Lesson 3: Surface Complexation

Overview

This lesson introduces general principles of surface complexation reactions, as well as how to set up surface complexation models in well-mixed batch reactors in CrunchFlow.

Learning Outcomes

By the end of this lesson, you should be able to:

Understand what are surface complexation reactions;
Comprehend thermodynamic controls of and important parameters for surface complexation.
Simulate surface complexation reactions in well-mixed batch reactors in CrunchFlow

Lesson Roadmap

Lesson Roadmap
To Read	Chapter 10 in Aqueous Environmental geochemistry (1997) by Langmuir, D.; Chapter 7 in Geochemistry, groundwater, and pollution, 2^nd edition, by C. A. J. Appelo and D. Postma, 2005; Page 63-64 and 69 of CrunchFlow manual; Example 4 of CrunchFlow exercise group.
To Do	Online reading materials Light board video Example videos Homework

Questions?

If you have any questions, please post them to our Questions? discussion forum (not e-mail), located in Canvas. The TA and I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.

3.1 Background

Sorption is the adhesion of chemicals to solid surfaces. Adsorption process occurs in many natural and engineered systems. Studies of contaminated systems have shown that sorption–desorption is an important geochemical process that regulates transport and fate of inorganic and organic contaminants in natural subsurface systems. For example, metals (Cd²⁺, Cr³⁺, Co²⁺, Cu²⁺, Fe³⁺, Pb²⁺or Zn²⁺) can become immobilized by sorbing on sediments and soils. They can also become mobilized through desorption from the solid surface and re-enter the aqueous phase when geochemical conditions allow. Sorption-desorption is widely used in industrial applications including charcoal activation, air conditioning, water purification, among others.

Sorption can occur either specifically or non-specifically as shown in Figure 1. Chemical sorption (Specific adsorption) is highly selective and occurs only between certain adsorptive and adsorbent species. A chemical bond involves sharing of electrons between the adsorbate and adsorbent and may be regarded as the formation of inner-sphere surface complexes. Chemical adsorption is difficult to reverse because of the strength of the formed bond. Physical adsorption (nonspecific adsorption). A physical attraction resulting from nonspecific, relatively weak Van der Waal's forces. Being only weakly bound, physical adsorption is easily reversed. Multiple layers form through outer-sphere surface complexes during physical adsorption [Goldberg 1991; Webb, 2003].

Sorption via surface complexation has been extensively studied. Surface complexation is the process where species in the aqueous phase form complexes with functional groups on solid surfaces, similar to aqueous complexation in lesson 1. Surface complexation function occurs between aqueous species and functional groups on solid surface, instead of the formation of complexes between aqueous species in aqueous complexation reactions. Surface complexation models use mass action laws that are analogous to aqueous geochemical conditions and solid phase properties.

Figure 1. Schematic illustration of the formation of inner-sphere and outer-sphere complexes at the solid–solution interface

Credit: [Goldberg et al., 2007]. Used with permission.

3.2 Surface Complexation Models (SCMs)

Surface complexation models describe sorption based on surface reaction equilibrium. Similar to aqueous complexation, surface complexation reactions are considered fast reactions and are controlled by reaction thermodynamics.

Surface Configuration of the Solid–Solution Interface

There are three commonly used SCMs, the constant capacitance model (CCM), the diffuse layer model (DLM), and the triple layer model (TLM). These models differ in complexity from the simplest CCM that has three adjustable model parameters, to the most complex TLM that has seven adjustable parameters [Hayes et al., 1991]. The double layers exist in practically all heterogeneous fluid-based systems. Here we introduce the principle and thermodynamics of DLM.

The double layer refers to two parallel layers of charge surrounding the solid surface. The first layer, the surface charge (either positive or negative), comprises ions sorbed onto the solid due to chemical interactions. The second layer (“diffuse” layer) is composed of counter ions attracted to the surface charges via the coulomb force, electrically screening the first layer. The schematic of double layer is shown in Figure 2.

