Problem 51 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write Lewis structures that obey the octet rule for each of the following, and assign oxidation numbers and formal charges to each atom: \((\mathbf{a}) \mathrm{OCS},(\mathbf{b}) \mathrm{SOCl}_{2}(\mathrm{~S}\) is the central atom), (c) \(\mathrm{BrO}_{3}^{-}\), (d) \(\mathrm{HClO}_{2}(\mathrm{H}\) is bonded to \(\mathrm{O})\).

Step-by-Step Solution

Answer

For the given molecules and ions, the Lewis structures that obey the octet rule are: 1. OCS: O=C=S with oxidation numbers O(-2), C(+4), and S(-2), and formal charges O(0), C(0), and S(0). 2. SOCl₂: O=S(Cl)₂ with oxidation numbers O(-2), S(+4), and Cl(-1) for each Cl, and formal charges O(0), S(0), and Cl(0) for each Cl. 3. BrO₃⁻: O--Br(--O)₂ with oxidation numbers O(-2) for each O, and Br(+5), and formal charges O(0) for each O, and Br(-1). 4. HClO₂: H--O--Cl(--O)₂ with oxidation numbers H(+1), O(-2), Cl(+3), and O(-2) for each O, and formal charges H(0), O(0), Cl(+1), and O(0) for each O.

Step 1: A. Drawing Lewis structures

To draw the Lewis structures, first, write the skeletal structure for each molecule, identify the total number of valence electrons available, and then distribute them around each atom to follow the octet rule. 1. OCS Skeletal structure: O=C=S Valence electrons: O (6) + C (4) + S (6) = 16 2. SOCl₂ (S is the central atom) Skeletal structure: O=S(Cl)₂ Valence electrons: S (6) + O (6) + 2 * Cl (7) = 26 3. BrO₃⁻ (with a negative charge) Skeletal structure: O--Br(--O)₂ Valence electrons: Br (7) + 3 * O (6) + 1 (from negative charge) = 26 4. HClO₂ (H is bonded to O) Skeletal structure: H--O--Cl(--O)₂ Valence electrons: H (1) + O (6) + Cl (7) + 2 * O (6) = 26

Step 2: B. Assign oxidation numbers

To assign oxidation numbers, consider each bond as if the electron pairs were completely transferred to the more electronegative atom. 1. OCS O (Ox#: -2), C (Ox#: +4), S (Ox#: -2) 2. SOCl₂ O (Ox#: -2), S (Ox#: +4), Cl (Ox#: -1) for each Cl 3. BrO₃⁻ O (Ox#: -2) for each O, Br (Ox#: +5) 4. HClO₂ H (Ox#: +1), O (Ox#: -2), Cl (Ox#: +3), O (Ox#: -2) for each O

Step 3: C. Calculate formal charges

To calculate formal charges, compare the number of valence electrons in the atom when not bonded to the number of electrons assigned to the atom in the molecule/ion. Formal Charge (FC) = Valence electrons - Nonbonding electrons - ½ * bonding electrons. 1. OCS Formal charges: O (FC: 0), C (FC: 0), S (FC: 0) 2. SOCl₂ Formal charges: O (FC: 0), S (FC: 0), Cl (FC: 0) for each Cl 3. BrO₃⁻ Formal charges: O (FC: 0) for each O, Br (FC: -1) 4. HClO₂ Formal charges: H (FC: 0), O (FC: 0), Cl (FC: +1), O (FC: 0) for each O. These Lewis structures with the assigned oxidation numbers and formal charges should obey the octet rule when drawn correctly.

Key Concepts

Octet Rule

The Octet Rule is a fundamental concept in chemistry, mainly for drawing Lewis structures. It states that atoms tend to bond in such a way that each atom has eight electrons in its valence shell, achieving a more stable electron configuration similar to noble gases. In practice, this means that atoms share, donate, or accept electrons to fill their outer layer.

When drawing the Lewis structures for different molecules, ensure each element follows the octet rule whenever possible. For instance, in the OCS molecule, the skeletal structure O=C=S uses lines to illustrate the bonds. The line represents a shared electron pair. In this example, carbon is forming double bonds with both oxygen and sulfur, giving it a total of eight electrons in its valence shell.

Keep in mind that while the octet rule applies widely, there are exceptions. For elements on the third period or higher, they can exceed this rule due to the presence of "d" orbitals capable of holding more electrons.

Oxidation Numbers

Oxidation numbers are a way to keep track of electrons during chemical reactions and bonding. They provide insight into the electron distribution in molecules, helping us understand which atoms gain or lose electrons.

• Consider each bond in the molecule as having completely transferred electrons to the more electronegative atom. For example, in the OCS molecule, oxygen generally takes a -2 oxidation state because it's more electronegative compared to sulfur and carbon.
• The oxidation number for carbon in this compound is +4, balancing the oxidation state of oxygen and maintaining the neutrality of the molecule.

These numbers are essential for understanding redox reactions, where one atom decreases its oxidation state by gaining electrons and another increases its oxidation state by losing electrons.

In some complex molecules, like SOCl₂, the central atom sulfur has an oxidation number of +4, balancing the contributions from the more electronegative oxygen and chlorine atoms.

Formal Charges

Calculating the formal charges in a molecule helps identify the most stable Lewis structure among possible resonance forms. The formal charge is determined by comparing the number of valence electrons in the neutral atom to those assigned in the molecule.

The formula for determining the formal charge (FC) is as follows:

\[FC = \text{(Valence electrons)} - \text{(Nonbonding electrons)} - \frac{1}{2} \times \text{(Bonding electrons)}\]

Let's look at the molecule BrO₃⁻ as an example:

• Each oxygen contributes to the octet of the central bromine atom, which, when satisfied, carries a formal charge of -1. This is consistent with the presence of the extra electron due to the negative charge of the ion.
• This makes the structure more stable and explains that BrO₃⁻ prefers to exist as an ion rather than a neutral molecule.

Applying formal charges correctly ensures that the drawn Lewis structure is representative of the molecule. It's crucial that the sum of formal charges in a molecule or ion equals the overall charge of the molecule or ion.