Chemical Bonding and Molecular Geometry

Ionic and Covalent Bonding

Chemical bonds form because bonded atoms are lower in energy than separated atoms - nature always seeks the energy minimum. The two fundamental bond types - ionic and covalent - lie on a continuum defined by electronegativity difference (DEN). Ionic bonds form when DEN > 1.7-2.0: one atom strips an electron from another, producing a cation and anion held together by Coulombic attraction (F = k * q1 * q2 / r^2). NaCl is the textbook example: Na (EN = 0.93) transfers its 3s1 electron to Cl (EN = 3.16), yielding Na+ and Cl- in a crystalline lattice. Ionic compounds have high melting points, dissolve in polar solvents, and conduct electricity when molten or dissolved. Covalent bonds form when DEN is small: atoms share electrons to complete their octets. Nonpolar covalent bonds occur between identical atoms (e.g., H2, Cl2, O2) or atoms with DEN < 0.4; polar covalent bonds occur when 0.4 < DEN < 1.7, creating bond dipoles - partial positive and negative charges separated along the bond axis. The percent ionic character increases with DEN. Metallic bonding (electron sea model) and coordinate covalent bonds (where one atom donates both electrons, as in NH3 -> BF3) complete the bonding spectrum. Bond energy (bond dissociation energy, D) quantifies bond strength: triple bonds > double bonds > single bonds; shorter bonds are stronger bonds. Bond length is the equilibrium distance where attractive and repulsive forces balance, producing the minimum potential energy on a Morse potential curve.

Lewis Structures

Lewis structures map valence electrons onto a molecular skeleton, showing bonding and nonbonding (lone-pair) electrons. The procedure is algorithmic: (1) Count total valence electrons - add one for each negative charge, subtract one for each positive charge. (2) Draw a skeleton with the least electronegative atom as the central atom (never H). (3) Connect each outer atom to the central atom with a single bond (2 electrons). (4) Distribute remaining electrons as lone pairs to satisfy the octet rule: main-group elements (C, N, O, F, and below) want 8 electrons. (5) If the central atom lacks an octet, convert lone pairs on outer atoms to multiple bonds. Hydrogen is satisfied with 2 electrons (duet rule). Beryllium (Be, 4 electrons) and boron (B, 6 electrons) are common octet-deficit exceptions. Third-row elements (P, S, Cl, etc.) can expand their octets into d orbitals, accommodating 10, 12, or even 14 electrons - this is why SF6 (12 electrons around S), PCl5 (10 around P), and SO4(2-) exist, but no analogous first-row compounds do (NF5 is impossible). Free radicals - molecules with an odd number of valence electrons like NO (11 electrons) and NO2 (17 electrons) - violate the octet rule and are highly reactive. The MCAT frequently asks for the Lewis structure of polyatomic ions (NO3-, SO4(2-), CO3(2-), PO4(3-)) and unusual molecules like O3, CO, and NO - know these cold.

Formal Charge

Formal charge is a bookkeeping tool that assigns electron ownership in a Lewis structure to identify the most stable electron distribution. Formula: FC = (valence electrons in free atom) - (nonbonding electrons) - 1/2(bonding electrons). Key rules: (1) The sum of formal charges must equal the overall charge on the molecule or ion. (2) The best Lewis structure minimizes formal charges - ideally placing all formal charges at zero. (3) Negative formal charges should reside on the more electronegative atoms; positive formal charges on the more electropositive atoms. (4) Adjacent formal charges of the same sign are destabilizing. For example, in the cyanate ion (OCN-), three resonance structures are possible: O-C=N (all FC=0, impossible since ion has -1 charge) versus O(-)-C=N (FC: O=-1, C=0, N=0) versus O=C=N(-) (FC: O=0, C=0, N=-1). The most stable contributor places the negative charge on oxygen (more electronegative), making O(-)-C=N the major resonance form. Formal charge differs from oxidation state conceptually: formal charge assumes perfectly covalent sharing (each atom gets half of each bonding pair), while oxidation state assumes ionic bonding (more electronegative atom gets all electrons in the bond). The MCAT exploits this distinction in passage-based questions.

