van 't Hoff FactorJEE Main

Concept

Colligative properties count particles, not moles weighed out. An electrolyte splitting into n ions multiplies the effect by the van 't Hoff factor $i = 1 + \alpha(n-1)$. Measured i below the ideal n reveals partial dissociation; i < 1 reveals association (like benzoic acid dimerising in benzene).

Key formula

Derivation

Start with 1 mol; α mol dissociate into αn ions, leaving (1−α). Total particles = $1 - \alpha + \alpha n = 1 + \alpha(n-1)$.

Every colligative law simply gains the factor: $\Delta T_b = iK_bm$, $\Delta T_f = iK_fm$, $\pi = iCRT$. Association: replace n by 1/n_assoc, giving i < 1.

Scenarios to explore

• van 't Hoff Factor — i = 1 + α(n−1) — electrolytes amplify colligative effects.

Real-world applications

• Road salting (CaCl₂ beats NaCl per mole: i = 3 vs 2).
• Abnormal molar masses diagnose dissociation/association.
• IV fluids are dosed by osmolarity = i × molarity.

JEE exam tips

• Observed molar mass = calculated/i — 'abnormal' masses decode instantly.
• K₃[Fe(CN)₆] → 4 ions: i_max = 4; complexes count the whole complex ion as ONE particle.
• Equal ΔTf comparisons: rank by i×m, nothing else.

Common mistakes

• Using n instead of measured i for weak electrolytes.
• α from i: α = (i−1)/(n−1), not i/n.
• Forgetting association gives i < 1 (dimers halve the count).

Exam traps to avoid

• i for acetic acid in WATER is slightly >1 (weak dissociation) but in BENZENE it's ~0.5 (dimerisation).
• 100% dissociation is an idealisation — strong electrolytes at high concentration show i below n (ion pairing).