Adsorption IsothermsJEE Main

Concept

Gases stick to solid surfaces (adsorption — a surface phenomenon, not absorption). The Freundlich isotherm fits the middle range empirically: $x/m = kP^{1/n}$ with $0 < 1/n \le 1$. At low P uptake is linear; at high P the surface saturates — behaviour Langmuir explains mechanistically with a monolayer model.

Key formula

Derivation

Freundlich is empirical: plot $\log(x/m)$ vs $\log P$ → straight line, slope $1/n$, intercept $\log k$.

Langmuir derives saturation from monolayer kinetics: adsorption rate ∝ P(1−θ), desorption ∝ θ, equilibrium coverage $\theta = bP/(1+bP)$ — linear at low P, flat at high P. Freundlich ≈ Langmuir on heterogeneous surfaces.

Scenarios to explore

• Adsorption Isotherms — Freundlich x/m = kP^(1/n) vs Langmuir's monolayer.

Real-world applications

• Activated-charcoal gas masks & water filters.
• Heterogeneous catalysis begins with reactant adsorption.
• Chromatography separations.

JEE exam tips

• Physisorption DEcreases with temperature; chemisorption first increases (activation) then decreases.
• Easily liquefiable gases (NH₃, CO₂) adsorb more — higher van der Waals forces.
• 1/n → 0 means x/m constant (saturation); 1/n = 1 means Henry-like linearity.

Common mistakes

• Confusing adsorption (surface) with absorption (bulk).
• Physisorption vs chemisorption mix-ups (weak van der Waals & reversible vs bond-forming).
• Forgetting adsorption is exothermic — ΔH < 0 always.

Exam traps to avoid

• Adsorption decreases entropy (ΔS < 0), so it MUST be exothermic to be spontaneous.
• Freundlich fails at high pressure — no saturation built in; Langmuir handles it.