The Langmuir Isotherm Calculator lets you solve for any unknown in the Langmuir adsorption model — enter your known values across maximum adsorption capacity, Langmuir constant, equilibrium concentration, and adsorbed amount, then get your calculated value alongside surface coverage (θ) and the linear form (Ce/q) for easy plotting.
Calculated Value
--
Surface Coverage (θ)
--
Surface Coverage
--
Linear Form (Ce/q)
--
The Langmuir isotherm is a model that describes monolayer adsorption on a uniform surface with finite adsorption sites. It assumes that adsorption occurs at specific homogeneous sites and that there is no interaction between adsorbed molecules.
Use the equation q = (qmax × b × Ce) / (1 + b × Ce), where q is the adsorbed amount, qmax is the maximum adsorption capacity, b is the Langmuir constant, and Ce is the equilibrium concentration.
Surface coverage fraction (θ) represents the proportion of adsorption sites occupied by adsorbate molecules. It ranges from 0 (no coverage) to 1 (complete monolayer coverage).
The Langmuir constant (b) is related to the affinity of the adsorbent for the adsorbate. Higher b values indicate stronger adsorption affinity and steeper isotherm curves at low concentrations.
The linear form (Ce/q vs Ce) helps determine Langmuir parameters from experimental data. The slope equals 1/qmax and the intercept equals 1/(qmax × b).
Key assumptions include: uniform surface with identical adsorption sites, monolayer coverage only, no interaction between adsorbed molecules, and equilibrium between adsorption and desorption.
Use mass balance when you know the initial concentration, solution volume, and adsorbent mass. This helps calculate the adsorbed amount from the difference between initial and equilibrium concentrations.
Keep units consistent throughout. Common units are mg/L for concentrations, mg/g for adsorbed amounts, and L/mg for the Langmuir constant. The calculator handles standard units automatically.