## 4 Discussion
### Thermodynamics Analysis of Lactic Acid Adsorption  
The negative values of \(\Delta G^{0}\) (\(-9.9\) to \(-10.9\) kJ/mol) and \(\Delta H^{0}\) (\(-16.7\) kJ/mol) revealed that the lactic acid adsorption onto GAC was spontaneous and exothermic between 303.15 K and 353.15 K (Table 3). Similarly, the negative values of \(\Delta G^{0}\) (\(-4.5\) to \(-1.9\) kJ/mol) and \(\Delta H^{0}\) (\(-19.9\) kJ/mol) assures that the lactic acid adsorption onto the RLX425 resin was spontaneous and exothermic between 303.15 and 353.15 K (Table 3). On the contrary, the negative values of \(\Delta G^{0}\) (\(-5.5\) to \(-6.8\) kJ/mol) and positive values for \(\Delta H^{0}\) (\(+2.0\) kJ/mol) showed that the lactic acid adsorption onto the AMB400 resin was spontaneous, but endothermic between 303.15 K and 353.15 K due to ion exchange mechanisms (Table 3). [PERSON] et al. [25] calculated the thermodynamic parameters for the lactic acid adsorption onto a weakly basic anionic (Amberlite(r) IRA-67) resin between 293.15 K and 323.15 K. In that study, the \(\Delta H^{0}\) value for lactic acid adsorption onto Amberlite(r) IRA-67 was \(-32.8\) kJ/mol and the adsorption process was exothermic between 298.15 K and 323.15 K. [PERSON] et al. [40] reported that the \(\Delta H^{0}\) value for the lactic acid adsorption onto zeolite molecular sieves was \(+29\) (\(\pm 17\)) kJ/mol and the adsorption process was endothermic between 299.15 K and 339.15 K.  
The negative values of \(\Delta G^{0}\) descending with the increase of temperature indicated a decrease in lactic acid adsorption from the bulk solution at elevated temperatures (\(>\)313.15 K) for both GAC and RLX425. On the other hand, the negative values of \(\Delta G^{0}\) ascending with temperature increase indicated a slight increase in lactic acid adsorption with the AMB400 resin (Table 3). The study by [PERSON] et al. [25] showed that the \(\Delta G^{0}\) (\(-8.8\) to \(-6.7\) kJ/mol) decreased with an increase in the temperature between 298.15 and 323.15 K for lactic acid adsorption onto the Amberlite(r) IRA-67 resin.  
The negative \(\Delta S^{0}\) value (\(-0.05\) kJ/(mol K)) for the weakly-basic resin (RLX425) shows decreased randomness at the adsorbent-adsorbate interface during the adsorption of lactic acid onto the active sites of the resin, which was further validated by the negative \(\Delta S^{0}\) (\(-0.8\) kJ/(mol K)) value found in a previous study on a weakly-basic resin (Amberlite(r) IRA-67) [25]. In addition, the positive value of \(\Delta S^{0}\) (\(0.02\) kJ/(mol K)) indicates the increased randomness at the adsorbent-adsorbate interface during the adsorption of lactic acid onto the active sites of the AMB400 resin. From the adsorption results at varying temperature, the increase in temperature decreased the recovery efficiency for both GAC and RLX425 (Figure 2a), which was further validated by the \(\Delta G^{0}\) values in Table 3 as the reaction spontaneity was found to decrease with an increase in the temperature [26].  
Generally, the adsorption enthalpy for physical adsorption (or electrostatic interaction between adsorption sites and the adsorbate species) ranges between \(-20\) and \(40\) kJ/mol [43] and for chemisorption between \(-80\) and \(-400\) kJ/mol, respectively [25; 44]. The \(\Delta H^{0}\) (\(-16.7\) kJ/mol for GAC and \(-19.9\) kJ/mol for RLX425) values obtained in this study were within the range of physical adsorption. Hence, the adsorption experiments with GAC and anionic resins indicated a physical adsorption process for lactic acid adsorption. In a related study, adsorption of acetic, propionic and burytic acid onto activated carbon and a weak base anionic resin (Puralite A133S) showed a physical adsorption (i.e., \(\Delta H^{0}\) between \(-20\) and \(40\) kJ/mol) process based on the thermodynamic analysis and the favorability: burytic \(>\) acetic \(>\) propionic acid [45]. The amount of lactic acid adsorbed via ion exchange (AMB400) was slightly lower than that adsorbed by physical adsorption (GAC and RLX425) [37].