Question

What is the order of bond angle in $SO_4^{2-}$, $SO_3$, $SO_2$?

Answer 1

SO_3 > SO_2 > SO_4^{2-}

Answer 2

To determine the order of bond angles in $SO_4^{2-}$, $SO_3$, and $SO_2$, we need to analyze the hybridization and molecular geometry of each species using VSEPR theory.

1. $SO_4^{2-}$ (Sulfate ion)

   • Central Atom: Sulfur (S)
   • Valence Electrons: S (6) + 4 * O (4 * 6) + 2 (charge) = 6 + 24 + 2 = 32 electrons.
   • Lewis Structure & VSEPR: Sulfur is bonded to four oxygen atoms. To minimize formal charges, the structure is often depicted with two S=O double bonds and two S-O single bonds, exhibiting resonance. For VSEPR theory, we count electron domains. Each bond (single or double) counts as one bonding domain. There are 4 bonding domains and 0 lone pairs on the central sulfur atom.
   • Steric Number: 4 (4 bond pairs + 0 lone pairs)
   • Hybridization: $sp^3$
   • Electron Geometry: Tetrahedral
   • Molecular Geometry: Tetrahedral
   • Bond Angle: Approximately $109.5^\circ$.

2. $SO_3$ (Sulfur Trioxide)

   • Central Atom: Sulfur (S)
   • Valence Electrons: S (6) + 3 * O (3 * 6) = 6 + 18 = 24 electrons.
   • Lewis Structure & VSEPR: Sulfur is bonded to three oxygen atoms. To satisfy octets and minimize formal charges, sulfur forms three S=O double bonds (sulfur expands its octet). There are 3 bonding domains and 0 lone pairs on the central sulfur atom.
   • Steric Number: 3 (3 bond pairs + 0 lone pairs)
   • Hybridization: $sp^2$
   • Electron Geometry: Trigonal planar
   • Molecular Geometry: Trigonal planar
   • Bond Angle: $120^\circ$.

3. $SO_2$ (Sulfur Dioxide)

   • Central Atom: Sulfur (S)
   • Valence Electrons: S (6) + 2 * O (2 * 6) = 6 + 12 = 18 electrons.
   • Lewis Structure & VSEPR: Sulfur is bonded to two oxygen atoms. The most common resonance structures show one S=O double bond, one S-O single bond, and one lone pair on sulfur. For VSEPR, we count 2 bonding domains and 1 lone pair on the central sulfur atom.
   • Steric Number: 3 (2 bond pairs + 1 lone pair)
   • Hybridization: $sp^2$
   • Electron Geometry: Trigonal planar
   • Molecular Geometry: Bent (or V-shaped)
   • Bond Angle: Due to the presence of a lone pair, the lone pair-bond pair repulsion is greater than bond pair-bond pair repulsion. This compresses the bond angle from the ideal $120^\circ$ for $sp^2$ hybridization. The actual bond angle is approximately $119.5^\circ$.

Comparison of Bond Angles:

• $SO_3$: $120^\circ$
• $SO_2$: $\approx 119.5^\circ$
• $SO_4^{2-}$: $\approx 109.5^\circ$

Therefore, the order of bond angles from largest to smallest is: $SO_3 > SO_2 > SO_4^{2-}$

Explanation of the solution:

1. $SO_4^{2-}$: Sulfur is $sp^3$ hybridized with 4 bonding domains and 0 lone pairs, leading to a tetrahedral geometry and bond angle of approximately $109.5^\circ$.
2. $SO_3$: Sulfur is $sp^2$ hybridized with 3 bonding domains and 0 lone pairs, resulting in a trigonal planar geometry and a bond angle of $120^\circ$.
3. $SO_2$: Sulfur is $sp^2$ hybridized with 2 bonding domains and 1 lone pair, leading to a bent molecular geometry. The lone pair causes greater repulsion, compressing the bond angle to approximately $119.5^\circ$, which is slightly less than $120^\circ$.

Comparing these values, the order of bond angles is $SO_3 > SO_2 > SO_4^{2-}$.