Figure 2. A schematic diagram of solid surface, double layer, and bulk liquid with a negatively charged solid surface.

http://en.wikipedia.org/wiki/Double_layer_(interfacial) [1]

Surface Complexation Reactions

In traditional SCM models, all reactions are considered as at equilibrium. As an example, the surface protolysis reactions, where H⁺ transfers among chemicals, are given by:

\begin{equation}\equiv\mathrm{SOH}+\mathrm{H}^+\Leftrightarrow \equiv\mathrm{SOH}_2^+,K_1^{app}=\frac{\left[\equiv\mathrm{SOH}_2^+\right]}{[\equiv\mathrm{SOH}]\left[\mathrm{H}^+\right]}\end{equation}

\begin{equation}\equiv S O H \Leftrightarrow \equiv S O^{-}+H^{+}, K_{2}^{a p p}=\frac{\left[\equiv \mathrm{SO}^{-}\right]\left[\mathrm{H}^{+}\right]}{[\equiv \mathrm{SOH}]}\end{equation}

Here the $\equiv S O H$ represents a species or functional group on solid surface. In the first reaction, $\equiv S O H$ gains an H⁺ and becomes positively charged. In the second reaction, $\equiv S O H$ loses an H⁺ and becomes negatively charged. The apparent equilibrium constants K^app describe the relationship between activities of different species, written in the same format as we do for aqueous complexations except now we include activities of solid species.

Similarly, for a metal ion M with a positive charge m, the reactions are represented by:

\begin{equation}\equiv S O H+M^{m+} \Leftrightarrow \equiv S O M^{(\mathrm{m}-1)}+H^{+}, K_{M 1}^{a p p}=\frac{\left[\equiv \mathrm{SOM}^{(\mathrm{m}-1)}\right]\left[\mathrm{H}^{+}\right]}{[\equiv \mathrm{SOH}]\left[\mathrm{M}^{m+}\right]}\end{equation}

\begin{equation}2\equiv SOH+M^{m+}\Leftrightarrow\equiv(SO)_2M^{(\mathrm{m}-2)}+2H^+,\ K_{M2}^{app}=\frac{\left[\equiv(\mathrm{SO})_2\mathrm{M}^{(\mathrm{m}-2)}\right]\left[\mathrm{H}^+\right]^2}{[\equiv\mathrm{SOH}]^2\left[\mathrm{M}^{m+}\right]}\end{equation}

For an anionic ligand L with a negative charge of l, the reactions are represented by:

\begin{equation}\equiv S O H+L^{l-}+H^{+} \Leftrightarrow=S O H_{2}^{+}-L^{l-}, K_{L 1}^{a p p}=\frac{\left[\equiv \mathrm{SOH}_{2}^{+}-\mathrm{L}^{l-}\right]}{[\equiv \mathrm{SOH}]\left[\mathrm{L}^{l^{-}}\right]\left[\mathrm{H}^{+}\right]}\end{equation}

\begin{equation}\equiv S O H+L^{l-}+2 H^{+} \Leftrightarrow \equiv S O H_{2}^{+}-L H^{(l-1)-}, K_{L 2}^{a p p}=\frac{\left[\equiv \mathrm{SOH}_{2}^{+}-\mathrm{LH}^{(l-1)-}\right]}{[\equiv \mathrm{SOH}]\left[\mathrm{L}^{l-}\right]\left[\mathrm{H}^{+}\right]^{2}}\end{equation}

In these reactions, $\equiv S O H$ represents a surface site for the sorbent functional group, $\equiv S O H_{2}^{+}, \equiv S O^{-}, \equiv S O M^{(\mathrm{m}-1)}, \equiv(S O)_{2} M^{(\mathrm{m}-2)}, \equiv S O H_{2}^{+}-L^{l-} \text { and } \equiv S O H_{2}^{+}-L H^{(l-1)-}$ are surface complexes, [ ] represents the activity of each species or surface complex, $Mm+$ represents a metal ion of charge m⁺ and L^l- represents an anionic ligand of charge l⁻.

Apparent (K^app) and Intrinsic (K^intr) Equilibrium Constants

The apparent equilibrium constant of surface complexation reactions, K^app, is an important parameter because it determines the ion partition between aqueous and solid phases. Large K^app values indicate high affinity of the ions to the solid surface. The relationship between total Gibbs free energy $\Delta G_{\text {tot }}$ and K^app is as follows:

\begin{equation}\Delta G_{\text{tot }}=-RT\ln\mathrm{K}^{app}\end{equation}

Here the total Gibbs free energy $\Delta G_{\text {tot }}$ can be further expressed as follows:

\begin{equation}\Delta G_{\text {tot }}=\Delta G_{\text {chem }}^{0}+\Delta G_{\text {coul }}^{0}\end{equation}

