What is the Langmuir isotherm equation?

The Langmuir equation is q = (q_max * K_L * C) / (1 + K_L * C), where q is the amount adsorbed per gram of adsorbent, q_max is the maximum monolayer adsorption capacity, K_L is the Langmuir constant (affinity), and C is the equilibrium concentration.

What is the Langmuir constant K_L?

K_L (L/mg or L/mol) is the Langmuir adsorption equilibrium constant. A higher K_L indicates stronger affinity between the adsorbate and the adsorbent surface. It equals k_ads / k_des (rate of adsorption over rate of desorption).

What does surface coverage (theta) mean?

Surface coverage (theta) ranges from 0 to 1 and represents the fraction of available adsorption sites occupied. Theta = 0 means no adsorption; theta = 1 means full monolayer saturation.

What are the assumptions of the Langmuir model?

The Langmuir model assumes: (1) adsorption occurs on a fixed number of identical sites, (2) each site can hold only one adsorbate molecule (monolayer), (3) no interaction between adsorbed molecules, and (4) adsorption is reversible and reaches equilibrium.

How do I find q_max and K_L from experimental data?

Linearize the Langmuir equation as C/q = C/q_max + 1/(q_max * K_L). Plot C/q vs C; the slope is 1/q_max and the y-intercept is 1/(q_max * K_L). Alternatively, use nonlinear regression on the original equation.

What units should I use?

Units must be consistent. If C is in mg/L, K_L should be in L/mg, and q_max in mg/g; then q will be in mg/g. You can also use mol/L and L/mol. This calculator accepts any consistent unit system.

Langmuir Isotherm Calculator

Enter your adsorbate concentration and Langmuir constants to calculate surface coverage and amount adsorbed.

Langmuir Parameters

Maximum Adsorption Capacity, q_max

mg/g

Langmuir Constant, K_L

L/mg

Equilibrium Concentration, C_e

mg/L

Batch Mode

Enter one concentration per line to generate an isotherm table (uses q_max and K_L above).

Results

Enter parameters and click Calculate.

Isotherm Table

C_e (mg/L)	q (mg/g)	θ	C/q

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Summary

The Langmuir isotherm calculator computes the amount of adsorbate bound to a surface at a given equilibrium concentration. It models monolayer adsorption assuming uniform binding sites with no interaction between adsorbed molecules. Enter the equilibrium concentration, maximum adsorption capacity (q_max), and Langmuir constant (K_L) to instantly obtain surface coverage and adsorbed quantity.

How it works

Enter the equilibrium concentration of the adsorbate in solution.
Input the maximum monolayer adsorption capacity (q_max) of the adsorbent.
Input the Langmuir constant (K_L), which relates to adsorption affinity.
The calculator applies the Langmuir equation: q = (q_max * K_L * C) / (1 + K_L * C).
Results show the amount adsorbed (q) and the fractional surface coverage (theta).
Use the batch mode to enter multiple concentrations and generate an isotherm table.

Use cases

Analyzing heavy metal adsorption onto activated carbon or clay minerals.
Studying drug binding to protein surfaces in biochemical research.
Evaluating catalyst surface saturation in heterogeneous catalysis.
Fitting experimental adsorption data to the Langmuir model.
Determining maximum adsorption capacity for water treatment design.
Comparing adsorption behavior of different adsorbents.
Teaching physical chemistry and surface science concepts.
Verifying Langmuir linearity via 1/q vs 1/C plots.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu