Comprehensive Study Notes: From Formal Charge to Lewis Acids and Bases

Formal Charge

• Purpose: Atoms in molecules can carry formal charges that affect stability; analyze formal charges to understand overall charge distribution.

• Formal charge (FC) calculation (per atom):

  • Use valence electrons that SHOULD be associated with the atom vs. valence electrons actually associated.

  • Formula: FC = g - (u + b) where:

  • g = Group number (valence electrons for the atom in the periodic table)

  • u = Number of unshared (lone-pair) electrons on the atom

  • b = Number of bonds to the atom

• Worked examples:

  • Carbon in a typical neutral carbon center with 4 single bonds:

  • g = 4, \, u = 0, \, b = 4 \Rightarrow FC = 4 - (0 + 4) = 0 -> Carbon has no formal charge.

  • Oxygen with 6 valence electrons, 6 lone electrons, and a single bond:

  • g = 6, \, u = 6, \, b = 1 \Rightarrow FC = 6 - (6 + 1) = -1 -> Oxygen carries a -1 formal charge.

• Practice problem reference: 1-4 (Determine the formal charges in the given structure).

• Key takeaways:

  • Formal charge helps explain stability and reactivity; stable structures tend to minimize formal charges where possible or place negative charges on more electronegative atoms and positive charges on less electronegative atoms.

Atomic Orbitals & Electron Configurations

• In the 1920s, quantum mechanics established orbitals as solutions to wave equations describing electrons.

• An orbital is a region with a calculated 95% probability of finding an electron; 5% probability tapers off with distance from the nucleus.

• Electrons exhibit both particle-like and wave-like behavior; the wavefunction can have positive, negative, or zero values, but the sign of the wavefunction is not equal to electrical charge.

• 1s and 2s orbitals:

  • The 1s orbital is filled when it contains two electrons.

  • After 1s, the 2s orbital is filled; the 2s orbital has a node.

• 2p orbitals are degenerate (same energy) and possess nodal planes; their orientation matters for bonding and overlap in bonds.

• Visualizing orbitals:

  • In p-orbitals, lobes are out-of-phase across the nodal plane; sign of the wavefunction is not the same as charge and becomes important for orbital overlap in bonds.

• Common elements and their electron configurations are shown for reference (e.g., H, He, Li, Be, B, C, N, O, F, Ne).

• Rules governing electron placement (3 core principles):

  • Aufbau principle (build up by increasing energy)

  • Pauli exclusion principle (no two electrons in an atom can have the same set of quantum numbers)

  • Hund's rule (maximize unpaired spins for degenerate orbitals)

Bonding: Overlap, Bonds, and Hybridization

• A chemical bond occurs when atomic orbitals overlap; overlapping wave regions lead to constructive interference that creates bonding regions.

• H2 bond example: bond results from constructive interference; electron density is concentrated along the bond axis.

• Methane (CH4) and the need for four equivalent bonds:

  • To form four identical C–H bonds, carbon uses four equivalent orbitals of equal energy—sp3 hybrids.

  • Hybridization: the process of mixing two or more atomic orbitals to form the same number of new, equivalent orbitals with the same energy.

• Hybridization patterns and bonding:

  • sp3 hybrids: four equivalent orbitals, tetrahedral arrangement; used in methane (CH4).

  • sp2 hybrids: three equivalent orbitals plus one unhybridized p orbital; used in ethene (C2H4).

  • sp hybrids: two equivalent orbitals with two unhybridized p orbitals; used in acetylene (C2H2).

• Bonding in molecules:

  • Sigma (σ) bonds form by head-on overlap of orbitals (e.g., sp3–sp3, sp2–sp2, sp–sp overlap).

  • Pi (π) bonds form by side-by-side overlap of unhybridized p orbitals (present in double and triple bonds).

• Ethane, Ethene, Ethyne (overview):

  • Ethane: C–C single bond with sp3 hybridization; bond angle ~109.5°.

  • Ethene: C=C double bond; three sp2 orbitals per carbon form σ-bonds; remaining unhybridized p orbitals form π-bond.

  • Ethyne: C≡C triple bond; two sp orbitals form σ-bonds; two unhybridized p orbitals form two π-bonds.

