Problem 52 - Chemistry The Central Science

Question

For each of the following molecules or ions of sulfur and oxygen, write a single Lewis structure that obeys the octet rule, and calculate the oxidation numbers and formal charges on all the atoms: (a) SO \(_{2},(\mathbf{b}) \mathrm{SO}_{3},(\mathrm{c}) \mathrm{SO}_{3}^{2-}\) (d) Arrange these molecules/ions in order of increasing \(S-O\) bond length.

Step-by-Step Solution

Answer

The Lewis structures for the given molecules/ions are as follows: (a) SO2: O=S=O (b) SO3: O=S(=O)=O (c) SO3^2-: O=S(-O^−2)=O The oxidation numbers and formal charges are: (a) SO2: O(-2, 0), S(+4, 0) (b) SO3: O(-2, 0), S(+6, 0) (c) SO3^2-: O(-2/−1, 0/-1), S(+6, 0) The order of increasing S-O bond lengths is: SO2 < SO3 < SO3^2-.

Step 1: Drawing the Lewis Structures

We will start by drawing Lewis structures of the molecules/ions. (a) SO2: O=S=O (b) SO3: O=S(=O)=O (c) SO3^2-: O=S(-O^−2)=O Next, we will calculate the oxidation numbers for each atom in the molecules/ions.

Step 2: Calculating Oxidation Numbers

Oxidation numbers are hypothetical charges assigned to atoms, based on their electronegativity. (a) SO2: Oxygen: -2 (each oxygen atom) Sulfur: +4 (sum of oxygen charges = -4, sulfur has to cancel it out) (b) SO3: Oxygen: -2 (each oxygen atom) Sulfur: +6 (sum of oxygen charges = -6, sulfur has to cancel it out) (c) SO3^2-: Oxygen: -2 (each oxygen atom except the one with extra lone pair) and -1 (oxygen with extra lone pair) Sulfur: +6 (sum of oxygen charges = -5, sulfur has to cancel it out, and there's a -1 charge on the ion) Now, we move to calculating the formal charges for all atoms.

Step 3: Calculating Formal Charges

Formal charges are the charge on an atom if all shared electrons were equally shared between atoms. (a) SO2: Oxygen: 0 (6 - 6) Sulfur: 0 (6 - 6) (b) SO3: Oxygen: 0 (6 - 6) Sulfur: 0 (6 - 6) (c) SO3^2-: Oxygen: -1 (6 - 7) for the oxygen with extra lone pair; 0 (6 - 6) for the other two oxygen atoms Sulfur: 0 (6 - 6) Lastly, we will arrange the molecules/ions in order of increasing S-O bond length.

Step 4: Arrange the Molecules/Ions in Order of Increasing S-O Bond Length

To determine the S-O bond length order, we will consider the multiple bonds and the resonance structures. (a) SO2: There is one double bond between S and each O atom, the bond lengths will be shorter due to double bonds. (b) SO3: There are two resonance structures for SO3. Each S-O bond is a double bond in the resonance structure. The bond lengths will be shorter as compared to single bonds and will be similar to SO2 bond lengths. (c) SO3^2-: There are three resonance structures for SO3^2-. In each resonance structure, sulfur has one double bond with one oxygen atom and single bonds with other two oxygen atoms. This makes the average bond order between S-O higher than a single bond but less than a double bond. So, the bond lengths will be longer compared to the S-O bond length in SO2 and SO3. Based on this information, the order of increasing S-O bond lengths is as follows: SO2 < SO3 < SO3^2-

Key Concepts

Oxidation Numbers

Oxidation numbers are an essential concept in chemistry that help us understand the distribution of electrons in molecules. They allow us to track electron transfer in redox reactions. For molecules like sulfur dioxide (SO₂), sulfur trioxide (SO₃), and the sulfite ion (SO₃²⁻), determining oxidation numbers enables us to comprehend the sharing and transfer of electrons among atoms. In SO₂, each oxygen atom possesses an oxidation number of -2, due to its higher electronegativity, which pulls electrons away from sulfur. Sulfur in SO₂, therefore, gets an oxidation number of +4 to balance the overall charge to zero. Similarly, in SO₃, each oxygen remains at -2, giving sulfur an oxidation number of +6 to maintain neutrality. In the ion SO₃²⁻, although most oxygens are -2, the presence of extra lone pairs and charges slightly alter the count, assigning sulfur its original +6 to carry the -2 of the ion effectively.

Formal Charges

Formal charges provide another perspective on how electrons are distributed in a molecule. They differ from oxidation numbers in that formal charges assume equal sharing of electrons between bonded atoms, regardless of the actual electronegativity. For example, in SO₂, with structural representation as O=S=O, both the sulfur and oxygen atoms in this molecule hold a formal charge of zero. This reflects a stable configuration, as electrons from double bonds are shared equally. In SO₃, with three equal double bonds (in resonance), similar calculations apply, sending each oxygen and sulfur atom back to zero formal charge. However, with the sulfite ion SO₃²⁻, one oxygen atom bears an extra lone pair, hence a formal charge of -1 for one oxygen atom, while the other atoms retain zero, tallying up to the overall -2 charge of the ion.

S-O Bond Length

Understanding the bond length between sulfur and oxygen in various compounds can provide insights into molecular structure and stability. Bond length is often influenced by whether the bonds are single or double, as well as by resonance effects. In SO₂, the S-O bond consists of double bonds, implying shorter bonds because of more electron sharing and stable molecular structure. SO₃, on the other hand, although it appears with multiple resonance structures, maintains double-bond characteristics due to delocalized electrons participating equally. This resonance shortens the S-O bonds similarly to SO₂. However, in the sulfite ion SO₃²⁻, with resonance structures suggesting one double bond and two single bonds in play, the bond length elongates slightly beyond the double-bonded states in SO₂ and SO₃.

Resonance Structures

Resonance structures offer a way to visualize how electrons might be distributed in a molecule when a single Lewis structure does not suffice. They demonstrate the concept of delocalized electron sharing among atoms, affecting molecular stability and properties. In SO₂, typically, resonance is minimal as the molecule already has a clear double-bonded structure on each side. However, in SO₃, resonance plays a crucial role due to the circulation of double bonds among the three oxygen atoms, drastically affecting the hypothetical representation of electron distribution. As for SO₃²⁻, resonance provides a way to depict the one double bond varying positions across the three oxygen atoms, illustrating a dynamic electron distribution and slight variance in bond strength and length. These structures are critical in comprehending physical properties and reactivity across different sulfur-oxygen compounds.