CHM2045 Exam 3 Session 10 (CH 11) Study Guide

Valence Bond Theory (VBT), Hybridization, and Lewis Structures

Hybrid Orbitals

• Definition: When two different orbitals mix, the result is a hybrid orbital.
  • Example: An s and a p orbital form two sp hybrid orbitals that are equivalent in terms of energy.

Determining Hybridization of Central Atoms

• The hybridization of the central atom of a molecule can be determined by counting the number of electron groups around the central atom. The following table outlines the correlations:

Specific Hybridization Examples

Problem C1: Hybrid Orbital Overlap in OF2

• Examine the hybrid orbital overlap in a molecule of OF2.
  • Hybridization of O atom: _
  • According to valence bond theory, orbitals overlapping to form O-F bond: _
  • Note: Generally, halogens and hydrogens do not utilize hybrid orbitals, thus we consider partially filled/empty orbitals for determining overlap.

Problem C2: Hybridization in CH4

• The electron pair geometry:
• Number of electron groups around carbon atom:
• Resulting hybrid orbitals: Mixed one and three orbitals to form _ hybrid orbitals.
• Important Note: Double/triple bonds do not alter hybridization; count them as one electron group.
• VBT consideration: Counts single bonds, double bonds, triple bonds, lone pairs, and radicals all the same as areas of high electron density.

Problem C3: Identifying sp3d Hybridization

• Atoms/Ions to analyze:
  • I. CH2O
  • II. BrF3
  • III. I3-
  • IV. PO43-
  • V. XeOF4
• Options:
  (a) I & II
  (b) I & IV
  (c) II & III
  (d) IV & V
  (e) II, IV, & V only

Problem C4: True Statements Regarding Valence Bond Theory

• Select all that apply:
  • The nitrogen atom in NH3 is sp3 hybridized. [✓]
  • The carbon atom in CO2 is sp hybridized. [✓]
  • The equatorial orbitals in a sp3d hybridized molecule lie at 109.5° to each other. [✗]
  • There are 3 degenerate, coplanar sp2 orbitals around the central atom in BF3 that lie at 120° to each other. [✓]
  • In the XeF4 molecule, there are 6 regions of high electron density on the Xe atom. [✓]

Bonding Concepts

Sigma (σ) Bonds

• Definition: A single bond is referred to as a sigma bond in a compound.
• Formation: A sigma bond is formed by the “end-to-end” overlap of two atomic orbitals, two hybrid orbitals, or one hybrid orbital with an atomic orbital.
• Characteristics:
  • Delocalizes electron density around the central atom.
  • Concentrates bonding electrons’ density along bond axis.
  • Creates space around nucleus for stronger bonding.
  • Reduces overall energy of the element.

Pi (π) Bonds

• Definition: A double bond contains 1 pi bond, and a triple bond contains 2 pi bonds in a compound.
• Formation:
  • A pi bond is formed by the “above and below” or “side-by-side” overlap of two unhybridized p orbitals.
• Characteristics:
  • Overlap of two unhybridized p orbitals oriented alike forms one pi bond.
  • Overlap of four unhybridized p orbitals oriented alike forms two pi bonds.
• Pre-requisite: For a pi bond to exist, a sigma bond must first occur.
• Comparison: A sigma bond is stronger than a pi bond.

Bonds Overview

• Single Bond: 1 sigma bond
• Double Bond: 1 sigma bond + 1 pi bond
• Triple Bond: 1 sigma bond + 2 pi bonds

Problem C5: Bonding in C2H4 Using VBT

• Analyze the following statements and select true ones:
  • There are three sigma bonds and two pi bonds. [✓]
  • A sigma bond formed by the overlap of sp hybridized orbitals. [✗]
  • Expected to have a linear geometry. [✗]
  • A pi bond formed by the overlap of two sp2 hybridized orbitals. [✗]
  • A pi bond formed by the overlap of two unhybridized p orbitals. [✓]

Problem C6: Sigma and Pi Bonds Count

• Count in molecule:
  • Sigma: ___
  • Pi: _

Molecular Orbital Theory

Overview

• VSEPR and VBT help determine shape and hybridization.
• Not effective in explaining energy or stability; utilize Molecular Orbital (MO) theory instead.
• Key Concepts:
  • Electrons are delocalized over the entire molecule.
  • Combination of atomic orbitals creates molecular orbitals.

