Chemical Bonding: Theory and Fundamentals

Molecular Structure and Bonding: Enhanced Detailed Notes

Introduction to Molecular Structure Models

  • Inorganic chemistry relies heavily on semi-quantitative models to interpret observed molecular structures, predict reactivity, and understand the properties of chemical compounds. These models bridge the gap between complex quantum mechanical calculations and intuitive chemical understanding.
  • This chapter delves into the foundational models used to describe molecular structure: Lewis structures (a foundational concept), the Valence Shell Electron Pair Repulsion (VSEPR) model for predicting shapes, Valence Bond (VB) theory (emphasizing localized bonds), and Molecular Orbital (MO) theory (emphasizing delocalized electrons).
  • A critical aspect is the dynamic interplay between these qualitative models, rigorous experimental observations (e.g., spectroscopy, diffraction), and advanced computational chemistry (e.g., density functional theory). Each approach offers unique insights and complements the others, leading to a more complete picture of chemical bonding.

Lewis Structures: The Foundation of Covalent Bonding

  • Covalent Bond Formation: G.N. Lewis proposed that atoms form covalent bonds by sharing electron pairs. This sharing allows atoms to achieve a more stable electron configuration, typically resembling that of a noble gas.
    • Single Bond: Involves the sharing of one pair of electrons, often represented by a single line (A–B) or two dots (A:B).
    • Double Bond: Consists of two shared electron pairs, represented by two lines (A=B) or four dots (A::B). This implies greater electron density between the bonded atoms.
    • Triple Bond: Involves three shared electron pairs, depicted by three lines (A≡B) or six dots (A:::B). These are the strongest and shortest covalent bonds between a given pair of atoms.
  • Lone Pairs (Non-bonding Electrons): These are unshared valence electron pairs residing on a particular atom (e.g., A:). While not directly involved in holding atoms together, lone pairs significantly influence:
    • Molecular Geometry: Their greater spatial demands (due to more diffuse electron clouds) lead to distortions in bond angles.
    • Molecular Polarity: They contribute to the overall electron distribution, impacting the molecule’s dipole moment.
    • Chemical Reactivity: Lone pairs often serve as sites for Lewis base behavior (electron pair donation).
  • The Octet Rule and Duplet Rule:
    • Octet Rule: For most main-group elements (especially Period 2 elements like C, N, O, F), the tendency is to share or transfer electrons such that each atom achieves a stable configuration of eight valence electrons, mimicking the electron configuration of the nearest noble gas (e.g., Ne). This results in a full s2p6 valence shell.
    • Duplet Rule: For hydrogen and helium, stability is achieved with two valence electrons (e.g., H in H2, He).
    • Limitations: The octet rule is a useful guideline but has exceptions, particularly for:
      • Electron-deficient compounds: e.g., BF3 (Boron only has 6 valence electrons).
      • Radicals: Molecules with an odd number of valence electrons, e.g., NO.
      • Hypervalent compounds: Elements from Period 3 and beyond (e.g., P, S, Cl, Xe) can accommodate more than eight valence electrons in their valence shell (e.g., PCl5, SF6, XeF4). This expansion is sometimes attributed to the involvement of d-orbitals, although modern explanations often involve delocalized bonding described by MO theory or packing considerations.
  • Resonance: Delocalization of Electrons:
    • When a single Lewis structure cannot adequately represent the true electron distribution in a molecule or ion, the concept of resonance is invoked.
    • Resonance Structures (Contributing Structures): These are hypothetical Lewis structures that differ only in the placement of electrons (usually pi electrons and lone pairs), not in the positions of the atoms.
    • Resonance Hybrid: The actual molecule is a resonance hybrid, an average or blend of all valid resonance structures. It is not an equilibrium between discrete structures, but a single, stable entity.
    • Key Characteristics of Resonance:
      • Electron Delocalization: Electrons are not confined to a single bond or atom but are spread over multiple atoms.
      • Bond Order Averaging: Bonds in a resonance hybrid often have intermediate bond orders (e.g., the C-C bonds in benzene are 1.5, not alternating single and double).
      • Resonance Stabilization: Delocalization of electrons lowers the overall potential energy of the molecule, making it more stable than any single contributing Lewis structure. This energy difference is called the resonance energy.
    • Example: Carbonate ion (CO3^2-), nitrate ion (NO3-), benzene (C6H6).

