Langmuir Isotherm Calculator
Predict adsorption capacity for a solute on a homogeneous surface using the classical Langmuir relation.
Adsorbed amount q
0.4865 mg/g
Surface coverage theta
0.3243
How to Use This Calculator
Measure isotherm parameters
Obtain Qmax and K from experimental fitting or literature for the adsorbent/adsorbate pair.
Enter fluid concentration
Use equilibrium solute concentration in the same units assumed when fitting K.
Calculate surface uptake
The Langmuir equation estimates amount adsorbed per unit mass and the fractional surface coverage.
Apply to process design
Use predicted uptake to size adsorbers, compare materials, or evaluate regeneration cycles.
Formula
q = (Qmax K C) / (1 + K C)
theta = (K C) / (1 + K C)
Qmax is saturation capacity, K affinity constant, C equilibrium concentration or pressure, theta dimensionless coverage.
Example
With Qmax = 1.5 mg/g, K = 0.8 L/mg, C = 0.6 mg/L: q = 0.72 mg/g, theta = 0.32.
Full Description
The Langmuir model assumes monolayer adsorption on uniform independent sites without interactions between adsorbed molecules.
Despite simplifications, it remains a standard tool for characterizing adsorbents and comparing affinities across different materials.
Frequently Asked Questions
Can the formula use pressure instead of concentration?
Yes. Replace concentration with partial pressure if K is fitted with pressure units.
What if the isotherm deviates from Langmuir?
Consider Freundlich, BET, or dual-site models for heterogeneous surfaces.
Why is theta limited to 0-1?
The Langmuir assumption enforces monolayer coverage, so theta represents the fraction of occupied sites.
Can K be negative?
No. Affinity constants should be positive. Negative values indicate fitting or unit errors.
Does temperature affect K?
Yes. K is temperature dependent. Use values measured under the same conditions as your system.