2.3.7
Ek molecule chhote-chhote charge arrows ka collection hai. Har polar bond ek arrow (vector) hai jo positive atom se negative atom ki taraf point karta hai. Molecule ki overall polarity bas yahi hai jo aapko milti hai jab aap in saare arrows ko head-to-tail add karte ho. Agar cancel ho jaayein → nonpolar. Agar nahi → polar.
YE KYUN ZAROORI HAI: Polarity boiling point, solubility ("like dissolves like"), aur ye control karti hai ki molecules electric fields mein kaise align hote hain. Ye ek aisa idea hai jo hazaaron substances ke real-world behaviour ko predict karta hai.
Definition Bond dipole momentJab do bonded atoms ki electronegativities alag-alag hoti hain, toh shared electrons zyada electronegative atom ke paas shift ho jaate hain. Isse ek atom par partial negative charge δ − δ + dipole kehte hain.
Bond dipole moment ye hota hai:
μ = q ⋅ d q d δ + se δ − vector hai.
Intuition Charges additive hote hain, toh unke moments bhi add hote hainDipole moment define hota hai charge × q i r i total dipole hai
μ net = ∑ i q i r i individual bond dipoles ka vector sum hota hai. Vectors head-to-tail add hote hain — direction matter karti hai, toh opposite arrows cancel ho sakte hain. Yahi poora secret hai.
Sanity checks (Forecast-then-Verify):
θ = 180° 2 μ cos 90° = 0 cancel ho jaate hain , nonpolar. ✓θ = 0° 2 μ cos 0° = 2 μ maximum . ✓θ = 104.5° 2 μ cos 52.25° ≈ 1.22 μ polar . ✓
Worked example CO₂ — polar bonds, nonpolar moleculeStructure: O = C = O linear , θ = 180° opposite directions mein.
μ net = 2 μ cos ( 180°/2 ) = 2 μ cos 90° = 0 Ye step kyun? Kyunki do equal arrows exactly opposite direction mein point karte hain, unka vector sum zero hai. Result: nonpolar, μ = 0 , chahe har bond polar ho. Ye classic trap hai.
Worked example H₂O — bent, polarBond angle 104.5° μ net = 2 μ OH cos ( 52.25° ) ≈ 2 ( 1.5 D ) ( 0.612 ) ≈ 1.84 D Ye step kyun? Bent shape ki wajah se arrows cancel nahi hote; dono "upar" O ki taraf point karte hain, add up ho jaate hain. Measured μ H 2 O = 1.85 D Polar.
Worked example BF₃ vs NH₃ — symmetry decide karti haiBF₃: trigonal planar, teen B–F dipoles 120° zero tak sum ho jaate hain. Nonpolar.
Proof: teen unit vectors 120° v 1 + v 2 + v 3 = 0 NH₃: trigonal pyramidal (lone pair use karke plane se bahar push ho jaata hai). Teen N–H dipoles ek plane mein nahi hote, isliye ek resultant axis ke along rehta hai, plus lone-pair contribution. Polar, μ ≈ 1.47 D
Fark kyun? "Teen bonds" same count hain, lekin geometry (planar vs pyramidal) ye decide karti hai ki arrows cancel hote hain ya nahi.
Worked example CH₄ — tetrahedral, nonpolarChar C–H dipoles tetrahedron ke corners ki taraf point karte hain. Koi bhi teen ek aisa vector add karte hain jo exactly chauthe ko cancel kar deta hai (ye ek perfectly symmetric set of directions mein point karte hain). μ = 0 Nonpolar.
Kyun? Full symmetry ⇒ δ + δ −
Worked example CHCl₃ (chloroform) — broken symmetryCH₄ ka ek H, Cl se replace karo. Ab char bonds identical nahi hain: teen C–Cl aur ek C–H cancel nahi hote. Net dipole H–C–Cl₃ axis ke along point karta hai. Polar, μ ≈ 1.04 D Substitution cancelling symmetry ko tod deti hai .
Common mistake "Polar bonds ⇒ polar molecule."Ye sahi kyun lagta hai: har bond genuinely ek dipole rakhta hai, toh surely molecule bhi rakhta hoga?
Fix: Dipoles vectors hain. Symmetric (linear/planar/tetrahedral) arrangements mein equal ones cancel ho jaate hain. CO₂, BF₃, CCl₄ mein bahut polar bonds hain phir bhi μ net = 0 geometry check karo, sirf bonds nahi.