The VSEPR Model (Valence Shell Electron Pair Repulsion): Predicting Molecular Shapes

  • Core Principle: The VSEPR model predicts the three-dimensional arrangement of atoms around a central atom by assuming that electron domains (bonding pairs, whether single, double, or triple, and lone pairs) in the valence shell of the central atom repel each other and will adopt geometries that maximize the distance between these domains, thereby minimizing electron-electron repulsion.
    • The geometry is based on the electron domain arrangement, but the molecular shape is described by the arrangement of the atoms only.
  • Hierarchy of Repulsions: The repulsive forces between electron domains are not equal, leading to distortions from ideal geometries:
    • Lone pair-lone pair (lp-lp) repulsion > Lone pair-bonding pair (lp-bp) repulsion > Bonding pair-bonding pair (bp-bp) repulsion.
    • Lone pairs are more diffuse and occupy more space around the central atom because they are only attracted by one nucleus, leading to greater repulsion and a tendency to compress bond angles between bonding pairs.
  • Steps for Applying VSEPR:
    1. Draw the correct Lewis structure.
    2. Count the total number of electron domains around the central atom (each lone pair, single bond, double bond, and triple bond counts as one domain).
    3. Determine the electron domain geometry that minimizes repulsion.
    4. Determine the molecular geometry by considering only the positions of the atoms.
  • Common Electron Domain Geometries and Molecular Shapes:
    • 2 Electron Domains: Linear (e.g., BeCl2, CO2). Bond angle: 180°.
    • 3 Electron Domains: Trigonal Planar (e.g., BF3, NO3-). Ideal bond angle: 120°.
      • 3 bonding, 0 lone pairs: Trigonal planar.
      • 2 bonding, 1 lone pair: Bent/V-shaped (e.g., SO2). Angle < 120°.
    • 4 Electron Domains: Tetrahedral (e.g., CH4, NH3, H2O). Ideal bond angle: 109.5°.
      • 4 bonding, 0 lone pairs: Tetrahedral (e.g., CH4).
      • 3 bonding, 1 lone pair: Trigonal pyramidal (e.g., NH3). Angle < 109.5° (approx. 107°).
      • 2 bonding, 2 lone pairs: Bent/V-shaped (e.g., H2O). Angle < 109.5° (approx. 104.5°).
    • 5 Electron Domains: Trigonal Bipyramidal (e.g., PCl5). Two types of positions: axial and equatorial. Lone pairs preferentially occupy equatorial positions to minimize stronger 90° repulsions.
      • 5 bonding, 0 lone pairs: Trigonal bipyramidal.
      • 4 bonding, 1 lone pair: Seesaw (e.g., SF4).
      • 3 bonding, 2 lone pairs: T-shaped (e.g., ClF3).
      • 2 bonding, 3 lone pairs: Linear (e.g., XeF2).
    • 6 Electron Domains: Octahedral (e.g., SF6). Ideal bond angles: 90°, 180°. Lone pairs occupy positions opposite to each other to maximize separation.
      • 6 bonding, 0 lone pairs: Octahedral.
      • 5 bonding, 1 lone pair: Square pyramidal (e.g., BrF5).
      • 4 bonding, 2 lone pairs: Square planar (e.g., XeF4).

