Chapter 6 – Molecular Shape & Intermolecular Forces

6.1 Drawing Simple Lewis Structures

Purpose of Lewis structures
- Visualize valence-electron arrangements, predict bonding/shape, assess octet completion.
- Most main-group atoms seek $8$ electrons (octet rule) → become isoelectronic with nearest noble gas.
General algorithm for simple molecules (4–step version)
1. Write a skeletal structure: place atoms in expected order; use dashes to indicate single bonds.
- Atom order guidelines: hydrogen is always terminal; the “unique” or least electronegative atom (usually) seats in the center.
1. Count total valence electrons = sum of group numbers (for main-group elements).
2. Subtract $2$ electrons for every dash drawn in step 1 → electrons still to distribute.
3. Distribute remaining electrons as lone-pair dots around atoms to complete octets (or $2$ for H).
Worked microscale examples
- Cl $_2$
- Valence e––count $7+7=14$ ; one bond consumes $2$ e–– → $12$ e–– to distribute; each Cl ends with $3$ lone pairs + the shared pair.
- HCl
- Valence $1+7=8$ ; after single bond $6$ remain; all $6$ go on Cl – H is satisfied with $2$ electrons.
Central-atom approach for polyatomics
- Central atom = unique or least electronegative element (except H). Surrounding atoms = terminal atoms.
- Arrange terminals symmetrically about center; draw one bond per pair.
Vocabulary
- Bonding (shared) pair = dash-line = $2$ electrons.
- Lone (non-bonding) pair = dot-pair not participating in a bond.
Lewis structure bookkeeping diagram (CCl $_4$ example)
- $4$ bond pairs (central C→4×Cl) = $8$ bonding e––.
- $12$ lone pairs overall (3 pairs/Cl) = $24$ non-bonding e––.
Polyatomic-ion adjustments
- Add $1$ e–– per negative charge; subtract $1$ e–– per positive charge.
- Enclose final diagram in brackets with overall charge as superscript (e.g.
  $[\text{NH}_4]^+$ ).
Sample Problem 6.1 highlights (SeBr $2$ , OH $3^+$ , PCl $_3$ )
- Electron counts, application of steps, final structures with octets/lone pairs, bracketed for charged species.

6.2 Lewis Structures Continued

Choosing among several potential central atoms
- Place the atom of greater metallic character in the center (more metallic = farther left/down).
Molecules with multiple central atoms
- E.g. C $2$ H $2$ contains two C atoms connected to each other; each C is a “central” for its side.
Introducing multiple bonds (5-step algorithm)
1–4. Same as before.
1. If any atom lacks an octet, convert lone pair(s) on an adjacent atom into additional bond pair(s) (double/triple bonds) until octets achieved.
Sample Problem 6.2 (CO $_2$ )
- Start: skeletal O–C–O, total $16$ e––, after initial single bonds $12$ remain.
- After lone-pair placement, C short of octet → convert one lone pair from each O into bond pairs → final $\,::O=C=O::$ with no formal charge.
Exceptions to the octet rule
1. Odd-electron species (e.g. $\text{NO}$ , $\text{NO}_2$ ).
2. Electron-deficient central atoms: $\text{Be}$ may have $4$ e––, $\text{B}$ may have $6$ .
3. Expanded octets: central atoms $\ge$ 3rd period (P, S, Cl, Xe…) can hold >8 e–– via $d$ subshell participation (e.g. $\text{PCl}5$ , $\text{SF}6$ ).

6.3 Resonance Structures

Definition
- When ≥2 valid Lewis structures differ only in electron placement (same atomic skeleton) → resonance structures; the true molecule is a resonance hybrid.
Delocalization concept
- Electrons are spread over several bonds → equalized bond lengths/strengths.
Typical systems
- Alternating single/double bonds (CO $3^{2-}$ , NO $3^-$ , SO $_3$ ).
Sample Problem 6.3 (SO $_3$ )
- Three equivalent structures depending on which S–O is double-bonded; depict with double-headed arrows.