Here $\Delta G_{c h e m}^{0}$ is the intrinsic free energy of the chemical reactions at the surface; $\Delta G_{\text {coul }}^{0}$ is the electrostatic or Coulombic term that accounts for the electrostatic interactions:

\begin{equation}\Delta G_{c o u l}^{0}=Z F \psi_{0}\end{equation}

Here Z is the charge of the ion, F is the Faraday constant (96485 C/mol), $\psi_{0}$ is the average potential of the surface plane (V). Therefore,

\begin{equation}K^{a p p}=\exp \left(-\frac{\Delta G_{t o t}}{R T}\right)=\exp \left(-\frac{\Delta G_{c h e m}^{0}+\Delta G_{c o u l}^{0}}{R T}\right)=K^{\mathrm{int} r} \exp \left(-\frac{Z F \psi_{0}}{R T}\right)\end{equation}

Where $K^{\mathrm{int} r}=\exp \left(-\frac{\Delta G_{c h e m}^{0}}{R T}\right)$, R is ideal gas constant $(1.987 \mathrm{cal} /(\mathrm{mol} \cdot \mathrm{K}))$; T is the absolute temperature (K). Take equation (1) as an example,

\begin{equation}K_{1}^{a p p}=\frac{\left[\equiv \mathrm{SOH}_{2}^{+}\right]}{[\equiv \mathrm{SOH}]\left[\mathrm{H}^{+}\right]}=\frac{\left[\equiv \mathrm{SOH}_{2}^{+}\right]}{[\equiv \mathrm{SOH}]\left[\mathrm{H}_{s}^{+}\right]} \exp \left(-\frac{Z_{H^{+}} F \psi_{0}}{R T}\right)=K_{1}^{\mathrm{int} r} \exp \left(-\frac{Z_{H^{+}} F \psi_{0}}{R T}\right)\end{equation}

Where $K_{1}^{\mathrm{int} r}=\frac{\left[\equiv \mathrm{SOH}_{2}^{+}\right]}{[\equiv \mathrm{SOH}]\left[\mathrm{H}_{s}^{+}\right]}$ , Z is the charge of the ion (1 in the case of H⁺); $\left[H_{s}^{+}\right]$ is H⁺ activity on the solid surface.

The electrostatic or coulombic effect can be quantified as:

\begin{equation}\left[\mathrm{H}_{s}^{+}\right]=\left[\mathrm{H}^{+}\right]_{b u l k} \exp \left(-\frac{Z_{H^{+}} F \psi_{0}}{R T}\right)\end{equation}

From equation (10), we know that $K_{1}^{\text {int } r}$ and $\psi_{0}$ are needed in order to calculate $K_{1}^{a p p}$. The $K_{1}^{\text {int } r}$ is typically estimated using zero charge extrapolation or using the double extrapolation method as discussed in literature. Under low ionic strength conditions where $\psi_{0} \cong 0$, the intrinsic and apparent constants are equivalent.

Surface sorption site

For different minerals, the number of surface sites differs significantly, depending on their surface properties. The abundance of surface sites is important in determining the total sorption capacity. The concentration of surface sites can be calculated as follows:

\begin{equation}C_{\text {site }}=\rho_{\text {site }} A_{\text {specific }}\end{equation}

Here C_site is the concentration of surface sites (mol/g mineral), ρ_sites is the surface density of surface hydroxyl sites (mol/m²), A_specific is the specific surface area (SSA)(m²/g). This equation says that surface site concentration depends on the surface site density and specific surface area. Please note that if you are working with porous media, you will need to calculate the total gram of minerals for surface complexation to get the total number of available sites.

Specific surface area (SSA) and site density values can be determined experimentally from Brunauer -Emmett-Teller (BET) surface area and tritium exchange measurements, respectively. The units of site/nm is often used in literature, where 1 site/nm = 1.66x10^-6 mol/m². Typical values of specific surface area (SSA) and site densities for different types of minerals are listed in Table 1. The total number of surface sites for a particular system (mol) can be calculated by multiplying site density (mol/m²) with SSA (m²/g) and the mineral mass (g). Minerals such as clays tend to have a large surface area and have a large capacity to sorb chemicals.

Table 1. Example specific surface area and site densities used in the base model
Absorbent	SAA (m²/g)	Site density (mol/m²) Strong Site	Site density (mol/m²) Weak Site	Reference
Goethite	14.7	1.76×10^-6	3.22×10^-6	(Müller and Sigg, 1992)
Kaolinite	19.5	2.20x10^-6	3.00×10^-6	(Lackovic et al., 2003)
Illite	66.8	1.30x10^-6	2.27x10^-6	(Gu and Evans, 2007)
Smectite	56.4	4.77x10^-8	9.54x10^-7	(Bradbury and Baeyens, 2005)

