Fajan's rules — covalent character in ionic compounds

2.3.4 · Chemistry › Chemical Bonding

Fajan's phenomenon KYA hai?

YEH KYUN hota hai: Ek chota, highly charged cation ek intense electric field create karta hai. Ek bada, loosely-held anion cloud squishy hota hai. Field cloud ko cation ki taraf squeeze karti hai → dono ions ke beech electron density ka build-up → wahi ek covalent bond ionic ke andar ban raha hai.

Chaar Rules (reasoning se derive kiye, memorise nahi kiye)

Hum electric field strength aur cloud softness se reason karte hain.

Rule 1 — Chota cation → zyada covalent

Ek point charge ka field $E = \frac{k q}{r ^{2}}$ hota hai. Chota cation radius $r$ ⇒ anion par bahut bada field (note karo $r^{2}$ ). Stronger field ⇒ zyada distortion ⇒ zyada covalent.

Rule 2 — High cation charge → zyada covalent

$E \propto q$ . Ek $+ 3$ cation $+ 1$ se teen guna zyada kheenchta hai (equal size par).

Rule 3 — Bada anion (aur high anion charge) → zyada covalent

Ek bada anion apne outer electrons ko apne nucleus se door rakhta hai → woh loosely held hote hain → easily distorted (high polarisability). Zyada negatively charged anion (2– vs 1–) mein bhi extra electrons per unit nuclear charge kam tightly held hote hain, isliye woh bhi zyada polarisable hota hai aur zyada covalent character deta hai.

Rule 4 — Non-noble-gas cation configuration → zyada covalent

Cations jinka $(n - 1) d^{10} n s^{0}$ pseudo-noble-gas shell ho (e.g. Cu⁺, Ag⁺, Zn²⁺, Cd²⁺, Hg²⁺) same size aur charge ke noble-gas-type cations (Na⁺, K⁺, Ca²⁺) se zyada polarise karte hain.

Sab kuch combine kaise karein: polarising power

Formula Charge-to-size ratio (ionic potential)

Yeh quantity kyun? Cation jo distorting field anion par exert karta hai woh Coulomb's law follow karta hai, lekin poore cation–anion separation ke across evaluate kiya jaata hai, sirf cation radius par nahi: $E \propto \frac{q _{cation}}{( r _{cation} + r _{anion} ) ^{2}}$ Yeh physically correct polarising field hai. Chemists phir ek rough ranking proxy use karte hain jise ionic potential kehte hain: $ϕ = \frac{q _{cation}}{r _{cation}}$ Scratch-se derivation (aur uski limits): distortion $\propto E$ . Agar anion fixed hai, $E$ cation charge $q$ ke saath badhta hai (Rule 2) aur separation badhne par girata hai (Rule 1). $ϕ = q / r_{cation}$ "higher charge, smaller cation" ko EK number mein capture karta hai — lekin yeh sirf ek bahut rough proxy hai: yeh anion ki radius ko ignore karta hai, $1/ r^{2}$ (vs $1/ r$ ) dependence ko ignore karta hai, aur anion charge/polarisability (Rule 3) aur cation configuration (Rule 4) ko ignore karta hai. Bada $ϕ$ ⇒ generally zyada covalent character, baaki sab equal hone par.

Figure — Fajan's rules — covalent character in ionic compounds

Covalent character ke observable consequences

Zyada covalent character (badi polarisation) generally matlab hai:

Lower melting/boiling point (weaker giant lattice, zyada discrete molecules).
Non-polar/organic solvents mein greater solubility, paani mein kam.
Molten hone par lower electrical conductivity.
Colour changes aksar strong polarisation ke saath associated hoti hain (e.g. AgI yellow hai jabki AgCl white hai). Lekin dhyan raho: actual colour solid mein charge-transfer / band-structure effects se aati hai, sirf Fajan's polarisation se koi transition energy lower hone se nahi. Polarisation correlate karta hai, lekin akele colour ko poori tarah explain nahi karta.

