Langmuir Isotherm Calculator

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Pick the unknown variable. All other fields become inputs.
Monolayer saturation capacity of the adsorbent. Must be greater than 0.
mg/g
Langmuir adsorption equilibrium constant. Related to adsorption energy.
L/mg
Concentration of adsorbate remaining in solution at equilibrium.
mg/L
Starting adsorbate concentration before any adsorption occurs. Used to compute the separation factor RL and optionally verify a mass balance.
mg/L
Toggle on to derive q from the mass balance: q = (C0 - Ce) * V / m instead of the isotherm equation.
Adsorbed amount (q)Favorable adsorption
7.5mg/g

Amount of adsorbate per gram of adsorbent at equilibrium

Equilibrium concentration (Ce)20mg/L
Maximum capacity (qmax)10mg/g
Langmuir constant (KL)0.15L/mg
Saturation fraction (q / qmax)75%
Separation factor (RL)0.1176
Linearized form (Ce / q)2.6667g/L
75% fraction
Low loading (<20%)<20%Moderate loading (20-50%)20%-50%High loading (50-80%)50%-80%Near saturation (80-95%)80%-95%Saturated (>95%)95%+

q = 7.5000 mg/g with 75.0% surface saturation.

  • The adsorbent surface is 75.0% saturated at this equilibrium concentration.
  • The separation factor RL = 0.1176 is between 0 and 1, confirming favorable adsorption under these initial conditions.
  • KL = 0.150000 L/mg indicates moderate binding affinity between adsorbate and adsorbent.

Next stepTo fit KL and qmax from experimental data, plot Ce/q against Ce: the slope gives 1/qmax and the intercept gives 1/(qmax*KL).

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