Different types of surface sites

Organic and inorganic chemicals are usually sorbed at hydroxyl surface functional groups that are located at the broken bonds and edge sites on minerals with excess negative charges [Baeyens and Bradbury, 1997]. We often classify two kinds of sorption sites: "strong" sites $\left(\equiv \mathrm{S}^{\mathrm{S}} \mathrm{OH}\right)$ and "weak" sites$\left(\equiv \mathrm{S}^{\mathrm{W}} \mathrm{OH}\right)$. "Strong" sites have a low capacity and a high sorption affinity and dominate the uptake of adsorbate at low concentrations. "Weak" sites have a considerably larger capacity however much lower sorption affinity. Table 2 shows reactions and equilibrium constants for U(VI) sorption on ferrihydrite, where Fe^sOH represents strong site with orders of magnitude higher intrinsic equilibrium constants than those of the weak sites $\left(\equiv \mathrm{FE}^{\mathrm{W}} \mathrm{OH}\right)$ (Zheng et al., 2003). In this soil with the presence of ferryhdrate, the site density ratio of weak to strong site is 476:1 (i.e., 0.21% of the total surface sites, 99.79% for the weak sites).

Table 2. Surface complexation reactions and equilibrium constants *[Zheng, et al., 2003]*
Reactions	LogK^intr
$2 \equiv \mathrm{Fe}^{S} \mathrm{OH}+\mathrm{UO}_{2}^{2+} \Leftrightarrow \equiv\left(\mathrm{Fe}^{S} \mathrm{O}\right)_{2} \mathrm{UO}_{2}+2 H^{+}$	-2.35
$2 \equiv \mathrm{Fe}^{W} \mathrm{OH}+\mathrm{UO}_{2}^{2+} \Leftrightarrow \equiv\left(\mathrm{Fe}^{W} \mathrm{O}\right)_{2} \mathrm{UO}_{2}+2 H^{+}$	-6.06
$2 \equiv \mathrm{Fe}^{S} \mathrm{OH}+\mathrm{UO}_{2}^{2+}+\mathrm{CO}_{3}^{2-} \Leftrightarrow \equiv\left(\mathrm{Fe}^{S} \mathrm{O}\right)_{2} \mathrm{UO}_{2} \mathrm{CO}_{3}^{2-}+2 \mathrm{H}^{+}$	4.33
$2 \equiv \mathrm{Fe}^{\mathrm{W}} \mathrm{OH}+\mathrm{UO}_{2}^{2+}+\mathrm{CO}_{3}^{2-} \Leftrightarrow \equiv\left(\mathrm{Fe}^{W} \mathrm{O}\right)_{2} \mathrm{UO}_{2} \mathrm{CO}_{3}^{2-}+2 H^{+}$	-0.24

Surface charge and point of zero charge (PZC)

Surface complexation leads to surface-charged solid surfaces. Electric surface charges govern characteristic chemical and physical phenomena such as ion exchange, adsorption, swelling, colloidal stability, and ﬂow behavior (Sposito, 1981). It is well known that the surface charges on layered silicates and insoluble oxides depend on the pH of aqueous solutions The pH of the point of zero charge (PZC), where the net total particle charge is zero, is a convenient reference for describing the pH dependence of surface charges. (Appel et al., 2003). When solution pH is above PZC, the solid surface has a negative charge and predominantly exhibits an ability to exchange cations, while the solid surface retains anions (electrostatically) if pH is below its PZC. A list of common substances and their associated PCZs is shown in Table 3.

Table 3. The Point of Zero Charge,pH_PZC, of clays and soil oxides and hydroxides (Table 7.3 (Appelo and Pstma, 2005), and references therin)
Chemical Formula	pH_PZC
$\text { Kaolinite }$	4.6
$\text { Montmorillonite }$	< 2.5
$\text { Corundum, } \alpha-\mathrm{Al}_{2} \mathrm{O}_{3}$	9.1
$\gamma-\mathrm{Al}_{2} \mathrm{O}_{3}$	8.5
$\text { alpha- } \mathrm{Al}(\mathrm{OH})_{3}$	5.0
$\text { Hematite, } \alpha-\mathrm{Fe}_{2} \mathrm{O}_{3}$	8.5
$\text { Goethite, } \alpha \text {-FeOOH }$	9.3
$\text { Birnessite, } \delta-\mathrm{MnO}_{2}$	2.2
$\mathrm{Fe}(\mathrm{OH})_{3}$	8.5
$\text { Quartz, } \mathrm{SiO}_{2}$	2.9
$\text { Calcite, } \mathrm{CaCO}_{3}$	9.5

3.3 Example 3.1

Cr(VI) sorption on illite in a batch reactor: Math formulation and CrunchFlow Setup

Example 3.1: Cr(VI) surface complexation on illite. Chromium is a common containment in natural subsurface due to its natural occurrence and wide industrial usage, including electroplating, pigmenting, and dye synthesis. Anionic Cr (VI) is highly mobile and poses a tremendous risk to human and ecosystem health. Clay minerals such as illite are important in controlling Cr(VI) sorption and natural attenuation due to its large surface area and ubiquitous presence (Wang and Li, 2015).

