Final answer:
The Langmuir adsorption isotherm becomes identical with the Freundlich adsorption isotherm when the Freundlich exponent approaches unity, indicating a homogeneous surface and no competition between adsorbed molecules.
Step-by-step explanation:
The Langmuir adsorption isotherm and the Freundlich adsorption isotherm describe different types of adsorption behavior. The Langmuir isotherm assumes that adsorption occurs only on specific sites without any interaction between adsorbed molecules. On the other hand, the Freundlich isotherm allows for interaction between adsorbed molecules and assumes that adsorption occurs on a heterogeneous surface.
Under certain conditions, the Langmuir isotherm becomes identical with the Freundlich isotherm. This happens when the Freundlich exponent, which represents the heterogeneity of the surface, approaches unity. When the exponent is close to one, the adsorption behavior described by the Freundlich isotherm resembles that of the Langmuir isotherm.
For example, if the surface is highly homogeneous and there is no competition between adsorbed molecules, the Freundlich adsorption isotherm may approach the Langmuir isotherm.