Freundlich equation
The Freundlich equation or Freundlich adsorption isotherm, an adsorption isotherm, is an empirical relationship between the quantity of a gas adsorbed into a solid surface and the gas pressure. The same relationship is also applicable for the concentration of a solute adsorbed onto the surface of a solid and the concentration of the solute in the liquid phase. In 1909, Herbert Freundlich gave an expression representing the isothermal variation of adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with gas pressure. This equation is known as Freundlich adsorption isotherm or Freundlich adsorption equation. As this relationship is entirely empirical, in the case where adsorption behavior can be properly fit by isotherms with a theoretical basis, it is usually appropriate to use such isotherms instead. The Freundlich equation is also derived by attributing the change in the equilibrium constant of the binding process to the heterogeneity of the surface and the variation in the heat of adsorption.
Freundlich adsorption isotherm
The Freundlich adsorption isotherm is mathematically expressed asIn Freundlich's notation, signifies the ratio between the adsorbed mass or adsorbate and the mass of the adsorbent, which in Freundlich's studies was coal. In the figure above, the x-axis represents, which denotes the equilibrium concentration of the adsorbate within the solvent.
Freundlich's numerical analysis of the three organic acids for the parameters and according to equation
were:
| acid type | K | n |
| acetic | 2.606 | 2.35 |
| propionic | 3.463 | 2.82 |
| succinic | 4.426 | 3.65 |
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.
| acid type | K | △ K | n | △ n |
| acetic | 2.56 | 0.035 | 2.565 | 0.075 |
| propionic | 3.292 | 0.0471 | 3.005 | 0.104 |
| succinic | 4.28 | 0.11 | 3.884 | 0.21 |
△ 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
Sometimes also this notation for experiments in the gas phase can be found:
and are constants for a given adsorbate and adsorbent at a given temperature.
At high pressure, 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 have a constant of adsorption. On the other hand, heterogeneous adsorption have a variable of adsorption depending on the percent of sites occupied. When the adsorbate pressure in the gas phase is low, high-energy sites will be occupied first. As the pressure in the gas phase increases, the low-energy sites will then be occupied resulting in a weaker of adsorption.