We have an initial solution listed in Table 4. The illite grains in the solution have specified surface area and site density of $\equiv \mathrm{SiOH}$. The surface site $\equiv \mathrm{SiOH}$ goes through several surface complexation reactions as listed in Table 4. Please calculate:

At the pH = 8.0, calculate the concentrations of different surface complexes on the surface sites; what is the pH value after the system reaches equilibrium?
If the initial pH is 4.0, calculate the concentration of different surface complexes on the surface sites; what is the pH value after the system reaches equilibrium?

Table 4. Initial conditions, surface complexation reactions and constants [Zachara et al., 1988]
Initial conditions (total concentrations)	Value
Temperature	25^oC
Solution volume	250 mL
pH	8.0
CrO₄^2-	9.61x10^-5mol/L
Na⁺	0.01 mol/L
Cl^-	0.01 mol/L
K⁺	1.93x10^-4mol/L
Al³⁺	1.00× 10^-6 mol/L
Mg²⁺	1.00× 10^-6mol/L
SiO_2(aq)	1.00× 10^-5mol/L
Site density $\equiv \mathrm{SiOH}$	1.00× 10^-6mol/L
Illite specific surface area	15.36 m²/g
Illite volume fraction	0.003
Reactions	Log K_app
$\equiv \mathrm{SiOH}+\mathrm{H}^{+} \Leftrightarrow \equiv \mathrm{SiOH}_{2}^{+}$	0.95
$\equiv \mathrm{SiOH} \Leftrightarrow \mathrm{SiO}^{-}+\mathrm{H}^{+}$	-6.59
$\equiv \mathrm{SiOH}+\mathrm{Na}^{+} \Leftrightarrow \equiv \mathrm{SiONa}+\mathrm{H}^{+}$	-6.60
$\equiv \mathrm{SiOH}+\mathrm{CrO}_{4}^{2-}+2 H^{+} \Leftrightarrow\left(\equiv \mathrm{SiOH}^{0}-\mathrm{H}_{2} \mathrm{Cr} O_{4}^{0}\right)^{0}$	14.50

Mathematical Representation:

Before setting up the simulations in CrunchFlow, let's think about how to represent this sytem, a well-mixed reactor, in a mathematical form, how many chemical species do we have, how many algebraic relationships that we have, and how many equations we need to solve. Please watch the following video (13:12).

Surface Complexation
Click for a transcript of the surface complexation video.

Surface Complexation

Presenter: We are going to show an example of Surface Complexation reaction today. This is somewhat similar to one of the previous lessons on Aqueous Complexation. But the difference is really, now we have solid phase and complexations are being formed between aqueous species and the species on a solid phase. So what I have here is example 3.1. You also have that in the online material. So this is the example, if we think about a system that you have well-mixed again a batch reactor.

So well-mixed meaning all the concentration in the water phase will remain the same. It's uniform. So we don't really solve for concentration difference in different parts of the batch reactor. Now in this system we have Illite grains, which is a very common type of clay. And then we have the water that has this chromium 6 (CrVI) on it. And we know that this species will solve our surface complexes with species on Illite. So what we have here is these grains and then this water.

But also there's some background species, like sodium chloride, that's providing some salinity. And Illite itself will be slowly dissolving up. So there are some other species, for example, magnesium silica. We'll talk about that later. So in order for solve for system, we think about this system again. Surface complexation is usually considered also a very fast reaction, similar to aqueous complexation. So we can usually think about the thermodynamics of these reactions instead of kinetics of these reactions.

So let's just go over the chemistry of the system. So first of all, we have these reactions, right? And we think about this as there's both reactions happening in water phase and also at the interface of water and solid. So in the water phase we actually will simplify the system to only include, for example, the water dissociation to become hydrogen ion (H⁺) and hydroxide (OH^-). This is a reaction that must be there. But also it includes a chromium related reaction.

Chromium 6 can have three different forms. You have H₂CrO₄(aq) can become H+ and then this species $$HCrO_4^-$$. And this can further dissociate to have hydrogen ion (H⁺) and this $CrO_4^-$ form. So in the water phase we are actually, there could be a lot of other reaction happening. But for simplicity we would only include these three.

