Identify Pyramidal Molecular Geometry Species

To determine the molecular geometry (shape) of each given species, we use the Valence Shell Electron Pair Repulsion (VSEPR) theory and steric number calculations:

$\text{Steric Number (SN)} = (\text{Number of }\sigma\text{-bonds}) + (\text{Number of lone pairs on the central atom})$

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1. Analysis of $\text{SO}_3$ (Sulfur trioxide)

• Central atom: Sulfur ($\text{S}$), which has 6 valence electrons.
• Bonding: $\text{S}$ forms double bonds with three oxygen atoms ($\text{S}=\text{O}$).
• $\sigma$-bonds: 3
• Lone pairs on $\text{S}$: $\frac{6 - (3 \times 2)}{2} = 0$
• Steric Number: $3 + 0 = 3$ ($sp^2$ hybridized)
• Geometry and Shape: Trigonal planar

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2. Analysis of $\text{BrF}_3$ (Bromine trifluoride)

• Central atom: Bromine ($\text{Br}$), which has 7 valence electrons.
• Bonding: $\text{Br}$ forms single bonds with three fluorine atoms ($\text{Br}-\text{F}$).
• $\sigma$-bonds: 3
• Lone pairs on $\text{Br}$: $\frac{7 - 3}{2} = 2$
• Steric Number: $3 + 2 = 5$ ($sp^3d$ hybridized)
• Geometry: Trigonal bipyramidal
• Shape: T-shaped

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3. Analysis of $\text{SiO}_3^{2-}$ (Silicate ion)

• Central atom: Silicon ($\text{Si}$), which has 4 valence electrons ($+ 2$ electrons from the 2- charge = 6 electrons available for bonding).
• Bonding: $\text{Si}$ forms one double bond ($\text{Si}=\text{O}$) and two single bonds ($\text{Si}-\text{O}^-$).
• $\sigma$-bonds: 3
• Lone pairs on $\text{Si}$: $\frac{6 - (2 + 1 + 1)}{2} = 0$
• Steric Number: $3 + 0 = 3$ ($sp^2$ hybridized)
• Geometry and Shape: Trigonal planar

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4. Analysis of $\text{OSF}_2$ (Thionyl fluoride)

• Central atom: Sulfur ($\text{S}$), which has 6 valence electrons.
• Bonding: $\text{S}$ forms one double bond with oxygen ($\text{S}=\text{O}$, using 2 electrons) and two single bonds with fluorine ($\text{S}-\text{F}$, using 2 electrons).
• $\sigma$-bonds: $1\,(\text{from S}=\text{O}) + 2\,(\text{from S}-\text{F}) = 3$
• Lone pairs on $\text{S}$: $\frac{6 - (2 + 1 + 1)}{2} = 1$
• Steric Number: $3 + 1 = 4$ ($sp^3$ hybridized)
• Electron Geometry: Tetrahedral
• Molecular Shape: Trigonal Pyramidal (or Pyramidal)

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Conclusion

Among the given options, $\text{OSF}_2$ has 3 bond pairs and 1 lone pair on the central sulfur atom, resulting in a pyramidal molecular shape.

Correct Option: D