Problem 90 - Chemistry The Central Science

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 PF4Cl has P as the central atom, bonded to four F atoms and one Cl atom, with a trigonal bipyramidal electron-domain geometry. A P-Cl bond takes up more space than a P-F bond due to Cl having a larger atomic radius. PF4Cl's molecular geometry is a seesaw or distorted tetrahedron, with Cl in an equatorial position and F atoms occupying the other positions. The molecule distorts from its ideal electron-domain geometry due to the differences in size and electronegativity of F and Cl atoms, minimizing electron repulsion.

Step 1: Lewis Structure and Electron-Domain Geometry Predictions

To draw the Lewis structure, first identify the central atom. Here, the central atom is phosphorus (P). There are four fluorine (F) atoms and one chlorine (Cl) atom bonded to the P atom. The valence electrons in each atom are as follows: P has 5, each F has 7, and Cl has 7. Therefore, the total number of valence electrons is 5 + 4(7) + 7 = 5 + 28 + 7 = 40. Arrange the F and Cl atoms around the P atom in a way that best minimizes electron repulsion, and draw single bonds between the P atom and the 5 surrounding atoms. Distribute the remaining valence electrons as lone pairs to complete the octets for all atoms (except P, which has an expanded octet). The resulting Lewis structure can be represented as P in the center, bonded to four F atoms, and then to one Cl atom. Next, determine the electron-domain geometry based on the number of electron groups around the central atom. In this case, P has a total of 5 electron groups (4 P-F bonds and 1 P-Cl bond), which indicates a trigonal bipyramidal electron-domain geometry. #Step 2: Comparing P-F and P-Cl Bond Sizes#

Step 2: Comparing P-F and P-Cl Bond Sizes

The bond size can be determined by comparing the atomic radius of the involved atoms. Generally, larger atomic radius leads to larger bond size. The atomic radius of chlorine is greater than that of fluorine, so we can expect that a P-Cl bond will take up more space compared to a P-F bond. #Step 3: Predicting the Molecular Geometry of PF4Cl#

Step 3: Molecular Geometry of PF4Cl

In a trigonal bipyramidal electron-domain geometry, there are two axial positions and three equatorial positions. As the P-Cl bond takes up more space, it is likely to be placed in an equatorial position to minimize repulsions. Therefore, the molecular geometry of PF4Cl will have Cl in one equatorial position, and the F atoms will occupy the two axial and the remaining two equatorial positions. The molecular geometry can be described as a seesaw or distorted tetrahedron. #Step 4: Distortion from Ideal Electron-Domain Geometry#

Step 4: Distortion from Ideal Electron-Domain Geometry

Yes, the molecule will likely distort from its ideal trigonal bipyramidal electron-domain geometry due to the differences in size and electronegativity of the F and Cl atoms. The distortion will result in a molecular geometry like a seesaw, where the Cl atom is in an equatorial position and the F atoms occupy the two axial and the remaining two equatorial positions. This distortion occurs to minimize electron repulsion caused by the larger P-Cl bond and the differences in electronegativity between the F and Cl atoms.

Key Concepts

Lewis Structure

A Lewis structure is a visual representation of the valence electrons in a molecule, showing how atoms are bonded together. To draw the Lewis structure for \(\mathrm{PF}_{4}\)Cl, we start by identifying the central atom, which is phosphorus (P).
Phosphorus can expand its octet, allowing it to bond with more than four atoms. In this case, it bonds with four fluorine (F) atoms and one chlorine (Cl) atom.

• Phosphorus starts with 5 valence electrons.
• Each fluorine atom contributes 7 electrons, totaling 28 for the four F atoms.
• Chlorine adds another 7 electrons.

This gives us a total of 40 valence electrons. These electrons are distributed to form single bonds between P and each of the surrounding atoms. P is at the center with F and Cl atoms forming a geometry that minimizes electron repulsion. Each F and Cl atom achieves an octet configuration, while P has an expanded octet.

Electron-Domain Geometry

The electron-domain geometry considers all electron groups around a central atom, including bonds and lone pairs. For \(\mathrm{PF}_{4}\)Cl, phosphorus is the central atom surrounded by five electron groups: four \(\mathrm{P-F}\) bonds and one \(\mathrm{P-Cl}\) bond.
These electron groups determine the electron-domain geometry. The five groups around phosphorus create a trigonal bipyramidal shape.

• This geometry features two distinct positions: axial and equatorial.
• Axial positions are aligned vertically, while equatorial ones are positioned horizontally.

In a perfect trigonal bipyramidal shape, the two axial positions experience more repulsion from other electron groups, making spatial consideration important for bond placements.

Bond Size Comparison

The size of a bond is often determined by the atomic radii of the bonded atoms. In \(\mathrm{PF}_{4}\)Cl, the \(\mathrm{P-F}\) and \(\mathrm{P-Cl}\) bonds differ in size due to the difference in atomic sizes.
Chlorine has a larger atomic radius than fluorine, which means that the \(\mathrm{P-Cl}\) bond will be larger than the \(\mathrm{P-F}\) bond.

• Larger bonds take up more space and lead to increased repulsion with other electron groups.
• This often results in strategic placement within the molecular geometry to reduce repulsion effects.

Understanding bond sizes is crucial for predicting molecular shape. In \(\mathrm{PF}_{4}\)Cl, the larger \(\mathrm{P-Cl}\) bond is likely placed in an equatorial position to minimize any increased electron repulsion, affecting overall molecular geometry.