So that's for the water phase reactions. And also at the water and solid interface, we're really talking about water and Illite interfaces. We have these solid species, like surface species, right? So this, if you look at the form, we are kind of using this to represent a solid surface. And then you have the SiOH as a functional group on the solid surface.

So this surface specie can react with hydrogen ion (H⁺) to form this. And also dissociate, the hydrogen ion comes out to become this. $\equiv \mathrm{SiOH}_{2}^{+} / \equiv \mathrm{SiOH} +\mathrm{H}^{+}=$, But also there's, for example, when there's sodium in the water and chromium in the water, they can also form these surface complexes. So you probably notice that in the different reactions here, these reactions, we write, for example, the same type of laws of mass action like in aqueous complexation.

So we had this activity of hydrogen ion, activity OH^- is timed together, equal to K_w. And similar for chromium A1, A2, right? I'm not writing everything out. Because this is all in similar form. You write activity of species in the right side of the reaction divided by activity of species in the left side of the reaction. So obviously the K's are constants. So again, we have these three reactions. But also then we have 4, 5, 6, 7. So we have three aqueous phase reactions and a another four reactions that occur at the water and solid interface.

And each of them you can have these expressions of laws of mass action, which I'm not detailing out. But also, as I mentioned, the Illite itself would dissolve slowly. So in control we actually also have this reaction in the background, except that it occurs so slowly it doesn't change much of the chemistry of the system. But when we set up the control, to input a file, we do need to have these reactions, these chemical species there. That is actually part of the Illite. But it's not really explicitly talked about in this aqueous phase.

So these are the chemical components of Illite that we have to put these there as primary species. Now, if we think about this sort of system, so we have this many reactions. And we think about how many different chemical species, we have, if we just list them out, you have H, of course, hydrogen ion, OH^-.

And then you have three chromium related species, which was different hydrogen ion there, $CrO_4^-$. And then you have these solid. We also need to solve the concentration for the solid species as well, right? So you have these $\equiv \mathrm{SiOH}_{2}^{+}$, SiOH self, SiO-. And then this forms complexly to have SiOHNa or SiO. And then you also have these OH with $\mathrm{H}_{2} \mathrm{CrO}_{4}^{0}$. So these are the five possible or potential surface complexes that can be formed. Now on top of that, you also have, for example, sodium chloride Na⁺,Cl^-. And then the chemical composition of these Illites, right? So you have Mg²⁺, potassium K⁺, aluminum, SiO₂, aqueous.

OK, so let's count. We need to solve for all these different species, right? So let's count this, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And then you have another 6. So in total we have 16 species, including all the possible aqueous species and solid species or surface species. So we have 16 species. That means that we are going to solve for 16 unknowns. And we already have 16 unknowns. Because we have 16 species.

Now we already know we have seven different relationships, 1, 2, 3, 4, 5, 6, 7, right? So these are the reaction we specify. And we know every time we specify one reaction, there's an algebraic relationship relative to that. So we have 16 minus 7 equal to 9. So we have 16 unknowns. 7 we know the relationship meaning these concentrations, all activity are dependent on each other, this relationship. That would mean we need to specify 9 additional conditions for completely solving these reactions.

So what we can do here is, for example, a lot of times we know PH. So these conditions should be already given to you. And what we have, for example, typically, let's say, we know PH. Then we should know the activity of hydrogen ion. Or we know the question should give the total concentration of chromium 6. And this would be equal to, for example, concentration of CrO₄^2- plus concentration of $\mathrm{H}_2\mathrm{CrO}_4^{ }$ plus concentration of $\mathrm{H}_{2} \mathrm{CrO}_{4}^{0}$ aqueous, right? And this together should be equal to whatever constant they gave to you. Which, I'm not writing those.

And you also should know, it should also give you a concentration of sodium, give the concentration of chloride, and give you a concentration of potassium, aluminum, magnesium, and SiO₂(aq). Another condition they should give you is also, how much total site you have. So this would be something like so this is a total site on the solid surface should be the concentration of all these five potential species adding together, right?

So you can think about this as total sites, C sites. And this would be adding all the surface complex species. For example, $\mathrm{SiOH}_{2}^{+}$ plus CSiOH plus CSiO^- and then the Csi of sodium plus CsiOHH2CrO4. So these are the five different surface complexes that can be formed. And this should be equal to a constant total concentration of sites on the Illite grain. And the total concentration of sites should be equal to, for example, how much Illite grain you have, how many grams. And also the site density, times the site density times the surface area.

