Which has trigonal bipyramidal shape?

To determine which compound has a trigonal bipyramidal shape, we use VSEPR theory. This theory predicts molecular geometry based on the number of electron domains (bonding pairs and lone pairs) around the central atom. A trigonal bipyramidal shape occurs when there are five electron domains with no lone pairs on the central atom.

We analyze each option by calculating the total valence electrons, drawing the Lewis structure, and finding the steric number (number of bonded atoms plus lone pairs on the central atom). Xenon (Xe) has 8 valence electrons.

Option A: XeOF₄
Total valence electrons = Xe (8) + O (6) + 4F (4 × 7 = 28) = 42.
Lewis structure: Xe bonded to O via a double bond and to four F atoms via single bonds.
Electrons used in bonding: Double bond (4 electrons) + four single bonds (8 electrons) = 12 electrons.
Non-bonding electrons = 42 - 12 = 30 electrons → 15 lone pairs.
On Xe: Electrons used = 2 (for O double bond) + 1 each for four F single bonds = 6 electrons.
Remaining electrons on Xe = 8 - 6 = 2 electrons → 1 lone pair.
Steric number = bonded atoms (5) + lone pairs (1) = 6.
Electron geometry: Octahedral. Molecular geometry: Square pyramidal (due to one lone pair). Not trigonal bipyramidal.

Option B: XeO₃
Total valence electrons = Xe (8) + 3O (3 × 6 = 18) = 26.
Lewis structure: Xe bonded to three O atoms via double bonds.
Electrons used in bonding: Three double bonds (12 electrons).
Non-bonding electrons = 26 - 12 = 14 electrons → 7 lone pairs.
On Xe: Electrons used = 2 per double bond × 3 = 6 electrons.
Remaining electrons on Xe = 8 - 6 = 2 electrons → 1 lone pair.
Steric number = bonded atoms (3) + lone pairs (1) = 4.
Electron geometry: Tetrahedral. Molecular geometry: Trigonal pyramidal (due to one lone pair). Not trigonal bipyramidal.

Option C: XeO₃F₂
Total valence electrons = Xe (8) + 3O (18) + 2F (14) = 40.
Lewis structure: Xe bonded to three O atoms via double bonds and to two F atoms via single bonds.
Electrons used in bonding: Three double bonds (12 electrons) + two single bonds (4 electrons) = 16 electrons.
Non-bonding electrons = 40 - 16 = 24 electrons → 12 lone pairs.
On Xe: Electrons used = 2 per double bond × 3 + 1 per single bond × 2 = 6 + 2 = 8 electrons.
Remaining electrons on Xe = 8 - 8 = 0 electrons → 0 lone pairs.
Steric number = bonded atoms (5) + lone pairs (0) = 5.
Electron geometry: Trigonal bipyramidal. Molecular geometry: Trigonal bipyramidal (no lone pairs). This matches the required shape.

Option D: XeOF₂
Total valence electrons = Xe (8) + O (6) + 2F (14) = 28.
Lewis structure: Xe bonded to O via a double bond and to two F atoms via single bonds.
Electrons used in bonding: Double bond (4 electrons) + two single bonds (4 electrons) = 8 electrons.
Non-bonding electrons = 28 - 8 = 20 electrons → 10 lone pairs.
On Xe: Electrons used = 2 (for O double bond) + 1 each for two F single bonds = 4 electrons.
Remaining electrons on Xe = 8 - 4 = 4 electrons → 2 lone pairs.
Steric number = bonded atoms (3) + lone pairs (2) = 5.
Electron geometry: Trigonal bipyramidal. Molecular geometry: T-shaped (due to two lone pairs in equatorial positions). Not trigonal bipyramidal.

Only XeO₃F₂ has a trigonal bipyramidal molecular geometry. Hence, the correct answer is Option C.