Sep 18: VSEPR, Steric Number, Electron and Molecular Geometry – Comprehensive Notes

VSEPR, Steric Number, Electron Geometry, and Molecular Geometry – Comprehensive Notes

• Core idea (VSEPR): atoms around a central atom repel each other via their electron domains (bonding pairs and lone pairs), shaping the three‑dimensional geometry of the molecule.

• Steric number (SN): the number of electron domains around the central atom. This equals
  $ext{SN} = N<em>{ ext{bonded}} + N</em>{ ext{lone}}$
  where $N<em>{ ext{bonded}}$ is the number of atoms bonded to the central atom and $N</em>{ ext{lone}}$ is the number of lone pairs on the central atom.

• Two related geometries to know:

  • Electron geometry: considers all electron domains around the central atom (the actual positions of electrons in space).

  • Molecular geometry: the arrangement of atoms around the central atom, taking into account lone pairs (lone pairs occupy space and influence bond angles).

• Five common electron geometries (based on SN):

  • Linear (SN = 2)

  • Trigonal Planar (SN = 3)

  • Tetrahedral (SN = 4)

  • Trigonal Bipyramidal (SN = 5)

  • Octahedral (SN = 6)

• Important analogy: lone pairs act like balloons in space and exert greater repulsion than bonding pairs, which pushes bonding pairs closer together and alters bond angles.

• General rule of thumb (bond angles and lone pairs): the more lone pairs around the central atom, the smaller the bond angles between bonding pairs tend to be.

• Resonance vs. lone pairs in counting SN: in molecules with resonance structures (e.g., ozone, ${O_3}$), you still count the number of bonded atoms and lone pairs on the central atom for SN; resonance affects bond order and formal charges, not the basic SN count.

Electron geometry vs molecular geometry with examples

• CO₂

  • Central atom: C with two double bonds to O

  • Bonded atoms: 2; Lone pairs on C: 0

  • SN = 2; Electron geometry: Linear; Molecular geometry: Linear; Bond angle: $180^ ext{\circ}$

• BH₃

  • Central atom: B with 3 single bonds to H; Lone pairs on B: 0

  • SN = 3; Electron geometry: Trigonal Planar; Molecular geometry: Trigonal Planar; Bond angle: $120^ ext{\circ}$

• SO₂ (example with resonance structure)

  • Central atom: S; Bonded to two O atoms; Lone pairs on S: 1

  • SN = 3; Electron geometry: Trigonal Planar; Molecular geometry: Bent (due to lone pair); Bond angle: < $120^ ext{\circ}$

  • Lone pair repulsion compresses the angle between the two S–O bonds.

• NH₃

  • Central atom: N; Bonded to three H; Lone pairs on N: 1

  • SN = 4; Electron geometry: Tetrahedral; Molecular geometry: Trigonal Pyramidal; Bond angle: < $109.5^ ext{\circ}$

• CH₄

  • Central atom: C; Bonded to four H; Lone pairs: 0

  • SN = 4; Electron geometry: Tetrahedral; Molecular geometry: Tetrahedral; Bond angle: $109.5^ ext{\circ}$

• H₂O

  • Central atom: O; Bonded to two H; Lone pairs on O: 2

  • SN = 4; Electron geometry: Tetrahedral; Molecular geometry: Bent; Bond angle: < $109.5^ ext{\circ}$ (approximately ~104.5° in water)

• PF₅

  • Central atom: P; Bonded to five F; Lone pairs: 0

  • SN = 5; Electron geometry: Trigonal Bipyramidal; Molecular geometry: Trigonal Bipyramidal; Bond angles: axial–axial ~ $90^ ext{\circ}$, equatorial–equatorial ~ $120^ ext{\circ}$, axial–equatorial ~ between these values

• SF₄

  • Central atom: S; Bonded to four F; Lone pairs: 1

  • SN = 5; Electron geometry: Trigonal Bipyramidal; Molecular geometry: Seesaw; Bond angles: ~

  • Some bonds closer to ≈ $90^ ext{\circ}$, some closer to ≈ $120^ ext{\circ}$ (overall asymmetric shape)

• T-shaped example (SN = 5, two lone pairs)

  • Geometry: T-shaped; Bond angles: < $90^ ext{\circ}$ between the two ligands in the axis and the third ligand

• SF₆

  • Central atom: S; Bonded to six F; Lone pairs: 0

  • SN = 6; Electron geometry: Octahedral; Molecular geometry: Octahedral; Bond angles: $90^ ext{\circ}$ between any two bonds

• BrF₅ (SN = 6, 1 lone pair)

  • Electron geometry: Octahedral; Molecular geometry: Square Pyramidal; Bond angles: < $90^ ext{\circ}$ (between the base and the apex bond is reduced by lone-pair repulsion)

