Problem 52 - Chemistry: The Central Science in SI Units, Global Edition

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 length.

Step-by-Step Solution

Answer

The Lewis structures, oxidation numbers, and formal charges for the given molecules or ions are: (a) SO2: O=S=O, oxidation numbers: S(+4), O(-2); formal charges: S(0), O(0). (b) SO3: O=S(=O)(=O), oxidation numbers: S(+6), O(-2); formal charges: S(0), O(0). (c) SO3 2-: O-S(-O)(-O), oxidation numbers: S(+4), O(-2); formal charges: S(+1), O(-1). In order of increasing S-O bond length: SO3, SO2, SO3 2-.

Step 1: (a) SO2 Lewis Structure

1. Count the valence electrons: Sulfur has 6 valence electrons, and Oxygen has 6 valence electrons each. So, the total number of valence electrons for SO2 is 18. 2. Place the least electronegative atom (S) in the center and connect it with the other atoms (O) with single bonds. 3. Complete the octet of each surrounding atom (O) by adding lone pairs of electrons. 4. Check if the central atom (S) has an octet. If not, form a double bond by moving a lone pair from the surrounding atom (O) to form a bonding pair with the central atom (S). The Lewis structure of SO2 is: O=S=O

Step 2: SO2 Oxidation Numbers and Formal Charges

Oxidation numbers: S: +4 (it has 4 electrons less than the neutral atom) O: -2 (each oxygen atom has 2 electrons more than the neutral atom) Formal charges: For S: Formal charge = Valence electrons - Non-bonding electrons - (1/2 * Bonding electrons) = 6 - 0 - (1/2 * 8) = 0 For each O: Formal charge = 6 - 4 - (1/2 * 4) = 0

Step 3: (b) SO3 Lewis Structure

1. Count the valence electrons: Sulfur has 6 valence electrons, and Oxygen has 6 valence electrons each. So, the total number of valence electrons for SO3 is 24. 2. Place the least electronegative atom (S) in the center and connect it with the other atoms (O) with single bonds. 3. Complete the octet of each surrounding atom (O) by adding lone pairs of electrons. 4. Check if the central atom (S) has an octet. If not, form double bonds by moving a lone pair from the surrounding atom (O) to form a bonding pair with the central atom (S) until the central atom has an octet. Once complete, SO3 will have one double bond with each of the three oxygen atoms.

Step 4: SO3 Oxidation Numbers and Formal Charges

Oxidation numbers: S: +6 (it has 6 electrons less than the neutral atom) O: -2 (each oxygen atom has 2 electrons more than the neutral atom) Formal charges: For S: Formal charge = 6 - 0 - (1/2 * 12) = 0 For each O: Formal charge = 6 - 4 - (1/2 * 4) = 0

Step 5: (c) SO3 2- Lewis Structure

1. Count the valence electrons: Sulfur has 6 valence electrons, Oxygen has 6 valence electrons each, and there are 2 additional electrons from the 2- charge. The total number of valence electrons for SO3 2- is 26. 2. Place the least electronegative atom (S) in the center and connect it with the other atoms (O) with single bonds. 3. Complete the octet of each surrounding atom (O) by adding lone pairs of electrons. 4. Check if the central atom (S) has an octet. It does, so there are no additional steps. In this case, all sulfur-oxygen bonds are single bonds.

Step 6: SO3 2- Oxidation Numbers and Formal Charges

Oxidation numbers: S: +4 (it has 4 electrons less than the neutral atom) O: -2 (each oxygen atom has 2 electrons more than the neutral atom) Formal charges: For S: Formal charge = 6 - 2 - (1/2 * 6) = +1 For each O: Formal charge = 6 - 6 - (1/2 * 2) = -1 Note: The overall charge of the ion is -1 * 3 + 1 = -2, which is consistent with the given charge.

Step 7: (d) Arrange Molecules/Ions in Order of Increasing S-O Bond Length

S-O bond length increases with decreasing bond order. Bond order can be determined by the number of bonds between the atoms. The Lewis structures show the bond orders. SO2 has an average bond order of 3/2 (since there is one double bond and one single bond), SO3 has a bond order of 2 (all double bonds), and SO3 2- has a bond order of 1 (all single bonds). In order of increasing S-O bond length: 1. SO3 (highest bond order, which means the shortest bond length) 2. SO2 (intermediate bond order and bond length) 3. SO3 2- (lowest bond order, which means the longest bond length)

Key Concepts

Oxidation Numbers

Understanding oxidation numbers is key to identifying how electrons are distributed in molecules, particularly in sulfur and oxygen compounds like SO_2, SO_3, and SO_3^{2-}. Oxidation numbers indicate the hypothetical charge that an atom would have if all bonds were completely ionic. This allows chemists to deduce the electron flow in a reaction. For example:

• In SO_2, sulfur has an oxidation number of +4, meaning it is electron-deficient compared to its neutral state.
• Each oxygen in SO_2 holds an oxidation number of -2, indicating it has gained electrons.

This pattern helps us comprehend the central sulfur atom's role in sharing electrons to meet the octet rule. By determining these values, we can better understand the reactivity and stability of these compounds.

Formal Charges

Formal charges help to assess how valence electrons are allocated in a molecule. They can predict the likelihood of atoms to donate or accept electrons in chemical reactions. Here’s how formal charges are calculated:

• The formula is: Formal charge = Valence electrons - Non-bonding electrons - (1/2 * Bonding electrons)

Taking SO_3 as an example, sulfur has 6 valence electrons, no lone pairs, and shares 12 electrons through double bonds, leading to a formal charge of 0. Oxygen, on the other hand, has four non-bonding electrons and forms two bonds, resulting in zero formal charge as well. Correct assignment of formal charges helps determine the most stable Lewis structure, ensuring our representation abides by the octet rule without unusual electron distributions.

Bond Length

Bond length refers to the distance between two bonded atoms. It is influenced by the bond order – more shared electrons result in shorter bonds. In sulfur-oxygen compounds, noticing differences in bond length is significant:

• In SO_3, each sulfur-oxygen bond is a double bond, meaning they share two electrons, resulting in shorter and stronger bonds.
• Conversely, in SO_3^{2-}, all are single bonds due to the surplus electrons from the negative charge, leading to longer bond lengths.

SO_2’s bond order is intermediate, reflecting its mixed bonding nature—a single and a double bond on sulfur. Recognizing these relationships aids in predicting molecular geometry and reactivity.

Octet Rule

The octet rule is a guiding principle in drawing Lewis structures, reflecting atoms' preference to have eight electrons in their valence shell to achieve stability similar to noble gases. Here's how it applies:

• Sulfur and oxygen strive to fill their valence shells in compounds like SO_2, SO_3, and SO_3^{2-}.
• Sulfur can have an expanded octet, meaning it can hold more than eight electrons, especially in SO_3 where it forms multiple double bonds, involving 12 electrons.

In contrast, both oxygen atoms in these examples adhere strictly to the octet rule. By ensuring that during the drawing of Lewis structures, the octet rule is satisfied, we make certain that the representation aligns with realistic and probable molecular structures.