VSEPR theory — geometry from electron pairs (linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral, etc

WHY does VSEPR exist?

WHY: Bonding pairs and lone pairs are clouds of negative charge. Like charges repel. If you have several such clouds tied to one central atom, they will orient themselves to minimise total repulsion, i.e. maximise the angles between them.

WHAT: VSEPR = Valence Shell Electron Pair Repulsion. It predicts the 3D geometry of a molecule from the number of electron domains (regions of electron density) around the central atom.

HOW: Count the domains → place them at the max-separation positions on a sphere → then decide where lone pairs sit → describe the shape of the atoms (not the electrons).

Deriving the shapes from first principles

We are placing $N$ points on a sphere so the minimum pairwise distance is maximised (the "Thomson-like" problem). Each geometry below is that optimal solution.

SN	Points maximally spread →	Ideal angle	Name
2	opposite ends of a line	$180^\circ$	linear
3	corners of a flat triangle	$120^\circ$	trigonal planar
4	corners of a tetrahedron	$109.5^\circ$	tetrahedral
5	3 equatorial + 2 axial	$120^\circ$ & $90^\circ$	trigonal bipyramidal
6	corners of an octahedron	$90^\circ$	octahedral

Formula Deriving the tetrahedral angle

$109.47^\circ$ Place 4 vertices of a cube that form a tetrahedron: $(+1,+1,+1),(+1,-1,-1),(-1,+1,-1),(-1,-1,+1)$ , centre at origin. Take two bond vectors $\mathbf{a}=(1,1,1)$ , $\mathbf{b}=(1,-1,-1)$ . $\cos\theta=\frac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{a}||\mathbf{b}|}=\frac{1-1-1}{\sqrt3\cdot\sqrt3}=\frac{-1}{3}$ $\theta=\arccos\!\left(-\tfrac13\right)=109.47^\circ$ Why this step? The dot product measures the angle between the two bonds directly — no experiment needed; the shape is mathematics.

Figure — VSEPR theory — geometry from electron pairs (linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral, etc

Lone pairs: the shape-benders

Worked derivation: from CH₄ → NH₃ → H₂O (all SN = 4)

Molecule	Bonds	Lone pairs	Electron geom	Molecular shape	Angle
$CH_4$	4	0	tetrahedral	tetrahedral	$109.5^\circ$
$NH_3$	3	1	tetrahedral	trigonal pyramidal	$107^\circ$
$H_2O$	2	2	tetrahedral	bent / V-shape	$104.5^\circ$

Why the angle shrinks $109.5\to107\to104.5$ ? Each added lone pair pushes harder on the bonds, closing them. Two lone pairs (water) squeeze more than one (ammonia).

The clever trick for SN = 5 (trigonal bipyramidal)

Worked Examples

Common Mistakes (Steel-manned)

Recall Feynman: explain to a 12-year-old

Imagine you're holding a bunch of balloons tied together at one knot. They automatically push apart to make a nice round arrangement — 2 balloons make a straight line, 3 make a flat triangle, 4 make a little pyramid. Molecules do the same with their electron "balloons." And if one balloon is fatter (a lone pair — an electron balloon not sharing with another atom), it shoves the others closer together. The shape you see is just where the atoms end up after all the balloons finish pushing.

Flashcards

What defines an electron domain in VSEPR?

One region of electron density — a lone pair OR any single/double/triple bond (a multiple bond = one domain).

Formula for steric number?

SN = (number of bonded atoms) + (number of lone pairs on the central atom).

SN=2 shape and angle?

Linear, 180°.

SN=3 shape and angle?

Trigonal planar, 120°.

SN=4 shape and angle?

Tetrahedral, 109.5°.

SN=5 electron geometry?

Trigonal bipyramidal (90° axial, 120° equatorial).

SN=6 shape and angle?

Octahedral, 90°.

Repulsion strength order?

lone–lone > lone–bond > bond–bond.

Why is H₂O's angle 104.5° not 109.5°?

