Langmuir Isotherm

The Langmuir isotherm is a model that describes the adsorption of a gas or a solute onto a solid surface. It is named after the scientist Irving Langmuir, who first proposed the model in 1916. The Langmuir isotherm is based on the assumption that adsorption occurs at specific sites on the surface of the solid, and that once a site is occupied by a gas molecule or solute particle, no further adsorption can occur at that site.

Key Concepts

Monolayer coverage: The Langmuir isotherm assumes that adsorption occurs in a single layer on the solid surface, and that once all the sites are occupied, further adsorption is not possible.
Equilibrium: The Langmuir isotherm describes the equilibrium between the adsorbed molecules or particles and the gas or solute in the bulk phase.
Langmuir equation: The Langmuir isotherm is described by the Langmuir equation, which relates the fraction of sites occupied by adsorbed molecules to the pressure or concentration of the gas or solute in the bulk phase.

Langmuir Equation

The Langmuir isotherm is described by the Langmuir equation, which is given by:

θ = (K * P) / (1 + K * P)

Where:

θ is the fraction of sites occupied by adsorbed molecules
K is the equilibrium constant
P is the pressure of the gas or the concentration of the solute in the bulk phase

Applications

The Langmuir isotherm is widely used in the study of adsorption processes in fields such as surface chemistry, chemical engineering, and environmental science. It is used to model the adsorption of gases onto solid surfaces, the adsorption of solutes onto solid adsorbents, and the behavior of molecular monolayers on solid substrates.

Study Tips

Understand the assumptions of the Langmuir isotherm and how they apply to real-world adsorption processes.
Practice using the Langmuir equation to calculate the fraction of sites occupied by adsorbed molecules at different pressures or concentrations.
Explore the applications of the Langmuir isotherm in different scientific and engineering contexts.
Compare and contrast the Langmuir isotherm with other adsorption models, such as the Freundlich isotherm and the BET theory.

◂Physics Worksheets and Study Guides High School. Thermodynamics

The resources above cover the following skills:

PHYSICAL SCIENCE (NGSS)

Matter and Its Interactions

Students who demonstrate understanding can:

Develop a model to illustrate that the release or absorption of energy from a chemical reaction system depends upon the changes in total bond energy.

Energy

Students who demonstrate understanding can:

Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).