• XeF₄ (SN = 6, 2 lone pairs)

  • Electron geometry: Octahedral; Molecular geometry: Square Planar; Bond angles: ~ $90^ ext{\circ}$ between the adjacent ligands (in a square plane)

• Note on octet exceptions

  • BF₃: boron has only 6 valence electrons; forms an incomplete octet around B (an exception to the octet rule)

  • SF₆: sulfur expands its octet beyond 8 electrons (allowed for third-row and heavier elements) and is a classic example of an expanded octet

  • In these exception cases, the SN framework still applies for predicting electron geometry, but the octet rule does not strictly apply to the central atom

How to solve SN and predict geometry (step-by-step)

1) Count valence electrons and draw a Lewis structure

• Example: SF₆ → valence electrons: $V = 6 + 6\times 7 = 48$

• Place S in the center; arrange six F around it; connect with single bonds; complete octets (or expand as needed)

• Note: for sulfur with 6 bonds, this is an expanded octet (not a violation in this context)
  2) Determine SN: count bonded atoms to the central atom + lone pairs on the central atom

• For SF₆: $N{bonded}=6$, $N{lone}=0$ → $SN=6$
  3) Identify electron geometry from SN

• SN 2 → Linear; SN 3 → Trigonal Planar; SN 4 → Tetrahedral; SN 5 → Trigonal Bipyramidal; SN 6 → Octahedral
  4) Determine molecular geometry from SN and lone pairs

• Use the number of lone pairs to modify the base electron geometry into the molecular shape

• Examples:

  • SN 4, 0 lone → Tetrahedral

  • SN 4, 1 lone → Trigonal Pyramidal (NH₃)

  • SN 4, 2 lone → Bent (H₂O)

  • SN 5, 0 lone → Trigonal Bipyramidal

  • SN 5, 1 lone → Seesaw (SF₄)

  • SN 5, 2 lone → T-shaped

  • SN 6, 0 lone → Octahedral (SF₆)

  • SN 6, 1 lone → Square Pyramidal (BrF₅)

  • SN 6, 2 lone → Square Planar (XeF₄)
    5) Recall key bond-angle values to set expectations (approximate):

• Linear: $180^ ext{\circ}$

• Trigonal Planar: $120^ ext{\circ}$

• Tetrahedral: $109.5^ ext{\circ}$

• Trigonal Bipyramidal: axial–axial ≈ $90^ ext{\circ}$, equatorial–equatorial ≈ $120^ ext{\circ}$

• Octahedral: all ≈ $90^ ext{\circ}$

• With lone pairs, bond angles are reduced below these values (e.g., NH₃ < 109.5°, H₂O < 109.5°, etc.)
  6) Check for resonance and formal charges when relevant

• For molecules with resonance (e.g., O₃), multiple valid Lewis structures exist; the actual geometry follows the SN and the average bonding arrangement

• Formal charges are not the focus for the basic SN-based geometry; they come into play when choosing the best resonance form
  7) Practice with an established worksheet/table

• Canvas has an “empty VSEPR table” worksheet to fill in for different SN cases

• Use it to visualize how electron geometry, molecular geometry, and bond angles relate to different configurations

Worked examples and notes on interpretation

• Sulfur hexafluoride (SF₆)

  • Valence electron count: $V = 6 + 6\times 7 = 48$

  • Lewis structure: S in center with six F atoms; 12 S–F bonds electrons assigned to satisfy octets; S uses expanded octet

  • SN = 6; Electron geometry = Octahedral; Molecular geometry = Octahedral; Bond angles ≈ $90^ ext{\circ}$

  • Key takeaway: more bonding domains around the central atom can yield highly symmetric, multi-coordinate geometries (octahedral in this case)

• Boron trifluoride (BF₃) as an octet exception

  • B has only 3 bonds and incomplete octet (BF₃) – an exception to the typical octet rule; helps illustrate why sometimes expanded or incomplete octets occur in chemistry

• Ozone (O₃): resonance and SN analysis

  • Central atom: O; bonds to two O atoms; lone pairs: 1 on the central O

  • SN = 3; Electron geometry = Trigonal Planar; Molecular geometry = Bent (due to lone pair)

  • Ozone has resonance structures that are equivalent; the actual bond order is an average of the resonance forms

• Nitrogen hydride family and water (NH₃, CH₄, H₂O)

  • NH₃: SN = 4; Electron geometry = Tetrahedral; Molecular geometry = Trigonal Pyramidal; angle < 109.5°

  • CH₄: SN = 4; Electron geometry = Tetrahedral; Molecular geometry = Tetrahedral; angle ≈ 109.5°

  • H₂O: SN = 4; Electron geometry = Tetrahedral; Molecular geometry = Bent; angle < 109.5° (about 104–105° in real water)

• Trigonal bipyramidal family (SN = 5)