Valence Bond (VB) Theory: Localized Bonds from Overlapping Orbitals

  • Core Concept: A chemical bond is formed when atomic orbitals from two different atoms overlap, and the region of overlap is occupied by a pair of electrons with opposite spins (Pauli principle). The greater the overlap, the stronger the bond.
  • Hydrogen Molecule (H2) Example: The simplest case, formed by the constructive overlap of two H1s atomic orbitals. The energy minimum in the potential energy curve signifies bond formation.
  • Homonuclear Diatomic Molecules (beyond H2):
    • Sigma (σ) Bonds: Formed by the direct, head-on (axial) overlap of atomic orbitals (s-s, s-p, p-p end-on). Electron density is concentrated along the internuclear axis. All single bonds are sigma bonds. They have cylindrical symmetry around the internuclear axis.
    • Pi (π) Bonds: Formed by the sideways overlap of parallel p-orbitals (or sometimes d-orbitals). The electron density is concentrated above and below (or in front and behind) the internuclear axis, with a nodal plane along the internuclear axis. Double bonds consist of one σ and one π bond; triple bonds consist of one σ and two π bonds.
  • Polyatomic Molecules: The Need for Hybridization:
    • Simple overlap of pure atomic orbitals (s, p, d) often fails to explain the observed geometries and equivalence of bonds in polyatomic molecules (e.g., methane, CH4, should have 90° angles if only p-orbitals are used, but it’s tetrahedral with 109.5° angles).
    • Promotion: A hypothetical step where an electron is excited from a lower-energy orbital to a higher-energy orbital within the same atom to create more unpaired electrons for bonding (e.g., Carbon: 2s22p2 → 2s12p3). This energy investment is compensated by the formation of a greater number of stronger bonds.
    • Hybridization: The mathematical mixing of a specific number of atomic orbitals (s, p, d) on a single central atom to form an equal number of new, degenerate (equal energy) hybrid orbitals. These hybrid orbitals are spatially directed in a way that minimizes electron repulsion and maximizes orbital overlap, leading to stronger, more stable bonds and correct molecular geometries.
      • sp3 Hybridization: One s orbital and three p orbitals combine to form four equivalent sp3 hybrid orbitals. These orbitals point towards the corners of a regular tetrahedron, explaining the tetrahedral geometry and equivalent C-H bonds in methane (109.5°).
      • sp2 Hybridization: One s orbital and two p orbitals combine to form three equivalent sp2 hybrid orbitals, arranged in a trigonal planar fashion (120°). One unhybridized p orbital remains perpendicular to the plane, available for π bonding (e.g., ethene, C2H4).
      • sp Hybridization: One s orbital and one p orbital combine to form two equivalent sp hybrid orbitals, arranged linearly (180°). Two unhybridized p orbitals remain perpendicular to the linear axis, available for two π bonds (e.g., ethyne, C2H2).
      • Hybridization involving d-orbitals: For hypervalent molecules, d-orbitals can participate in hybridization to accommodate more than eight electrons (e.g., sp3d for trigonal bipyramidal; sp3d2 for octahedral). However, the extent of d-orbital participation is a subject of ongoing debate in advanced inorganic chemistry, with MO theory offering alternative explanations.