Electron Overlap Possibilities

• Two overlapping electron conditions:
  • In-phase (Constructive):
  • Reinforces attraction forming bonding molecular orbital (lower energy).
  • Out-of-phase (Destructive):
  • Weakens attraction forming anti-bonding molecular orbital (higher energy).

Molecular Orbital (MO) Diagrams

• For diatomic molecules:
  • Add total electrons and position them starting from lowest energy MOs.
• Orbital configuration includes:
  • Sigma (σ) orbitals: Max 2 electrons per box.
  • Pi (π) orbitals: Max 4 electrons (2 boxes).
  • Anti-bonding orbitals indicated with (*).

Molecular Orbital Order for Mixing 2s & 2p (B2, C2, N2)

• Order:
  • ext{σ } 1s < ext{σ* } 1s < ext{σ } 2s < ext{σ* } 2s < ext{π } 2p = ext{π } 2p < ext{σ } 2p < ext{π* } 2p = ext{π* } 2p < ext{σ* } 2p

Molecular Orbital Order for No Mixing (O2, F2, Ne2)

• Order:
  • ext{σ } 1s < ext{σ* } 1s < ext{σ } 2s < ext{σ* } 2s < ext{σ } 2p < ext{π } 2p = ext{π } 2p < ext{π* } 2p = ext{π* } 2p < ext{σ* } 2p

Problem C7: MO Filling Diagrams

• Draw and label MO filling diagrams for substances to determine paramagnetic or diamagnetic behavior.
  • Example MO sequence: ext{σ } 1s < ext{σ* } 1s < ext{σ } 2s < ext{σ* } 2s < ext{π } 2p = ext{π } 2p < ext{σ } 2p < ext{π* } 2p = ext{π* } 2p < ext{σ* } 2p

Principles of MO Theory

Valid Principles in MO Theory

• Many principles from electron configurations apply to MO Theory:
  • Hund’s Rule: Obeyed / Not Obeyed
  • Pauli Exclusion Principle: Obeyed / Not Obeyed
  • Aufbau Principle: Obeyed / Not Obeyed (electrons are assigned to orbitals of successively higher energy)

Bond Order

• Definition:
  • ext{Bond Order} = rac{1}{2} imes ([ ext{# of electrons in bonding MO}] - [ ext{# of electrons in anti-bonding MO}])
• Implications:
  • Bond orders > 0 indicate stability and potential for existence.
  • Higher bond orders correlate with stronger, shorter bonds.
  • Bond orders = 0 indicate a lack of stability.

Example Bond Order Calculation

• In MO Theory, mixing two s orbitals creates: (bonding) and (anti-bonding) molecular orbitals.
• Mixing two p orbitals creates: , , , and molecular orbitals.

Problem C8: Bond Orders in O2, F2, Ne2

• Energy sequence: ext{σ } 2s < ext{σ* } 2s < ext{σ } 2p < ext{π } 2p < ext{π* } 2p < ext{σ* } 2p
• Determine bond orders of O2^{1-} and Ne2^{1+} respectively, and evaluate stability comparison.

Problems and Questions

Packet Problem Set

• P1: Identify sp3 hybridization in:
  • 1) ClO3^{-} 2) CO3^{2-} 3) SF4 4) PH3 5) SO3
• P2: Identify which has 2 pi bonds:
  • I) HCN II) N2O4 III) CO3^{2-}
• P3: Analyze nitrogen hybridization change in reaction:
  • NH3 + 2CO2 → CH3CN + 2O2
• P4: Determine which MO is represented by given p atomic orbitals in n = 2.
• P5: Identify sp2-hybridized carbon atoms in:
  • HCOOH, CS2, CF2CHCl, CH3CCH

Advanced Analysis

• P9: Order increasing molecular polarity for: I. CCl2Br2 II. CH2Br2 III. CBr4 IV. CH2F2 V. CF4
• P10: Identify incorrect statement regarding MO theory principles.
• P11: Match molecule with central atom hybridization.
• P12: Determine hybridization for PF3, SF4, AsO4^{3-}.