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

BACKGROUND: The adsorption equilibrium constant of the Langmuir model (K_L; L mol⁻¹) has been applied as the standard thermodynamic equilibrium constant, (Formula presented.), 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 (Formula presented.) 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 ∆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 (Formula presented.) 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.