## 3 Results
### Precipitation
The detailed species distribution of saturated Ca(OH)\({}_{2}\), CaCO\({}_{3}\) and CaCO\({}_{4}\) can be found in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Formulas** & **Possible Chemical Reactions** & **Log\({}_{\text{10}}\)(\(K\)) 1** \\ \hline H\({}^{+}\)/OH\({}^{+}\) & H\({}_{2}\)O \(\leftrightarrow\) H\({}^{+}\) + OH\({}^{-}\) & (1) & \(-\)13.99 \\ Ca\  
\[C_{CaO_{3}(s)}+C_{CaHCO_{3}}+C_{CaHCO_{3}}+C_{HCO_{3}^{-}}+C_{HCO_{3}^{-}}+C_{H_{2}CO_{ 3}}+C_{CO_{2}}+C_{CO_{2}(g)}=C_{CO_{3}^{2-}total} \tag{7}\]  
\[C_{CaHCO_{3}}+C_{HCO_{3}^{-}}+2\times\left(C_{H_{2}CO_{3}}+C_{CO_{2}}+C_{CO_{2}( g)}\right)=C_{OH^{-}} \tag{8}\]  
Figure 1: Calculated species distributions of 30 mM Ca(OH)2 at different pH: (**a**) with log concentration vs. pH; (**b**) with fraction of calcium vs. pH. \begin{table}
\begin{tabular}{c c c c} \hline Pb3(OH)2+ & 2 Pb2+ + 4H2O \(\leftrightarrow\) Pb3(OH)2+ + 4H+ & (50) & \(-\)23.88 \\ PbOH+ & Pb2+ + H2O \(\leftrightarrow\) PbOH+ + H+ & (51) & \(-\)7.71 \\ PbSO4 & Pb2+ + SO42+ \(\leftrightarrow\) PbSO4 & (52) & 2.69 \\ Pb(OH)2(s) & Pb2+ + 2H2O \(\leftrightarrow\) Pb(OH)2(s) + 2H+ & (53) & \(-\)13.6 \\ PbO(s) & Pb2+ + 2H2O \(\leftrightarrow\) PbO(s) + 2H+ & (54) & \(-\)12.9 \\ PbSO4(s) & Pb2+ + SO42+ \(\leftrightarrow\) PbSO4(s) & (55) & 7.79 \\ Pb(CO)32-2 & Pb2+ + 2H2O + 2 CO2 \(\leftrightarrow\) PbCO32-2 + 4H+ & (56) & \(-\)23.26 \\ PbCO3 & Pb2+ + H2O + CO2 \(\leftrightarrow\) PbCO3 + 2H+ & (57) & \(-\)10.08 \\ PbCO3 OH- & Pb2+ + 2H2O + 2 CO2 \(\leftrightarrow\) PbCO3 OH + 3H+ & (58) & \(-\)18.48 \\ PbHCO3+ & Pb2+ + H2O + CO2 \(\leftrightarrow\) PbHCO3+ H+ & (59) & \(-\)3.331 \\ Pb3(CO3)2(OH)2(s) & 3 Pb2+ + 3H2O + 2 CO2 \(\leftrightarrow\) PbSO3(CO)2(OH)2(s) + 6H+ & (60) & \(-\)13.96 \\ PbCO3(s) & Pb2+ + H2O + CO2 \(\leftrightarrow\) PbCO3(s) + 2H+ & (61) & \(-\)3.48 \\ \hline \end{tabular} Note: 1. \(K\) data obtained from HSC Chemistry® 6.0 database.  
\end{table} 
Table 1: Cont. Figure 2: Calculated species distributions of 10 mM CaCO3 at different pH: (**a**) with log concentration vs. pH; (**b**) with fraction of calcium vs. pH. According to the ICP-OES measurement results, the concentration of SO42- in the spent electrolyte sample was 1.53 M. Figure 4 shows the reaction equilibriums of 1.53 M SO42- reacting with 1.55 M \begin{table}
\begin{tabular}{c c c} \hline \hline
**Contents** & **Species** & **Concentrations (mM)** \\ \hline \multirow{4}{*}{Saturated Ca(OH)2 (30 mM)} & Ca(OH)2 (s) & 7.203 \\  & Ca2+ & 19.48 \\  & OH- & 28.44 \\  & CaOH+ & 3.318 \\ \hline \multirow{4}{*}{Saturated CaCO3 (10 mM)} & CaCO3 (s) & 9.847 \\  & CaCO3 & \(1.094\times 10^{-2}\) \\  & CaCO3+ & \(1.415\times 10^{-4}\) \\  & OH- & \(8.886\times 10^{-2}\) \\  & Ca2+ & \(0.1415\) \\  & CO32- & \(4.318\times 10^{-2}\) \\  & HCO3- & \(9.840\times 10^{-2}\) \\  & H2 CO3 & \(2.560\times 10^{-5}\) \\  & CO2 & \(2.468\times 10^{-5}\) \\ \hline \multirow{4}{*}{Saturated CaSO4 (20 mM)} & OH- & \(1.212\times 10^{-4}\) \\  & SO42- & 12.03 \\  & CaOH+ & \(9.681\times 10^{-6}\) \\ \cline{1-1}  & CaSO4 (20 mM) & CaSO4 & 4.457 \\ \cline{1-1}  & H2 SO4 & \(3.236\times 10^{-13}\) \\ \cline{1-1}  & HSO4- & \(6.279\times 10^{-5}\) \\ \cline{1-1}  & Ca2+ & 12.03 \\ \cline{1-1}  & CaSO4-2H2O & 3.516 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated concentrations of different species in saturated Ca(OH)2, CaCO3, and CaSO4 solutions. Figure 3: Calculated species distributions of 20 mM CaO4 at different pH: (**a**) with log concentration vs. pH; (**b**) with fraction of calcium vs. pH; (**c**) with fraction of sulfate vs. pH. Ca(OH)\({}_{2}\) at different pH. Extra Ca(OH)\({}_{2}\) was introduced to ensure the removal of SO\({}_{4}\)\({}^{2-}\) ions. As can be seen from Figure 4, the main precipitates were CaSO\({}_{4}\)\(\cdot\)2H\({}_{2}\)O in a wide pH range (pH: 2\(\sim\)12), according to Equation (9), and when pH \(<\) 2 [19], CaSO\({}_{4}\)\(\cdot\)2H\({}_{2}\)O would dissolve into the solution and become Ca\({}^{2+}\) and SO\({}_{4}\)\({}^{2-}\) ions, according to Equation (10).