Recall Forecast-then-verify: NaCl, MgCl₂, AlCl₃ ke melting points rank karo

Forecast: charge $+ 1, + 2, + 3$ jaata hai; size Na⁺>Mg²⁺>Al³⁺ shrink hoti hai, toh $ϕ$ badhta hai → covalent character badhta hai → MP girna chahiye. Verify: NaCl 801 °C, MgCl₂ 714 °C, AlCl₃ ~180 °C par sublimes. ✅ Prediction sahi.

Common Mistakes (steel-manned)

Feynman check

Recall Ek 12-saal ke bachche ko explain karo

Ek strong magnet (chota, high-charge cation) imagine karo ek electrons se bhari soft water balloon (anion) ke paas. Magnet bas baitha nahi rehta — woh balloon ki skin ko apni taraf kheenchta hai, toh kuch paani dono ke beech ke gap mein bulge kar jaata hai. Woh shared bulge waise hai jaise do bachche ek hi rope hold kar rahe hain apni alag-alag rope ki jagah — wahi ek ionic mein covalent bond ghus raha hai. Ek tiny strong magnet aur ek bada, extra-bhari floppy balloon (bada bhi aur zyada charged bhi) sabse bada bulge banate hain.

Flashcards

Fajan's rules "ionic" bonds ki kya property describe karte hain?

Cation dwara anion ki polarisation se hone wale covalent character ki degree.

Polarising power vs polarisability kya hai?

Polarising power = cation ki cloud distort karne ki ability (chota, high charge). Polarisability = anion ki distort hone ki tendency (bada size AUR high negative charge).

Cation size ghataane ka covalent character par kya effect hota hai?

Badhta hai — field

E \propto 1/ r^{2}

toh chota cation kaafi zyada kheenchta hai.

Anion size badhane ka covalent character par kya effect hota hai?

Badhta hai — bada anion zyada polarisable hota hai (loosely held outer electrons).

Anion charge badhane (1– → 2–) ka covalent character par kya effect hota hai?

Badhta hai — extra electrons zyada loosely held hote hain, toh 2– anion similar size ke 1– anion se zyada polarisable hota hai.

Cu⁺ similar size ke Na⁺ se zyada covalent bonds kyun deta hai?

Cu⁺ ka

(n - 1) d^{10}

pseudo-noble-gas core poorly shield karta hai, ek badi effective pull deta hai (Rule 4).

Ionic potential formula, meaning, aur uski limitation?

ϕ = q_{c a t i o n} / r_{c a t i o n}

; bada

ϕ

⇒ greater polarising power. Limitation: sirf ek rough proxy — true field

\propto q / (r_{c a t i o n} + r_{ani o n})^{2}

hai aur yeh anion charge/config ko ignore karta hai.

Covalent character rank karo: AlF₃, AlCl₃, AlBr₃, AlI₃.

AlF₃ < AlCl₃ < AlBr₃ < AlI₃ (anion polarisability group mein neeche jaane par badhti hai).

Kya AgI purely isliye yellow hai kyunki Fajan's polarisation transition energy lower karti hai?

Nahi — colour charge-transfer/band-structure effects se aata hai; polarisation sirf trend ke saath correlate karta hai.

High covalent character ke do reliable physical signs?

Lower melting point aur organic (non-polar) solvents mein higher solubility.

Real polarising field

q / (r_{c a t i o n} + r_{ani o n})^{2}

kyun hai, sirf

q / r_{c a t i o n}

kyun nahi?

Coulomb's law poore cation–anion separation par evaluate hota hai;

q / r_{c a t i o n}

sirf ek ranking approximation hai.

Connections

Ionic bonding — lattice energy (Fajan's ideal ionic model se deviations explain karta hai)
Covalent bonding — electron sharing (polarisation trend ki destination)
Coulomb's law and electric fields (rules ka physical basis)
Electronegativity and bond polarity (partial covalent/ionic character tak complementary route)
Effective nuclear charge and shielding (Rule 4 explain karta hai, d-electron poor shielding)
Charge-transfer transitions and colour (kyun AgI colour pure Fajan's effect nahi hai)
Solubility and lattice/hydration energy (kyun covalent character solvent behaviour shift karta hai)