# Batch and Column Adsorption of Phosphorus by Modified Montmorillonite
## 3 Results and Discussion
### The Batch Adsorption of Phosphorus by Al\({}_{13}\)-O-MMt
#### 3.2.3 Effect of the Amount of Al\({}_{13}\)-O-MMt on Phosphorus Adsorption  
Figure 5 illustrates that the adsorption efficiency of phosphorus onto Al\({}_{13}\)-O-MMt increased with the increase in the dosage of the adsorbent and became stable at -95% when the dosage was 0.1 g. An increasing dosage of adsorbent could adsorb more phosphorus in the aqueous solution. When the dosage reached 0.1 g, the adsorption of phosphorus onto Al\({}_{13}\)-O-MMt approached the equilibrium status, in which nearly the optimal amount of phosphorus was adsorbed. For reasons of cost-effectiveness, based on the experimental data, 0.1 g adsorbent is the optimal amount for the removal of 30 mL of 200 mg/L phosphorus. Column Adsorption of Phosphorus by Al\({}_{13}\)-O-MMt in the Elution Column and Breakthrough Time Analysis  
In Figure 6, the adsorption efficiency dropped rapidly after day 10 in the column experiment. The adsorption efficiency was about 85%, which was lower than the efficiency of batch adsorption, implying that the adsorption approached saturation within 10 days. The calculation reveals that the phosphorus adsorption capacity of Al\({}_{13}\)-O-MMt in column adsorption is 60 mg/g, which is higher compared to that of other montmorillonite-based sorbents (Table 1). Figure 5: Dosage of Al\({}_{13}\)-O-MMt used in the adsorption of 30 mL 200 mg/L phosphorus solution with pH = 8, related to adsorption efficiency. To verify the adsorption capacity of Al\({}_{13}\)-O-MMt in the column experiment as to whether it met the expectation, the breakthrough time was calculated via Equation (2). In Equation (2), the Thomas rate constant (\(k_{TH}\)) can be calculated using Equation (3):  
\[k_{TH}=\frac{v}{m} \tag{3}\]  
where \(v\) denotes the flow rate, and \(m\) represents the mass of phosphorus flowing in 1 min. Therefore,  
\[k_{TH}=\frac{0.417\ \text{mL}\cdot\text{min}^{-1}}{200\ \text{mg}\cdot\text{L}^{-1} \times(0.417\times 10^{-3})\ \text{L}}=5\ \text{mL}\cdot\text{min}^{-1}\cdot\text{mg}^{-1}\]  
If the values of the initial and equilibrium concentrations of solute in solution (\(c_{0}\) and \(c\)), the adsorption capacity (\(q_{0}\)), the quantity of the montmorillonite used (\(x\)), the flow \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Sorbent**} & \multicolumn{3}{c}{**Experiment Condition**} & \multirow{2}{*}{**Sorption Capacity**} \\ \cline{2-2} \cline{4-6}  & **Adsorbent** & & & **Phosphorus** & **(mg/g)** & **Reference** \\  & **Dosage (g)** & & & **Concentration (mg/L)** & & \\ \hline Chitosan/Ca–organically modified & & & & & \\ montmorillonite beads & 10 & 7 & 50 & 48.35 & [16]- \\ \hline Fe-loaded ceramic adsorbent & & & & & \\ (contain montmorillonite) & 10 & 6 & 10 & 45.88 & [61] \\ \hline Zirconium (Zr)-modified & & & & & \\ calcium-montmorillonite (Zr-CaMs) & & & & & \\ \hline Keggin Al\({}_{13}\) & & & & & \\ complex–HDTMA-modified & & & & & \\ montmorillonite (Al\({}_{13}\)-O-MMt) & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of phosphorus adsorption capacity and sorption condition among various montmorillonite-based adsorbents. Figure 6: Column adsorption for 12 days (8 h/day) with a total of 2400 mL phosphorus solution (200 mg/L) with pH = 8.  
rate (\(v\)), and the Thomas rate constant (\(k_{TH}\)) are known, the breakthrough time (\(t\)) can be calculated based on Equation (2).