Adsorption Isotherm Calculator
Compute equilibrium adsorption capacity using Langmuir or Freundlich isotherm models. Used by environmental and chemical engineers to design activated carbon beds, ion-exchange columns, and water treatment systems.
About this calculator
Adsorption isotherms describe how much solute a solid adsorbent retains per unit mass at equilibrium, at constant temperature. The Langmuir model assumes monolayer adsorption on a finite number of identical sites: q = (q_max × K_L × C) / (1 + K_L × C), where q_max is maximum adsorption capacity (mg/g), K_L is the Langmuir constant (L/mg), and C is equilibrium concentration (mg/L). It predicts saturation behaviour at high concentrations. The Freundlich model is empirical and suits heterogeneous surfaces: q = K_F × C^(1/n), where K_F is the Freundlich capacity constant and 1/n is the intensity exponent (this calculator uses 1/n = 1/3). At low concentrations both models converge toward a linear (Henry's Law) relationship. Choosing the right model requires fitting experimental data; R² values from linear regression on Langmuir (C/q vs. C) or Freundlich (log q vs. log C) plots determine the better fit.
How to use
Langmuir example: activated carbon with q_max = 200 mg/g and K_L = 0.05 L/mg treating water with an equilibrium concentration C = 20 mg/L. q = (200 × 0.05 × 20) / (1 + 0.05 × 20) = (200) / (1 + 1) = 200 / 2 = 100 mg/g. The carbon adsorbs 100 mg of contaminant per gram at this equilibrium. Freundlich example: K_F = 50, C = 27 mg/L, 1/n = 1/3. q = 50 × 27^(1/3) = 50 × 3 = 150 mg/g. Compare results from both models against experimental data to confirm which isotherm best represents your adsorbent–adsorbate system before scaling up to a full column design.
Frequently asked questions
What is the difference between Langmuir and Freundlich adsorption isotherms and which one should I use?
The Langmuir isotherm assumes a homogeneous surface with a fixed number of equivalent adsorption sites, leading to a maximum (saturation) capacity — it is ideal for chemisorption and systems like activated alumina removing fluoride. The Freundlich isotherm is empirical, assumes surface heterogeneity and multi-layer adsorption, and has no theoretical saturation limit — it often fits physisorption on activated carbon more accurately across wide concentration ranges. To decide, linearise both models using your experimental batch equilibrium data and compare R² values: Langmuir linearisation plots C/q versus C; Freundlich plots log(q) versus log(C). Use the model with the higher R² and physically meaningful constants for your design.
How do I determine Langmuir and Freundlich constants from experimental data?
Run a series of batch equilibrium experiments by contacting a fixed mass of adsorbent with solutions at different initial concentrations, then measuring the final (equilibrium) concentration C and calculating q = (C₀ − C) × V / m, where V is solution volume and m is adsorbent mass. For the Langmuir model, plot C/q versus C — the slope gives 1/q_max and the intercept gives 1/(K_L × q_max). For the Freundlich model, plot log(q) versus log(C) — the slope is 1/n and the intercept is log(K_F). At least 6–8 data points spanning the expected operating concentration range are recommended for reliable parameter estimation.
Why does equilibrium concentration matter when designing an adsorption column or bed?
The equilibrium concentration defines the theoretical maximum loading of the adsorbent at a given operating condition — it directly sets the amount of adsorbent required and therefore column size and cost. If the inlet concentration changes (e.g., due to seasonal variation in a water source), the equilibrium loading shifts along the isotherm curve, potentially reducing bed life and breakthrough time. Isotherm data collected at a single concentration point cannot predict column behaviour across varying feed conditions; a full isotherm curve is needed. Engineers use isotherm data together with mass transfer models (e.g., LDF or pore diffusion) and the Empty Bed Contact Time (EBCT) concept to translate batch equilibrium results into practical column designs.