Question

Write Lewis structures for each molecule or ion. Include resonance structures if necessary and assign formal charges to all atoms. If you need to, expand the octet on the central atom to lower formal charge. \begin{equation}\mathrm{ a.} {SO}_{4}^{2-} \quad \text { b. } \mathrm{HSO}_{4}^{-} \quad \text { c. } \mathrm{SO}_{3} \quad \text { d. } \mathrm{BrO}_{2}^{-}\end{equation}

Short answer

For \( {SO}_4^{2-} \) and \( \text{HSO}_4^- \) each oxygen atom is bonded to \text{S} with one double bond or two with single bonds and one with a double bond, respectively, and additional electron pairs complete the octet. \( \text{SO}_3 \) has each oxygen either with a double bond to \text{S} or with one double bond and two single bonds. For \( \text{BrO}_2^- \), \text{Br} is connected to each \text{O} with a single bond and has one lone pair left, with the possibility of forming a double bond with one oxygen for charge minimization.

Step-by-step solution

Writing the Lewis Structure for \( {SO}_4^{2-} \)

Start by calculating the total number of valence electrons: sulfur (\text{S}) has 6, each oxygen (\text{O}) has 6, and the ion carries an extra 2 negative charges, giving a total of \(6 + 4\times6 + 2 = 32\) valence electrons. Place \text{S} at the center and surround it with four \text{O} atoms. Connect each \text{O} to \text{S} with a single bond, distributing the remaining electrons to fulfill the octet rule for the \text{O} atoms first, then place any leftover pairs on the \text{S} atom. If necessary, share electron pairs between \text{S} and \text{O} to form double bonds and minimize formal charges. Make sure that the structure obeys the octet rule and the formal charges are minimized.

Writing the Lewis Structure for \( \text{HSO}_4^- \)

Compute the total valence electrons: \text{S} has 6, each \text{O} has 6, hydrogen (\text{H}) has 1, and the ion has an extra negative charge, giving a total of \(6 + 4\times6 + 1 + 1 = 32\) valence electrons. Place \text{S} at the center, attach one \text{H} to one of the \text{O} atoms, and place the remaining three \text{O} atoms around \text{S}. Form single bonds between \text{S} and \text{O} and between \text{H} and its \text{O}. Distribute the remaining electrons to complete the octets, and if needed, form double bonds between \text{S} and \text{O} to reduce the formal charges.

Writing the Lewis Structure for \( \text{SO}_3 \)

Calculate the total valence electrons: \text{S} has 6 and each \text{O} has 6, giving a total of \(6 + 3\times6 = 24\) electrons. Place \text{S} at the center, arrange three \text{O} atoms around it, and connect them with single bonds. Distribute the remaining electrons to satisfy the octets of the \text{O} atoms. \text{S} can have an expanded octet, so form double bonds between \text{S} and \text{O} atoms as necessary to minimize formal charges while adhering to the 24 available electrons.

Writing the Lewis Structure for \( \text{BrO}_2^- \)

Determine the total number of valence electrons: bromine (\text{Br}) has 7 and each \text{O} has 6, with an additional negative charge for the ion, totaling \(7 + 2\times6 + 1 = 20\) valence electrons. Position \text{Br} at the center, bond it with two \text{O} atoms using single bonds, and add one extra electron as a lone pair on \text{Br} to account for the negative charge. Distribute the remaining electrons to satisfy the octets, and consider forming double bonds if it can reduce the formal charges.

Key concepts

Formal Charge Calculation

Calculating the formal charge of an atom in a molecule or ion is crucial for understanding its chemical behavior and stability. The formal charge is the charge an atom would have if all bonding electrons were shared equally between bonded atoms. To calculate the formal charge, use the formula:

\[ \text{Formal Charge} = (\text{Valence Electrons}) - (\text{Non-bonding Electrons}) - \frac{1}{2}(\text{Bonding Electrons}) \]
Begin by identifying the number of valence electrons the atom normally has (its group number on the periodic table). Then count the number of non-bonding (lone pair) electrons and the number of bonding electrons (each bond counts as two electrons). Remember, bonding electrons are split equally between the bonded atoms. The goal of drawing Lewis structures, where formal charge calculation is relevant, is to have the formal charge on each atom as close to zero as possible. For polyatomic ions, ensure that the sum of the formal charges equals the overall charge of the ion.

When addressing an exercise involving complex molecules, like sulfate (\( {SO}_{4}^{2-} \)) or bromite (\( {BrO}_{2}^{-} \)), knowing how to calculate formal charges can clarify which resonance structure is more stable or predominant.

Valence Electrons

Understanding the concept of valence electrons is fundamental for constructing Lewis structures. Valence electrons are the electrons in the outermost shell of an atom that are available for bonding. The number of valence electrons is typically the same as the group number for main group elements on the periodic table.

For instance, in the exercise solutions, sulfur (S) has 6 valence electrons as it belongs to group 6A(16), and oxygen (O) also has 6, as it is in the same group. Similarly, hydrogen (H) has 1 valence electron, and bromine (Br) has 7, corresponding to their respective group numbers. These valence electrons are depicted as dots around the atom's symbol in Lewis structures and are used to form bonds with other atoms or as lone pairs.

The total number of valence electrons is vital when predicting molecular structures. In polyatomic ions like \( {SO}_{4}^{2-} \) and \( {BrO}_{2}^{-} \), the charge of the ion alters the total count of valence electrons that need to be considered during the Lewis structure construction. It's important to add or subtract electrons equal to the ionic charge if the compound is an ion.

Resonance Structures

Resonance structures are different ways of drawing the Lewis structure for a molecule where the placement of electrons can vary. These structures are a tool used to depict the delocalization of electrons within molecules that cannot be accurately represented by a single Lewis structure. In reality, the molecule exists as a hybrid of all possible resonance structures, with the true electron distribution being an average of those represented.

Each valid Lewis structure with the same arrangement of atoms but different electron placements is called a resonance structure, and collectively, they better describe the potential electron configurations of the molecule. It is essential that each resonance form has the same number of valence electrons and that atoms maintain proper valence except in cases where expanded octets are permissible due to available d orbitals, as seen with sulfur in sulfate (\( {SO}_{4}^{2-} \)).

One must remember that all resonance structures must be valid Lewis structures on their own—obeying the octet rule where applicable—and the depiction of a resonance structure does not imply that the electrons are rapidly moving or oscillating between one form or another. They are static representations of a dynamic electron distribution. For example, when working with sulfate (\( {SO}_{4}^{2-} \)), one might draw several resonance structures to convey the equal sharing of negative charge between the oxygen atoms, but in reality, the negative charges are delocalized evenly across all oxygens.