Freundlich equation

Lore & Background

Herbert Freundlich gave an expression in 1909 for the isothermal variation of adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with gas pressure. The equation is entirely empirical, though it can also be derived by attributing changes in the equilibrium constant to surface heterogeneity and variation in heat of adsorption. Freundlich's original experiments involved the adsorption of organic acids on coal in aqueous solutions, where he used the ratio x/m (adsorbed mass per mass of adsorbent) and the equilibrium concentration c_eq.

Reader's Guide

The Freundlich equation is mathematically expressed as x/m = K * c_eq^(1/n) or, in logarithmic form, log(x/m) = log K + (1/n) log c_eq. For gas-phase experiments, pressure p replaces concentration. The constants K and n are specific to a given adsorbate and adsorbent at a given temperature. The equation is unique in that if data fit it, it suggests but does not prove surface heterogeneity; calorimetry can confirm this. A limitation is that at higher pressures, the equation fails because adsorption saturates. When adsorption behavior can be properly fit by theoretically based isotherms (e.g., Langmuir or BET), those are usually preferred.

Did You Know?

• The Freundlich equation is entirely empirical, though it can be derived from surface heterogeneity and variation in heat of adsorption.
• Freundlich's original experiments used the adsorption of organic acids on coal in aqueous solutions.
• At high pressure, the exponent 1/n approaches zero, making the extent of adsorption independent of pressure.
• The equation fails at higher pressures because adsorption saturates beyond a certain point.