6.4 Molecular Shape (VSEPR Theory)

Core postulates
- Electron groups (single, double, triple bonds or lone pairs) repel → arrange around central atom to minimize repulsion.
- Electron-group geometry depends solely on number of electron groups; molecular shape depends on positions of nuclei (ignore lone pairs).
Common electron-group counts & geometries
- $2$ groups → linear (bond angle $180^\circ$ ).
- $3$ groups → trigonal planar (ideal $120^\circ$ ).
- $4$ groups → tetrahedral (ideal $109.5^\circ$ ).
Deriving molecular shapes from electron geometries
- Tetrahedral EG:
- 0 lone pairs → tetrahedral shape (e.g. CH $_4$ ).
- 1 lone pair → trigonal pyramidal (e.g. NH $_3$ ) with bond angles $\approx109.5^\circ$ (slightly <).
- 2 lone pairs → bent (e.g. H $_2$ O) with bond angle $\approx104.5^\circ$ .
- Trigonal-planar EG:
- 0 lone pairs → trigonal planar (e.g. BF $_3$ ).
- 1 lone pair → bent (e.g. SO $_2$ ) with $\sim120^\circ$ .
Linear cases (EG $=2$ )
- Any combination of two electron groups (single/double/triple bonds) gives linear shape: CO $2$ , H–C≡N, BeCl $2$ .
Stepwise procedure for predicting shape (summary)
1. Draw correct Lewis structure.
2. Count electron groups on central atom.
3. Assign electron-group geometry via VSEPR.
4. Remove lone-pair positions → identify molecular shape; quote approximate bond angles.
Sample Problem 6.4 results
- NO $_3^-$ → $3$ electron groups, trigonal planar, $120^\circ.
- NCl $_3$ → $4$ electron groups (3 bonds +1 LP), trigonal pyramidal, $\approx109.5^\circ$ .

6.5 Electronegativity & Polarity

Electronegativity (EN)
- Scale of atom’s ability to attract shared e–– toward itself.
- Periodic trend: EN increases up a group and left→right across a period; F highest.
Bond polarity categories (qualitative)
- Nonpolar covalent: $\Delta\text{EN}\lesssim0.4$ (e.g. C–C).
- Polar covalent: $0.5\lesssim\Delta\text{EN}\lesssim1.7$ (e.g. H–Cl).
- Ionic: $\Delta\text{EN}\gtrsim1.8$ (e.g. CsBr).
Partial charge depiction: $\delta^-$ on more EN atom, $\delta^+$ on less.
Molecular polarity
- Vector sum of individual bond dipoles; cancellation depends on shape.
- Example: BCl $3$ (trigonal planar) non-polar despite three polar B–Cl bonds; AsCl $3$ (trigonal pyramidal) polar.
Sample problems
- Most EN in pairs: Li vs Rb → Li; Ca vs Br → Br.
- Bond classification: ClF polar (ΔEN $=1.0$ ); CsBr ionic (ΔEN $=2.1$ ); C=C in C $2$ H $4$ non-polar (ΔEN $=0$ ).

6.6 Intermolecular Forces (IMFs)

Hierarchy (similar molar mass): \text{dispersion}<\text{dipole–dipole}<\text{hydrogen bonding}.
Dipole–dipole interactions
- Operate between polar molecules; align $\delta^+$ of one with $\delta^-$ of another.
- Absent in nonpolar Br $2$ ; present in SeCl $2$ ; absent in symmetric BF $_3$ .
Hydrogen bonding (special dipole–dipole)
- Requirements: H directly bonded to N, O, or F, and the molecule must be polar.
- Consequences: stronger IMF → higher b.p./m.p., anomalous water properties.
- Example outcomes: NH $3$ exhibits H-bonding; CH $2$ F $2$ and H2$Se do not.
Dispersion (London) forces
- Instantaneous dipole in one molecule induces dipole in neighbor → present in all species, dominant in non-polar ones.
- Strength ∝ molar mass/polarizability & elongated shape.
- Comparisons (nonpolar pairs): N2 $(M$ =28 $) vs Br$ 2 $(M$ =160 $) → Br$ 2 $stronger; CO$ 2 $vs I$ 2 $→ I$ 2 $; SiF$ 4 $vs SiBr$ 4 $→ SiBr$ _4 $.</li></ul></li> <li>Integrated IMF analysis (Sample Problem 6.11) <ul> <li>CCl$ _4 $: nonpolar → dispersion only.</li> <li>CH$ _3$COOH: polar + $\text{O–H}$ → H-bonding, dipole–dipole, dispersion.
- CH3$COCH3 $(acetone): polar, no$ \text{N/O/F–H} $→ dipole–dipole + dispersion.</li> <li>H$ _2$S: polar, no $\text{N/O/F–H}$ → dipole–dipole + dispersion.
Physical property link:
- Br $2$ (nonpolar, M=159.8) is liquid at $25^{\circ}\text{C}$ ; I $2$ (nonpolar, M=253.8) is solid → larger molar mass enhances dispersion to offset lower IMF category.

Skills & Conceptual Connections

Lewis-structure proficiency underpins VSEPR, polarity, and IMF predictions—errors propagate.
Octet exceptions & resonance demonstrate limits of simple models, segueing into molecular orbital theory.
IMFs explain macroscopic observations (boiling points, solubility, state of matter) → key for biochemistry (protein folding via H-bonding) and materials science (polymer crystallinity).
Ethical/environmental note (from SO $3$ example): coal combustion produces SO $2$ /SO $_3$ , precursor to acid rain—understanding molecular structure informs mitigation strategies.