Langmuir Isotherm Calculator — Adsorption Equilibrium
Enter the Langmuir constant (KL), equilibrium concentration (C), and maximum adsorption capacity (qmax) to compute adsorption at equilibrium, fractional surface coverage, and the complete isotherm curve.
Amount of adsorbate adsorbed per unit mass of adsorbent at equilibrium
- 1
Denominator (1 + KL × C)
1 + 0.5 × 10 = 6 - 2
Numerator (qmax × KL × C)
50 × 0.5 × 10 = 250 - 3
Adsorption capacity q
250 ÷ 6 = 41.6667q = qmax · KL · C / (1 + KL · C) — the Langmuir isotherm equation.
How does this calculator work?
Langmuir isotherm: q = qmax·KL·C / (1 + KL·C). Enter the Langmuir constant KL, equilibrium concentration C, and maximum capacity qmax to get the adsorbed amount q, fractional surface coverage θ, and dimensionless separation factor RL — key parameters for adsorption system design in water treatment, catalysis, and materials science.
Formula
How this is calculated
The Langmuir isotherm describes adsorption of molecules from a solution onto a solid surface under the assumptions that (1) adsorption occurs in a monolayer — only one molecule can adsorb at each site; (2) all surface sites are energetically equivalent and independent; and (3) adsorbed molecules do not interact with each other. The resulting equation q = qmax·KL·C / (1 + KL·C) gives the mass of adsorbate per unit mass of adsorbent at equilibrium concentration C, where qmax is the theoretical maximum loading and KL is the Langmuir adsorption constant.
The fractional surface coverage θ = q / qmax tells you what fraction of the maximum capacity is occupied. When KL·C ≫ 1 the surface is nearly full (θ → 1); when KL·C ≪ 1 adsorption is in the linear (Henry) region (θ ≈ KL·C). The concentration at which q = qmax/2 is simply 1/KL — the half-saturation point. The dimensionless separation factor RL = 1/(1 + KL·C₀) indicates isotherm favorability: RL < 1 is favorable, RL = 0 is irreversible, RL > 1 is unfavorable.
The Langmuir model is widely used in water treatment (activated carbon, ion exchange), catalysis, pharmacology (receptor binding), and materials science. It fails when multilayer adsorption occurs (use the BET model instead) or when surface sites are heterogeneous (Freundlich isotherm may be more accurate). KL and qmax are typically determined experimentally by linearising the equation and performing linear regression.
Frequently asked questions
KL (L/mg or L/mol) is the affinity constant — it measures how strongly the adsorbate binds to the adsorbent surface. A high KL means a small concentration is enough to achieve significant loading; a low KL means you need high concentrations to saturate the surface.
RL = 1 / (1 + KL·C₀) where C₀ is the initial concentration. RL indicates whether adsorption is favorable: 0 < RL < 1 means favorable (the preferred case), RL = 1 means linear (Henry-type), RL > 1 means unfavorable, and RL = 0 means irreversible adsorption.
Run batch adsorption experiments at different initial concentrations, measure the equilibrium concentration C and the adsorbed amount q. Then linearise the Langmuir equation as C/q = C/qmax + 1/(qmax·KL) and plot C/q vs C — the slope gives 1/qmax and the intercept gives 1/(qmax·KL).
Also known as
TG we-Calculate Editorial Team. (2026). Langmuir Isotherm Calculator — Adsorption Equilibrium [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/langmuir-isotherm-calculator
TG we-Calculate Editorial Team. "Langmuir Isotherm Calculator — Adsorption Equilibrium." TG we-Calculate. 2026. https://we-calculate.com/calculator/langmuir-isotherm-calculator.
TG we-Calculate Editorial Team, "Langmuir Isotherm Calculator — Adsorption Equilibrium," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/langmuir-isotherm-calculator
@misc{wecalculate_langmuir_isotherm_calculator, title = {Langmuir Isotherm Calculator — Adsorption Equilibrium}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/langmuir-isotherm-calculator}}, year = {2026}, note = {TG we-Calculate} }
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