4.2.3
Carbon ko 109.5° s p 3 ring mein force karte ho, to wo angles 109.5° angle strain . Baeyer ne socha tha ki saari rings flat hoti hain, isliye usne predict kiya ki badi rings bahut zyada strained hongi. Woh galat tha — rings PUCKER (3D mein fold) ho jaati hain strain se bachne ke liye. Cyclohexane ek "chair" mein fold hoti hai jo itni perfect hai ki usmein zero angle strain hota hai. Yeh ek idea — ki molecules total strain minimize karne ke liye twist hoti hain — poore topic ka dil hai.
Definition Cycloalkanes mein strain ke types
Angle (Baeyer) strain 109.5° Torsional (eclipsing) strain eclipsed (ek line mein) hote hain staggered ki jagah.Steric (van der Waals) strain
YEH KYUN matter karte hain: sabse stable conformation/ring woh hai jisme total strain sabse kam ho. Cycloalkanes ki stability (heat of combustion per CH₂ se measure ki jaati hai) inhe teen strain ko add karke determine hoti hai.
Intuition Baeyer ki (galat) assumptionBaeyer (1885) ne assume kiya ki har ring ek flat regular polygon hai . Agar ring flat polygon hai, to uska internal angle geometry se fix hota hai, aur carbon ko apne bonds us mein fit karne ke liye bend karne padte hain. Har bond ka 109.5° deviation strain measure karta hai.
Deviation KAISE compute karein (derive karein):
n internal angle hai
θ internal = n ( n − 2 ) × 180° .
Kyun? Kisi bhi n ( n − 2 ) × 180° n
Baeyer ki angular strain (har bond ka tetrahedral direction se deviation) per bond:
d = 2 1 ( 109.5° − θ internal ) .
2 1 aadhe total mismatch se deviate karta hai.
Ring (n
θ internal d Reality
3 (cyclopropane)
60° + 24.75° bahut strained ✔
4 (cyclobutane)
90° + 9.75° strained ✔
5 (cyclopentane)
108° + 0.75° almost strain-free ✔
6 (cyclohexane)
120° − 5.25° Baeyer: strained ✗ — actually strain-FREE
larger
—
aur zyada negative
Baeyer: bahut strained ✗ — actually theek
Common mistake Steel-man: "Badi rings strained honi chahiye kyunki unka flat angle109.5° Kyun sahi lagta hai: formula literally bade n agar ring flat ho.
Fix: rings flat nahi hoti. Woh pucker karke 3D mein aa jaati hain. Cyclohexane is tarah fold hoti hai ki har carbon ka angle sach mein 111° 109.5° maths nahi . Strain theory chhoti rings (3,4) ke liye bahut achha kaam karti hai jo zyada pucker nahi kar sakti .
Definition Cyclohexane ke conformations
Chair Saare bonds staggered , saare angles ≈ 111° Sabse stable (global minimum).Boat ek hi side se upar fold hote hain. Sides mein eclipsing strain hoti hai + ek flagpole interaction (do H's ek doosre ki taraf point karte hain). ~29 kJ/mol Twist-boat : thoda twisted boat, boat se thoda kam energy par lekin chair se zyada.
Intuition Chair > boat kyunChair mein, kisi bhi C–C bond se neeche dekho → H's perfectly staggered hain (staggered ethane ki tarah) → minimum torsional strain. Boat mein, side bonds eclipsed hain, AUR do "flagpole" hydrogens aage/peechhe ek doosre se bhid jaate hain (steric strain). Zyada strain → kam stable.
Definition Axial & equatorial bondsChair mein, har carbon ke do C–H bonds hote hain:
Axial upar ya niche point karta hai, ring ke main (vertical) axis ke parallel. Yeh ring ke around up–down–up–down alternate karte hain.Equatorial baahir ki taraf point karta hai (roughly ring ke "equator" mein), apne axial partner ke opposite thoda upar/niche.
Intuition Ring flip (chair–chair interconversion)Chair doosre chair mein flip ho sakta hai. Jab aisa hota hai, har axial bond equatorial ban jaata hai aur har equatorial axial . Molecule iske liye higher-energy twist-boat se guzarti hai (barrier ≈ 45 kJ/mol
Intuition Bade groups equatorial kyun prefer karte hain (1,3-diaxial strain)Ek axial substituent upar ki taraf us space mein point karta hai jo same face par dono doosre axial groups (1,3-diaxial positions) share karte hain. Wahan ek bada group clash karta hai (steric strain). Equatorial position mein woh safely baahir ki taraf point karta hai. Isliye bulky substituents equatorial prefer karte hain , e.g. methylcyclohexane ~95% equatorial-methyl chair hota hai.
