3.4 Homework assignment

Homework Question 1: extension of example 3.1 (total 90 points):

If instead we have two types of surface sites on illite surface with the reactions and parameters shown in Tables 5. All other conditions remain the same as in example 3.1.

(10 points) At the pH of 8.0, calculate the concentrations of surface complexes on the surface sites; what is the pH at equilibrium?
(10 points) At the pH = 4.0, calculate the concentrations of surface complexes on the surface sites; what is the pH value at equilibrium?
(30 points) Change pH also to 2.0, 6.0, and 10.0 and run simulations. Combining simulation results from 1) – 3), plot total sorbed Cr(VI) and Na(I) as a function of pH. How does pH change the sorbed concentration for Na(I) and Cr(VI)?
(40 points) At the pH of 8.0, run the simulation using the specific surface area of 1, 5, 25, 50 m²/g. Combining simulation results from 1), plot total sorbed Cr(VI) and Na(I) as a function of specific surface area. How does specific surface area change the sorbed concentration for Na(I) and Cr(VI)?

Table 5. Initial conditions, surface complexation reactions and constants (Zachara et al., 1988)
Initial conditions	Value
Temperature	25^oC
Solution volume	250 mL
pH	8.0
Total CrO₄^--	$9.61 \times 10^{-5} \mathrm{~mol} / \mathrm{L}$
Na+	0.01 mol/L
Cl^-	0.01 mol/L
K⁺	$18.5 \times 10^{-5} \mathrm{~mol} / \mathrm{L}$
Site density $\equiv \mathrm{SiOH}$	$1.0 \times 10^{-6} \mathrm{~mol} / \mathrm{m}^{2}$
Site density $\equiv A l O H$	0.1 10^-6mol/m²
Illite specific surface area	15.36 m²/g
Illite volume fraction	0.003

Reactions	Log K
$\equiv\mathrm{SiOH}+\mathrm{H}^+\Leftrightarrow\ \equiv\mathrm{SiOH}_2^+$	0.95
$\equiv\mathrm{SiOH}\quad\Leftrightarrow\ \equiv\mathrm{SiO}^-+\mathrm{H}^+$	-6.59
$\equiv\mathrm{SiOH}+\mathrm{Na}^+\Leftrightarrow\ \equiv\mathrm{SiONa}+\mathrm{H}^+$	-6.60
$\equiv \mathrm{SiOH}+\mathrm{CrO}_{4}^{2-}+2 \mathrm{H}^{+} \Leftrightarrow\left(\equiv \mathrm{SiOH}^{0}-\mathrm{H}_{2} \mathrm{CrO}_{4}^{0}\right)^{0}$	14.50
$\equiv\mathrm{AlOH}+\mathrm{H}^+\Leftrightarrow\ \equiv\mathrm{AlOH}_2^+$	5.70
$\equiv AlOH\quad\Leftrightarrow\ \equiv AlO^-+H^+$	-11.40
$\equiv AlOH+Na^+\Leftrightarrow\ \equiv AlONa+H^+$	-9.15
$\equiv\mathrm{AlOH}+\mathrm{Cl}^-+\mathrm{H}^+\Leftrightarrow\ \equiv\mathrm{AlOH}_2\mathrm{Cl}$	7.90
$\equiv \mathrm{AlOH}+\mathrm{CrO}_{4}^{2-}+\mathrm{H}^{+} \Leftrightarrow\left(\equiv \mathrm{AlOH}_{2}^{+}-\mathrm{CrO}_{4}^{2-}\right)^{-}$	9.42
$\equiv \mathrm{AlOH}+\mathrm{CrO}_{4}^{2-}+2 \mathrm{H}^{+} \Leftrightarrow\left(\equiv \mathrm{AlOH}_{2}^{+}-\mathrm{HCrO}_{4}^{-}\right)^{0}$	16.30

Click here for HW3 solution package. [1]