So these should be conditions you should have. So if you look at this, you have 7, and then 8, 9, 10, 11, 12, 13, 14, 15, 16. So this is close to form, right? You have 16 unknowns. You have 16 relationships to-- You have seven relationships, but you also know nine conditions that specify the system that you can solve for the whole system.

Now what you end up with is the concentration of each species, both aqueous and solid at equilibrium. Because the system reaches equilibrium really quickly. So essentially you have 7 relationships and then 9 conditions to completely solve the concentration of all species involved in the system.

Credit: Li Li @ Penn State University is licensed under CC BY-NC-SA 4.0 [2]

Here are the equations and key points.

Setting up a simulation for surface complexation involves both input and database file. Relevant reading materials on surface complexation in CrunchFlow includes keywords on pages 63, 64, 69.

In the input file, the keyword block for surface complexation is the SURFACE_COMPLEXATION block. Complexation must occur on a specific mineral, so a valid mineral name (listed in the MINERALS keyword block) must be given in the MINERAL keyword block as well. An example:

SURFACE_COMPLEXATION
$\equiv \mathrm{SiOH}$ on Illite
END

Here the $\equiv \mathrm{SiOH}$ is a surface site on the mineral Illite. The mineral must be present in the database. To specify a non-electrostatic model, the mineral name should be followed by the keyword –no_edl. For example:

$\equiv \mathrm{SiOH}$ on Illite -no_edl

The term “-no_edl” means no electrical double layer.

In the database file, you need to specify the surface complexation reactions in Table 4 in the “Begin Surface Complexation” section. In addition, you need to specify charges of the surface species in “Begin Surface Complexation parameters” section.

The exercise 4 in the CrunchFlowExampleExercise is also for surface complexation.

If you try to set up in Phreeqc, Phreeqc manual includes the introduction of surface complexation calculation and the key words such as SURFACE, SURFACE_MASTER_SPECIES, SURFACE_SPECIES. Example 8 in Phreeqc is a good reference for setting up surface complexation reactions.

Click here for a transcript of the Lesson 2 Ex CrunchFlow video.

Li Li: All right. Let's get started on Lesson 3. I suppose everyone has read through the online material. So at this point, you are ready to start the example. Hopefully, you have appreciated the importance of surface complexation and how common they occur and what are the applications as well as what governs surface complexation on clays and different type of material.

So in this video, we are going to go through the example 3.1, which essentially is about setting up a batch reactor for chromium absorption on illite. And we know chromium is a very common contaminant. It can occur in terms of natural occurrence. There are processes in natural system that actually would generate chromium.

It's also why they use it in industry for different type of applications. So chromium can be a tremendous risk to both human and ecosystem health. So clay in natural system usually has the capacity to absorb chromium. So what we are going through here in this example, I'm giving you Table 4 which is the initial conditions for the system.

And essentially, we are really kind of looking at a batch reactor at 25 degrees C. And let's say you have a beaker, 250 milliliters as the volume. And essentially we're adding. So you have this amount of water. This beaker is filled with 250 milliliters of water. And then imagine in that beaker, you have some amount of illite grains.

And I put here illite volume fraction is 0.003, which is 0.3% of the total volume. You can actually calculate what it is. Because we have a 250 milliliters as the total volume. And you also are given the illite-specific surface area, which is 15.36 meters squared per gram.

Now illite is a very common clay material. Some other common clay material like smectite, chlorite, the various type of clay minerals. Clay tend to be very complex its chemical compositions and all kinds of different type of So we pick illite as a representative one, essentially.

Now, so imagine you have all these. And then in the water, you are putting a pH 8.0 and this chromium. What I'm putting here is this concentration, it's before the speciation. So really, it's a total concentration of chromium 6. And then you have sodium chloride, potassium in the background.

So these are what's happened, what's the solution. And that means the second half of the table I'm telling you that there's this surface site SiOH. And this surface site can go through four different surface reactions. One is complexity with H plus to becomes this SiOH2 plus. And then it's log K, its apparent equivalent constant is listed in the right hand side.

Anyway, you have these four different reactions for the surface reaction part. But imagine you would also have all kinds of aqueous complexation reaction happening at the same time. You are not going to just have these surface reactions. So keep that in mind.

So what I'm asking, we went through this Table 4. And what I'm asking here is that, first of all, at the pH of 8.0, I'm asking you to calculate the concentration of the different surface complexes on the surface sites. And what is the pH value of the system which is equivalent?

And these are all equivalent reactions, so you would get a direct number after running the simulation. And if you have initial pH of 4.0, you would do the same thing. And how much difference do you see? So essentially, it's really trying to look at-- by comparing Question 1 and Question 2, you're looking at how much difference does pH make in terms of how much chromium absorbed on the surface.

