Problem 3 - Chemistry and Chemical Reactivity

Question

Specify the electron-pair and molecular geometry for each of the following. Describe the hybrid orbital set used by the underlined atom in each molecule or ion. (a) \(\underline{\mathrm{BBr}}_{3}\) (b) \(\underline{\mathrm{CO}}_{2}\) (c) \(\underline{\mathrm{CH}}_{2} \mathrm{Cl}_{2}\) (d) \(\underline{\mathrm{CO}}_{3}^{2-}\)

Step-by-Step Solution

Answer

BBr₃: Trigonal Planar, sp²; CO₂: Linear, sp; CH₂Cl₂: Tetrahedral, sp³; CO₃²⁻: Trigonal Planar, sp².

Step 1: Determine BBr₃ Geometry and Hybridization

For BBr₃, Boron (B) is the central atom. Boron has three valence electrons and forms three sigma bonds with Bromine. There are no lone pairs on Boron. - **Electron-Pair Geometry**: Trigonal Planar - **Molecular Geometry**: Trigonal Planar - **Hybridization of B**: sp² (Boron uses three sp² hybrid orbitals to bond with three Bromine atoms)

Step 2: Determine CO₂ Geometry and Hybridization

For CO₂, Carbon (C) is the central atom. Carbon forms two double bonds with Oxygen atoms, and there are no lone pairs on Carbon. - **Electron-Pair Geometry**: Linear - **Molecular Geometry**: Linear - **Hybridization of C**: sp (Carbon uses two sp hybrid orbitals for the double bonds with each Oxygen)

Step 3: Determine CH₂Cl₂ Geometry and Hybridization

For CH₂Cl₂, Carbon (C) is the central atom. Carbon forms two sigma bonds with Hydrogen and two sigma bonds with Chlorine, with no lone pairs on Carbon. - **Electron-Pair Geometry**: Tetrahedral - **Molecular Geometry**: Tetrahedral - **Hybridization of C**: sp³ (Carbon uses four sp³ hybrid orbitals to form bonds with two Hydrogens and two Chlorines)

Step 4: Determine CO₃²⁻ Geometry and Hybridization

For CO₃²⁻, Carbon (C) is the central atom. Carbon forms three sigma bonds and has a resonance structure with double bonds distributed among three Oxygen atoms. There are no lone pairs on Carbon. - **Electron-Pair Geometry**: Trigonal Planar - **Molecular Geometry**: Trigonal Planar - **Hybridization of C**: sp² (Carbon uses three sp² hybrid orbitals to bond with Oxygen atoms)

Key Concepts

Hybridization

The concept of hybridization is essential in understanding molecular geometry. It refers to the mixing of atomic orbitals in an atom to form a new set of hybrid orbitals. This occurs during the formation of chemical bonds to optimize the arrangement of electrons.

• In BBr₃, boron undergoes sp² hybridization. Here, one s and two p orbitals mix, resulting in three equivalent sp² hybrid orbitals. These orbitals form sigma bonds with the bromine atoms.
• In CO₂, carbon uses sp hybridization. One s orbital and one p orbital mix to form two sp hybrid orbitals. Each orbital forms a sigma bond with an oxygen atom, aligning linearly.
• CH₂Cl₂ involves carbon undergoing sp³ hybridization. All four hybridized orbitals are used to bond with hydrogen and chlorine atoms, leading to a tetrahedral shape.
• For CO₃²⁻, carbon is sp² hybridized. Similarly to BBr₃, this leads to three hybrid orbitals, but with resonance structures affecting electron distribution.

Understanding hybridization helps explain how different molecules achieve their specific shapes and bond types.

Electron-Pair Geometry

Electron-pair geometry considers the spatial arrangement of all electron pairs around a central atom, including both bonding and lone pairs. This helps in predicting the molecular structure.

• For BBr₃, the electron-pair geometry is trigonal planar. This symmetrical arrangement comes from the three shared electron pairs and zero lone pairs around boron.
• In CO₂, with only two regions of electron density, the geometry is linear, resulting from its two double bonds.
• CH₂Cl₂ has a tetrahedral electron-pair geometry because the four areas of electron density—bonds to two hydrogens and two chlorines—spread out evenly in three dimensions.
• CO₃²⁻ also shares a trigonal planar electron-pair geometry, with three equivalent bonding regions around carbon reflecting shared and resonance-affected double bonds.

Understanding electron-pair geometry is crucial to predicting how molecules interact and react in a three-dimensional space.

Sigma Bonds

Sigma bonds (\(\sigma\) bonds) are the first and strongest type of covalent bonds formed via the head-on overlap of atomic orbitals. They exist in all single bonds and are necessary for determining a molecule's structure and stability.

• In BBr₃, three sigma bonds form between boron and each bromine atom, securing a planar shape.
• CO₂ forms sigma bonds from sp hybridized orbitals of carbon bonded to oxygen atoms. The linear molecular shape features these bonds.
• CH₂Cl₂ contains four sigma bonds, with each sp³ hybridized orbital of carbon forming a bond with hydrogen or chlorine.
• For CO₃²⁻, three sigma bonds exist between carbon and oxygen atoms. The resonance structure alters bond characteristics but maintains sigma bond presence.

Sigma bonds are fundamental to the rigid framework in molecular structures.

Resonance Structure

Resonance structures are different ways of representing the electron distribution within a molecule that can't be captured by a single Lewis structure. They are critical for understanding the electron delocalization seen in many molecules.

• In CO₃²⁻, resonance plays a crucial role. While drawing one structure suggests a single double bond and two single bonds, resonance structures indicate that all C-O bonds are equivalent by sharing electron density.
• Unlike CO₃²⁻, BBr₃, CO₂, and CH₂Cl₂ do not exhibit resonance structures since they are adequately described by one traditional Lewis structure.

Recognizing the concept of resonance is pivotal for comprehending molecules' true electron arrangements and their resultant chemical properties.