Science & Lab Tools
Langmuir Isotherm Calculator
Calculate adsorption parameters using the Langmuir isotherm model
Enter values to calculate Langmuir isotherm parameters
The Langmuir Isotherm Calculator is based on Irving Langmuir's model for adsorption of molecules on a solid surface. The calculator implements the Langmuir equation to determine the extent of surface coverage and adsorption capacity at equilibrium conditions. The model assumes monolayer adsorption on a homogeneous surface with no interaction between adsorbed molecules.
Key Equations
Surface Coverage (θ) = (KL × Ce) / (1 + KL × Ce)
Adsorption Capacity (qe) = (Qm × KL × Ce) / (1 + KL × Ce)
Where:
- Ce is the equilibrium concentration of adsorbate in solution (mg/L)
- KL is the Langmuir constant related to the affinity of binding sites (L/mg)
- Qm is the maximum monolayer adsorption capacity (mg/g)
- θ is the fraction of surface coverage (dimensionless)
- qe is the amount of adsorbate adsorbed per unit mass of adsorbent (mg/g)
The calculator provides two main results: surface coverage (θ) and adsorption capacity (qe). The surface coverage indicates the fraction of available adsorption sites that are occupied, ranging from 0 to 1. The adsorption capacity represents the actual amount of adsorbate taken up per unit mass of adsorbent at the given equilibrium conditions.
Understanding the Graph
The graph shows the relationship between equilibrium concentration and surface coverage. The characteristic L-shaped curve demonstrates saturation behavior, where coverage increases rapidly at low concentrations and approaches a plateau at high concentrations, indicating surface saturation.
A surface coverage value close to 1 indicates near-complete monolayer coverage, while the adsorption capacity approaches the maximum capacity (Qm) as the surface becomes saturated. The shape of the isotherm can provide insights into the adsorption process and the strength of adsorbate-surface interactions.
1. What are the limitations of the Langmuir isotherm model?
The Langmuir model assumes monolayer adsorption on a homogeneous surface with no interaction between adsorbed molecules. It may not accurately describe systems with multilayer adsorption, heterogeneous surfaces, or significant adsorbate-adsorbate interactions.
2. How can I determine if my system follows Langmuir behavior?
Plot your experimental data as Ce/qe vs Ce. If the plot is linear, your system likely follows Langmuir behavior. The slope gives 1/Qm, and the intercept gives 1/(KL×Qm).
3. What does the Langmuir constant (KL) indicate?
The Langmuir constant (KL) represents the affinity between the adsorbate and adsorbent. A higher KL value indicates stronger binding and more favorable adsorption conditions.
4. Can the calculator be used for gas adsorption?
Yes, the calculator can be used for gas adsorption by using partial pressure instead of concentration. However, ensure to convert units appropriately and consider temperature effects on gas adsorption.
5. What is the scientific source for this calculator?
This calculator is based on Irving Langmuir's fundamental work published in "The Constitution and Fundamental Properties of Solids and Liquids" (1916) in the Journal of the American Chemical Society. The mathematical model and equations are derived from his theoretical treatment of adsorption processes, which has been extensively validated through decades of experimental research and is documented in standard physical chemistry textbooks such as Atkins' Physical Chemistry and Surface Science texts by Adamson and Gast. The implementation follows the standardized form of the Langmuir equation as recognized by the International Union of Pure and Applied Chemistry (IUPAC).