# Effect of Hydrogen Ion Presence in Adsorbent and Solution to Enhance Phosphate Adsorption
## 1 Introduction  
The presence of phosphorus in a water body has been acknowledged, although its concentration is relatively lower than that of nitrogen due to the main causes of eutrophication therein--the concentration of total phosphorus (T-P) was set to 0.2 mg/L in the effluent of the sewage treatment plant in Korea [1]. Since phosphorus (P) only rarely exists by itself in nature, instead P usually occurs as a form of phosphate [2], and improvement of the removal efficiency of the phosphate discharged is required to control the T-P. Since some issues such as ineffective removal efficiency and further treatment at low concentrations of phosphate remain [3], adsorption is a cost-effective and efficient approach, with low chemical sludge production and easy recovery of the adsorbed phosphate [4], when compared with chemical precipitation [5], biological removal [6], and ion exchange (IX)/adsorption [7, 8].  
Currently, although various adsorbents have been developed, as listed in Table S1, GAC is still widely applied in the field of organic and inorganic contaminant removal, with the benefits of high removal efficiency, easy operation, and availability of regeneration. To increase the removal efficiency of GAC, the following physical and chemical attempts have been made to modify GAC's properties: temperature control for altering the surface area, pore volume and diameter [9], acid and base treatment for use of the functional group [10], and impregnation of the metal [11].  
During the phosphate removal process, the adsorption capacity of the adsorbent is highly dependent on the adsorption conditions (e.g., pH, initial concentration, and thepresence of co-ions), which are also related to the adsorption mechanism. According to [PERSON] et al. [12], the effect of pH is important in the adsorption of phosphates to goethite and akaganeite, being closely related to factors such as the net positive charge of the adsorbent and concentration of the hydroxide and phosphate species. A possible explanation is that phosphate has three pKa values, i.e., 2.12, 7.21, and 12.44, and exists as a form of four species, i.e., H3 PO4, H2 PO4, HPO4, and PO4, depending on the pH of the solution. Table S1 shows various adsorbents for the removal of phosphates including activated carbon, and the optimized solution pH was found to vary, confirming that the adsorption capacity depended on the adsorbent, the experimental conditions, and the adsorption mechanism.  
Adsorption is the process of mass transfer of a target contaminant from the liquid phase to the solid phase. Adsorption isotherm and kinetic experiments have usually been undertaken to describe the adsorption mechanism. The adsorption isotherm model, which uses the relationship between the uptake at equilibrium and a certain time, is used to describe the mechanism and quantify the adsorbate distribution in the interface of the liquid and solid phases. Among a variety of isotherm models, currently, the Langmuir [13] and Freundlich [14] models are widely used. For a porous adsorbent, adsorption occurs over three stages, including external diffusion (film diffusion), internal diffusion (pore diffusion), and adsorption on the active sites [15; 16]. The pseudo-first-order model (PFO) [17] and the pseudo-second-order model (PSO) [18] have been developed, and furthermore, the intraparticle diffusion model has been applied to determine the rate-limit step [19].  
This study was to investigate the hydrogen-ion effect on the increase in phosphate adsorption and the mechanism onto porous GAC in the presence of the adsorbent and a solution of hydrogen. The specific objectives were to (1) assess the inherent physical properties of GAC; (2) test the optimized solution pH; (3) determine the effect of the pH on adsorption uptake using the isotherm and kinetic rates, the pseudo-first-order and pseudo-second-order reactions, and the interparticle diffusion model; and (4) estimate the enhancement in the fixed column.