Molecular Orbital (MO) Theory: Delocalized Electron Clouds

  • A More Global Perspective: MO theory offers a more advanced and powerful description of bonding, where electrons are not localized between specific atoms but are delocalized over the entire molecule. It successfully explains phenomena that VB theory struggles with, such as the paramagnetism of O2.
  • Key Concept: Electrons in a molecule occupy molecular orbitals (MOs), which are eigenfunctions of the molecular Hamiltonian. These MOs span the entire molecular framework, providing a delocalized view of electron density.
  • Linear Combination of Atomic Orbitals (LCAO) Approximation: The most common approach to constructing molecular orbitals is by mathematically combining atomic orbitals (AOs) from all atoms in the molecule.
    • Rules for LCAO:
      1. Only AOs of similar energy can combine effectively.
      2. Only AOs with significant overlap can combine effectively.
      3. Only AOs of appropriate symmetry can combine effectively.
    • If N atomic orbitals are combined, N molecular orbitals will be formed.
  • Types of Molecular Orbitals:
    • Bonding Molecular Orbitals (Ψbonding​): Formed by the constructive interference of atomic orbitals (AOs combine with the same sign). Electron density is concentrated between the nuclei, leading to attraction and lower energy (more stable).
    • Antibonding Molecular Orbitals (Ψantibonding​): Formed by the destructive interference of atomic orbitals (AOs combine with opposite signs). A nodal plane (a region of zero electron density) is created between the nuclei, leading to repulsion and higher energy (less stable). Denoted with an asterisk (), e.g., $\sigma^$, π∗.
    • Nonbonding Molecular Orbitals: Formed when AOs have incompatible symmetry or negligible overlap. Their occupation neither stabilizes nor destabilizes the molecule. They are typically localized on a single atom and have similar energy to the contributing atomic orbital.
  • Homonuclear Diatomic Molecules (e.g., H2, N2, O2):
    • Energy Level Diagrams: These diagrams illustrate the relative energies of the atomic orbitals and the molecular orbitals formed from their combination. Electrons are filled into the MOs according to the Aufbau principle, Hund’s rule, and the Pauli exclusion principle.
    • σ and π Molecular Orbitals: Similar to VB theory, MOs are classified as σ or π based on their symmetry around the internuclear axis.
    • g (gerade) and u (ungerade) Symmetry: For molecules with a center of inversion (centrosymmetric, e.g., H2, O2, N2), molecular orbitals are further classified:
      • gerade (g): The orbital’s sign remains the same upon inversion through the center of the molecule. Bonding σ MOs are typically g.
      • ungerade (u): The orbital’s sign changes upon inversion through the center of the molecule. Antibonding σ∗ MOs are typically u. Bonding π MOs are typically u, while antibonding π∗ MOs are typically g.
    • s-p Mixing (Orbital Reversal): For lighter diatomic molecules (Li2, Be2, B2, C2, N2), there is significant mixing between the 2s and 2p atomic orbitals. This mixing causes the σ2p​ molecular orbital to be pushed to a higher energy than the π2p​ orbitals. For heavier diatomics (O2, F2), this mixing is less pronounced, and the normal order (π2p​ above σ2p​) is restored. This explains the paramagnetism of O2 (two unpaired electrons in the π2p∗​ orbitals) and the diamagnetism of N2.
    • Bond Order (b): A quantitative measure of the net bonding in a molecule: b = ½ (number of electrons in bonding MOs – number of electrons in antibonding MOs) Nonbonding electrons do not contribute to bond order. A higher bond order indicates a stronger and typically shorter bond.
      • Examples: H2 (b=1), He2 (b=0, unstable), N2 (b=3), O2 (b=2), F2 (b=1).
  • Heteronuclear Diatomic Molecules (e.g., HF, CO):
    • The LCAO approach still applies, but due to differences in electronegativity and atomic orbital energies, the atomic orbital contributions to each molecular orbital are unequal.
    • Polarity: Bonding MOs will have a greater contribution from the more electronegative atom (whose AOs are lower in energy), leading to polar bonds.
    • Example: CO: The Highest Occupied Molecular Orbital (HOMO) of CO is an almost nonbonding orbital largely localized on the carbon atom, and the Lowest Unoccupied Molecular Orbital (LUMO) is an antibonding orbital also primarily on carbon. This electronic structure is crucial for understanding CO’s ability to coordinate to transition metals through the carbon atom.
  • Polyatomic Molecules (Beyond Diatomics):
    • MO theory extends naturally to polyatomic molecules. The MOs are even more delocalized, spanning multiple atoms.
    • Symmetry: Group theory (covered in Chapter 6) is essential for constructing and classifying molecular orbitals in complex polyatomic molecules, simplifying the process and allowing for the prediction of spectroscopic properties.
    • d-orbital Participation: For transition metals, d-orbitals participate extensively in bonding, forming not only σ and π bonds but also δ (delta) bonds. δ bonds arise from the sideways overlap of four lobes of d-orbitals (e.g., dx2-y2 with dx2-y2 or dxy with dxy), contributing to very high bond orders (e.g., quadruple and quintuple bonds in metal-metal bonds).