Resonance

Resonance describes the delocalization of electrons across multiple equivalent Lewis structures when a single structure cannot accurately represent the true electron distribution. The true structure is a resonance hybrid - a weighted average of the contributing resonance forms, not an equilibrium flipping between them. Rules for drawing resonance structures: (1) Only electrons move - nuclei stay fixed. (2) All resonance structures must be valid Lewis structures. (3) The number of unpaired electrons must remain constant. (4) Resonance involves pi electrons (double/triple bonds) and lone pairs; sigma-bond framework is unchanged. Electron movement is shown with curved arrows: tail at electron source (lone pair or pi bond), head at electron destination. Resonance stabilization energy is the difference between the energy of the hybrid and the energy of the most stable contributing structure. Species with extensive resonance are unusually stable: the carboxylate ion (R-COO-) has two equivalent resonance structures that distribute the negative charge equally over both oxygen atoms, making carboxylates far more stable than alkoxide ions (R-O-) and explaining why carboxylic acids (pKa ~5) are millions of times more acidic than alcohols (pKa ~16). Benzene's six pi electrons delocalized over a ring of six carbons give it an aromatic stabilization energy of ~150 kJ/mol - benzene does NOT have alternating single and double bonds; every C-C bond is identical (1.39 angstroms, intermediate between C-C single bond 1.54 A and C=C double bond 1.34 A). The MCAT frequently tests the recognition of resonance-stabilized intermediates: allylic and benzylic carbocations, enolate ions, carboxylate ions, and amide bonds (the C-N bond in peptides has partial double-bond character due to resonance, restricting rotation and biasing the trans conformation).

VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts molecular geometry from the principle that electron domains (bonding pairs and lone pairs) arrange themselves around a central atom to minimize repulsion. The steric number (SN) - the sum of atoms bonded to the central atom plus lone pairs - determines the electron-domain geometry, while the actual molecular shape depends on how many of those domains are lone pairs. SN = 2: linear, 180 degrees (BeCl2, CO2). SN = 3: trigonal planar electron geometry; molecular geometries = trigonal planar for 0 lone pairs, 120 degrees (BF3, SO3); bent for 1 lone pair, <120 degrees (SO2, O3). SN = 4: tetrahedral electron geometry; molecular geometries = tetrahedral for 0 lone pairs, 109.5 degrees (CH4, NH4+); trigonal pyramidal for 1 lone pair, <109.5 degrees (NH3, ~107 degrees); bent for 2 lone pairs, <109.5 degrees (H2O, ~104.5 degrees). SN = 5: trigonal bipyramidal electron geometry; molecular geometries = trigonal bipyramidal for 0 LP (PCl5); seesaw for 1 LP (SF4); T-shaped for 2 LP (ClF3); linear for 3 LP (XeF2). Lone pairs occupy equatorial positions in trigonal bipyramidal geometry because equatorial positions have fewer 90-degree interactions (2 vs 3 axial). SN = 6: octahedral electron geometry; geometries = octahedral 0 LP (SF6); square pyramidal 1 LP (BrF5); square planar 2 LP (XeF4), with lone pairs opposite each other (180 degrees apart). Repulsion hierarchy: lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair. This explains angle compression: water's H-O-H angle (104.5) < ammonia's H-N-H angle (107) < methane's H-C-H angle (109.5) - the increasing number of lone pairs (2, 1, 0) compresses the bonding angles. The MCAT loves to ask: which has the larger bond angle, NH3 or NH4+? (NH4+, 109.5 degrees vs. NH3, 107 degrees - NH4+ has no lone pair.)

Hybridization

Hybridization reconciles VSEPR geometry with atomic orbital theory by mathematically mixing s and p (and sometimes d) orbitals on a central atom to form equivalent hybrid orbitals that point in the directions required by VSEPR geometry. Steric number directly determines hybridization: SN = 2 -> sp (linear, 180 degrees), SN = 3 -> sp2 (trigonal planar, 120 degrees), SN = 4 -> sp3 (tetrahedral, 109.5 degrees), SN = 5 -> sp3d (trigonal bipyramidal, 90/120 degrees), SN = 6 -> sp3d2 (octahedral, 90 degrees). The number of hybrid orbitals equals the number of atomic orbitals mixed. Unhybridized p orbitals remain perpendicular to the hybrid framework and participate in pi bonding. Ethylene (C2H4): each carbon is sp2 hybridized - three sp2 orbitals form sigma bonds (two C-H, one C-C), leaving one unhybridized p orbital on each carbon that overlap sideways to form a pi bond. The C=C double bond consists of one sigma bond (head-on overlap, strong, ~350 kJ/mol) and one pi bond (sideways overlap, weaker, ~270 kJ/mol). Acetylene (C2H2): each carbon is sp hybridized, forming a C-C triple bond (one sigma + two pi bonds). In a triple bond, the two pi bonds occupy orthogonal planes. The geometry of hybrid orbitals dictates sigma-bond framework - pi bonds form only after sigma bonds, which explains why rotation about a double bond is restricted (rotating would break the pi bond) while rotation about a single bond (pure sigma) is free. Resonance-stabilized systems like benzene involve sp2 carbons with unhybridized p orbitals forming a continuous pi system above and below the ring plane. The MCAT also tests hybridization in unusual geometries: the amide nitrogen in a peptide bond is sp2 (not sp3), making the bond planar with restricted rotation - a critical concept linking structure to protein folding and enzyme specificity.