• Carbon–hydrogen bonding lengths and energies (typical values):

  • C–C: Ethane ≈ 1.54 Å, Ethene ≈ 1.34 Å, Ethyne ≈ 1.20 Å

  • Bond energies: Ethane ≈ 368 kJ/mol, Ethene ≈ 632 kJ/mol, Ethyne ≈ 820 kJ/mol

• Summary table of covalent bonding in carbon compounds:

  • 4 groups bonded to C: sp3, ~109.5°, example CH3–CH3 (ethane)

  • 3 groups bonded to C: sp2, ~120°, example CH2=CH2 (ethylene); one σ bond and one π bond

  • 2 groups bonded to C: sp, ~180°, example H–C≡C–H (acetylene); one σ bond and two π bonds

Recognizing Hybridization Patterns and Bonding Details

• Patterns of hybridization across molecules (examples): sp3, sp2, sp; often summarized in diagrams showing how many p-orbitals remain unhybridized and how many hybrid orbitals are formed.

• Practical recognition involves counting the number of electron domains (bonding and lone pairs) around the central atom and assigning the corresponding hybridization.

Bond Length, Bond Strength, and s-Character

• Bond length and bond strength depend on the s-character of the involved orbitals:

  • Higher s-character in the bonding orbital generally leads to shorter and stronger bonds.

• Table (example values):

  • Ethane (C–C): Bond length about 1.54 Å; Bond energy ≈ 368 kJ/mol

  • Ethylene (C=C): Bond length about 1.34 Å; Bond energy ≈ 632 kJ/mol

  • Acetylene (C≡C): Bond length about 1.20 Å; Bond energy ≈ 820 kJ/mol

• Sp3, sp2, and sp hybrids influence C–H bond lengths as well; more s-character in the C–H bond generally yields shorter bonds.

Valence Shell Electron Pair Repulsion (VSEPR) and Molecular Geometry

• VSEPR theory: Valence electrons (bonded and lone pairs) repel each other, guiding molecular shapes.

• How to determine geometry:
  1) Determine the steric (electron-group) number around the central atom (sigma bonds + lone pairs).
  2) Infer hybridization from steric number: 4 → sp3, 3 → sp2, 2 → sp.

• Electron-group geometry vs molecular geometry:

  • sp3: Electron groups form a tetrahedral arrangement; molecular geometry can be tetrahedral (CH4), trigonal pyramidal (NH3), or bent (H2O) depending on lone pairs.

• Examples:

  • CH4: steric number 4, sp3, electron group geometry = tetrahedral; molecular geometry = tetrahedral.

  • NH3: steric number 4, sp3; electron geometry = tetrahedral; molecular geometry = trigonal pyramidal (one lone pair).

  • H2O: steric number 4, sp3; electron geometry = tetrahedral; molecular geometry = bent (two lone pairs).

• Summary layout:

  • Steric number 4 → sp3 → Tetrahedral electron-pair geometry; molecular geometry depends on lone pairs

  • Steric number 3 → sp2 → Trigonal planar electron-pair geometry

  • Steric number 2 → sp → Linear electron-pair geometry

Molecular Representations: Lewis Structures, Resonance, and Delocalization

• Lewis structures: depict connectivity and lone pairs; various representations include Kekulé, partially condensed, and condensed forms; resonance structures illustrate delocalization of electrons.

• Resonance:

  • Delocalization stabilizes molecules by spreading charge over multiple atoms.

  • Rules for curved-arrow notation (to illustrate resonance forms and reaction mechanisms):

  • Don’t break existing sigma bonds in the process unless necessary; maintain octet for second-row elements; ensure electron count is conserved; avoid creating impossible charges.

  • Resonance contributors should be reasonable and avoid excessive formal charges; prefer contributing structures with full octets when possible.

• Curved arrows in reactions (mechanisms):

  • Arrows indicate the movement of electron pairs during chemical reactions.

  • In many acid–base steps, two curved arrows move simultaneously (concerted mechanism).

  • Example: base attacks an acid’s proton, leading to bond formation and proton transfer in a single-step mechanism.

Delocalization of Lone Pairs

• Delocalized lone pairs participate in resonance (e.g., in certain heterocycles and aromatic systems); localized lone pairs do not participate in resonance.

• Examples highlight the difference between conjugated systems and non-conjugated lone-pair participation.

Brønsted–Lowry Acids and Bases; Conjugates

• Definitions:

  • Acids donate a proton (H+).

  • Bases accept a proton.

• Conjugates:

  • Conjugate acid results when a base accepts a proton.

  • Conjugate base results when an acid donates a proton.

• Practice: identify acid, base, and conjugate partners in given reactions; water is neutral in many contexts but can act as both acid and base (amphiprotic).