Structure and Bond Properties: Experimental Connections

  • Bond Length: The average equilibrium distance between the nuclei of two bonded atoms. Measured experimentally (e.g., by X-ray diffraction).
    • Trend: Generally, as bond order increases between a given pair of atoms, the bond length decreases (e.g., C-C > C=C > C≡C).
  • Bond Strength (Bond Enthalpy): The energy required to break a specific bond in a gaseous molecule (homolytically, splitting into radicals).
    • Trend: Generally, as bond order increases, bond strength increases.
    • Correlation: Shorter bonds are typically stronger bonds.
    • Element-specific trends highlight unique chemistry:
      • Carbon-Carbon Bonds: A C=C double bond is less than twice as strong as a C-C single bond (∼614 kJ/mol vs. ∼348 kJ/mol). This relatively weaker π component explains why unsaturated organic compounds readily undergo addition reactions (e.g., polymerization).
      • Nitrogen-Nitrogen Bonds: The N≡N triple bond (∼945 kJ/mol) is significantly more than five times stronger than an N-N single bond (∼160 kJ/mol). This extraordinary strength explains the high stability and inertness of N2 gas, and why breaking it (e.g., in nitrogen fixation) is energetically demanding.
      • Phosphorus-Phosphorus Bonds: Unlike nitrogen, single P-P bonds are relatively more stable than multiple P-P bonds. This contributes to phosphorus’s tendency to form extended structures with P-P single bonds (e.g., P4, which has a tetrahedral arrangement of P atoms) rather than diatomic P2 molecules (which exist only at high temperatures).
  • Electronegativity: A measure of an atom’s ability to attract electrons in a chemical bond. Differences in electronegativity influence bond polarity and can also affect bond strength.
  • Oxidation States: Formal assignments based on electronegativity, reflecting the hypothetical charge an atom would have if all bonds were ionic. These are useful bookkeeping tools for tracking electron distribution and changes in chemical reactions.

Molecular Structure and Bonding: 30 New Multiple Choice Questions with Explanations

