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

Abstract

Abstract BACKGROUND The adsorption equilibrium constant of the Langmuir model ( K L ; 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 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 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 Δ G ° 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 Δ H ° 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 Δ H ° 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 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 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).