Common mistake Lone pairs ko ignore karna.Ye sahi kyun lagta hai: hum sirf bonds draw karte hain, toh hum sirf bond arrows add karte hain.
Fix: Lone pairs bhi charge ke regions hain aur μ
Common mistake Dipole magnitudes ko ordinary numbers ki tarah add karna.Ye sahi kyun lagta hai: arithmetic easy hai; 2 + 2 = 4 Fix: Aapko cosine rule μ net = μ 1 2 + μ 2 2 + 2 μ 1 μ 2 cos θ θ = 0
Common mistake Arrow direction galat karna.Ye sahi kyun lagta hai: physics dipole − + Fix: Chemistry mein arrow (crossed-plus symbol ↣ δ + se δ −
Recall Quick self-test (answers cover karo)
Ek molecule mein polar bonds hone ke bawajood nonpolar kyun ho sakta hai? → symmetric geometry bond dipoles ko cancel kar deti hai.
Do equal dipoles at angle θ 2 μ cos ( θ /2 )
CO₂ nonpolar kyun hai lekin H₂O polar kyun hai? → CO₂ linear hai (180° cancel), H₂O bent hai (104.5° cancel nahi hote).
NH₃ ya BF₃ mein se zyada polar kaun hai, aur kyun? → NH₃ (pyramidal, cancel nahi hota); BF₃ planar cancel ho jaata hai.
Define bond dipole moment μ = q d , ek vector
δ + se
δ − ki taraf, magnitude = charge × separation.
Unit of dipole moment and its SI value Debye (D); 1 D = 3.336 × 1 0 − 30 C⋅m
Net dipole of two equal bond dipoles at angle θ μ n e t = 2 μ cos ( θ /2 )
General two-dipole resultant formula μ n e t = μ 1 2 + μ 2 2 + 2 μ 1 μ 2 cos θ .
Why is CO₂ nonpolar despite polar bonds Linear (180°), do equal C=O dipoles opposite direction mein point karke cancel ho jaate hain.
Dipole moment of water and why nonzero ~1.85 D; bent (104.5°) isliye O–H dipoles cancel nahi hote.
Is BF₃ polar? Why Nahi; trigonal planar, teen 120° dipoles zero tak sum ho jaate hain.
Is NH₃ polar? Why Haan (~1.47 D); pyramidal shape + lone pair, dipoles cancel nahi hote.
Effect of replacing one H in CH₄ by Cl (CHCl₃) Symmetry tod deta hai, polar ban jaata hai (~1.04 D).
Condition for a symmetric molecule to be nonpolar Bond dipoles equal hon aur aisa arrange hon ki vector sum = 0 ho (linear, trigonal planar, tetrahedral, etc.).
Recall Feynman: 12-saal ke bachche ko samjhaoSocho har bond ek bachcha hai jo rope ko ek direction mein kheench raha hai. Agar saare bachche balanced directions mein equally kheenchein (ek perfect star), toh beech ki rope nahi hilti — wo molecule "balanced" hai (nonpolar). Lekin agar bachche unevenly kheenchein ya ek taraf bunch up kar lein, toh rope us taraf khich jaati hai — us molecule ka ek "pull direction" hai (polar). Water ke do bachche dono upar-aur-sideways kheenchte hain, isliye beech upar ki taraf khichti hai → water polar hai. Carbon dioxide ke do bachche exactly opposite kheenchte hain → koi drag nahi → nonpolar. Toh ye nahi ki har bachcha kitna zor se kheenchta hai, ye hai ki kheench cancel hoti hai ya nahi .
"Shape, not just bonds." Aur cancellation ke liye: "Straight, Flat-triangle, aur Tetra = zero" (linear, trigonal-planar, tetrahedral symmetric molecules nonpolar hote hain). Bent, pyramidal, aur asymmetric = polar.
Electronegativity — har bond dipole ka source .VSEPR Theory — geometry (angles) deta hai jo aap vector sum mein plug karte ho.Molecular Geometry and Shapes — cancellation decide karta hai.Intermolecular Forces — dipole–dipole forces μ n e t Solubility — Like Dissolves Like — polarity miscibility predict karti hai.Vectors and the Cosine Rule — addition ke peeche ka math engine.
Electronegativity difference
Debye, 1 D = 3.336e-30 C·m
Vector sum of bond dipoles
mu_net = 2 mu cos of theta over 2
Boiling point, solubility, alignment