  1. Which model is explicitly stated to bridge the gap between quantum mechanical calculations and intuitive chemical understanding? a) Lewis Structures b) VSEPR Model c) Molecular Orbital (MO) Theory d) All of the aboveAnswer: d) All of the above Explanation: The introduction states that the “dynamic interplay between these qualitative models, rigorous experimental observations… and advanced computational chemistry… leads to a more complete picture of chemical bonding.” This implies all the models listed contribute to this understanding.
  2. According to Lewis, how many electron pairs are shared in a triple bond? a) One b) Two c) Three d) FourAnswer: c) Three Explanation: The “Covalent Bond Formation” section under Lewis Structures explicitly states, “Triple bond: Involves three shared electron pairs…”
  3. What is a direct consequence of lone pairs having greater spatial demands compared to bonding pairs? a) Increased bond strength b) Distortions in molecular polarity c) Compression of bond angles d) Formation of pi bondsAnswer: c) Compression of bond angles Explanation: The “Lone Pairs (Non-bonding Electrons)” section and the “Hierarchy of Repulsions” under VSEPR state that lone pairs occupy more space and lead to “greater repulsion and a tendency to compress bond angles between bonding pairs.”
  4. Which of the following elements is explicitly mentioned as an exception to the Octet Rule, forming electron-deficient compounds? a) Carbon b) Nitrogen c) Boron d) OxygenAnswer: c) Boron Explanation: Under “Limitations” of the Octet Rule, BF3 (Boron only has 6 valence electrons) is given as an example of an “Electron-deficient compound.”
  5. What is the defining characteristic of a “resonance hybrid”? a) It is a single Lewis structure with delocalized electrons. b) It is an equilibrium between discrete contributing structures. c) It is an average or blend of all valid resonance structures. d) It only applies to molecules with odd numbers of electrons.Answer: c) It is an average or blend of all valid resonance structures. Explanation: The “Resonance Hybrid” section clarifies that the actual molecule “is an average or blend of all valid resonance structures. It is not an equilibrium between discrete structures, but a single, stable entity.”
  6. In the VSEPR model, what is the count for a double bond when determining the total number of electron domains around the central atom? a) Two domains b) One domain c) Zero domains d) Depends on the elements involvedAnswer: b) One domain Explanation: The “Steps for Applying VSEPR” explicitly states: “…each lone pair, single bond, double bond, and triple bond counts as one domain.”
  7. Which VSEPR electron domain geometry corresponds to a T-shaped molecular geometry? a) 3 electron domains b) 4 electron domains c) 5 electron domains d) 6 electron domainsAnswer: c) 5 electron domains Explanation: Under “Common Electron Domain Geometries and Molecular Shapes” for “5 Electron Domains,” it lists “3 bonding, 2 lone pairs: T-shaped (e.g., ClF3).”
  8. What is the ideal bond angle for a molecule with three electron domains around the central atom, all of which are bonding pairs? a) 90° b) 109.5° c) 120° d) 180°Answer: c) 120° Explanation: For “3 Electron Domains: Trigonal Planar (e.g., BF3, NO3-). Ideal bond angle: 120°.”
  9. According to Valence Bond Theory, what is the effect of greater orbital overlap on bond strength? a) It decreases bond strength. b) It has no effect on bond strength. c) It increases bond strength. d) It leads to pi bond formation only.Answer: c) It increases bond strength. Explanation: Under “Core Concept” of VB Theory, it states, “The greater the overlap, the stronger the bond.”
  10. What kind of bond is formed by the sideways overlap of parallel p-orbitals, with electron density concentrated above and below the internuclear axis? a) Sigma (σ) bond b) Delta (δ) bond c) Pi (π) bond d) Ionic bondAnswer: c) Pi (π) bond Explanation: Under “Homonuclear Diatomic Molecules” in VB Theory, it’s defined as “formed by sideways overlap of parallel p-orbitals… The electron density is concentrated above and below… the internuclear axis, with a nodal plane along the internuclear axis.”
  11. Why was the concept of “Promotion” introduced in Valence Bond Theory? a) To explain electron delocalization. b) To account for the observed paramagnetism of molecules. c) To create more unpaired electrons for bonding. d) To describe the formation of antibonding orbitals.Answer: c) To create more unpaired electrons for bonding. Explanation: The “Promotion” section states it’s “a hypothetical step where an electron is excited from a lower-energy orbital to a higher-energy orbital within the same atom to create more unpaired electrons for bonding.”
