Langmuir Isotherm Calculator
Calculate the fractional surface coverage and amount adsorbed using the Langmuir adsorption isotherm model. Used in surface chemistry and environmental engineering.
Maximum adsorption capacity (mg/g or mmol/g)
Affinity constant related to adsorption energy (L/mg)
Concentration at equilibrium (mg/L or mol/L)
What is the Langmuir isotherm?
The Langmuir isotherm describes monolayer adsorption onto a homogeneous surface with a finite number of identical adsorption sites. It assumes that each site can hold only one adsorbate molecule, there is no interaction between adsorbed molecules, and all sites have equal energy. The equation: q = (Qm × b × Ce) / (1 + b × Ce), where q is amount adsorbed, Qm is monolayer capacity, b is Langmuir constant, and Ce is equilibrium concentration.
What does the Langmuir constant (b) represent?
The Langmuir constant (b) is related to the enthalpy of adsorption - it represents the affinity between the adsorbent and adsorbate. A larger b value indicates higher adsorption affinity, meaning the adsorbate is more strongly attracted to the surface. The constant b can be determined experimentally from the slope of a Langmuir plot of 1/q versus 1/Ce. Typical values range from 0.1 to 10 L/mg for many adsorption systems.
How do you determine if Langmuir isotherm fits the data?
Linearize the Langmuir equation: Ce/q = (1/Qm × b) + (Ce/Qm). Plot Ce/q versus Ce - a straight line indicates Langmuir adsorption. The slope gives 1/Qm and the intercept gives 1/(Qm × b). The separation factor RL = 1/(1 + b × C₀) also indicates adsorption favorability: 0 < RL < 1 = favorable, RL = 1 = linear, RL > 1 = unfavorable. The dimensionless equilibrium parameter R² close to 1 confirms good fit.
What is surface coverage (θ)?
Surface coverage (θ) is the fraction of available adsorption sites that are occupied at a given equilibrium concentration. It ranges from 0 (no adsorption) to 1 (complete monolayer coverage). At θ = 0.5, half the surface is covered. The Langmuir isotherm predicts that coverage increases with concentration but asymptotically approaches 1 as concentration becomes very high, reaching monolayer saturation.
What are the limitations of the Langmuir isotherm?
The Langmuir model assumes: (1) homogeneous surface with identical adsorption sites, (2) monolayer adsorption only, (3) no interactions between adsorbed molecules, (4) all adsorption occurs at the same energy. Real systems often violate these assumptions - heterogeneous surfaces, multilayer adsorption, and lateral interactions all reduce model accuracy. For complex systems, Freundlich or BET isotherms may be more appropriate.