Freundlich adsorption isotherm is a relationship between the amount of adsorbate x/m (adsorbate per unit mass of the adsorbent) and the pressure p (or concentration) at a constant temperature. This is represented by the equation:

x/m = k * p^(1/n)

where k and n are constants that depend on the nature of the adsorbent-adsorbate system and the temperature.

Explanation:

Freundlich adsorption isotherm is a model that describes the adsorption of a gas or a solute onto a solid surface at equilibrium. It was first proposed by Fritz Freundlich in 1906.

The plot between x/m and p is called the Freundlich adsorption isotherm. Here, x/m represents the amount of adsorbate per unit mass of the adsorbent, and p represents the pressure (or concentration) of the adsorbate in the gas (or liquid) phase.

The Freundlich adsorption isotherm assumes that the adsorption process occurs on a heterogeneous surface, where the adsorbate molecules are adsorbed onto active sites of different energies. This results in a non-linear relationship between the amount of adsorbate and the pressure (or concentration).

The Freundlich adsorption isotherm is represented by a logarithmic plot of x/m versus log p. The slope of this plot is equal to 1/n, and the intercept is equal to log k. The constant k is related to the adsorption capacity of the adsorbent, while n is related to the degree of heterogeneity of the surface.

Applications of Freundlich adsorption isotherm:

The Freundlich adsorption isotherm is widely used in various fields, such as:

1. Environmental science: To study the adsorption of pollutants on soil, water, and air.

2. Materials science: To design and optimize adsorbent materials for gas separation, catalysis, and energy storage.

3. Chemical engineering: To model and simulate adsorption processes in industrial applications, such as gas purification, chromatography, and ion exchange.

In conclusion, the Freundlich adsorption isotherm is a useful tool for understanding and predicting the adsorption behavior of gases and solutes on solid surfaces. The plot between x/m and p (or c) provides valuable insights into the adsorption mechanism and the properties of the adsorbent-adsorbate system.