Problem 61 - Chemistry: The Central Science

Question

Draw the Lewis structures for each of the following ions or molecules. Identify those that do not obey the octet rule, and explain why they do not. (a) \(\mathrm{SO}_{3}{\underline{\phantom{xx}}}^{2-}\), (b) \(\mathrm{AlH}_{3}\), (c) \(\mathrm{N}_{3}^{-}\), (d) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), (e) \(\mathrm{SbF}_{5}\).

Step-by-Step Solution

Answer

In summary, ions/molecules (a) \(\mathrm{SO}_{3}{\underline{\phantom{xx}}}^{2-}\), (b) \(\mathrm{AlH}_{3}\), and (e) \(\mathrm{SbF}_{5}\) do not obey the octet rule. In \(\mathrm{SO}_{3}{\underline{\phantom{xx}}}^{2-}\) and \(\mathrm{SbF}_{5}\), sulfur and antimony have expanded octets with 10 electrons around them. In \(\mathrm{AlH}_{3}\), aluminum has an incomplete octet with only 6 electrons around it.

Step 1: Find the number of valence electrons for each ion/molecule

The first step for drawing Lewis structures is to determine the number of valence electrons for each ion/molecule. (a) \(\mathrm{SO}_{3}{\underline{\phantom{xx}}}^{2-}\): Sulfur has 6 valence electrons, oxygen has 6 valence electrons, and a total of \(2\) extra electrons are present due to the \(2-\) charge. So, the total valence electrons are \(6+3(6)+2=26\). (b) \(\mathrm{AlH}_{3}\): Aluminum has 3 valence electrons, and hydrogen has 1 valence electron. So, the total valence electrons are \(3+3(1)=6\). (c) \(\mathrm{N}_{3}^{-}\): Nitrogen has 5 valence electrons, and \(1\) extra electron due to the \(1-\) charge. So, the total valence electrons are \(3(5)+1=16\). (d) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\): Carbon has 4 valence electrons, hydrogen has 1 valence electron, and chlorine has 7 valence electrons. So, the total valence electrons are \(4+2(1)+2(7)=20\). (e) \(\mathrm{SbF}_{5}\): Antimony has 5 valence electrons, and fluorine has 7 valence electrons. So, the total valence electrons are \(5+5(7)=40\).

Step 2: Draw the Lewis structures

Next, we will draw Lewis structures for the given ions/molecules and then identify if there is any violation of the octet rule. (a) \(\mathrm{SO}_{3}{\underline{\phantom{xx}}}^{2-}\): With 26 valence electrons, we draw the following Lewis structure: \[ \mathrm{S} \equiv \mathrm{O} - \mathrm{S} \equiv \mathrm{O} - \mathrm{O} - \mathrm{S} \] In this structure, each oxygen follows the octet rule (double bonds), but the sulfur has an expanded octet with 10 electrons around it. (b) \(\mathrm{AlH}_{3}\): With 6 valence electrons, we draw the following Lewis structure: \[ \mathrm{H} - \mathrm{Al} - \mathrm{H} \] \[ \quad \quad \quad \mathrm{H} \] In this structure, each hydrogen has 2 electrons (duet rule), but the aluminum has an incomplete octet with only 6 electrons around it. (c) \(\mathrm{N}_{3}^{-}\): With 16 valence electrons, we draw the following Lewis structure: \[ \mathrm{N} = \mathrm{N} - \mathrm{N}^{+} \] In this structure, all three nitrogen atoms follow the octet rule (8 electrons around each). (d) \(\mathrm{CH}_{2}\mathrm{Cl}_{2}\): With 20 valence electrons, we draw the following Lewis structure: \[ \mathrm{H} - \mathrm{C} - \mathrm{H} \] \[ \quad \quad \mathrm{Cl} - \mathrm{Cl} \] In this structure, carbon and both chlorine atoms follow the octet rule (8 electrons around each), and each hydrogen follows the duet rule (2 electrons each). (e) \(\mathrm{SbF}_{5}\): With 40 valence electrons, we draw the following Lewis structure: \[ \mathrm{F} - \mathrm{Sb} - \mathrm{F} \] \[ \quad \quad \mathrm{F} \quad \quad \mathrm{F} \] \[ \quad \quad \quad \mathrm{F} \] In this structure, all five fluorine atoms follow the octet rule (8 electrons around each), but the antimony has an expanded octet with 10 electrons around it.

Step 3: Identify and explain the violations

Based on the Lewis structures drawn, we can conclude that: (a) \(\mathrm{SO}_{3}{\underline{\phantom{xx}}}^{2-}\) violates the octet rule, as sulfur has an expanded octet. (b) \(\mathrm{AlH}_{3}\) violates the octet rule, as aluminum has an incomplete octet. (c) \(\mathrm{N}_{3}^{-}\) obeys the octet rule. (d) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) obeys the octet rule. (e) \(\mathrm{SbF}_{5}\) violates the octet rule, as antimony has an expanded octet. Therefore, ions/molecules (a), (b), and (e) do not obey the octet rule.

Key Concepts

Octet Rule

The octet rule is a fundamental chemical principle that helps us understand the bonding behavior of atoms in a molecule. It states that atoms tend to form bonds until they are surrounded by eight valence electrons, thereby achieving a stable electronic configuration similar to that of the noble gases.

However, there are exceptions to this rule, particularly for molecules or ions involving elements in the third period or below of the periodic table. These elements can have expanded octets, meaning they can hold more than eight electrons, due to available d-orbitals. Elements such as sulfur in (SO3)^{2-} or antimony in SbF5 diverge from the rule and exhibit an expanded octet, showing that the rule is more a guideline than a strict law.

In contrast, molecules like AlH3 do not satisfy the octet rule because aluminum ends up with only six valence electrons. This is known as an incomplete octet and is often observed in elements like boron and aluminum, which can form stable compounds despite not having a complete octet.

Valence Electrons

Valence electrons are the outermost electrons of an atom and determine its chemical properties and bonding behavior. They are responsible for the formation of chemical bonds through either sharing with or transferring to other atoms.

Understanding Valence Electrons in Lewis Structures

When drawing Lewis structures, the number of valence electrons for each atom is crucial in determining the arrangement and connectivity in the molecule.

For instance, the sulfite ion (SO3)^{2-} has a total of 26 valence electrons, which must be distributed among the sulfur and oxygen atoms to maintain stability. On the other hand, a simple molecule like AlH3 has significantly fewer valence electrons, only six, which are used to form bonds with hydrogen atoms albeit without completing the octet for aluminum.

Counting and properly distributing valence electrons across atoms is pivotal for accurately predicting the molecular structures and understanding both the physical and chemical properties of substances.

Molecular Geometry

Molecular geometry indicates the three-dimensional arrangement of atoms within a molecule, greatly influencing the molecule's physical and chemical characteristics. The geometry is determined by the number of electron pairs, both bonding and lone pairs, around the central atom, following the VSEPR (Valence Shell Electron Pair Repulsion) theory.

Impact on Properties and Behaviors

The shape of a molecule plays a significant role in determining properties such as polarity, reactivity, and phase at room temperature.

For instance, the tetrahedral geometry of CH2Cl2 helps predict its polarity and consequent solubility in organic solvents, while the trigonal bipyramidal shape of SbF5 explains the distribution of electron pairs and can be used to infer the compound's reactivity.

Understanding molecular geometry helps in visualizing molecules and predicting their interactions in chemical reactions, making it an integral part of studying chemistry.