Curved Arrows in Reactions

• Revisit the idea that curved arrows depict electron movement during reaction mechanisms (acid–base, nucleophilic attack, etc.).

• Each step is often depicted with two electrons moving via curved arrows; arrows show how bonds break and form in a single or consecutive steps.

• Practice: provide products and curved arrows for given acid–base reactions; identify acid, base, conjugate acid, and conjugate base.

Acids and Bases: Quantifying Strengths (pKa) and Equilibria

• Strong vs. weak acids/bases:

  • Strength is reflected by how easily protons are donated/accepted and by the position of the equilibrium.

  • Quantitative strength analysis uses pKa values; qualitative analysis uses structural stability (MARIO/ARIO).

• Definitions of Ka and pKa:

  • K_a is the equilibrium constant for the reaction between an acid and water.

  • Relationship: Ka = rac{[H^+][A^-]}{[HA]}; pKa = -\, ext{log}{10}Ka.

• Typical ranges:

  • K_a ext{ values range from } 10^{-50} ext{ to } 10^{10}.

  • Therefore, pKa ext{ values range roughly from } - ext{log}{10}(10^{10}) = -10 ext{ to } - ext{log}_{10}(10^{-50}) = 50.

• Strong acids have low pKa values; weak acids have high pKa values.

• Examples (common anchors):

  • Acetic acid: pK_a ext{ approximately } 4.75

  • Example strong inorganic acids in water (e.g., HCl): pK_a ext{ ~ } -7 ext{ (in water context)} (illustrative; exact values depend on solvent).

• Using pKa to compare acid strengths:

  • A lower pKa means a stronger acid; a higher pKa means a weaker acid.

  • When comparing two acids in equilibrium, the side with the conjugate base having the higher pKa (weaker acid) is favored by the reaction direction depending on the proton transfer context.

• Using pKa to analyze equilibria:

  • If you subtract pKa values, a larger difference corresponds to a stronger bias toward the side with the higher pKa (in many cases, products).

  • Example heuristic: if pKa(HB) − pKa(HA) ≈ 11, the equilibrium heavily favors the side with the higher pKa (roughly 10^11 difference).

• MARIO: A quantitative/qualitative framework to analyze acidity:

  • M = Measured Value (actual pKa when available)

  • A = Atom type carrying the charge

  • R = Resonance stabilization

  • I = Induction effects

  • O = Orbital type hosting the charge

• ARIO: A related framework used when MARIO’s measured value is not available (Atom, Resonance, Induction, Orbital).

• MARIO/ARIO are general guidelines; they may fail in some cases, and experimental pKa values should be used when available.

• Ranking hydrogens by acidity or comparing conjugate bases is common practice (qualitative MARIO-guided) but exact ordering can require pKa values or ARIO analysis.

• Special cases: acids bearing a formal positive charge can be evaluated directly with MARIO to stabilize positive charge; ranking follows similar stabilizing considerations.

Practical Use: Predicting Equilibria, Reagents, and Solvents

• Predicting equilibrium position:

  • If pKa values are known, compare to predict direction of proton transfer and the favored side (products vs reactants).

  • If pKa values are not known, qualitatively compare conjugate base stabilities using MARIO/ARIO.

• Choosing reagents for acid–base reactions:

  • Select an acid (from table 3.1) that can protonate the target molecule.

  • Select a conjugate base that can deprotonate the target molecule.

  • Pick a solvent that stabilizes charges and does not react with reactants; water has a leveling effect.

• Leveling effect of water:

  • Acids stronger than H3O+ cannot be meaningfully studied in water because water will protonate to form H3O+. Therefore, in water, the effective acidity is limited by the leveling effect.

  • Bases stronger than OH− cannot be studied in water for similar leveling reasons.

• Solvation:

  • Solvent molecules stabilize charges via solvent–solute interactions (ion–dipole attractions, etc.).

  • Solvation can significantly affect acidity constants; e.g., pKa of acetic acid is ~4.75 in water but ~23.5 in acetonitrile.

• Counterions (spectator ions):

  • Counterions balance the overall charge in solution but are often not drawn explicitly in mechanisms or condensed equations.

• Lewis acids and bases:

  • Definition: A Lewis acid accepts an electron pair; a Lewis base donates an electron pair.

  • All Bronsted–Lowry acids/bases are Lewis acids/bases, but not all Lewis acid/base reactions fit the Bronsted–Lowry scheme.

  • Some reactions are best described only by the Lewis framework.

• Solvation and counterions are integral to understanding acidity, basicity, and reaction mechanisms in solution.