mathrm{Cl}\) bonds, leading to a decrease in equatorial bond angles, but it should not drastically change the overall molecular geometry.

Step 1: (a) Drawing Lewis Structure and Predicting Electron-domain Geometry

First, find the total number of valence electrons in the molecule which is composed of: 5 valence electrons from \(\mathrm{P}\), 7 valence electrons from \(\mathrm{Cl}\), and 4 × 7 (7 from four \(\mathrm{F}\) atoms) = 28 valence electrons from the \(\mathrm{F}\) atoms. The total number of valence electrons in the molecule is 5 + 7 + 28 = 40. To draw the Lewis structure, arrange the atoms in such a way that \(\mathrm{P}\) is the central atom surrounded by \(\mathrm{F}\) atoms and \(\mathrm{Cl}\). Next, place one pair of electrons between each two bonded atoms (one \(\mathrm{P}-\mathrm{F}\) and one \(\mathrm{P}-\mathrm{Cl}\)), and then fill the octets of the surrounding atoms (both \(\mathrm{F}\) and \(\mathrm{Cl}\)). Since \(\mathrm{P}\) has 5 valence electrons and it is bonded with 5 other atoms (4 \(\mathrm{F}\) atoms and 1 \(\mathrm{Cl}\)), its electron-domain geometry is described by five electron domains: 5 bonds around the \(\mathrm{P}\) atom (no lone pairs). Therefore, the electron-domain geometry of \(\mathrm{PF}_{4}\mathrm{Cl}\) is trigonal bipyramidal.

Step 2: (b) Comparing \(\mathrm{P}-\mathrm{F}\) and \(\mathrm{P}-\mathrm{Cl}\) Bond Sizes

Although both fluorine and chlorine belong to Group 17, chlorine is larger in size than fluorine. The larger the atom, the longer the bond will be. Therefore, a \(\mathrm{P}-\mathrm{Cl}\) bond is expected to take up more space than a \(\mathrm{P}-\mathrm{F}\) bond.

Step 3: (c) Predicting Molecular Geometry of \(\mathrm{PF}_{4}\mathrm{Cl}\)

In a trigonal bipyramidal electron-domain geometry, there are two types of positions: axial (two positions) and equatorial (three positions). The less bulky groups (or those that take up less space) occupy axial positions, whereas the bulkier groups/events occupy equatorial positions to minimize the electronic repulsion. Based on our conclusion in part (b), the \(\mathrm{P}-\mathrm{Cl}\) bond takes up more space, so it will occupy one of the three equatorial positions to minimize electronic repulsion. The remaining positions will be occupied by \(\mathrm{F}\) atoms. Therefore, the molecular geometry of \(\mathrm{PF}_{4}\mathrm{Cl}\) can be described as a trigonal bipyramid, with three \(\mathrm{F}\) atoms and one \(\mathrm{Cl}\) atom in the equatorial plane and two more \(\mathrm{F}\) atoms at axial positions.

Step 4: (d) Considering Possible Distortions

Due to the size difference between the \(\mathrm{P}-\mathrm{F}\) and \(\mathrm{P}-\mathrm{Cl}\) bonds, there might be some distortion in the molecular geometry of \(\mathrm{PF}_{4}\mathrm{Cl}\) from the ideal trigonal bipyramidal structure. The equatorial \(\mathrm{P}-\mathrm{Cl}\) bond may slightly push the equatorial \(\mathrm{P}-\mathrm{F}\) bonds away from the ideal 120° angle, leading to a decrease in the equatorial bond angles and a slight distortion of the molecule. Axial bond angles may also differ from 180°. However, this distortion should not be significant enough to cause drastic changes in the overall molecular geometry.

Key Concepts

Lewis Structure

The Lewis structure is a diagrammatic way of representing molecules. It shows how atoms are bonded and the arrangement of valence electrons around those atoms. For our molecule, \(\mathrm{PF}_{4}\mathrm{Cl}\), we need to count the total valence electrons to draw its Lewis structure.

• Phosphorus (\(\mathrm{P}\)) has 5 valence electrons.
• Each Fluorine (\(\mathrm{F}\)) atom contributes 7 valence electrons, adding up to 28 for four fluorines.
• Chlorine (\(\mathrm{Cl}\)) also contributes 7 valence electrons.

So, the molecule as a whole has 40 valence electrons. Placing \(\mathrm{P}\) in the center, it is surrounded by four \(\mathrm{F}\) atoms and one \(\mathrm{Cl}\). Each bond represents a pair of electrons.
After accounting for bonds, ensure each surrounding atom fulfills its octet. This understanding forms the basis to predict the molecule's properties and structure.

Electron-Domain Geometry

Electron-domain geometry refers to the spatial arrangement of electron domains (bonding and nonbonding electron pairs) around the central atom. In \(\mathrm{PF}_{4}\mathrm{Cl}\), phosphorous is the central atom. It is bonded with five other atoms, making five bonding pairs or electron domains.
The electron-domain geometry is described as trigonal bipyramidal due to these five domains.

The understanding of electron geometry helps predict molecular shapes and how atoms are arranged in space, which is crucial for understanding molecular behavior and interactions.

Bond Angles

Bond angles are the angles between adjacent bonds around a central atom. In a trigonal bipyramidal electron-domain geometry, ideal bond angles are set by the domain arrangement:

• 120° between equatorial positions.
• 90° between axial and equatorial positions.
• 180° between two axial positions.

However, atoms differ in size; hence, differences in bond length and atomic size can cause deviations from these ideal angles. For \(\mathrm{PF}_{4}\mathrm{Cl}\), with a larger \(\mathrm{P}-\mathrm{Cl}\) bond, equatorial \(\mathrm{P}-\mathrm{F}\) bond angles could be slightly less than 120° due to crowding by the larger \(\mathrm{Cl}\) atom.

Trigonal Bipyramidal Geometry

Trigonal bipyramidal geometry appears when a central atom is surrounded by five groups of electrons, making five bonds. This arrangement features two different types of positions around the central atom:

• Axial positions: two positions aligned with the molecule’s axis.
• Equatorial positions: three positions forming an equatorial plane.

In our molecule, \(\mathrm{PF}_{4}\mathrm{Cl}\), the \(\mathrm{P}-\mathrm{Cl}\) bond, which is bulkier, takes an equatorial position to minimize electron repulsion, influencing the specific molecular geometry. Such a geometry allows for the most efficient distribution, minimizing repulsions and stabilizing the structure. Understanding this geometry helps to predict physical and chemical properties of molecules.