Problem 1 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Draw Lewis structures for the following compounds. \\[ \mathrm{BF}_{3} \quad \mathrm{SiH}_{4} \quad \mathrm{CS}_{2} \quad \mathrm{PCl}_{3} \quad \mathrm{PF}_{5} \quad \mathrm{KrF}_{2} \\] For each molecule, indicate whether the central atom obeys the octet rule, is hypervalent, or is electron poor. (Section 5.1 )

Step-by-Step Solution

Answer

BF3 is electron-deficient, SiH4 obeys the octet rule, CS2 obeys the octet rule, PCl3 obeys the octet rule, PF5 is hypervalent, and KrF2 is hypervalent.

Step 1: Determine Valence Electrons (BF3)

Boron has 3 valence electrons and each Fluorine has 7. The total number of valence electrons for BF3 is \(3 + 3 \times 7 = 24\) electrons.

Step 2: Draw the Lewis Structure (BF3)

Place Boron (B) in the center and connect it with three single bonds to each Fluorine (F). Distribute the remaining electrons to satisfy Flurorine's octet.

Step 3: Evaluate Octet Rule (BF3)

Boron has only 6 electrons around it, thus it is electron-deficient and does not obey the octet rule.

Step 4: Determine Valence Electrons (SiH4)

Silicon has 4 valence electrons and each Hydrogen has 1. The total number of valence electrons for SiH4 is \(4 + 4 \times 1 = 8\) electrons.

Step 5: Draw the Lewis Structure (SiH4)

Silicon (Si) is placed in the center with four single bonds connecting it to each Hydrogen (H). Each hydrogen has access to 2 electrons, satisfying its requirement.

Step 6: Evaluate Octet Rule (SiH4)

Silicon is surrounded by 8 electrons, thus it obeys the octet rule.

Step 7: Determine Valence Electrons (CS2)

Carbon has 4 valence electrons, and each Sulfur has 6. The total for CS2 is \(4 + 2 \times 6 = 16\) electrons.

Step 8: Draw the Lewis Structure (CS2)

Carbon (C) is central with double bonds to each Sulfur (S). Each sulfur has access to 8 electrons.

Step 9: Evaluate Octet Rule (CS2)

Carbon and both Sulfurs have full octets, so CS2 satisfies the octet rule.

Step 10: Determine Valence Electrons (PCl3)

Phosphorus has 5 valence electrons, and each Chlorine has 7. The total for PCl3 is \(5 + 3 \times 7 = 26\) electrons.

Step 11: Draw the Lewis Structure (PCl3)

Place Phosphorus (P) in the center with single bonds to each Chlorine (Cl), and distribute remaining electrons to attain full octets around Cl atoms.

Step 12: Evaluate Octet Rule (PCl3)

Phosphorus is surrounded by 8 electrons, including lone pairs and bond pairs, thus meets the octet rule.

Step 13: Determine Valence Electrons (PF5)

Phosphorus has 5 valence electrons, and each Fluorine has 7. The total for PF5 is \(5 + 5 \times 7= 40\) electrons.

Step 14: Draw the Lewis Structure (PF5)

Phosphorus is central with five single bonds to each Fluorine, using all available electrons.

Step 15: Evaluate Octet Rule (PF5)

Phosphorus has 10 electrons around it making it hypervalent, exceeding the octet rule.

Step 16: Determine Valence Electrons (KrF2)

Krypton has 8 valence electrons, and each Fluorine has 7. The total for KrF2 is \(8 + 2 \times 7 = 22\) electrons.

Step 17: Draw the Lewis Structure (KrF2)

Krypton is in the center with single bonds to each Fluorine atom, distributing remaining electron pairs around Krypton to complete valence shell accessibility.

Step 18: Evaluate Octet Rule (KrF2)

Krypton has access to 10 electrons, thus it is hypervalent, not strictly following the octet rule.

Key Concepts

Octet Rule

The octet rule is a fundamental concept in chemistry that guides us in understanding the formation of chemical bonds in molecules. According to this rule, atoms tend to form bonds until they are surrounded by eight electrons in their valence shell, giving them a noble gas electron configuration. This configuration is associated with maximum stability.

It's important to remember that the octet rule primarily applies to the main group elements, especially carbon, nitrogen, oxygen, and the halogens. For example, in the molecule \( \text{SiH}_4 \), silicon is bound to four hydrogen atoms, each hydrogen atom shares an electron with silicon, leading to an electron count of eight for silicon, thereby obeying the octet rule.

• Atoms aim for an electron configuration similar to the nearest noble gas.
• Elements in period 3 and below, such as phosphorus in \( \text{PCl}_3 \), often follow the octet rule due to their ability to accommodate more electrons through expanded octets.

However, there are exceptions. Boron in \( \text{BF}_3 \) only has six electrons, making it electron-deficient, which violates the octet rule, illustrating one of the exceptions to this guideline.

Valence Electrons

Valence electrons are the outermost electrons of an atom and play a pivotal role in bond formation. These electrons determine how an atom interacts with others and are, therefore, crucial when constructing a Lewis structure.

To determine valence electrons, we often look at the group number in the periodic table for main-group elements. For instance, looking at the compound \( \text{BF}_3 \): Boron, belonging to group 13, has three valence electrons, and each fluorine, belonging to group 17, has seven. To get the total number of valence electrons, we add these: \(3 + 3 \times 7 = 24\). Understanding these electron numbers helps in crafting precise Lewis structures.

• Satisfying the full octet depicts a stable configuration, as seen in \( \text{PCl}_3 \) where phosphorus and chlorine achieve full octets.
• Valence electrons directly help to visualize potential bond formations and molecular geometry.

Valence electrons serve as a backbone for both chemical bonding and Lewis structure representation, highlighting their significance in molecular chemistry.

Electron Deficiency

Electron deficiency occurs when an atom in a molecule lacks enough electrons to complete its valence shell to the point typically required by the octet rule. This condition leads to fewer than eight electrons surrounding an atom.

An example of electron deficiency is seen in \( \text{BF}_3 \). The boron atom is surrounded by only six electrons, making it electron-deficient. This often compels the atom to seek additional electrons through different forms of bonding, such as forming complexes. Boron's inability to reach a stable octet demonstrates a key aspect of electron deficiency, often leading to reactive or donor-acceptor interactions.

• Electron-deficient compounds tend to be highly reactive due to their need to fill electron gaps.
• They are frequently involved in forming Lewis acid-base complexes or accepting electron pairs from other molecules.

Electron-deficient atoms are interesting in chemistry because they often participate in unique reactions to achieve stability, highlighting their reactive nature.

Hypervalency

Hypervalency occurs when central atoms in molecules have valence electron counts exceeding eight. This phenomenon is prevalent in elements from the third period onward, where empty d orbitals become available.

In \( \text{PF}_5 \) and \( \text{KrF}_2 \), phosphorus and krypton exceed the standard octet. Phosphorus in \( \text{PF}_5 \) has ten electrons around it through five single bonds with fluorine atoms, while krypton in \( \text{KrF}_2 \) supports a similar count. These examples demonstrate how hypervalency allows for the stabilization of unusual molecular geometries and coordination numbers.

• Hypervalent molecules often display expanded coordination numbers, such as five for phosphorus in \( \text{PF}_5 \).
• Elements in period 3 or beyond can exceed the octet due to available d orbitals, leading to various bonding arrangements.

Understanding hypervalency helps in predicting molecular structures and explaining why certain compounds can exist despite seemingly violating the octet rule.