# Evaluation of Agricultural Soil-Improving Zeolite for Improving Irrigation Water Quality
## 2 Materials and Methods
### Batch Kinetic Sorption Tests  
Based on the results obtained from the experimental factorial design, kinetic sorption tests were conducted to identify and define the most appropriate kinetics that describe the process. This knowledge is crucial, as it provides valuable information about the mechanism of the process and indicates the sorption rate, which, in treating an effluent, determines the residence time of the sorbate at the interface between the solution and the sorbent material.  
For this purpose, 100 mL of irrigation water was placed in non-sterile polypropylene Erlenmeyer flasks with a maximum capacity of 250 mL, containing 4.93 g of zeolite/L, and a total contact time of 6200 min at a constant controlled temperature (22 \(\pm\) 1 \({}^{\circ}\)C). In all cases, the flasks were covered with a transparent biofilm to prevent dust and/or impurities from entering. The quantity of zeolite and the total contact time were predetermined through factorial experimental planning.  
At various predefined times, each Erlenmeyer flask was opened for sampling and monitoring of cation concentrations. A total of 17 tests were conducted. Before the characterization analyses, the aqueous samples were filtered with cellulose acetate filters of 0.20 \(\upmu\)m and 47 mm in diameter (Teknokroma, Barcelona, Spain). The percentage removal of sodium and boron was determined using Equation (1), where C\({}_{0}\) and C\({}_{t}\) represent the initial concentration of cations and the concentration at time t (mg/L), respectively.  
\[\%\text{ removal}=\frac{\text{C}_{0}-\text{C}_{t}}{\text{C}_{0}}\times 100 \tag{1}\]  
The assessment of the kinetic mechanism of the sorption process was conducted by applying the three most commonly used kinetic models to the experimental data. These models are (_i_) [PERSON]'s pseudo-first-order model, commonly employed for liquid-solid sorption, as it considers the rate of occupation of active sites to be proportional to the number of available active sites in the adsorbent material, also known as physisorption [36; 37]; (_ii_) [PERSON]'s pseudo-second-order model, based on solid-phase sorption, presupposing it as a chemical sorption process involving the participation of valence forces or electron exchange between sorbate and sorbent, thus describing chemisorption [38]; and (_iii_) [PERSON] and [PERSON]'s intraparticle diffusion model, wherein the limiting stage of the sorption process may be caused by the slowness of the intraparticle diffusion mechanism [39]. The corresponding equations of the kinetic models are shown in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Equation** \\ \hline Pseudo-first-order & \(\frac{d\mu_{t}}{dt}=k_{1}(q_{e}-q_{t})\) \\ \hline where \(q_{e}\) and \(q_{t}\) represent the amounts of sorbate retained (mg) per gram of sorbent at equilibrium and time \(t\), respectively., and \(k_{1}\) (min\({}^{-1}\)) is the rate constant of the pseudo-first-order. \\ \hline Pseudo-second-order & \(\frac{dP_{t}}{dt}=k(HP_{e}-HP_{t})^{2}\) \\ \hline where \(P_{t}\) and \(HP_{t}\) correspond to the number of occupied active sites on the sorbent at time \(t\), while \(P_{e}\)\(yHP_{e}\) refers to the number of available active sites on the sorbent at equilibrium. \\ \hline Intraparticle diffusion & \(q_{t}=k_{in}t^{\frac{1}{2}}+C\) \\ \hline where \(k_{in}\) is the rate of intraparticle diffusion (mg g\({}^{-1}\) min\({}^{-0.5}\)) and \(C\) is the constant related to the thickness of the diffusion layer (mg g\({}^{-1}\)). \\ \hline \hline \end{tabular}
\end{table}
Table 2: Equations of kinetic models used in this study.