To determine the shape of a molecule, we need to find the hybridization of the central atom and the number of lone pairs and bond pairs around it. The VSEPR theory helps predict the molecular geometry.

The Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the geometry of molecules based on minimizing the repulsion between electron pairs (both bonding and non-bonding) in the valence shell of the central atom. Hybridization is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds.

Let's analyze each option:

• A) ${\mathrm{SO}}_3$: The central atom is Sulfur (S). Sulfur has 6 valence electrons. It forms three double bonds with three oxygen atoms. There are no lone pairs on sulfur. The steric number is 3 (3 bond pairs + 0 lone pairs). This corresponds to ${\mathrm{sp}}^2$ hybridization and a trigonal planar geometry.
• B) ${\mathrm{BrF}}_5$: The central atom is Bromine (Br). Bromine has 7 valence electrons. It forms five single bonds with five fluorine atoms. The remaining two electrons form one lone pair. The steric number is 6 (5 bond pairs + 1 lone pair). This corresponds to ${\mathrm{sp}}^3{\mathrm{d}}^2$ hybridization and a square pyramidal geometry.
• C) ${\mathrm{SiO}}_3^{2-}$: The central atom is Silicon (Si). Silicon has 4 valence electrons. In ${\mathrm{SiO}}_3^{2-}$, silicon forms three bonds with oxygen atoms. To satisfy the valency and charge, it typically forms a cyclic or polymeric structure. However, if we consider a single ${\mathrm{SiO}}_3^{2-}$ unit, it would have a trigonal planar arrangement around silicon if all oxygens are double-bonded, or a tetrahedral arrangement if it's part of a larger silicate structure. Isolated ${\mathrm{SiO}}_3^{2-}$ is not a stable discrete species with a simple pyramidal shape. More commonly, silicates form extended structures. If we consider a hypothetical monomeric unit with 3 single bonds and 1 double bond, it would be trigonal planar. If we consider it as part of a ring, the silicon is tetrahedral. It does not have a pyramidal shape.
• D) ${\mathrm{OSF}}_2$: The central atom is Sulfur (S). Sulfur has 6 valence electrons. It forms one double bond with oxygen and two single bonds with two fluorine atoms. The remaining two electrons form one lone pair. The steric number is 4 (3 bond pairs + 1 lone pair). This corresponds to ${\mathrm{sp}}^3$ hybridization and a trigonal pyramidal geometry (similar to ${\mathrm{NH}}_3$).

Therefore, ${\mathrm{OSF}}_2$ has a pyramidal shape.

• A) ${\mathrm{SO}}_3$: Trigonal planar. Incorrect.
• B) ${\mathrm{BrF}}_5$: Square pyramidal. Incorrect (the question asks for pyramidal, which usually refers to trigonal pyramidal).
• C) ${\mathrm{SiO}}_3^{2-}$: Typically forms extended structures or is considered trigonal planar in a monomeric unit. Incorrect.
• D) ${\mathrm{OSF}}_2$: Trigonal pyramidal. Correct.

Correct Answer: (D)