van der Waals forces — London dispersion, dipole-dipole, dipole-induced dipole

1. What are van der Waals forces?

WHAT they are NOT: they are not chemical bonds. They act between molecules, not within them.

2. Deriving the physics from first principles

The parent of all these forces is Coulomb's law between charges: $F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2}, \qquad U = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r}$

But molecules are neutral, so the net charge product is zero. The attraction survives only because charge is separated into + and − regions (a dipole). Let's build up each force.

2.1 The dipole potential (foundation block)

2.2 Dipole–dipole interaction energy

HOW: Molecule 1 has permanent dipole $\mu_1$ ; it creates field $E_1 \propto \mu_1/r^3$ . Molecule 2's dipole $\mu_2$ sits in that field. Interaction energy $U = -\mu_2 E_1$ :

$U_{\text{dd}} \propto -\frac{\mu_1\mu_2}{r^3}\quad(\text{fixed, aligned orientation})$

Why the extra averaging? In a gas, molecules tumble. Thermal motion partly randomises orientations. Averaging over all angles (Boltzmann-weighted) gives the Keesom result: $\boxed{U_{\text{dd}} \propto -\frac{\mu_1^2\mu_2^2}{k_B T\, r^6}}$

2.3 Dipole–induced dipole (Debye) interaction

WHAT: A polar molecule (dipole $\mu$ ) sits next to a non-polar (but polarisable) molecule. The dipole's field distorts the neighbour's cloud, inducing a dipole.

HOW (derivation):

Induced dipole size: $\mu_{\text{ind}} = \alpha E$ , where $\alpha$ = polarisability.
The field is $E \propto \mu/r^3$ .
Interaction energy $U \propto -\mu_{\text{ind}}\,E \propto -\alpha E^2$ :

$\boxed{U_{\text{di}} \propto -\frac{\alpha\,\mu^2}{r^6}}$

Why $r^6$ again? One factor $E \propto r^{-3}$ to induce, another $E \propto r^{-3}$ to interact → $r^{-6}$ . This is orientation-independent (always attractive) because the induced dipole always lines up favourably.

2.4 London dispersion (instantaneous dipole – induced dipole)

WHY it's the deepest idea: even a non-polar atom like Ar has NO permanent dipole. Yet electrons move constantly, so at any instant the cloud is momentarily lopsided → instantaneous dipole. This flickering dipole induces a matching dipole in the neighbour, and the two correlate to give net attraction.

HOW (scaling argument):

Instantaneous dipole $\propto$ how easily the cloud distorts $= \alpha$ .
It induces $\mu_{\text{ind}} \propto \alpha$ in the neighbour → energy $\propto \alpha^2/r^6$ .
London's quantum result includes ionisation energy $I$ :

$\boxed{U_{\text{London}} \propto -\frac{\alpha_1\alpha_2}{r^6}\cdot\frac{I_1 I_2}{I_1+I_2}}$

Figure — van der Waals forces — London dispersion, dipole-dipole, dipole-induced dipole

3. What controls their strength?

4. Worked examples

5. Common mistakes (Steel-manned)

6. Active recall

Recall Forecast-then-verify: predict before revealing

Q: Rank Cl₂, Br₂, I₂ by boiling point. → I₂ > Br₂ > Cl₂ (more electrons → larger α → stronger London). Q: Why is neopentane's BP lower than n-pentane's (same formula)? → n-pentane is more linear/larger surface area, so more London contact; neopentane is spherical/compact.

Which van der Waals force acts between ALL molecules, polar or not?

London dispersion forces

What is the instantaneous origin of London forces?

Momentary fluctuations in the electron cloud create a temporary (instantaneous) dipole

How does van der Waals attraction energy scale with distance?

-1/r^6

What molecular property makes London forces stronger?

Higher polarisability (more electrons / larger, softer electron cloud)

Which force operates between a polar and a non-polar molecule?

Dipole–induced dipole (Debye) force

Why do noble gases liquefy at all despite having no bonds?

They still experience London dispersion forces

Why does HCl boil higher than F₂ despite similar electron count?

HCl has permanent dipole–dipole attraction in addition to London forces

Which term dominates for heavy molecules like HI?

London dispersion, because electron count/polarisability dominates over the (small) dipole

Formula-scaling for dipole–induced dipole energy?

U \propto -\alpha\mu^2/r^6

Are van der Waals forces chemical bonds?

No — no electron sharing/transfer; they are weak intermolecular electrostatic attractions

Recall Feynman: explain to a 12-year-old

Imagine two fluffy clouds of tiny buzzing bees (electrons) around two magnets. Even though each cloud is balanced, sometimes more bees crowd on one side by accident, making that side a little sticky-negative. The neighbour cloud feels it and rearranges its own bees so the two clouds gently pull together. This happens for a split second, over and over, and adds up to a tiny "stickiness" between all molecules — that's why even gases with no real magnets inside can turn into liquids when you cool them.

7. Connections

Dipole moment and molecular polarity
Polarisability and Fajans' rules
Hydrogen bonding (stronger special case of dipole–dipole)
Lennard-Jones potential
Boiling point and intermolecular forces
Coulomb's law (parent principle)
States of matter and condensation

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, har molecule ke andar electrons ek fuzzy cloud ki tarah ghumte rehte hain. Chahe molecule neutral ho, yeh cloud thoda idhar-udhar hilta rehta hai. Isi hilne se temporary ya permanent charge ka imbalance banta hai, aur padosi molecules ke beech halki si electrostatic attraction lag jaati hai — inhe hum van der Waals forces kehte hain. Ye chemical bond nahi hote (koi electron share ya transfer nahi hota), sirf weak intermolecular pull hote hain.

Teen types samajh lo. London dispersion — yeh sabse important hai kyunki ye har molecule me hota hai, polar ho ya non-polar. Electron cloud me ek instant ke liye lopsidedness aati hai (instantaneous dipole), jo padosi me dipole induce kar deti hai. Zyada electrons matlab zyada polarisability ( $\alpha$ ) matlab strong London force — isiliye Ar, Kr, Xe ka boiling point badhta jaata hai. Dipole–dipole tab lagta hai jab dono molecules me permanent dipole ho (jaise HCl), aur iski strength dipole moment $\mu$ pe depend karti hai. Dipole–induced dipole tab jab ek polar molecule non-polar padosi me dipole induce kare (jaise water O₂ ko ghol leta hai).

Ek super important point: teeno forces distance ke saath $1/r^6$ ki tarah girti hain — yaani thodi door hote hi lagbhag khatam. Aur ek classic exam trap: "bada dipole matlab bada boiling point" — ye galat hai! HI ka dipole HCl se kam hai par boiling point zyada, kyunki HI me electrons zyada hain to London force jeet jaata hai. Heavy molecules me London usually dominate karta hai.

Yeh matter isliye karta hai kyunki boiling point, melting point, gases ka liquefy hona, solubility, gecko ka wall pe chipakna — sab in choti-choti forces se decide hote hain. Bina bond ke bhi noble gases liquid ban jaate hain, sirf London dispersion ki wajah se. To in teeno ko trend ke saath yaad rakho, formula ratne se zyada important hai unka WHY samajhna.