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) \(\mathrm{SO}_{2}\), (b) \(\mathrm{SO}_{3}\), (c) \(\mathrm{SO}_{3}{ }^{2-}\). (d) Arrange these molecules/ions in order of increasing \(\mathrm{S}-\mathrm{O}\) bond distance.

Short answer

The Lewis structures, oxidation numbers, and formal charges for the given molecules/ions are as follows: (a) SO2: - Lewis structure: O=S=O - Oxidation numbers: S (+4), O (-2) - Formal charges: S (0), O (0) (b) SO3: - Lewis structure: O=S(-O)-O - Oxidation numbers: S (+6), O (-2) - Formal charges: S (0), O (0) (c) SO3^2-: - Lewis structure: O^-=S(-O^-)-O^- - Oxidation numbers: S (+6), O (-2) - Formal charges: S (0), O (-1) Based on the bond distances being inversely proportional to bond orders, the order of increasing S-O bond distance is: SO2 < SO3 ≈ SO3^2-

Step-by-step solution

(a) Lewis structure for SO2

To determine the Lewis structure for SO2, we first count the total number of valence electrons: Sulfur (S) has 6 valence electrons, and Oxygen (O) has 6 valence electrons. Since there are two oxygen atoms, the total number of valence electrons is 6 + 2(6) = 18. The Lewis structure for SO2 can be represented as: O=S=O where Sulfur (S) is double bonded with both Oxygen atoms.

(b) Lewis structure for SO3

We determine the total number of valence electrons for SO3: Sulfur (S) has 6 valence electrons, and each Oxygen (O) atom has 6 valence electrons. Since there are three oxygen atoms, the total number of valence electrons is 6 + 3(6) = 24. The Lewis structure for SO3 can be represented as: O || S-O-S \\ O where Sulfur (S) is double bonded with one Oxygen and single bonded with the other two Oxygen atoms.

(c) Lewis structure for SO3^2-

We determine the total number of valence electrons for SO3^2-: Sulfur (S) has 6 valence electrons, and each Oxygen (O) atom has 6 valence electrons. As there are three oxygen atoms, the total number of valence electrons is 6 + 3(6) = 24. Since it is a 2- ion, we add 2 additional electrons, making the total electron count 26. The Lewis structure for SO3^2- can be represented as: O- || S-O-S / \\ O O- where Sulfur (S) is double bonded with one Oxygen and single bonded with the other two Oxygen atoms, and each O atom has an extra lone pair of electrons, giving them a formal charge of -1. #Step 2: Calculate the oxidation numbers for each atom in the molecule or ion#

(a) Oxidation numbers for SO2

Sulfur (S): +4 (double bonded to two O atoms) Oxygen (O): -2 (each oxygen atom is double bonded to S)

(b) Oxidation numbers for SO3

Sulfur (S): +6 (double bonded to one O atom and single bonded to two O atoms) Oxygen (O): -2 (each oxygen atom bonded to S)

(c) Oxidation numbers for SO3^2-

Sulfur (S): +6 (double bonded to one O atom and single bonded to two O atoms) Oxygen (O): -2 (each oxygen atom bonded to S) #Step 3: Calculate the formal charge of each atom in the molecule or ion#

(a) Formal charges for SO2

Sulfur (S): 0 (no formal charge) Oxygen (O): 0 (each oxygen atom has no formal charge)

(b) Formal charges for SO3

Sulfur (S): 0 (no formal charge) Oxygen (O): 0 (each oxygen atom has no formal charge)

(c) Formal charges for SO3^2-

Sulfur (S): 0 (no formal charge) Oxygen (O): -1 (each oxygen atom has a formal charge of -1) #Step 4: Compare the S-O bond distances and arrange the molecules/ions in order# In general, bond distances are inversely proportional to bond orders. - For SO2, the bond order is 2 (double bonds). - For SO3, the average bond order is (2 + 1 + 1) / 3 = 1.33. - For SO3^2-, the average bond order is also (2 + 1 + 1) / 3 = 1.33. Since bond distances are inversely proportional to bond orders, we can arrange the molecules/ions in order of increasing S-O bond distance as follows: SO2 < SO3 ≈ SO3^2-