Molecular Polarity

A molecule is polar if it has a net dipole moment - an asymmetric distribution of electron density resulting from polar bonds that do not cancel vectorially. Polarity depends on two factors: (1) bond polarity (electronegativity difference creates bond dipoles) and (2) molecular geometry (whether those bond dipoles sum to zero). For a molecule to be polar, it must have polar bonds AND a non-canceling geometry. CO2 has two polar C=O bonds (DEN = 1.0) but is nonpolar because its linear geometry places the two equal bond dipoles at 180 degrees, canceling each other. H2O has two polar O-H bonds and a bent geometry (~104.5 degrees), so the bond dipoles add to give a net dipole moment (mu = 1.85 D). CCl4 has four polar C-Cl bonds but tetrahedral symmetry cancels them completely - nonpolar. CHCl3 (chloroform) has tetrahedral geometry but the bond dipoles are unequal (three C-Cl bonds, one C-H bond), so they do NOT cancel - polar. NH3 is polar (trigonal pyramidal, net dipole upward); BF3 is nonpolar (trigonal planar, dipoles cancel). For molecules with lone pairs, the lone-pair dipole (electron density on one side of the atom) contributes to overall polarity. This is why NF3 has a smaller dipole moment (0.24 D) than NH3 (1.47 D) - in NH3, the N-H bond dipoles and the lone-pair contribution both point in the same direction (away from the H atoms), while in NF3 the N-F bond dipoles point toward the fluorines (opposite the lone-pair dipole), partially canceling. The MCAT expects you to predict solubility from polarity: polar molecules dissolve in polar solvents (water, alcohols); nonpolar molecules dissolve in nonpolar solvents (hexane, benzene). This principle - 'like dissolves like' - underpins membrane permeability, drug design, chromatography, and extraction techniques across C/P and B/B passages.

How it works

The bonding unit operates on a layered logic that builds from the atomic scale to the molecular scale. Step 1: Determine whether bonds are ionic, polar covalent, or nonpolar covalent using electronegativity differences. Step 2: Draw the Lewis structure - count valence electrons, build a skeleton, satisfy octets, and check formal charges to find the best electron distribution. Step 3: Identify resonance if pi electrons or lone pairs can delocalize; evaluate relative stability of contributors using formal charge rules and electronegativity. Step 4: Apply VSEPR - count steric number, determine electron-domain geometry, then deduce molecular shape by subtracting lone pairs. Step 5: Assign hybridization based on steric number. Step 6: Assess molecular polarity by summing bond dipole vectors based on molecular geometry. This six-step protocol transforms a molecular formula into a complete structural portrait, and the MCAT will test every step - often in sequence within a single passage.

How it works

The bonding unit operates on a layered logic that builds from the atomic scale to the molecular scale. Step 1: Determine whether bonds are ionic, polar covalent, or nonpolar covalent using electronegativity differences. Step 2: Draw the Lewis structure - count valence electrons, build a skeleton, satisfy octets, and check formal charges to find the best electron distribution. Step 3: Identify resonance if pi electrons or lone pairs can delocalize; evaluate relative stability of contributors using formal charge rules and electronegativity. Step 4: Apply VSEPR - count steric number, determine electron-domain geometry, then deduce molecular shape by subtracting lone pairs. Step 5: Assign hybridization based on steric number. Step 6: Assess molecular polarity by summing bond dipole vectors based on molecular geometry. This six-step protocol transforms a molecular formula into a complete structural portrait, and the MCAT will test every step - often in sequence within a single passage.

Comparisons

• C/P (Bonding): Electronegativity-based bond-type classification; ionic versus covalent lattice energy; Coulomb's law and bond strength trends; percent ionic character from dipole moment measurements.
• C/P (Lewis/Resonance): Drawing Lewis structures of polyatomic ions (NO3-, SO4(2-), CO3(2-)); formal charge minimization; resonance stabilization energies; aromaticity criteria (4n + 2 pi electrons).
• C/P (VSEPR/Hybridization): Predicting geometries from molecular formulas; explaining bond-angle deviations due to lone pairs; sp/sp2/sp3 hybrid orbital formation; sigma versus pi bonding; restricted rotation in double bonds and amide linkages.
• B/B (Biochemistry): Peptide bond planarity from resonance (amide C-N has partial double-bond character, sp2 nitrogen); enzyme active-site geometry determined by VSEPR; drug-receptor binding relies on molecular shape complementarity; phosphate group tetrahedral geometry in DNA/ATP.
• B/B (Membrane biology): Molecular polarity governs membrane permeability - nonpolar molecules cross lipid bilayers; polar/charged molecules require transporters; phospholipid amphipathicity (polar head + nonpolar tails) drives bilayer self-assembly.
• B/B (Hemoglobin): Heme iron coordination geometry (octahedral Fe2+ with four pyrrole nitrogens, proximal histidine, and O2 binding site); CO poisoning competes for the sixth coordination site with 200x greater affinity.

