In this applet we explore the Langmuir isotherm.

An adsorption isotherm is a plot of the fractional coverage of the surface, , against pressure. The simplest physically plausible isotherm is based on three assumptions:

- Adsorption cannot proceed beyond monolayer coverage.
- All sites are equivalent and the surface is uniform.
- The ability of a molecule to adsorb at a given site is independent of the occupation of neighbouring sites.

The resulting isotherm is called the **Langmuir isotherm**:

Where **K** = **k _{a}** /

Select the **Simple Adsorption** tab to plot this equation.

The **Data**, **Plot** and **Least Squares Analysis** tabs consider the adsorption of CO
on charcoal at 273 K. The fractional coverage is calculated as

Where **V _{infinity}** is the volume corresponding to complete coverage.

We rewrite the Langmuir isotherm as

It follows that a plot of **p/V** against **V** should be a straight line, and

where slope( **p**, **p _{V_ratio}** ) and intercept(

When a molecule dissociates upon adsorption, the Langmuir isotherm is

Select the **with Dissociation** tab to plot this equation.

Different isotherms are obtained at different temperatures on account of the temperature dependence of **K**.
It follows that we can use the van 't Hoff equation to determine the isosteric enphalpy of adsorption,
,
the standard enthalpy of adsorption at a fixed surface coverage:

We again consider the adsorption of CO on charcoal. The pressures of CO needed for the volume of adsorption
(corrected to 1.00 atm and 273 K) to be 10.0 cm^{3} are entered on the **Data** tab below.

The Langmuir isotherm can be rearranged to

Therefore, a plot (**Plot** tab) of **ln(p)** against **1/T** should be a straight line of slope
/ R. It follows that the isosteric
enthalpy of adsorption is

This value is calculated on the **Least Squares Analysis** tab below.