  12. What is the geometry of the hybrid orbitals formed from sp2 hybridization? a) Linear b) Tetrahedral c) Trigonal planar d) OctahedralAnswer: c) Trigonal planar Explanation: Under “Hybridization,” it states, “sp2 hybridization… form three equivalent sp2 hybrid orbitals, arranged in a trigonal planar fashion (120°).”
  13. Which theory is described as more sophisticated and capable of explaining phenomena like the paramagnetism of O2? a) Lewis Structure Theory b) VSEPR Model c) Valence Bond (VB) Theory d) Molecular Orbital (MO) TheoryAnswer: d) Molecular Orbital (MO) Theory Explanation: The “A More Global Perspective” section of MO Theory states it “successfully explains phenomena that VB theory struggles with, such as the paramagnetism of O2.”
  14. What is the fundamental concept in Molecular Orbital Theory regarding electron distribution? a) Electrons are localized between two specific atoms. b) Electrons occupy atomic orbitals only. c) Electrons are delocalized over all atoms in the molecule. d) Electrons are always found in nonbonding orbitals.Answer: c) Electrons are delocalized over all atoms in the molecule. Explanation: The “Key Concept” of MO Theory states, “Electrons in a molecule occupy molecular orbitals (MOs), which are eigenfunctions of the molecular Hamiltonian. These MOs span the entire molecular framework, providing a delocalized view of electron density.”
  15. According to the LCAO approximation rules, which atomic orbitals can effectively combine to form molecular orbitals? a) Only AOs with very different energies. b) Only AOs with no overlap. c) Only AOs of appropriate symmetry. d) All AOs, regardless of properties.Answer: c) Only AOs of appropriate symmetry. Explanation: One of the “Rules for LCAO” is: “Only AOs of appropriate symmetry can combine effectively.” The other options contradict the rules stated.
  16. Which type of molecular orbital has a nodal plane between the nuclei and is higher in energy? a) Bonding molecular orbital b) Nonbonding molecular orbital c) Antibonding molecular orbital d) Atomic orbitalAnswer: c) Antibonding molecular orbital Explanation: Under “Types of Molecular Orbitals,” antibonding MOs are described as having “a nodal plane… between the nuclei, leading to repulsion and higher energy (less stable).”
  17. For centrosymmetric molecules, what does the ‘g’ (gerade) designation for a molecular orbital indicate? a) The orbital’s sign changes upon inversion. b) The orbital is nonbonding. c) The orbital’s sign remains the same upon inversion. d) The orbital has a nodal plane.Answer: c) The orbital’s sign remains the same upon inversion. Explanation: Under “g (gerade) and u (ungerade) Symmetry,” it states, “gerade (g): The orbital’s sign remains the same upon inversion through the center of the molecule.”
  18. What phenomenon explains the reversal of the σ2p​ and π2p​ molecular orbital energy order in lighter diatomics (Li2-N2) compared to heavier ones (O2-F2)? a) Pauli exclusion principle b) Hund’s rule c) s-p mixing d) Electronegativity differencesAnswer: c) s-p mixing Explanation: The “s-p Mixing (Orbital Reversal)” section explicitly attributes this phenomenon to “significant mixing between the 2s and 2p atomic orbitals.”
  19. A molecule has 8 electrons in bonding MOs and 4 electrons in antibonding MOs. What is its bond order? a) 1 b) 2 c) 3 d) 4Answer: b) 2 Explanation: Bond Order (b) = ½ (n – n*) = ½ (8 – 4) = ½ (4) = 2.
  20. What is a key characteristic of the HOMO of carbon monoxide (CO) that influences its coordination chemistry? a) It is highly bonding and localized on oxygen. b) It is an antibonding orbital. c) It is primarily nonbonding and largely localized on carbon. d) It is a sigma (σ) bonding orbital.Answer: c) It is primarily nonbonding and largely localized on carbon. Explanation: Under “Heteronuclear Diatomic Molecules,” the text states, “The Highest Occupied Molecular Orbital (HOMO) of CO is an almost nonbonding orbital largely localized on the carbon atom…”
  21. What type of bond, beyond σ and π, is formed by the sideways overlap of four lobes of d-orbitals? a) Ionic bond b) Hydrogen bond c) Delta (δ) bond d) Metallic bondAnswer: c) Delta (δ) bond Explanation: Under “d-orbital Participation,” it states that d-orbitals can form “δ (delta) bonds. δ bonds arise from the sideways overlap of four lobes of d-orbitals.”
