Analyzing Planar Molecular Geometries

The question asks us to identify the set containing only planar species. A planar species is one where all the constituent atoms are located within the same plane. We can determine the shape of molecules using the Valence Shell Electron Pair Repulsion (VSEPR) theory, which helps predict the geometry based on minimizing electron pair repulsions around the central atom.

Determining Molecular Geometry Using VSEPR Theory

The VSEPR theory involves the following steps:

• Identify the central atom.
• Calculate the total number of valence electrons of the central atom.
• Determine the number of bonding pairs (BP) and lone pairs (LP) around the central atom.
• Calculate the steric number (SN), where SN = BP + LP.
• Determine the electron geometry based on SN.
• Determine the molecular geometry by considering the spatial arrangement of bonded atoms only.
• Assess if the molecular geometry is planar.

Analysis of Chemical Species

Let's analyze the geometry and planarity of each species mentioned:

Xenon Tetrafluoride ($XeF_4$)

• Central Atom: Xenon (Xe)
• Valence electrons of Xe: 8
• Bonding Pairs (BP) with Fluorine (F): 4
• Lone Pairs (LP): (8 valence electrons - 4 bonding pairs * 2 electrons/pair) / 2 = 4 / 2 = 2
• Steric Number (SN): 4 (BP) + 2 (LP) = 6
• Electron Geometry: Octahedral
• Molecular Geometry: Square Planar (4 BP and 2 LP arranged opposite each other)
• Planarity: Yes

Boron Trifluoride ($BF_3$)

• Central Atom: Boron (B)
• Valence electrons of B: 3
• Bonding Pairs (BP) with Fluorine (F): 3
• Lone Pairs (LP): (3 valence electrons - 3 bonding pairs * 2 electrons/pair) / 2 = 0 / 2 = 0
• Steric Number (SN): 3 (BP) + 0 (LP) = 3
• Electron Geometry: Trigonal Planar
• Molecular Geometry: Trigonal Planar
• Planarity: Yes

Boron Trichloride ($BCl_3$)

• Central Atom: Boron (B)
• Valence electrons of B: 3
• Bonding Pairs (BP) with Chlorine (Cl): 3
• Lone Pairs (LP): (3 valence electrons - 3 bonding pairs * 2 electrons/pair) / 2 = 0 / 2 = 0
• Steric Number (SN): 3 (BP) + 0 (LP) = 3
• Electron Geometry: Trigonal Planar
• Molecular Geometry: Trigonal Planar
• Planarity: Yes

Phosphorus Trichloride ($PCl_3$)

• Central Atom: Phosphorus (P)
• Valence electrons of P: 5
• Bonding Pairs (BP) with Chlorine (Cl): 3
• Lone Pairs (LP): (5 valence electrons - 3 bonding pairs * 2 electrons/pair) / 2 = 2 / 2 = 1
• Steric Number (SN): 3 (BP) + 1 (LP) = 4
• Electron Geometry: Tetrahedral
• Molecular Geometry: Trigonal Pyramidal
• Planarity: No

Nitrogen Trichloride ($NCl_3$)

• Central Atom: Nitrogen (N)
• Valence electrons of N: 5
• Bonding Pairs (BP) with Chlorine (Cl): 3
• Lone Pairs (LP): (5 valence electrons - 3 bonding pairs * 2 electrons/pair) / 2 = 2 / 2 = 1
• Steric Number (SN): 3 (BP) + 1 (LP) = 4
• Electron Geometry: Tetrahedral
• Molecular Geometry: Trigonal Pyramidal
• Planarity: No

Xenon Hexafluoride ($XeF_6$)

• Central Atom: Xenon (Xe)
• Valence electrons of Xe: 8
• Bonding Pairs (BP) with Fluorine (F): 6
• Lone Pairs (LP): (8 valence electrons - 6 bonding pairs * 2 electrons/pair) / 2 = 2 / 2 = 1
• Steric Number (SN): 6 (BP) + 1 (LP) = 7
• Electron Geometry: Pentagonal Bipyramidal
• Molecular Geometry: Distorted Octahedral (due to lone pair influence)
• Planarity: No

Aluminium Trifluoride ($AlF_3$)

• Central Atom: Aluminium (Al)
• Valence electrons of Al: 3
• Bonding Pairs (BP) with Fluorine (F): 3
• Lone Pairs (LP): (3 valence electrons - 3 bonding pairs * 2 electrons/pair) / 2 = 0 / 2 = 0
• Steric Number (SN): 3 (BP) + 0 (LP) = 3
• Electron Geometry: Trigonal Planar
• Molecular Geometry: Trigonal Planar (in monomeric form)
• Planarity: Yes

Aluminium Trichloride ($AlCl_3$)

• Central Atom: Aluminium (Al)
• Valence electrons of Al: 3
• Bonding Pairs (BP) with Chlorine (Cl): 3
• Lone Pairs (LP): (3 valence electrons - 3 bonding pairs * 2 electrons/pair) / 2 = 0 / 2 = 0
• Steric Number (SN): 3 (BP) + 0 (LP) = 3
• Electron Geometry: Trigonal Planar
• Molecular Geometry: Trigonal Planar (in monomeric form)
• Planarity: Yes

Evaluating the Options for Planar Species

Now, let's check each option provided:

Conclusion on Planar Species Set

Based on the VSEPR theory analysis, the set {$XeF_4$, $BF_3$, $BCl_3$} consists solely of planar species. $XeF_4$ exhibits a square planar geometry, while both $BF_3$ and $BCl_3$ display trigonal planar geometries. These shapes ensure all atoms lie within a single plane.