Two lone pairs on O repel harder than bonding pairs, squeezing the H–O–H angle.

Shape of NH₃ and why not trigonal planar?

Trigonal pyramidal; SN=4 (3 bonds + 1 lone pair), tetrahedral electron geometry.

Where do lone pairs sit in trigonal bipyramidal and why?

Equatorial — fewer 90° neighbours (2 vs 3), so less repulsion.

Molecular shape of SF₄ (1 lone pair, SN=5)?

See-saw.

Molecular shape of ClF₃ (2 lone pairs, SN=5)?

T-shaped.

Molecular shape of XeF₂ (3 lone pairs, SN=5)?

Linear.

Molecular shape of XeF₄ (2 lone pairs, SN=6)?

Square planar.

Derive the tetrahedral angle.

cosθ = (a·b)/(|a||b|) = -1/3 → θ = arccos(-1/3) = 109.47°.

When does molecular geometry equal electron geometry?

When there are zero lone pairs on the central atom.

Connections

Lewis Structures — you need the Lewis dot picture first to count lone pairs.
Hybridization — sp/sp²/sp³/sp³d/sp³d² map 1-to-1 onto SN = 2/3/4/5/6.
Bond Polarity and Dipole Moment — geometry decides if bond dipoles cancel (CO₂ nonpolar, H₂O polar).
Molecular Orbital Theory — a deeper model where VSEPR's simple picture breaks down.
Formal Charge — helps choose the best Lewis structure before applying VSEPR.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, VSEPR ka funda bilkul simple hai. Central atom ke around jitne bhi electron ke "cloud" hain — chahe wo bonding pair ho ya lone pair — sab negative charge wale hote hain, isliye ek doosre ko dhakka dete hain (repulsion). Ye clouds itni door spread ho jaate hain ki total repulsion minimum ho jaye. Bas usi arrangement se molecule ki shape ban jaati hai. Sabse pehle steric number nikalo: bonded atoms + central atom ke lone pairs. Yehi number decide karta hai geometry: 2 = linear, 3 = trigonal planar, 4 = tetrahedral, 5 = trigonal bipyramidal, 6 = octahedral.

Ek important cheez — multiple bond ko ek hi domain count karo. Double ya triple bond ke saare electrons ek hi direction mein hote hain, isliye wo ek fat cloud hai, do nahi. Ye galti bahut students karte hain. Aur doosri baat, lone pair extra fat hota hai kyunki use sirf ek nucleus pakadta hai, dusra atom share nahi karta. Isliye lone pair zyada zor se dhakka maarta hai aur bond angles ko chhota kar deta hai. Isi wajah se CH₄ mein 109.5°, NH₃ mein 107°, aur H₂O mein 104.5° angle hota hai — jaise-jaise lone pairs badhte hain, angle ghatta jaata hai.

Ek aur clever point trigonal bipyramidal (SN=5) ke liye: lone pair hamesha equatorial position pe baithta hai, axial pe nahi. Kyun? Axial position ke 3 padosi 90° pe hote hain, jabki equatorial ke sirf 2. Kam 90° neighbours matlab kam repulsion, isliye fat lone pair equatorial choose karta hai. Yaad rakho: electron geometry matlab saare clouds ki arrangement, aur molecular geometry matlab sirf atoms kahan hain. Dono tabhi same hote hain jab koi lone pair na ho. Ye chhoti si difference exam mein marks dilwati hai — aur shape se hi decide hota hai molecule polar hai ya nahi (CO₂ nonpolar, H₂O polar).

VSEPR theory — geometry from electron pairs (linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral, etc

WHY does VSEPR exist?

Deriving the shapes from first principles

Lone pairs: the shape-benders

Worked derivation: from CH₄ → NH₃ → H₂O (all SN = 4)

The clever trick for SN = 5 (trigonal bipyramidal)

Worked Examples

Common Mistakes (Steel-manned)

Flashcards

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Chemical Bonding

Connections