Langmuir Adsorption Isotherm Calculator

Calculate adsorbed amount, maximum capacity, or Langmuir constant using the Langmuir isotherm equation.

Input any three of the four parameters (equilibrium concentration, Langmuir constant, maximum adsorption capacity, adsorbed amount) to solve for the unknown. Includes step-by-step solutions and real-world examples.

Examples

See how to use the calculator with real-world scenarios.

Calculate adsorbed amount (q)

Calculate Adsorbed Amount

Given C=10 mg/L, K=0.2 L/mg, qmax=50 mg/g, find the adsorbed amount (q).

Equilibrium Concentration (C): 10

Langmuir Constant (K): 0.2

Maximum Adsorption Capacity (qmax): 50

Adsorbed Amount (q):

Unit: mg/L

Find maximum adsorption capacity (qmax)

Find Maximum Adsorption Capacity

Given C=8 mg/L, K=0.15 L/mg, q=18 mg/g, find qmax.

Equilibrium Concentration (C): 8

Langmuir Constant (K): 0.15

Maximum Adsorption Capacity (qmax):

Adsorbed Amount (q): 18

Unit: mg/L

Find Langmuir constant (K)

Find Langmuir Constant

Given C=12 mg/L, qmax=40 mg/g, q=24 mg/g, find K.

Equilibrium Concentration (C): 12

Langmuir Constant (K):

Maximum Adsorption Capacity (qmax): 40

Adsorbed Amount (q): 24

Unit: mg/L

Find equilibrium concentration (C)

Find Equilibrium Concentration

Given qmax=60 mg/g, K=0.25 L/mg, q=30 mg/g, find C.

Equilibrium Concentration (C):

Langmuir Constant (K): 0.25

Maximum Adsorption Capacity (qmax): 60

Adsorbed Amount (q): 30

Unit: mg/L

Other Titles
Understanding Langmuir Adsorption Isotherm Calculator: A Comprehensive Guide
Master the Langmuir isotherm and adsorption calculations with this step-by-step tool.

What is the Langmuir Isotherm?

  • Definition and Background
  • Langmuir Equation
  • Assumptions of the Model
The Langmuir isotherm describes the adsorption of molecules onto a solid surface, assuming a fixed number of identical sites and monolayer coverage. It is widely used in surface chemistry and environmental engineering.
Langmuir Isotherm Formula

Adsorption in Action

  • Adsorption of dyes onto activated carbon.
  • Removal of heavy metals from water using adsorbents.

Step-by-Step Guide to Using the Calculator

  • Input Required Data
  • Choose the Unknown
  • Interpret Results
Enter any three of the four parameters (C, K, qmax, q). The calculator will solve for the unknown using the Langmuir isotherm equation and provide a step-by-step solution.
How to Use the Tool

Practical Usage

  • Calculate the adsorbed amount for a given concentration.
  • Find the Langmuir constant from experimental data.

Real-World Applications of the Langmuir Isotherm

  • Water Treatment
  • Industrial Adsorption
  • Surface Science Research
The Langmuir isotherm is used to design water treatment systems, optimize industrial adsorption processes, and study surface interactions in research labs.
Applications in Science and Industry

Applications

  • Designing filters for pollutant removal.
  • Optimizing adsorbent materials for maximum efficiency.

Common Misconceptions and Correct Methods

  • Monolayer vs. Multilayer Adsorption
  • Unit Consistency
  • Input Accuracy
The Langmuir model assumes monolayer adsorption. Always use consistent units for all parameters and double-check your inputs for accuracy to avoid calculation errors.
Avoiding Mistakes

Tips

  • Using multilayer adsorption data with the Langmuir model gives incorrect results.
  • Mixing units (e.g. mg/L and mmol/L) leads to errors.

Mathematical Derivation and Examples

  • Langmuir Equation Rearrangement
  • Sample Calculations
  • Interpreting Results
The Langmuir equation can be rearranged to solve for any parameter. The calculator applies algebraic manipulation to provide accurate results and step-by-step solutions.
Worked Examples

Math in Action

  • Given C=10, K=0.2, qmax=50, q=?
  • Given q=18, C=8, K=0.15, qmax=?