Fajan's Rules — Covalent Bonding in Ionic Compounds

Fajan's rules state that the more covalent character (less ionic character) a bond has, the more the cation polarises the anion's electron cloud.

Covalent character is GREATER (bond is more covalent) when:

Rule 1: High charge on the cation • Higher charge → more polarising power • Al³⁺ is more polarising than Mg²⁺, which is more polarising than Na⁺ • Example: AlCl₃ (more covalent) vs NaCl (more ionic)

Rule 2: Small size of the cation • Smaller cation → higher charge density (charge/size ratio) → more polarising power • Li⁺ (small) more polarising than K⁺ (large), both +1 charge • Example: LiCl more covalent than KCl

Rule 3: Large size of the anion • Larger anion → more polarisable (outer electrons farther from nucleus, less tightly held) • I⁻ (large) more polarisable than F⁻ (small) • Covalent character order: AgI > AgBr > AgCl > AgF

Rule 4: Pseudo-noble gas / 18-electron configuration of cation • Cations with 18 electrons in outermost shell (d¹⁰ configuration) are more polarising than cations with noble gas (8-electron) configuration of similar size/charge • Example: Cu⁺ (18e⁻ config) is more polarising than Na⁺ (8e⁻ config) • AgCl is more covalent than NaCl (both MX type, but Ag⁺ has 18e⁻ vs Na⁺ has 8e⁻)

Conversely, ionic character is GREATER when: • Low charge cation (Na⁺ over Al³⁺) • Large cation (K⁺ over Li⁺) • Small anion (F⁻ over I⁻) • Noble gas (8e⁻) configuration of cation

Two key concepts in Fajan's rules:

1. Polarising Power (of the cation): • Ability of the cation to distort the electron cloud of the anion • Increases with: higher charge, smaller size (↑ charge density = charge/radius) • Charge density ∝ charge / radius

Order of polarising power: • Al³⁺ > Mg²⁺ > Na⁺ (increasing charge) • Li⁺ > Na⁺ > K⁺ > Rb⁺ (decreasing size, same charge)

2. Polarisability (of the anion): • Ease with which the anion's electron cloud is distorted • Increases with: larger size (electrons farther from nucleus, more loosely held) • Higher charge on anion also increases polarisability

Order of polarisability of halide ions: • I⁻ > Br⁻ > Cl⁻ > F⁻ (increasing size → decreasing polarisability; largest = most polarisable)

Effect of polarisation: • When cation polarises anion significantly, electron cloud of anion shifts toward cation • The bond character shifts from ionic to covalent • Highly polarised ionic bond ≈ covalent bond

Examples: • NaF: mostly ionic (Na⁺ low polarising, F⁻ low polarisability) • AlI₃: significant covalent character (Al³⁺ high polarising, I⁻ high polarisability) • AgI: significant covalent character (Ag⁺ has 18e⁻ config; I⁻ is large)

Q: According to Fajan's rules, covalent bonding is favoured by: Answer: (a) A small cation with high charge (high polarising power) and (b) A large anion (high polarisability)

Q: Arrange AlCl₃, MgCl₂, NaCl in increasing covalent character. Answer: NaCl < MgCl₂ < AlCl₃ (Al³⁺ has highest charge density → most polarising → most covalent)

Q: Which has more covalent character — LiCl or CsCl? Answer: LiCl. Li⁺ is smaller than Cs⁺ with the same +1 charge → Li⁺ has higher polarising power.

Q: Which has more covalent character — AgCl or NaCl? Answer: AgCl. Ag⁺ has 18-electron (pseudo-noble gas) configuration vs Na⁺'s 8-electron noble gas configuration. 18e⁻ configuration is more polarising.

Q: Why does AgI have significant covalent character? Answer: Ag⁺ has 18e⁻ configuration (more polarising than Na⁺) AND I⁻ is the largest and most polarisable halide ion. Both factors combine to give AgI significant covalent character.

Q: Among HF, HCl, HBr, HI, which is most covalent? Answer: HI — I⁻ (or the H–I bond) has the largest anion/atom. (Note: for hydrogen halides, it's about bond polarity — HF is most polar/ionic character; HI is least polar/most covalent.)