11.2 Adsorption, Heterogeneous Catalysis and Colloids

11.2.1 Physisorption and chemisorption ★★

• Temperature: physisorption needs no activation and is exothermic, so heating only drives gas off. Chemisorption first needs its activation energy (rate ∝ e^−E_a/RT), so uptake rises with T until equilibrium is reached; beyond that, being exothermic, it falls Geo 2024 Q5(b) 5m.SN
• Entropy: a gas molecule held on a surface loses translational freedom, so ΔS_ads < 0. Since adsorption is spontaneous (ΔG < 0), ΔH = ΔG + TΔS must be negative: adsorption is exothermic. The statement “adsorption increases entropy” is wrong for the adsorbate; it can hold only for the whole system in special cases (water released from a surface when a solute adsorbs from solution, dissociative adsorption) Geo 2023 Q9(c) 2m.SN
• Finely divided adsorbents: adsorption is a surface effect, x/m ∝ specific area. A 1 cm cube (6 cm²) cut into 1 µm cubes gives 10¹² cubes, 6 m²: 10⁴ times the area, plus more edges, corners and defects (active sites). Activated charcoal 500–1500 m² g⁻¹ Geo 2021 Q1(g) 5m.SN
• Water on glass: glass below the dew point; its Si–OH groups hydrogen-bond water, so a flat nucleus forms at very small supersaturation (heterogeneous nucleation; a free tiny droplet would need much more, Kelvin equation) and spreads into a film; greasy glass gives droplets (fogging) CSE 2024 Q5(b)(i) 5m.

11.2.2 Langmuir adsorption isotherm ★★★ asked every year

Assumptions Geo 2024 Q7(a) 5m:SN

1. A fixed number of equivalent sites; each holds one molecule; adsorption stops at a monolayer.
2. No interaction between adsorbed molecules, so ΔH_ads does not depend on θ.
3. Dynamic equilibrium: rate of adsorption = rate of desorption.

Derivation. Let θ = fraction of sites covered.

• Low p (Kp ≪ 1): θ = Kp, amount ∝ p¹, “first order”. High p (Kp ≫ 1): θ → 1, amount ∝ p⁰, “zero order”: the monolayer is full CSE 2021 Q6(c) 20m CSE 2025 Q6(c) 20m IFoS 2025 Q5(b) 8m IFoS 2022 Q5(b) 8m.SN
• Where it fails: at high p real isotherms keep rising (multilayers, type II); real surfaces have sites of different energy and ΔH_ads falls with θ; adsorbed molecules do interact. The Langmuir isotherm holds at low p and for chemisorption best.SN
• Dissociative adsorption (H₂ → 2H on a metal): θ = (Kp)^½/(1 + (Kp)^½).

11.2.3 Freundlich isotherm ★★

• Empirical; a log–log plot is a straight line of slope 1/n, intercept log k. Works at intermediate pressures and for adsorption from solution (concentration c for p); fails at high p (no saturation) IFoS 2023 Q6(c) 10m.SN
• From Langmuir: at intermediate p, θ = Kp/(1 + Kp) varies between p¹ and p⁰, so it behaves as p^1/n with 0 < 1/n < 1. Theory: Freundlich is exact for a surface whose sites have an exponential spread of adsorption energies IFoS 2021 Q7(a) 15m.SN
• Five features of a catalyst: gives a new path of lower E_a; unchanged at the end; small amounts suffice; often specific; does not change ΔG° or K (speeds forward and back equally) IFoS 2023 Q6(c).

11.2.4 BET isotherm and the five isotherm types ★★★

• Terms: p = equilibrium pressure; p° = saturation vapour pressure of the adsorbate; V = volume adsorbed (STP); V_m = volume for one complete monolayer; c ≈ e^{(ΔH₁ − ΔH_L)/RT}, set by the heat of adsorption of the first layer over the heat of liquefaction Geo 2024 Q1(h) 5m Geo 2022 Q14(a) 10m.SN
• Model: Langmuir's ideas applied layer by layer; the first layer is held by the surface, the second and higher layers like a liquid; when only one layer can form it reduces to Langmuir. Large c gives type II, small c (weak first layer) type III; pores add capillary condensation (IV, V) IFoS 2022 Q7(a) 10m.SN
• Surface area by BET: measure N₂ uptake at 77 K for p/p° ≈ 0.05–0.30; plot p/[V(p° − p)] against p/p°: slope s, intercept i, so V_m = 1/(s + i), c = 1 + s/i. Then area per gram IFoS 2024 Q4(c) 10m:SN