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 (c)? (d) Would you expect the molecule to distort from its ideal electron-domain geometry? If so, how would it distort?

Short answer

The electron-domain geometry of \(\mathrm{PF}_{4}\mathrm{Cl}\) is trigonal bipyramidal. The P-Cl bond is larger than the P-F bonds, causing the molecular geometry to be a distorted trigonal bipyramid. Due to the size difference between P-Cl and P-F bonds, the molecule will distort from its ideal electron-domain geometry with slightly different bond angles.

Step-by-step solution

Drawing Lewis Structure for \(\mathrm{PF}_{4} \mathrm{Cl}\)

To draw the Lewis structure, we need to consider the total number of valence electrons available for all atoms: - P has 5 valence electrons - F has 7 valence electrons each, and there are 4 F atoms, so 4 * 7 = 28 - Cl has 7 valence electrons Total valence electrons = 5 (P) + 28 (F) + 7 (Cl) = 40 Place the central atom (P) in the middle and surround it with the others: P – F – F – F – F – Cl Now, distribute the 40 electrons around atoms to fulfill the octet rule (each atom should have 8 electrons around it, including shared electrons): ``` P - F ||( ) ||( ) F--F (||)|| )||( ) F Cl (||) ||( ) ``` The Lewis structure for \(\mathrm{PF}_{4} \mathrm{Cl}\) is now complete.

Predicting Electron-Domain Geometry

The electron-domain geometry of a molecule is determined by the number of electron pairs, both bonding and nonbonding, around the central atom. In this case, the central atom P has five bonded pairs (4 P-F bonds and 1 P-Cl bond). There are no lone pairs on the central atom. As there are 5 electron pairs around the central atom, the electron-domain geometry is trigonal bipyramidal.

Comparing P-F and P-Cl Bond Sizes

In general, a bond between an atom with a larger size and another atom will take up more space than a bond between the same atom and a smaller atom. In this case, Cl is larger than F, so the P-Cl bond will take up more space than the P-F bond.

Predicting Molecular Geometry

Based on the electron-domain geometry being trigonal bipyramidal, and the fact that P-Cl bond is larger and takes up more space than the P-F bonds, the molecular geometry will have the P-Cl bond in an equatorial position, and the P-F bonds in axial and equatorial positions. So, the molecular geometry of \(\mathrm{PF}_{4} \mathrm{Cl}\) is a distorted trigonal bipyramid.

Discussing Distortion from Ideal Electron-Domain Geometry

As the P-Cl bond is larger than the P-F bonds, it will cause a difference in bond angles on one side of the molecule. This will make the molecule distort from its ideal electron-domain geometry (trigonal bipyramid). Instead of the ideal angles of 90° and 120°, they will be slightly different due to the distortion. In conclusion, for the \(\mathrm{PF}_{4} \mathrm{Cl}\) molecule, the electron-domain geometry is trigonal bipyramidal, with the molecular geometry being a distorted trigonal bipyramid. The larger P-Cl bond will cause the molecule to distort from its ideal electron-domain geometry with slightly different bond angles.

Key concepts

Lewis Structure

The Lewis structure is a symbolic representation showing how atoms share or transfer electrons to form molecules. To draw the Lewis structure for the molecule \( \mathrm{PF}_{4} \mathrm{Cl} \), you begin by counting the total number of valence electrons available. Each atom contributes its outer shell electrons: Phosphorus (P) contributes 5, each of the four Fluorine (F) atoms contributes 7, and Chlorine (Cl) also contributes 7. This totals to 40 valence electrons, which will be distributed among the atoms to satisfy their octet rule.
Place the central atom, Phosphorus (P), in the center and arrange the Fluorine and Chlorine atoms symmetrically around it. The availability of these 40 electrons helps in forming the necessary bonds ensuring each atom achieves a stable electron configuration. Thus, each F and Cl atom connects to the Phosphorus atom through single covalent bonds, forming a complete Lewis structure for \( \mathrm{PF}_{4} \mathrm{Cl} \).

• Central atom: Phosphorus
• Peripheral atoms: 4 Fluorine, 1 Chlorine
• Total valence electrons: 40

Electron-Domain Geometry

Electron-domain geometry refers to the spatial arrangement of electron groups around the central atom, which includes both bonding pairs and lone pairs of electrons. In the case of \( \mathrm{PF}_{4} \mathrm{Cl} \), Phosphorus is surrounded by five bonds (four \( \mathrm{P-F} \) bonds and one \( \mathrm{P-Cl} \) bond), and no lone pairs. The geometry that accommodates five electron domains around a central atom is known as "trigonal bipyramidal." This configuration includes two different bond angles, 90° between axial and equatorial bonds, and 120° among equatorial bonds.
This electron configuration ensures that electron pairs are positioned to minimize repulsions, leading to predictable and specific geometric formations.

• Five electron domains
• Trigonal bipyramidal geometry
• Bond angles: 90° and 120°

Trigonal Bipyramidal

When discussing molecular shapes, trigonal bipyramidal is a key concept. This geometry is significant for molecules with five electron domain regions, which \( \mathrm{PF}_{4} \mathrm{Cl} \) exhibits. In a trigonal bipyramidal geometry, there is a distinction between the axial positions (above and below the equatorial plane) and the equatorial positions (around the central plane). Typically, larger substituents or those that require more space, due to bond length or size, occupy equatorial positions to minimize repulsion.
Due to the differences in atom sizes and bond lengths, arrangment affects molecular shape. In this context, \( \mathrm{P-Cl} \) is positioned in an equatorial place because Chlorine requires more space due to its larger atomic radius, influencing the molecular geometry from perfect symmetry.

• Geometry: Trigonal bipyramidal
• Axial and equatorial positions
• Effect of substituent size

Bond Distortion

Ideally, trigonal bipyramidal geometries have precise bond angles of 90° and 120°; however, these can vary due to bond distortions. Bond distortion refers to the variations from ideal bond angles due to disparities in bond lengths and different atom sizes. In \( \mathrm{PF}_{4} \mathrm{Cl} \), the \( \mathrm{P-Cl} \) bond is larger than the \( \mathrm{P-F} \) bonds, which results in alterations from the original trigonal bipyramidal geometry. This enlarges the equatorial plane positions, pushing the axial \( \mathrm{P-F} \) bonds slightly closer together, changing from the ideal bond angles.
When bond lengths vary, more significant atoms such as Chlorine in \( \mathrm{PF}_{4} \mathrm{Cl} \) lead to a distorted shape rather than a perfect trigonal bipyramidal geometry. This distortion is crucial for understanding molecular behavior, affecting reactivity and interaction with other molecules.

• Substituent size affects angles
• Bonds deviate from ideal positions
• Molecular distortion impacts reactivity