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

2.3.17 · Chemistry › Chemical Bonding

1. Van der Waals forces kya hain?

YEH kya NAHI hain: yeh chemical bonds nahi hain. Yeh molecules ke beech act karti hain, molecules ke andar nahi.

2. Physics ko first principles se derive karna

In sab forces ki parent Coulomb's law hai charges ke beech: $F = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r ^{2}}, U = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r}$

Lekin molecules neutral hain, isliye net charge product zero hai. Attraction tabhi bachta hai jab charge + aur − regions mein separate hota hai (ek dipole). Chalte hain har force build up karte hain.

2.1 Dipole potential (foundation block)

2.2 Dipole–dipole interaction energy

KAISE: Molecule 1 ka permanent dipole $μ_{1}$ hai; yeh field $E_{1} \propto μ_{1} / r^{3}$ create karta hai. Molecule 2 ka dipole $μ_{2}$ us field mein baitha hai. Interaction energy $U = - μ_{2} E_{1}$ :

$U_{dd} \propto - \frac{μ _{1} μ _{2}}{r ^{3}} (fixed, aligned orientation)$

Extra averaging kyun? Gas mein molecules tumble karte hain. Thermal motion orientations ko partially randomise karti hai. Sab angles par average karne se (Boltzmann-weighted) Keesom result milta hai: $U_{dd} \propto - \frac{μ _{1}^{2} μ _{2}^{2}}{k _{B} T r ^{6}}$

2.3 Dipole–induced dipole (Debye) interaction

KYA: Ek polar molecule (dipole $μ$ ) ek non-polar (lekin polarisable) molecule ke paas baitha hai. Dipole ka field distort karta hai neighbour ke cloud ko, ek dipole induce karta hai.

KAISE (derivation):

Induced dipole size: $μ_{ind} = α E$ , jahan $α$ = polarisability.
Field hai $E \propto μ / r^{3}$ .
Interaction energy $U \propto - μ_{ind} E \propto - α E^{2}$ :

$U_{di} \propto - \frac{α μ ^{2}}{r ^{6}}$

Phir se $r^{6}$ kyun? Ek factor $E \propto r^{- 3}$ induce karne ke liye, doosra $E \propto r^{- 3}$ interact karne ke liye → $r^{- 6}$ . Yeh orientation-independent hai (hamesha attractive) kyunki induced dipole hamesha favourably line up ho jaata hai.

2.4 London dispersion (instantaneous dipole – induced dipole)

YEH sabse deep idea kyun hai: ek non-polar atom jaise Ar ka KOI permanent dipole nahi hota. Phir bhi electrons constantly move karte hain, isliye kisi bhi instant par cloud momentarily lopsided ho jaata hai → instantaneous dipole. Yeh flickering dipole neighbour mein ek matching dipole induce karta hai, aur dono correlate ho ke net attraction dete hain.

KAISE (scaling argument):

Instantaneous dipole $\propto$ cloud kitni easily distort hota hai $= α$ .
Yeh neighbour mein $μ_{ind} \propto α$ induce karta hai → energy $\propto α^{2} / r^{6}$ .
London ka quantum result ionisation energy $I$ include karta hai:

$U_{London} \propto - \frac{α _{1} α _{2}}{r ^{6}} \cdot \frac{I _{1} I _{2}}{I _{1} + I _{2}}$

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

3. Inki strength ko kya control karta hai?

4. Worked examples

5. Common mistakes (Steel-manned)

6. Active recall

Recall Forecast-then-verify: pehle predict karo phir reveal karo

Q: Cl₂, Br₂, I₂ ko boiling point se rank karo. → I₂ > Br₂ > Cl₂ (zyada electrons → larger α → stronger London). Q: Neopentane ka BP n-pentane se lower kyun hai (same formula)? → n-pentane zyada linear/larger surface area wala hai, isliye zyada London contact; neopentane spherical/compact hai.

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

London dispersion forces

What is the instantaneous origin of London forces?

Electron cloud mein momentary fluctuations ek temporary (instantaneous) dipole create karte hain

How does van der Waals attraction energy scale with distance?

- 1/ r^{6}

What molecular property makes London forces stronger?

Higher polarisability (zyada electrons / bada, 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?

Unhe phir bhi London dispersion forces experience hoti hain

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

HCl ka permanent dipole–dipole attraction hai London forces ke addition mein

Which term dominates for heavy molecules like HI?

London dispersion, kyunki electron count/polarisability (chhote) dipole par dominate karta hai

Formula-scaling for dipole–induced dipole energy?

U \propto - α μ^{2} / r^{6}

Are van der Waals forces chemical bonds?

Nahi — koi electron sharing/transfer nahi; yeh weak intermolecular electrostatic attractions hain

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho do fluffy clouds buzzing bees (electrons) ki do magnets ke around. Chahe har cloud balanced ho, kabhi kabhi zyada bees ek side mein accident se crowd ho jaati hain, us side ko thodi sticky-negative bana deti hain. Neighbour cloud usse feel karta hai aur apni bees ko rearrange kar leta hai taaki dono clouds gently ek doosre ko pull karein. Yeh ek split second ke liye hota hai, baar baar, aur add up ho ke sab molecules ke beech ek chhoti "stickiness" banata hai — isliye chahe gases mein koi real magnets andar na hon, phir bhi woh liquids mein turn ho sakti hain jab unhe thanda karo.

7. Connections

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