Determining T-shaped Molecular Geometry using VSEPR Theory

To determine the molecular geometry of a molecule, we use the Valence Shell Electron Pair Repulsion (VSEPR) theory. This theory predicts the arrangement of electron domains (bonding pairs and lone pairs) around the central atom to minimize repulsion. The molecular geometry is then determined by the arrangement of only the bonding pairs.

Applying VSEPR Theory to the Given Molecules

Molecular Geometry of \(SF_4\)

• Central atom: Sulfur (S).
• Valence electrons: S has 6 valence electrons. Each F has 7 valence electrons. Total valence electrons = \(6 + 4 \times 7 = 6 + 28 = 34\).
• Total electron pairs = \(34 / 2 = 17\).
• Number of bonding pairs: 4 (S-F bonds).
• Number of lone pairs = Total pairs - Bonding pairs = \(17 - (4 \text{ bonds} + 4 \text{ F atoms}) = 17 - 4\). This calculation approach using total pairs is incorrect for VSEPR domains. A simpler approach is to find the number of electron domains around the central atom.
• Let's recalculate domains for the central atom:
  • Central atom: S. Valence electrons of S = 6.
  • Number of atoms bonded to S = 4 (F atoms). These form 4 bonding pairs.
  • Total electrons contributed by F atoms = \(4 \times 1 = 4\) (one electron each for bonding).
  • Remaining valence electrons on S = \(6 - 4 = 2\).
  • Number of lone pairs on S = \(2 / 2 = 1\).
• Electron domains around S = Bonding pairs + Lone pairs = \(4 + 1 = 5\).
• Electron domain geometry for 5 electron domains is trigonal bipyramidal.
• In a trigonal bipyramidal arrangement, lone pairs occupy equatorial positions to minimize repulsion.
• Molecular geometry is determined by the arrangement of the 4 bonding pairs and 1 lone pair. With 4 bonding pairs and 1 lone pair, the molecular geometry is see-saw.

Molecular Geometry of \(ClF_3\)

• Central atom: Chlorine (Cl).
• Valence electrons: Cl has 7 valence electrons. Each F has 7 valence electrons. Total valence electrons = \(7 + 3 \times 7 = 7 + 21 = 28\).
• Total electron pairs = \(28 / 2 = 14\).
• Let's find electron domains around Cl:
  • Central atom: Cl. Valence electrons of Cl = 7.
  • Number of atoms bonded to Cl = 3 (F atoms). These form 3 bonding pairs.
  • Total electrons contributed by F atoms = \(3 \times 1 = 3\).
  • Remaining valence electrons on Cl = \(7 - 3 = 4\).
  • Number of lone pairs on Cl = \(4 / 2 = 2\).
• Electron domains around Cl = Bonding pairs + Lone pairs = \(3 + 2 = 5\).
• Electron domain geometry for 5 electron domains is trigonal bipyramidal.
• The 2 lone pairs occupy equatorial positions to minimize repulsion.
• Molecular geometry is determined by the arrangement of the 3 bonding pairs and 2 lone pairs in a trigonal bipyramidal electron domain. This results in a T-shaped molecular geometry.

Molecular Geometry of \(XeF_4\)

• Central atom: Xenon (Xe).
• Valence electrons: Xe has 8 valence electrons. Each F has 7 valence electrons. Total valence electrons = \(8 + 4 \times 7 = 8 + 28 = 36\).
• Total electron pairs = \(36 / 2 = 18\).
• Let's find electron domains around Xe:
  • Central atom: Xe. Valence electrons of Xe = 8.
  • Number of atoms bonded to Xe = 4 (F atoms). These form 4 bonding pairs.
  • Total electrons contributed by F atoms = \(4 \times 1 = 4\).
  • Remaining valence electrons on Xe = \(8 - 4 = 4\).
  • Number of lone pairs on Xe = \(4 / 2 = 2\).
• Electron domains around Xe = Bonding pairs + Lone pairs = \(4 + 2 = 6\).
• Electron domain geometry for 6 electron domains is octahedral.
• The 2 lone pairs occupy positions opposite to each other (axial positions) to minimize repulsion.
• Molecular geometry is determined by the arrangement of the 4 bonding pairs and 2 lone pairs in an octahedral electron domain. This results in a square planar molecular geometry.

Conclusion on T-shaped Geometry

Based on the VSEPR analysis:

• \(SF_4\) has see-saw geometry.
• \(ClF_3\) has T-shaped geometry.
• \(XeF_4\) has square planar geometry.

Therefore, \(ClF_3\) is the molecule that has T-shaped geometry.