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

Abstract

AbstractBACKGROUNDThe adsorption equilibrium constant of the Langmuir model (KL; L mol−1) has been applied as the standard thermodynamic equilibrium constant, , for calculating the thermodynamic parameters (∆G°, ∆S°, and ∆H°) of an adsorption processes by using the van't Hoff equation. Some authors have (directly and indirectly) applied the constant KRP (L kg−1) of the Redlich–Peterson model for such calculations. However, this is an incorrect application because the unit of KRP is not suitable (it is not an equilibrium constant). Its new adsorption equilibrium constant, Ke(RP) (L mol−1), was revisited based on aRP (L mol−1)g. In the literature, there is still uncertainty regarding the application of aRP as for calculating the thermodynamic parameters. Therefore, the present study aimed to evaluate the feasibility of applying Ke(RP) to calculate thermodynamic parameters using available literature data. The thermodynamic parameters obtained from Ke(RP) were compared to those from KL. A case study using a biosorbent for adsorbing methylene blue dye at different temperatures was carried out to re‐verify the feasibility.RESULTSThe 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 Ke(RP) (11.7–47.6 kJ mol−1) were significantly different (p = 2.98 × 10−12) from those on KL (12.2–40.8 kJ mol−1). The magnitudes of ΔH° obtained based on Ke(RP) were significantly different (P < 0.05) to those on KL; 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 ∆H° (kJ mol−1) and ∆S° [J mol−1 × K−1] values calculated based on Ke(RP) (11.65 and 111.5) were like those on KL (11.34 and 110.4, respectively).CONCLUSIONA new equilibrium constant, Ke(RP) (L mol−1), of the Redlich–Peterson model can be applied as for calculating the thermodynamic parameters (∆G°, ∆S°, and ∆H°) 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. © 2022 Society of Chemical Industry (SCI).