# Langmuir Isotherm Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Apr 06, 2022

The Langmuir Isotherm calculator is an easy-to-use tool for computing the fraction or percent of the adsorbent surface covered by an adsorbate using the Langmuir model.

Our Langmuir Isotherm calculator allows you to use either the partial pressure or the molarity of the substance, depending whether you're calculating the isotherm for a gas or for a liquid.

## What is Langmuir adsorption isotherm?

Firstly, we'd like to remind you of a few basic definitions:

• Adsorption - is a process of adhesion that connects molecules, atoms, or ions to a surface (or a phase boundary).

• In this process, the adsorbate creates a thin layer on the surface of the adsorbent.

• Chemisorption - a type of adsorption that creates strong chemical bonds between the adsorbate and the adsorbent.

• Isotherm - is a function that describes the change in the amount of adhered substance, depending on the substance's partial pressure or concentration. The reaction must take place in (that is, with constant temperature). 🌡️

Coming back to the Langmuir theory:

The Langmuir isotherm assumes that the adsorbate can only create a monolayer of particles on the adsorbent's surface. These particles interact only with the adsorbent (vertical interactions) and do not interact with each other (horizontal interactions).

Langmuir isotherm is based on these assumptions:

• The adsorbate particles behave as an ideal gas;
• The energy of the surface is homogeneous (identical and flat in all the places); and
• The adsorbate particles can not create multi-layers.

🙋 Want to know how ideal gas behaves? Check out our ideal gas law calculator.

## How to calculate Langmuir isotherm?

We understand that even the best of Langmuir isotherm calculators can not replace the actual, decent knowledge. In this section, you can discover the formula we used in the smallest details possible.

Our tool uses the following Langmuir isotherm equation:

θ = (Keq * P) / (1 + (Keq * P))

Where:

• θ - fraction of the surface covered by adsorbate
• Keq - equilibrium constant of adsorbtion
• P - partial pressure of the gas, or the molar concentration of the liquid

In order to receive percent of the surface covered by adsorbate, use the equation below:

θpercent = θfraction * 100

## How to plot Langmuir adsorption isotherm?

This is one of the most common questions on adsorption isotherm; in order to answer that, we first need to understand the rules of Langmuir adsorption model.

• The adsorbate particles hit the surface of adsorbent just like little bullets into the shooting target. The greater the surface, the bigger the shooting target, the easier it is to hit the target.

• Imagine that we're increasing concentration (or partial pressure) of a mixture - that results in us having more bullets to shoot, so that the probability of hitting the target (and adhesion!) increases.

• After a while, however, the shooting target becomes full of bullets and cannot accept any new shots. That's exactly what's happening to the adsorbent surface - it becomes filled with particles, since then can form only one layer.

As a result, the Langmuir isotherm graph is pretty steep at the beginning, when we increase the pressure or concentration, supplying the system with new bullets. After a while, however, all the places on the surface of the adsorbent are taken. The coverage becomes full - as a result, the graph becomes flat.

Łucja Zaborowska, MD, PhD candidate Equilibrium constant (K eq)
Partial pressure (P)
Pa
Surface fraction (θ)
Surface percent
%
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