Key concepts

Oxidation Numbers

Understanding oxidation numbers is crucial for determining how electrons are distributed in a molecule. Oxidation numbers help us identify the charge an atom would have if the compound was composed entirely of ions. Consider the oxidation numbers in our example molecules:

• For \( \mathrm{SO}_2 \), sulfur (S) has an oxidation number of +4, meaning it has "lost" 4 electrons considering its sharing with oxygen atoms. Each oxygen (O) atom in \( \mathrm{SO}_2 \) possesses an oxidation number of -2.
• In \( \mathrm{SO}_3 \), sulfur exhibits an oxidation number of +6, reflecting a greater electron-sharing disparity with its oxygen partners. Every oxygen atom maintains an oxidation number of -2.
• For \( \mathrm{SO}_3^{2-} \), sulfur retains the oxidation number of +6, while each oxygen continues to show -2. The -2 charge overall is explained by the additional two electrons in the structure.

This insight assists in understanding electron arrangements and chemical properties, such as reactivity and oxidation-reduction behavior.

Formal Charges

Formal charges offer a way to keep track of electrons in a structure and help in predicting molecular geometry and reactivity. Formal charges tell us the hypothetical charge an atom would possess if electrons in individual bonds were equally shared, which is slightly different from oxidation numbers. Here's how we can evaluate them step by step for each molecule:

• For \( \mathrm{SO}_2 \), the formal charges for sulfur and oxygen are all zero, indicating a stable electron arrangement with sulfur being central and doubly bonded to each oxygen.
• In \( \mathrm{SO}_3 \), similar stability is observed as formal charges for all intervening atoms are zero. This neutrality suggests a relatively symmetrical distribution of electrons.
• When considering \( \mathrm{SO}_3^{2-} \), sulfur still maintains a formal charge of zero, while each oxygen atom exhibits a formal charge of -1 due to extra electrons associated with the 2- ion charge. This imbalance is what confers the overall negative charge to the ion.

Understanding formal charges helps chemists predict structural formulas that minimize charge separation, steering molecules toward more stable forms, hence adhering to real-world molecular behavior.

Bond Distances

Bond distances refer to the average bond length between two atoms in a molecule. Shorter bonds are generally stronger and have higher bond orders, meaning more shared electrons are between the two bonded atoms. Let's see how this looks in our sulfur-oxygen compounds:

• In \( \mathrm{SO}_2 \), each S-O bond is a double bond, with a bond order of 2, leading to the shortest bond distance among the examples.
• For \( \mathrm{SO}_3 \), not all bonds are double. The average bond order here is 1.33, combining double and single bonds, thus, the bond distance is longer compared to \( \mathrm{SO}_2 \).
• The structure of \( \mathrm{SO}_3^{2-} \) also has an average bond order of 1.33 since it has a similar electron sharing pattern as \( \mathrm{SO}_3 \), resulting in comparable bond distances.

Greater bond length implies lower bond energy. Therefore, among our compounds, the sequence of increasing bond distance is: \( \mathrm{SO}_2 < \mathrm{SO}_3 \approx \mathrm{SO}_3^{2-} \). Understanding bond distance is vital as it affects molecular shape, reactivity, and how molecules interact with light and heat.

Octet Rule

The octet rule is a fundamental concept in chemistry that dictates many of the rules for creating stable molecules. This principle states that atoms tend to form bonds so each atom has eight electrons in its valence shell, resembling a noble gas configuration. Let's apply this to our sulfur and oxygen molecules:

• In \( \mathrm{SO}_2 \), sulfur forms a double bond with each oxygen, achieving a complete octet around all participating atoms. This guarantees stability following the octet rule.
• For \( \mathrm{SO}_3 \), sulfur makes two single bonds and one double bond with the three oxygen atoms, maintaining an expanded octet as it's able to hold more than eight electrons, which is permissible for elements in the third period of the periodic table.
• In \( \mathrm{SO}_3^{2-} \), the additional electrons are used to fulfill the octet requirement for each oxygen atom, while sulfur again exceeds the octet, accommodating the extra electrons.

The adherence to the octet rule underscores why certain molecular structures are preferred, affecting stability and chemical reactivity. The rule provides a pretext for predicting the formation of bonds and the resulting molecule geometries.