Revisiting the calculation of thermodynamic parameters of adsorption processes from the modified equilibrium constant of the Redlich–Peterson model

Abstract

BACKGROUND:The adsorption equilibrium constant of the Langmuir model (K L ; L mol −1 ) has been applied as the standard thermodynamic equilibrium constant, K o Eq , for calculating the thermodynamic parameters (ΔG°, ΔS°, and ΔH°) of an adsorption processes by using the van't Hoff equation. Some authors have (directly and indirectly) applied the constant K RP (L kg −1 ) of the Redlich-Peterson model for such calculations. However, this is an incorrect application because the unit of K RP is not suitable (it is not an equilibrium constant). Its new adsorption equilibrium constant, K e(RP) (L mol −1 ), was revisited based on a RP (L mol −1 ) g . In the literature, there is still uncertainty regarding the application of a RP as K o Eq for calculating the thermodynamic parameters. Therefore, the present study aimed to evaluate the feasibility of applying K e(RP) to calculate thermodynamic parameters using available literature data. The thermodynamic parameters obtained from K e(RP) were compared to those from K L . A case study using a biosorbent for adsorbing methylene blue dye at different temperatures was carried out to re-verify the feasibility. RESULTS:The Redlich-Peterson model is only valid when its exponent is in a strict range (0 ≤ g ≤ 1). The Redlich-Peterson model (68%; 227 observations collected from 52 published papers) describes adsorption equilibrium datasets better than the Langmuir model. The negative ΔG°values obtained based on K e(RP) (11.7-47.6 kJ mol −1 ) were significantly different (p = 2.98 × 10 −12 ) from those on K L (12.2-40.8 kJ mol −1 ). The magnitudes of ΔH°obtained based on K e(RP) were significantly different (P < 0.05) to those on K L ; however, such differences did not affect conclusions drawn on dominant mechanism adsorption (physical or chemical). The magnitude of ΔH°for chemisorption (involved in covalent bonds) is higher than 200 kJ mol −1 . For the case study, the ΔH°(kJ mol −1 ) and ΔS°[J mol −1 × K −1 ] values calculated based on K e(RP) (11.65 and 111.5) were like those on K L (11.34 and 110.4, respectively). CONCLUSION: A new equilibrium constant, K e(RP) (L mol −1 ), of the Redlich-Peterson model can be applied as K o Eq for calculating the thermodynamic parameters (ΔG°, ΔS°, and ΔH°) of an adsorption processes under specific cases (i.e., F, H, and L-shaped adsorption isotherms). Most of the adsorption processes (98%) involve physical adsorption.

Biochar as Alternative Material for Heavy Metal Adsorption from Groundwaters: Lab-Scale (Column) Experiment Review

“…From a thermodynamic point of view, it can be stated that adsorption is a spontaneous process (∆G < 0) and is characterised by a decrease in the entropy of the adsorbed substance incorporated into the solid (∆S < 0). Adsorption is an exothermic phenomenon (∆H < 0) and is therefore favoured by low-temperature values; the amount of heat generated by the process is a function of the type of bonds formed [227]. Depending on the nature of the interactions that occur between the adsorbate and the adsorbent, and thus on the extent of the energy of the bonds with which the particles are retained on the surface, adsorption can be defined as physical, also called physisorption, or chemisorption [228].…”