Common confusions

• Confusing electron-domain geometry with molecular geometry: VSEPR answers must report the molecular shape (atom positions), not the electron-domain arrangement. SF4 has trigonal bipyramidal electron geometry but seesaw molecular geometry - answer the question being asked.
• Forgetting to count formal charges on ALL atoms: the sum of formal charges must equal the ion's total charge. A neutral Lewis structure for SO4(2-) is WRONG - two of the oxygen atoms must carry a -1 formal charge.
• Assuming all resonance structures contribute equally: they do not. The major contributor has the fewest formal charges, with negative charges on the most electronegative atoms. The true hybrid resembles the major contributor more than the minor ones.
• Misassigning hybridization from a Lewis structure that violates the octet rule: count the steric number, not the number of bonds. Sulfur in SF6 makes 6 bonds (SN=6) yielding sp3d2, even though S is in period 3 and can expand its octet.
• Treating expanded octets as always available: only period 3 and below (P, S, Cl, Br, I, Xe, etc.) can expand their octets. Period 2 elements (C, N, O, F) NEVER exceed 8 electrons - this is why NO3- uses resonance (not an expanded octet on N) to satisfy formal charge requirements.
• Miscounting steric number for molecules with multiple bonds: a double bond counts as ONE electron domain (one region of electron density), not two. CO2 has SN = 2 (two double bonds), so it's linear with sp hybridization - not SN = 4.
• Predicting polarity from bond polarity alone: a molecule with polar bonds can be nonpolar if symmetry cancels the dipoles. CO2, CCl4, BF3, XeF4, and PF5 are all nonpolar despite having polar bonds.
• Assuming NH3 and NF3 have similar dipole moments: NH3 (1.47 D) has a much larger dipole than NF3 (0.24 D) because the N-F bond dipoles oppose the nitrogen lone-pair contribution, while N-H and the lone pair reinforce each other.
• Overlooking resonance in bond-length questions: all S-O bonds in SO4(2-) are equivalent and intermediate between S=O and S-O due to resonance. There are no discrete single and double bonds in resonance-stabilized ions.
• Confusing VSEPR predictions for radicals: NO2 has 17 valence electrons - an odd-electron species with one unpaired electron on nitrogen. Its geometry is bent (~134 degrees) due to SN=3 (two bonding domains + one lone electron).

Quick review

• DEN > 1.7 -> ionic; 0.4 < DEN < 1.7 -> polar covalent; DEN < 0.4 -> nonpolar covalent.
• Lewis steps: valence electrons -> skeleton (least EN central) -> single bonds -> lone pairs -> multiple bonds if needed.
• Formal charge = valence e- - nonbonding e- - 1/2(bonding e-); best structure minimizes FC with negative on most EN atom.
• Resonance delocalizes pi electrons; hybrid is weighted average, not equilibrium; amide C-N has double-bond character -> planar, restricted rotation.
• VSEPR steric number = bonded atoms + lone pairs. SN 2=linear, 3=trigonal planar, 4=tetrahedral, 5=trig bipyramidal, 6=octahedral.
• Lone pair repulsion hierarchy: LP-LP > LP-BP > BP-BP. Bond angles compressed: H2O (104.5 deg) < NH3 (107 deg) < CH4 (109.5 deg).
• Hybridization: SN 2=sp, 3=sp2, 4=sp3, 5=sp3d, 6=sp3d2. Double bond = 1 sigma + 1 pi; triple bond = 1 sigma + 2 pi.
• Period 2 elements (C, N, O, F) NEVER exceed octet; period 3+ (P, S, Cl) can expand (d orbitals).
• Molecular polarity: polar bonds + asymmetric geometry = polar molecule. CO2 (linear), CCl4 (tetrahedral), BF3 (trigonal planar) are nonpolar despite polar bonds.
• Peptide bond: sp2 nitrogen (not sp3), C-N partial double bond -> planar, trans preferred; fundamental to protein structure.
• Molecular shapes with LP: 1 LP = bent/pyramidal/seesaw; 2 LP = bent/T-shaped/square planar; LP occupy equatorial in trig bipyramidal.
• Resonance key species: carbonate, nitrate, sulfate, phosphate, ozone, benzene, carboxylate, amide (peptide), allylic/benzylic carbocations and radicals.