  • PF₅: 5 bonded, 0 lone; Electron geometry = Trigonal Bipyramidal; Molecular geometry = Trigonal Bipyramidal; bond angles: 90° (axial–bond interactions) and 120° (equatorial)

  • SF₄: 4 bonded, 1 lone; Electron geometry = Trigonal Bipyramidal; Molecular geometry = Seesaw; angles mix around 90° and ~120° depending on orientation

  • T-shaped (SN = 5, 2 lone pairs): bond angles < 90° between the two bonds and the third

• Octahedral family (SN = 6)

  • SF₆: 6 bonded, 0 lone; Electron geometry = Octahedral; Molecular geometry = Octahedral; all angles ≈ 90°

  • BrF₅: 5 bonded, 1 lone; Molecular geometry = Square Pyramidal; angles < 90° due to lone-pair repulsion

  • XeF₄: 4 bonded, 2 lone; Molecular geometry = Square Planar; angles ≈ 90° between adjacent ligands

• Practical note on study approach

  • You don’t need to memorize every exotic geometry name for every SN beyond SN = 4 for many exams; focus on understanding how lone pairs alter geometry and the general trends (more lone pairs → smaller bond angles)

  • If you can correctly draw the Lewis structures and identify SN, bonded vs lone pairs, you’ll be able to predict the major geometry and approximate bond angles

• The “flip-to-work” strategy used in class

  • Use the Canvas worksheet to practice filling in SN, electron geometry, and molecular geometry for a variety of configurations

  • The instructor will cover more advanced cases (e.g., SN > 4 with multiple lone pairs) as needed; expect to know up to SN 4 for many assessments, with awareness of trends extending to higher SN

Quick practice prompts you can try

• Rank NH₃, CH₄, H₂O in order of decreasing bond angle (largest to smallest)

  • NH₃: bond angles < 109.5° (due to 1 lone pair)

  • CH₄: bond angle ≈ 109.5°

  • H₂O: bond angles < 109.5° (due to 2 lone pairs)

  • Order (largest to smallest): CH₄ > NH₃ > H₂O

  • Note: this aligns with the idea that more lone pairs lead to smaller bond angles

• For CO₂, SO₂, and BF₃, identify SN and predict electron vs molecular geometry

  • CO₂: SN = 2 → Linear, bond angle 180°

  • SO₂: SN = 3 → Electron geometry: Trigonal Planar; Molecular geometry: Bent (bond angle < 120°)

  • BF₃: SN = 3, 0 lone pairs → Electron geometry: Trigonal Planar; Molecular geometry: Trigonal Planar; bond angle ~120° but note this is an exception to octet behavior for B

Connections to broader chemistry concepts

• Real molecules show that lone-pair repulsion shapes polarity and reactivity (e.g., water’s bent shape confers strong polarity and hydrogen bonding)

• The SN framework connects to foundational ideas in bonding orbitals and electron density distribution around a central atom

• While formal charges are not the focus in the SN-based geometry discussion, they become important when considering resonance structures and determining the most stable Lewis form

• The VSEPR approach provides a practical predictive tool for molecular structure, geometry, and approximate bond angles used in spectroscopy, material science, and biochemistry

Guidance for exam preparation

• Be comfortable computing SN from a given Lewis structure and predicting the corresponding electron geometry

• Memorize the standard geometries associated with SN values (2–6) and the typical bond angles associated with those geometries

• Practice distinguishing electron geometry from molecular geometry, especially in cases with lone pairs (e.g., SO₂, NH₃, H₂O, SF₄)

• Understand the qualitative effect of lone pairs on bond angles via the “balloon” analogy and remember the order of repulsions: lone pair–bonding pair > bonding pair–bonding pair; lone pair–lone pair > lone pair–bonding pair

• Use the VSEPR worksheet (empty VSEPR table) on Canvas to reinforce the mapping from SN to geometries and to view concrete examples

Summary of key takeaways

• SN = number of bonded atoms to the central atom + number of lone pairs on the central atom

• Electron geometry depends on SN; molecular geometry depends on SN and the number of lone pairs

• Lone pairs take up more space than bonding pairs and reduce bond angles

• Common geometries and typical bond angles (approximate):

  • SN = 2 → Linear, 180°

  • SN = 3 → Trigonal Planar, 120°

  • SN = 4 → Tetrahedral, 109.5° (with lone pairs leading to bent or trigonal pyramidal shapes)

  • SN = 5 → Trigonal Bipyramidal with various molecular geometries (Seesaw, T‑shape, Linear) depending on lone pairs

  • SN = 6 → Octahedral with possible square pyramidal or square planar molecular geometries depending on lone pairs

• Always verify by drawing the Lewis structure, counting electrons, and then applying SN and geometry rules; for more complex cases, consult the practice worksheet and instructor guidance