## 2 Materials and Methods
### Arsenic Sorption and Sorption Efficiency  
The arsenic sorption capacity of each treated soil was determined, compared to the control soil, using the conventional batch equilibration technique. In brief, a unit mass of the treated soil sample (0.2 g) was mixed with 20 mL As solution of known concentration (0, 5, 50, 100, 200, 300, 400, 500, 600, 700, and 800 mg/L as NaAsO\({}_{2}\)) in a flask, and the flask was placed on a shaker at 120 rpm at 25 \({}^{\circ}\)C for 24 h (i.e., the equilibrium time from kinetics experiment). Then, the treated soil samples with the As (III) solution was centrifuged at 5000\(\times\)\(g\) for 15 min prior to sampling. The difference in As (III) sorption between un-amended and nWTRs-amended soils were quantified. At the end of this experiment, final As concentrations in the solutions were measured by Inductively-coupled Plasma/Mass Spectroscopy (ICP/MS). The amount of As adsorbed to the soil was calculated using the following equation:  
\[\mathrm{q_{e}=V\ (C_{0}-C_{e})/m} \tag{1}\]  
where \(\mathrm{q_{e}}\) is the amount of As sorbed by a unit mass of soil at equilibrium (mg/kg), V is the solution volume (mL), m is the mass of soil sorbent (g), and \(C_{0}\) and \(C_{e}\) are the initial and equilibrium concentrations of As, respectively.  
To describe the As sorption in treated soils, the isotherm classification concept was applied to distinguish four main types of isotherms corresponding to different solute adsorbent interactions, named as L, H, C, and S curves. Soil isotherms were characterized by a decreasing slope as equilibrium concentration increased. The As sorption efficiency of sorbent for arsenic was calculated using the following equation:  
\[\mathrm{E\ (\%)=[(C_{i}-C_{e})/C_{i}]\times 100} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Soil** & **nWTRs** & **Biosolids** \\ \hline pH & 8.32 \(\pm\) 0.06 & 7.66 \(\pm\) 0.09 & 6.38 \(\pm\) 0.05 \\ Electrical conductivity (EC) (dS/m) & 2.13 \(\pm\) 0.04 & 1.12 \(\pm\) 0.03 & 8.33 \(\pm\) 0.17 \\ Organic Matter (g/kg) & 2.60 \(\pm\) 0.18 & 48.00 \(\pm\) 2.33 & 410.00 \(\pm\) 3.77 \\ Cation Exchange Capacity (CEC) (cmol(+)/kg) & 21.00 \(\pm\) 1.07 & 39.45 \(\pm\) 1.38 & 77.77 \(\pm\) 2.58 \\ Sand (g/kg) & 738.00 \(\pm\) 3.70 & N/A \({}^{\dagger}\) & N/A \\ Slit (g/kg) & 106.40 \(\pm\) 1.90 & N/A & N/A \\ Clay (g/kg) & 155.60 \(\pm\) 3.20 & N/A & N/A \\ Soil Texture & Sandy loam & N/A & N/A \\ CaCO\({}_{3}\) (g/kg) & 326.20 \(\pm\) 3.69 & N/A & N/A \\ KCl-Al (mg/kg) & 0.12 \(\pm\) 0.03 & 18.12 \(\pm\) 1.07 & 3.82 \(\pm\) 0.14 \\ Olsen-P (mg/kg) & 15.30 \(\pm\) 0.50 & 20.00 \(\pm\) 2.11 & 44.40 \(\pm\) 1.74 \\ Total As (mg/kg) & 1.23 \(\pm\) 0.11 & 1.55 \(\pm\) 0.13 & 6.22 \(\pm\) 0.58 \\ Exchangeable As (mg/kg) & 0.07 \(\pm\) 0.01 & 0.06 \(\pm\) 0.01 & 0.16 \(\pm\) 0.06 \\ Soluble As (mg/kg) & 0.04 \(\pm\) 0.01 & 0.03 \(\pm\) 0.01 & 0.09 \(\pm\) 0.02 \\ \hline \hline \end{tabular} \({}^{\dagger}\): not applicable.  
\end{table}
Table 1: General physical and chemical properties of experimental soil, nanoscale drinking water treatment residuals (nWTRs), and biosolids.  
where E is the sorption efficiency, while C\({}_{i}\) and C\({}_{e}\) are the initial and equilibrium As concentrations, respectively.