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Adsorption Isotherms | Langmuir & Freundlich | Complete Guide

Adsorption Isotherms

Langmuir, Freundlich, and the models that describe how molecules adhere to surfaces

1. What are Adsorption Isotherms?

An adsorption isotherm is a curve that relates the amount of adsorbate (gas or solute) adsorbed on a solid surface to its concentration (or pressure) at constant temperature. It describes how the adsorbed quantity varies with equilibrium concentration. Two of the most widely used models are the Langmuir isotherm (monolayer adsorption on homogeneous surfaces) and the Freundlich isotherm (empirical model for heterogeneous surfaces).

q_e = amount adsorbed per unit mass of adsorbent at equilibrium (mg/g)
C_e = equilibrium concentration of adsorbate in solution (mg/L or M)

2. Interactive Isotherm Explorer

Adjust the parameters for Langmuir and Freundlich models to see how the adsorption curve changes. The graph shows adsorbed amount (q_e) vs. equilibrium concentration (C_e).

Langmuir q_m (mg/g): 100
Langmuir K_L (L/mg): 0.50
Freundlich K_F (mg/g): 15
Freundlich 1/n: 0.50
📊 Langmuir: q_m = 100 mg/g, K_L = 0.50 L/mg 📈 Freundlich: K_F = 15, 1/n = 0.50

Langmuir assumes monolayer coverage on a uniform surface; Freundlich allows for heterogeneous surfaces with exponential distribution of site energies.

3. Langmuir Isotherm

The Langmuir isotherm assumes that adsorption occurs at specific homogeneous sites within the adsorbent, and once a molecule occupies a site, no further adsorption can take place there (monolayer coverage). It also assumes that all sites are equivalent and there is no interaction between adsorbed molecules.

q_e = (q_m * K_L * C_e) / (1 + K_L * C_e)

Linear form: C_e / q_e = 1/(q_m K_L) + C_e / q_m

Parameters:
– q_e = amount adsorbed at equilibrium (mg/g)
– C_e = equilibrium concentration (mg/L)
– q_m = maximum monolayer adsorption capacity (mg/g)
– K_L = Langmuir equilibrium constant (L/mg) related to affinity.

Example: Adsorption of methylene blue dye onto activated carbon. If q_m = 100 mg/g and K_L = 0.5 L/mg, at C_e = 50 mg/L, q_e = (100×0.5×50)/(1+0.5×50) = (2500)/(26) ≈ 96.15 mg/g.

Separation factor (R_L): R_L = 1/(1 + K_L * C_0), where C_0 is initial concentration. R_L > 1: unfavorable; 0 < R_L < 1: favorable; R_L = 0: irreversible.

4. Freundlich Isotherm

The Freundlich isotherm is an empirical model applicable to multilayer adsorption on heterogeneous surfaces. It assumes an exponential distribution of active sites and that the adsorption energy decreases exponentially with surface coverage.

q_e = K_F * C_e^(1/n)

Linear form: log q_e = log K_F + (1/n) log C_e

Parameters:
– K_F = Freundlich capacity constant (mg/g) (L/mg)^(1/n)
– 1/n = heterogeneity factor; n > 1 indicates favorable adsorption.

Example: Adsorption of heavy metal ions (e.g., Pb²⁺) onto biosorbent. If K_F = 15 (mg/g) and 1/n = 0.5, then at C_e = 50 mg/L, q_e = 15 × (50)^0.5 = 15 × 7.07 = 106.05 mg/g. The model works well over limited concentration ranges.

Note: Unlike Langmuir, Freundlich does not predict a saturation plateau; it continues to increase with concentration, which may not reflect reality at very high concentrations.

5. Langmuir vs. Freundlich: Quick Comparison

FeatureLangmuirFreundlich
AssumptionHomogeneous surface, monolayer, no interactionHeterogeneous surface, multilayer, exponential site energy distribution
Equation formq_e = (q_m K_L C_e)/(1 + K_L C_e)q_e = K_F C_e^(1/n)
Linear plotC_e/q_e vs. C_e → slope = 1/q_m, intercept = 1/(q_m K_L)log q_e vs. log C_e → slope = 1/n, intercept = log K_F
Maximum capacityq_m (finite)No theoretical limit
Favorability indicatorR_L = 1/(1+K_L C_0)1/n < 1 → favorable

6. Other Important Isotherms

BET (Brunauer–Emmett–Teller)
Used for multilayer adsorption. Extends Langmuir to multiple layers. Equation: 1/( (C_e/C_0) * (1 – C_e/C_0) ) = (C-1)/(C·q_m) * (C_e/C_0) + 1/(C·q_m). Commonly used for surface area determination (e.g., nitrogen adsorption).
Temkin Isotherm
Assumes that the heat of adsorption decreases linearly with coverage due to indirect adsorbate–adsorbate interactions. q_e = (RT/b_T) ln(A_T C_e), where A_T and b_T are constants.
Langmuir and Freundlich remain the most widely used models for liquid-phase adsorption due to their simplicity and applicability to a wide range of systems.

7. Applications of Adsorption Isotherms

  • Water treatment: Designing activated carbon filters for removal of dyes, heavy metals, and organic pollutants.
  • Gas purification: Using zeolites or MOFs to capture CO₂, methane, or volatile organic compounds.
  • Catalysis: Understanding how reactants adsorb onto catalyst surfaces to predict reaction rates.
  • Pharmaceuticals: Drug delivery systems where drugs are adsorbed onto carriers.
  • Environmental remediation: Soil remediation and adsorption of pesticides.

8. Video Lecture: Adsorption Isotherms (Urdu/Hindi)

Watch Complete Lecture in Urdu/Hindi for Comprehensive Understanding

Detailed step‑by‑step explanation of Langmuir and Freundlich isotherms, derivations, linear forms, and practical examples.

9. Summary

  • Langmuir isotherm: homogeneous monolayer adsorption; gives finite capacity q_m.
  • Freundlich isotherm: empirical model for heterogeneous surfaces; does not saturate.
  • Both models have linearised forms for parameter estimation from experimental data.
  • R_L (Langmuir) and 1/n (Freundlich) indicate whether adsorption is favourable.
  • BET isotherm extends to multilayer coverage; used for surface area measurement.
Choosing the right isotherm is essential for accurate process design and understanding adsorbent–adsorbate interactions.
Complete guide to adsorption isotherms – all content original, with interactive graphs, equations in plain text, and integrated video lecture.

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