Question

Consider the following statement: "For some molecules and ions, a Lewis structure that satisfies the octet rule does not lead to the lowest formal charges, and a Lewis structure that leads to the lowest formal charges does not satisfy the octet rule." Illustrate this statement using the hydrogen sulfite ion, \(\mathrm{HSO}_{3}^{-}\), as an example (the \(\mathrm{H}\) atom is bonded to one of the \(\mathrm{O}\) atoms).

Short answer

In the hydrogen sulfite ion ($\mathrm{HSO}_{3}^{-}$), the Lewis structure that satisfies the octet rule ends up having formal charges that are not the lowest possible. In this structure, sulfur exhibits an expanded octet state. The Lewis structure, which leads to the lowest formal charges, results in an incomplete octet in the sulfur atom, now having only 6 electrons. Thus, for some molecules and ions like HSO3-, a Lewis structure satisfying the octet rule does not lead to the lowest formal charges, and a structure that leads to the lowest formal charges does not satisfy the octet rule.

Step-by-step solution

Determine the total number of valence electrons

To begin, count the total valence electrons present in the HSO3- ion. Hydrogen has 1, sulfur has 6, and each oxygen has 6 valence electrons. There is also an extra electron due to the negative charge. Therefore, the total number of valence electrons is: \[1 + 6 + 3\times 6 + 1 = 26\]

Draw the Lewis structure satisfying the octet rule

To satisfy the octet rule (hydrogen follows duet rule), each atom (except hydrogen) must have 8 electrons around it. Start with a single bond between H and O, single bonds between S and the other two O atoms, and then distribute the remaining electrons accordingly: O | H - S - O | O Now, complete the octet for all O and S atoms: O - (8 electrons for O) H - S - O | (2 electrons for the bond) | H - S (6 electrons to complete octet) - O | (2 electrons for the bond) O - (8 electrons for O) There are now 26 electrons in the structure, so all valence electrons have been accounted for.

Calculate formal charges for the structure satisfying the octet rule

Now, let's calculate the formal charges. Formal charge is based on the difference between the number of valence electrons an atom has in its neutral state and how many electrons it's effectively "using" in the bonded state. For hydrogen: Formal charge = Valence electrons - (Non-bonding electrons + 1/2 × Bonding electrons) Formal charge = 1 - (0 + 1/2 × 2) = 0 For sulfur: Formal charge = 6 - (6 + 1/2 × 6) = 0 For each oxygen atom: Formal charge = 6 - (6 + 1/2 × 2) = 6 - 7 = -1 The sum of the formal charges is zero, which matches the overall charge of the ion (HSO3-). However, S is in an expanded octet state, where it has more than eight electrons around it.

Draw a new Lewis structure with the lowest formal charges

To reduce the formal charges on the oxygen and sulfur atoms, let's create a double bond between sulfur and one of the oxygen atoms: O || H - S - O | O

Calculate the formal charges for the structure with the lowest formal charges

Again, let's calculate the formal charges for the new structure: For hydrogen: Formal charge = 1 - (0 + 1/2 × 2) = 0 For sulfur: Formal charge = 6 - (4 + 1/2 × 8) = 6 - 8 = -2 For oxygen atom with a double bond: Formal charge = 6 - (4 + 1/2 × 4) = 2 For each of the other two oxygen atoms: Formal charge = 6 - (6 + 1/2 × 2) = -1 Adding up the formal charges, we still get zero, but we notice that the lowest formal charges are not achieved while also satisfying the octet rule. While the oxygen atoms have reduced their formal charges, sulfur now has an incomplete octet (6 electrons).

Key concepts

Octet Rule

The octet rule is a fundamental concept in chemical bonding that states atoms tend to form compounds in ways that give them eight electrons in their valence shell, resembling the electron configuration of noble gases. This rule explains the stability associated with noble gases and why other elements bond to achieve a similar stable configuration.

For example, in the hydrogen sulfite ion (\(\mathrm{HSO}_{3}^{-}\)), sulfur and oxygen are the central atoms. Sulfur, being the less electronegative, often forms the core of the molecule, while oxygen atoms are distributed around it. Hydrogen attaches typically to one oxygen atom. To satisfy the octet rule, sulfur and the oxygen atoms will form bonds in such a way that each, except for hydrogen which follows the duet rule, ends up with eight electrons in their valence shell. This leads to a satisfaction of the octet rule but not necessarily to the most stable or favorable Lewis structure.

Formal Charge Calculation

The concept of formal charge is used to estimate the distribution of electrons among atoms within a molecule. It's calculated with the formula:
\( \text{Formal charge} = (\text{Valence electrons}) - (\text{Non-bonding electrons}) - \frac{1}{2}(\text{Bonding electrons}) \).

This calculation helps us determine which Lewis structure is more likely to occur in nature by comparing the theoretical charge on atoms to the actual charge on the molecule or ion. A Lewis structure is generally predicted to be more stable if the atoms have formal charges close to zero, and the sum of formal charges equals the overall charge of the molecule or ion.

In the hydrogen sulfite ion (\(\mathrm{HSO}_{3}^{-}\)), when the formal charges are calculated by assigning electrons to atoms based on their bonds, it can result in a structure where some or all atoms have non-zero formal charges, which indicates that alternative structures may need to be considered for better stability.

Expanded Octet

The expanded octet refers to the ability of certain elements, particularly those in the third period or higher of the periodic table, to have more than eight electrons in their valence shell. This occurs due to the presence of vacant d-orbitals which can accommodate additional electrons, thus expanding the octet.

Sulfur, a third period element, can often exceed the octet rule as seen in the hydrogen sulfite ion (\(\mathrm{HSO}_{3}^{-}\)). When constructing the Lewis structure, you may find that sulfur is surrounded by more than eight electrons. This 'expansion' allows for a more favorable distribution of formal charges in certain cases, even though it defies the octet rule. It's an example of the flexibility of the octet 'rule', which is more accurately seen as a guideline than a strict law.

Lewis Structure for Polyatomic Ions

Creating a Lewis structure for polyatomic ions, such as \(\mathrm{HSO}_{3}^{-}\), follows the same principles as for neutral molecules but also incorporates the overall charge of the ion. To do this, the total number of valence electrons is adjusted by adding an electron for each negative charge or subtracting one for each positive charge.

The ultimate goal in drawing the Lewis structure for polyatomic ions is not merely following the octet rule but also minimizing formal charges across the ion. This can result in structures that make use of double or triple bonds or even expanded octets for central atoms. For the \(\mathrm{HSO}_{3}^{-}\) ion, this approach can lead to different structures, where the traditional application of the octet rule does not lead to the best representation in terms of formal charge distribution.