Homework Question 2 (Optional) (total 30 bonus points for students who do the work and develop a neat solution)
Set up a batch reactor model for AsO43- sorption on Fe(OH)3 given initial conditions and parameters in Tables 6. Run the simulation to understand how sorbed concentrations are affected by different parameters and geochemical conditions.
- Effects of initial pH: Compare the surface concentration of AsO43-, PO43- and Na+ at the initial pH at 2, 4, 6, 7, 8 and 10, respectively. Plot the concentrations of the three ions as a function of pH. Describe the differences and explain your observations.
- Effects of Na+ concentration: compare the surface concentrations of AsO43-, PO43- and Na+ by setting the Na+ conc. at 10-4, 10-3, 10-2, 10-1 and 100 mol/L, respectively. Plot the sorbed concentration of the three ions as a function of Na+ conc. Describe the difference and explain your observations.
- Effect of equilibrium constants: compare the surface concentrations of AsO43-, PO43- and Na+ by setting the LogKapp for $A s 0_{4}^{3-}$ surface complexation reaction at 15.6, 16.6, 17.6, respectively. Plot the sorption amount of the three ions as a function of LogKapp. Describe the observations and explain why.
Table 6. Initial conditions, surface complexation reactions and constants (Riese, 1982; Zeng et al., 2008)
| Initial conditions |
Value |
| Temperature |
25oC |
| pH |
7.0 |
| AsO4--- |
0.005 mol/L |
| Na+ |
0.001 mol/L |
| Fe+++ |
0 |
| PO4--- |
0.001 mol/L |
| Site density $\equiv \mathrm{FeOH}$ |
$1.0 \times 10^{-6} \mathrm{~mol} / \mathrm{m}^{2}$ |
| Specific surface area |
50 m2/g |
| Fe(OH)3 volume fraction |
0.2 |
| Reactions |
Log K |
| $\equiv\mathrm{FeOH}+\mathrm{H}^+\Leftrightarrow\ \equiv\mathrm{FeOH}_2^+$ |
5.10 |
| $\equiv \mathrm{FeOH} \Leftrightarrow \quad \equiv \mathrm{FeO}^{-}+\mathrm{H}^{+}$ |
-10.70 |
| $\equiv\mathrm{FeOH}+\mathrm{Na}^+\Leftrightarrow\ \equiv\mathrm{FeO}-\mathrm{Na}+\mathrm{H}^+$ |
-9.00 |
| $\equiv \mathrm{FeOH}+\mathrm{AsO}_{4}^{3-}+\mathrm{H}^{+} \Leftrightarrow\left(\equiv \mathrm{FeOAsO}_{3}\right)^{2-}+\mathrm{H}_{2} \mathrm{O}$ |
16.6 |
| $\equiv \mathrm{FeOH}+\mathrm{PO}_{4}^{3-}+\mathrm{H}^{+} \Leftrightarrow\left(\equiv \mathrm{FeOPO}_{3}\right)^{2-}+\mathrm{H}_{2} \mathrm{O}$ |
16.9 |