Question

Which of the following statements concerning \(\mathrm{SO}_{2}\) is(are) true? a. The central sulfur atom is \(s p^{2}\) hybridized. b. One of the sulfur-oxygen bonds is longer than the other(s). c. The bond angles about the central sulfur atom are about 120 degrees. d. There are two \(\sigma\) bonds in \(\mathrm{SO}_{2}\). e. There are no resonance structures for \(\mathrm{SO}_{2}\).

Short answer

The true statements about \(\mathrm{SO}_{2}\) are: a. The central sulfur atom is \(s p^{2}\) hybridized, c. The bond angles about the central sulfur atom are about 120 degrees, and d. There are two \(\sigma\) bonds in \(\mathrm{SO}_{2}\).

Step-by-step solution

Drawing the Lewis structure and determining the hybridization

: To analyze the molecular structure of \(\mathrm{SO}_{2}\), we need to first draw the Lewis structure. O=S=O The sulfur atom has a double bond with each oxygen atom, and there is a lone pair of electrons on it. The sulfur atom is surrounded by three electron groups (two double bonds and one lone pair). According to the VSEPR theory, with three electron groups, the central atom exhibits \(\mathrm{sp^2}\) hybridization.

Checking bond length

: In \(\mathrm{SO}_{2}\), the sulfur atom has double bonds with the two oxygen atoms, and the bond lengths should be the same. Therefore, one bond is not longer than the other.

Finding bond angles

: With three electron groups around the central atom sulfur in \(\mathrm{SO}_{2}\), the ideal bond angle should be 120 degrees.

Identifying sigma bonds

: In a double bond, there is one sigma bond and one pi bond. Since \(\mathrm{SO}_{2}\) has two double bonds, we can conclude that it has two sigma bonds.

Checking for resonance structures

: There are no valid resonance structures for \(\mathrm{SO}_{2}\) where we can draw a different arrangement of the double bonds or preserve the octet rule. Based on our analysis, the true statements are: a. The central sulfur atom is \(s p^{2}\) hybridized. c. The bond angles about the central sulfur atom are about 120 degrees. d. There are two \(\sigma\) bonds in \(\mathrm{SO}_{2}\).

Key concepts

VSEPR Theory

VSEPR, or Valence Shell Electron Pair Repulsion theory, helps us understand the geometry of molecules. This theory is based on the idea that electron groups around a central atom will repel each other and, thus, arrange themselves as far apart as possible to minimize repulsion.
In the case of sulfur dioxide ( SO_2 ), the sulfur atom has two double bonds with oxygen atoms and one lone pair of electrons. These three electron groups lead to a trigonal planar geometry according to VSEPR theory.

• Remember, each double bond counts as one electron group in this context.
• The presence of the lone pair slightly distorts the shape, but the ideal bond angle remains close to 120 degrees.

The key takeaway is that VSEPR theory predicts molecular shapes based on electron group repulsion, providing insight into the spatial arrangement and bond angles.

Hybridization

Hybridization is a concept used to describe how atomic orbitals mix to form new hybrid orbitals. These hybrid orbitals are responsible for the bonding properties of atoms in a molecule.
In SO_2 , the sulfur atom undergoes sp^2 hybridization. This occurs because sulfur needs three hybrid orbitals to accommodate two sigma bonds (one with each oxygen) and one lone pair of electrons.

• Each sp^2 hybrid orbital is formed by the mixing of one s orbital and two p orbitals.
• This results in three equivalent sp^2 hybrid orbitals arranged in a trigonal planar formation.

The concept of hybridization helps explain the bonding and the structure of SO_2 , namely, why the molecule has specific bond angles and a planar geometry.

Lewis Structure

Lewis structures are diagrams that show the bonding between atoms and the lone pairs of electrons in a molecule. To draw the Lewis structure for SO_2 , follow these steps:

• First, count the total number of valence electrons available. Sulfur has 6, and each oxygen has 6, totaling 18 electrons.
• Place the sulfur atom in the center and form double bonds with two oxygen atoms. This accounts for 16 electrons.
• The remaining two electrons form a lone pair on the sulfur atom.

The Lewis structure of SO_2 thus shows two double bonds and a lone pair on sulfur.

It is essential to verify that each atom fulfills the octet rule, which means they generally have eight electrons in their valence shell. The Lewis structure provides a good visual framework for understanding how the atoms in SO_2 are connected.

Sigma and Pi Bonds

Sigma ( σ ) and Pi ( π ) bonds are fundamental in understanding molecular bonding. A sigma bond represents the first bond formed between two atoms. It involves the head-on overlapping of orbitals, providing rotational freedom to the bonded atoms.
In SO_2 , each double bond consists of one sigma bond and one pi bond:

• The sigma bond is the primary bond formed by the direct overlap of orbitals, which lies along the axis connecting the two bonded nuclei.
• The pi bond is formed from the side-to-side overlap of p orbitals, located above and below the axis of the bond.

Therefore, in SO_2 , there are two sigma bonds (one for each S-O double bond). Understanding the distinction between sigma and pi bonds is crucial for explaining molecular rigidity, bond strength, and characteristics.