Freundlich equation

Freundlich adsorption isotherm

The Freundlich adsorption isotherm is mathematically expressed as

In Freundlich's notation (used for his experiments dealing with the adsorption of organic acids on coal in aqueous solutions), ${\displaystyle x/m}$ signifies the ratio between the adsorbed mass or adsorbate ${\displaystyle x}$ and the mass of the adsorbent ${\displaystyle m}$, which in Freundlich's studies was coal. In the figure above, the x-axis represents ${\displaystyle c_{\mathrm{e}\mathrm{q}}}$, which denotes the equilibrium concentration of the adsorbate within the solvent.

Freundlich's numerical analysis of the three organic acids for the parameters ${\displaystyle K}$ and ${\displaystyle n}$ according to equation were:

Freundlich's experimental data can also be used in a contemporary computer based fit. These values are added to appreciate the numerical work done in 1907.

△ K and △ n values are the error bars of the computer based fit. The K and n values itself are used to calculate the dotted lines in the figure.

Equation can also be written as

${\displaystyle \log \frac{x}{m}=\log K+\frac{1}{n}\log c_{eq}}$

Sometimes also this notation for experiments in the gas phase can be found:

${\displaystyle \log \frac{x}{m}=\log K+\frac{1}{n}\log p}$

x = mass of adsorbate

m = mass of adsorbent

p = equilibrium pressure of the gaseous adsorbate in case of experiments made in the gas phase (gas/solid interaction with gaseous species/adsorbed species)

K and n are constants for a given adsorbate and adsorbent at a given temperature (from there, the term isotherm needed to avoid significant gas pressure fluctuations due to uncontrolled temperature variations in the case of adsorption experiments of a gas onto a solid phase).

K = distribution coefficient

n = correction factor

At high pressure 1/n = 0, hence extent of adsorption becomes independent of pressure.

The Freundlich equation is unique; consequently, if the data fit the equation, it is only likely, but not proved, that the surface is heterogeneous. The heterogeneity of the surface can be confirmed with calorimetry. Homogeneous surfaces (or heterogeneous surfaces that exhibit homogeneous adsorption (single site)) have a constant ΔH of adsorption. On the other hand, heterogeneous adsorption (multi-site) have a variable ΔH of adsorption depending on the percent of sites occupied. When the adsorbate pressure in the gas phase (or the concentration in solution) is low, high-energy sites will be occupied first. As the pressure in the gas phase (or the concentration in solution) increases, the low-energy sites will then be occupied resulting in a weaker ΔH of adsorption.