Langmuir Isotherm Calculator

The Langmuir Isotherm Calculator models how molecules adsorb onto a surface at equilibrium — a core concept in water treatment, catalysis, and materials science. Select what you want to calculate: adsorbed amount (q), equilibrium concentration (Ce), surface coverage fraction (θ), or Langmuir constant (b). Enter your maximum adsorption capacity, Langmuir constant, and system conditions to get the calculated value along with surface coverage (θ) and the linear form (Ce/q) for isotherm plotting.

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Results

Calculated Value

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Surface Coverage (θ)

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Surface Coverage

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Linear Form (Ce/q)

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Frequently Asked Questions

What is the Langmuir adsorption isotherm?

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.

How do I calculate the Langmuir isotherm?

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.

What does the surface coverage fraction (θ) represent?

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).

What is the Langmuir constant (b)?

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.

How is the linear form of Langmuir isotherm useful?

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).

What are the assumptions of the Langmuir model?

Key assumptions include: uniform surface with identical adsorption sites, monolayer coverage only, no interaction between adsorbed molecules, and equilibrium between adsorption and desorption.

When should I use mass balance calculations?

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.

What units should I use for the calculations?

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.