  22. For a given pair of atoms, what is the relationship between bond order and bond length? a) As bond order increases, bond length increases. b) As bond order increases, bond length decreases. c) Bond order and bond length are unrelated. d) Bond length is directly proportional to bond order.Answer: b) As bond order increases, bond length decreases. Explanation: Under “Bond Length,” the trend states, “Generally, as bond order increases between a given pair of atoms, the bond length decreases.”
  23. Which element’s unique bond enthalpy trends explain why it readily undergoes addition reactions like polymerization due to a relatively weaker pi component in its double bonds? a) Nitrogen b) Oxygen c) Carbon d) PhosphorusAnswer: c) Carbon Explanation: Under “Element-specific trends,” it states, “Carbon-Carbon Bonds: A C=C double bond is less than twice as strong as a C-C single bond… This relatively weaker π component explains why unsaturated organic compounds readily undergo addition reactions (e.g., polymerization).”
  24. What best describes the stability of the N≡N triple bond based on its bond enthalpy? a) It is relatively unstable due to strong repulsions. b) It is significantly stronger than single N-N bonds, making N2 highly stable. c) It is weaker than two N-N single bonds combined. d) Its strength is comparable to that of a single N-N bond.Answer: b) It is significantly stronger than single N-N bonds, making N2 highly stable. Explanation: Under “Element-specific trends,” it highlights: “Nitrogen-Nitrogen Bonds: The N≡N triple bond (∼945 kJ/mol) is significantly more than five times stronger than an N-N single bond (∼160 kJ/mol). This extraordinary strength explains the high stability and inertness of N2 gas…”
  25. What is the primary role of “Oxidation States” in chemistry, as described in the notes? a) To determine bond lengths. b) To track electron distribution and changes in chemical reactions. c) To predict molecular geometry. d) To calculate bond enthalpy.Answer: b) To track electron distribution and changes in chemical reactions. Explanation: The “Oxidation States” section states they are “useful bookkeeping tools for tracking electron distribution and changes in chemical reactions.”
  26. Which of the following is a direct influence of lone pairs on molecular properties? a) Reducing overall molecular stability. b) Increasing the effective nuclear charge. c) Contributing to the molecule’s dipole moment. d) Decreasing the formal charge on the central atom.Answer: c) Contributing to the molecule’s dipole moment. Explanation: Under “Lone Pairs (Non-bonding Electrons),” it states they “contribute to the overall electron distribution, impacting the molecule’s dipole moment.”
  27. If a molecule has 4 electron domains, with 3 bonding pairs and 1 lone pair, what is its molecular geometry? a) Tetrahedral b) Trigonal pyramidal c) Bent/V-shaped d) SeesawAnswer: b) Trigonal pyramidal Explanation: Under “Common Electron Domain Geometries and Molecular Shapes” for “4 Electron Domains,” it lists “3 bonding, 1 lone pair: Trigonal pyramidal (e.g., NH3).”
  28. What is the term for the energy difference that arises when electron delocalization lowers the overall potential energy of a molecule? a) Promotion energy b) Ionization energy c) Resonance energy d) Hybridization energyAnswer: c) Resonance energy Explanation: Under “Resonance Stabilization,” it states, “This energy difference is called the resonance energy.”
  29. In the context of Molecular Orbital Theory, what is the role of Group Theory (mentioned in Chapter 6)? a) To determine bond polarity. b) To calculate bond order. c) To simplify the construction and classification of molecular orbitals. d) To predict hybridization states.Answer: c) To simplify the construction and classification of molecular orbitals. Explanation: Under “Polyatomic Molecules (Beyond Diatomics),” it states, “Symmetry: Group theory… is essential for constructing and classifying molecular orbitals in complex polyatomic molecules, simplifying the process…”
  30. Why is phosphorus more likely to form extended structures with P-P single bonds rather than diatomic P2 molecules? a) P-P single bonds are weaker than multiple P-P bonds. b) Phosphorus is too electronegative for multiple bonds. c) Single P-P bonds are relatively more stable than multiple P-P bonds. d) P2 is a radical and unstable.Answer: c) Single P-P bonds are relatively more stable than multiple P-P bonds. Explanation: Under “Element-specific trends,” it states, “Phosphorus-Phosphorus Bonds: Unlike nitrogen, single P-P bonds are relatively more stable than multiple P-P bonds. This contributes to phosphorus’s tendency to form extended structures with P-P single bonds…”

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