Worked example Methylcyclohexane preferenceKyun? Axial-CH₃ mein do 1,3-diaxial H···CH₃ interactions hote hain, har ek ~3.8 kJ/mol 7.6 kJ/mol axial ⇌ equatorial define karo K = [ eq ] / [ ax ] Δ G ≈ − 7.5 kJ/mol Δ G = − R T ln K ⇒ ln K = − R T Δ G K = e − Δ G / R T = e − ( − 7500 ) / ( 8.314 × 298 ) = e + 7500/ ( 8.314 × 298 ) ≈ 21 21 : 1 Yeh step kyun? Δ G < 0 positive hai, jo K > 1 K = e − Δ G / R T Δ G
Worked example Example 1 — Cyclopropane ka Baeyer strainn = 3 θ = 3 ( 3 − 2 ) 180 = 60° d = 2 109.5 − 60 = + 24.75° Yeh step kyun? Bahut bada positive d
Worked example Example 2 — Cyclohexane stability mein cyclopentane seper CH₂ kyun better hai
Flat formula cyclopentane ke liye d = + 0.75° d = − 5.25° Formula kyun mislead karta hai: cyclohexane flat nahi hai. Real cyclohexane mein 0 658.7 kJ/mol Lesson: n ≥ 6
Worked example Example 3 —cis - vs trans -1,4-dimethylcyclohexane
trans -1,4: dono methyls equatorial,equatorial (e,e) ho sakte hain → sabse stable.
cis -1,4: ek axial hoga, ek equatorial (a,e) → 1,3-diaxial strain hai → kam stable.
Kyun? Chair par, same up/down "tag" wali 1,4 positions ek ko axial force karti hain; cis mein tum dono ko equatorial nahi bana sakte. Isliye trans -1,4 winner hai.
Recall Test yourself (answers chhupao)
Q: Baeyer bade rings ke baare mein galat kyun tha? → Woh 3D mein pucker hoti hain, angle strain se bach jaati hain.
Q: Chair ya boat, kaun zyada stable hai, aur kyun? → Chair; staggered bonds + koi flagpole clash nahi.
Q: Ring flip par axial/equatorial labels ka kya hota hai? → Woh completely swap ho jaate hain.
Q: Bulky groups equatorial kyun prefer karte hain? → 1,3-diaxial steric strain se bachne ke liye.
Q: Flat-ring strain per bond ka formula? → d = 2 109.5 − ( n − 2 ) 180/ n
Recall Feynman: ek 12-saal ke bacche ko explain karoCarbon ki "baahein" ek aaram-deh angle par spread hona chahti hain, jaise tumhare paon relaxed stance mein hote hain. Agar tum carbons ko ek chhote triangle ring mein baandh do, to unki baahein squeeze ho jaati hain aur uncomfortable ho jaati hain — yahi strain hai, aur chhoti rings isse hate karti hain. Lekin ek 6-carbon ring bahut smart hai : flat lie karne ki jagah, woh ek lawn chair ki tarah fold hoti hai (ek part upar, ek part neeche). Us folded "chair" mein har baah aaram se baith jaati hai aur koi do haath nahi bhidate — isliye woh super happy hai. Kuch baahein seedha upar/niche stick karti hain (axial) aur kuch baahir stick karti hain (equatorial). Agar tum ek bada backpack (bulky group) pehno, to tum use baahir ki taraf point karna chahoge taaki woh tumhare upar aur neeche ki cheezon se na takraaye.
"AXial = vertical AXis" (axial bonds ek axis ki tarah upar/niche jaate hain)."Bade groups OUT jaana chahte hain (eQuatorial)" — Q for "Quit the crowding."Chair Champion, Boat Bummer — chair jeetta hai, boat haarta hai.Strain trio: A-T-S = A ngle, T orsional, S teric.
Conformations of Ethane and Butane (staggered vs eclipsed — same torsional idea)sp3 Hybridization and Tetrahedral Geometry (kyun 109.5° Heat of Combustion as a Stability Measure Geometrical Isomerism cis-trans (cis/trans dimethylcyclohexanes)Newman Projections Free Energy and Equilibrium ΔG = -RT lnK
Baeyer's strain theory assume karti hai ki rings hain flat (planar) regular polygons
Regular n-gon ka internal angle n ( n − 2 ) × 180°
Baeyer strain per bond formula d = 2 109.5° − ( n − 2 ) 180°/ n
Cyclopropane ka Baeyer strain + 24.75°
Baeyer bade rings ke liye galat kyun tha rings 3D mein pucker hoti hain, angle strain remove ho jaati hai
Cyclohexane ka sabse stable conformation chair
Chair sabse stable kyun hai saare bonds staggered, ≈111° angles, koi flagpole clash nahi
Boat ke do destabilizing features eclipsing (torsional) strain + flagpole steric strain
Axial bonds point karte hain seedha upar/niche, ring axis ke parallel
Equatorial bonds point karte hain ring ke equator ke around baahir
Ring flip substituents ke saath kya karta hai saare axial↔equatorial swap ho jaate hain
Bulky groups equatorial kyun prefer karte hain 1,3-diaxial steric strain se bachne ke liye
Teen types of strain angle (Baeyer), torsional (eclipsing), steric (van der Waals)
Sabse stable 1,4-dimethylcyclohexane trans (dono equatorial, e,e)
Ek axial-methyl 1,3-diaxial interaction ki cost ≈3.8 kJ/mol
ΔG = –RT ln K ka correct rearrangement K = e − Δ G / R T
Ideal angle 109.5 tetrahedral
Baeyer assumes flat polygons
