Mastering Fajans Rules and Polarizing Power for JEE/NEET

Fajans' rules predict how much covalent character an ionic compound has. A small, highly charged cation drags the anion's electron cloud toward itself, so the bond stops being purely ionic.

They matter because they explain melting point crashes (NaCl melts at 801 C but AlCl3 sublimes near 180 C), solubility puzzles (AgF dissolves but AgI does not), and why some chlorides hydrolyse in water.

Key Concepts

• Polarizing power of the cation: increases with charge and decreases with size. Order: Na+ < Mg2+ < Al3+; also Li+ > Na+ > K+ down the group.
• Polarizability of the anion: increases with size, since large electron clouds distort easily. Order: F- < Cl- < Br- < I-.
• Fajans' rules: covalent character is maximum when the cation is small and highly charged and the anion is large. It is minimum for large, low-charge cations with small anions.
• Pseudo noble gas cations: ions like Ag+, with an 18-electron shell, polarize more strongly than noble-gas-core ions of similar size (Ag+ > Na+), so silver halides are more covalent than sodium halides.
• Consequences: more covalent character means lower melting point, lower solubility in water, higher solubility in organic solvents, and easier hydrolysis.

Formulas

• Polarizing power scale: proportional to Z / r squared, where Z is the cation charge and r its radius. Doubling the charge quadruples the polarizing power at the same size.
• Melting point evidence: NaCl (801 C) > MgCl2 (714 C) > AlCl3 (sublimes near 180 C). Rising cation charge from +1 to +3 converts an ionic lattice into substantially covalent molecules.
• Solubility evidence: AgF is very soluble in water while AgCl, AgBr, and AgI are nearly insoluble: the growing, more polarizable anion makes each silver halide more covalent.
• Limit: the rules are qualitative; they rank compounds reliably but do not give numerical percent-covalent values.

Worked Example

Question: Arrange NaCl, MgCl2, and AlCl3 in order of increasing covalent character and justify it.

Step 1: The anion (Cl-) is the same, so only the cation's polarizing power matters.

Step 2: Charges rise Na+ (+1) < Mg2+ (+2) < Al3+ (+3), while radii shrink: 102 pm > 72 pm > 53 pm. Polarizing power scales with Z/r squared, so Al3+ polarizes far more strongly than Mg2+, which beats Na+.

Step 3: Order of covalent character: NaCl < MgCl2 < AlCl3.

Step 4: Check against reality: NaCl is a high-melting ionic solid (801 C), MgCl2 melts lower (714 C), and AlCl3 exists as covalent Al2Cl6 dimers that sublime near 180 C. The ranking holds.

Common Misconceptions

• "Ionic and covalent are two separate boxes." Bonding is a spectrum; Fajans' rules place each compound on it. Even NaCl has slight covalent character.
• "Larger cations are more polarizing." The reverse: smaller cations concentrate their charge. Li+ polarizes more than Cs+.
• "Only the cation matters." The anion matters equally: fluorides are the most ionic halides and iodides the most covalent for any fixed cation.

Real-World Applications

• Predicting solubility for qualitative analysis: AgI and PbI2 precipitate because of covalent character, the basis of classic salt-analysis tests.
• Explaining why AlCl3 and FeCl3 are used as covalent Lewis-acid catalysts while NaCl is an inert ionic solid.
• Designing battery electrolytes: lithium salts are chosen with large, poorly polarizing anions to stay ionic and mobile.
• Geochemistry: the covalent character of heavy-metal sulphides explains ore formation and metal extraction chemistry.

Fajans' rules say covalent character grows with a small, highly charged cation and a large, polarizable anion. The NaCl-MgCl2-AlCl3 melting point collapse and the AgF-to-AgI solubility drop are the textbook proofs. Apply the Z/r-squared ranking and ionic-vs-covalent questions answer themselves.