So let's go through this. There's two things that you actually would need to set up. I talk briefly in the online material texts. One is the database. In order to set up the reactions, you would need the surface reaction. You would need to go through the database.

And in the database, let's see if we start from the beginning. And before that, from previous lessons, you have all the different blocks. We have touched through primary species block, second species block. And then mineral reaction kinetics in the previous lessons.

Here, let's go through the surface complexation. So there's a block listing all these minerals as a surface complexation block. So let's do Control-F to search for surface complexation. And it directly come to me with the beginning surface complexation reaction.

So I already, what I did different in this lecture, a little bit different from previous. Previous one, I tend to start from beginning and we go kind of one-by-one step. Here, I'm already putting in these reactions. Because that will save us a little bit of time. I don't want the video to be too long. Because at some point, it gets boring.

So in this, so what you will need to do in the beginnings of the complexation part you will be putting all the different reactions listed in table. You have four reactions. So you would need four different surface reactions included here.

Now the way I load it is using the products, the absorbed species. So if you observe, for example, the first one here, it's SiOH2 plus. It's actually this one, SiOH2 plus.

Whether you use this like three line equal or you use this larger It doesn't really matter. Because the code we're reading essentially is a text file. And as long as you have consistent representation in the input file and in the database, it can recognize it. It doesn't matter if you use this larger than or if you use this triple equal sign. But the problem will come if you are not consistent between input file and database.

So anyway here, in the input file, I write this way. So essentially, you can see it's this species, similar to the aqueous complexation. So you have this species and equals to 1.0 H plus press 1.0 this SiOH species.

Now it's opposite way of writing as in this table. And this apparent K is written in terms of the reaction in this form. So when we do this form, since it needs to be negative now, so it's minus 0.95. Again, we are looking at 25 degrees C.

This, as a whole form, it is very similar. It's essentially the same as what you see before for the aqueous complexation. So you can see think about surface mixing as really almost like aqueous complexation, except that you are having a reaction with species on the surface. And so, all these different reactions are written similarly.

So this first item is for the first reaction. And then the second one, you have SiO minus as on the surface. And this is equal to essentially minus 1 from this SiOH. So this is another reaction. Now again, in the table, you have minus 6.59. And it's because the reaction is in opposite directions. This needs to be 6.59.

And all these other 500.0's as I mentioned, these are for-- you could have a constant at a different temperature. And you can really ignore them. But you do need to have eight items to represent the eight temperature points. And similarly, you have SiO sodium and SiOH and H2 chromium species. So as long as you pay attention to the sign of the log K values, be consistent with how these terms in terms of reaction are written, it's in the opposite way that is listed in the table, you should be fine.

So this is for the surface complexation block in the database. And then a second item in the database for surface complexation is giving the charge for each of these surface complexes. What is the charge of each of these species? So for example, SiOH is zero. SiOH2 plus is 1.0. Minus is minus 1.0. And you have all these other species. So your list is there. So essentially, two items in the database block.

And then in the input file block, let's look at this. Again, I already put everything in. But we walk through and you kind of need to know. So all these ones we talked about before, these are kind of computation long time

And then, the discretization is for, essentially, total volume. So we have 250 milliliters. I'm putting centimeters as units. This is essentially OK. We only input 250 for x zone as one cell. But essentially, the default is the y zones. And z zones is 1.

So it's like one group block in each direction, so giving you a well-mixed one group block, essentially. If you want to specifically put in y zones, 1 1 and then z zones 1, that's fine too. You can look up the discretization in the Crunch menu.

And then you do need to put in illite. The reason is that because in CrunchFlow, all the surface sites, you need to specify which mineral is this on. So here, this SiOH site is on illite. So you have to have illite there. So in the mineral, you would need to put illite as a mineral.

For systems that you have, for example, you have mineral dissolution precipitation and you also have surface complex. So you might have multiple minerals there. And you might have multiple minerals that have surface complexation sites. And you can put more than these when you have more complex systems.

So this is for surface complexation. And then we go to the condition. Now in the condition, we set up the initial. Because this unit should be really mole per liter. I think in the table, we put mole per liter. So this is mole per liter. Temperature, 25. And then you have pH 8.0. Chromium, sodium, chloride, potassium, they are all listed in the Table 4 in the online material.

Now I do have a few more primary species than what you have in what I have in the table. And the reason, why do I need to do that? The reasoning is that we have illite. So as long as you have-- let's go through what is illite into mineral dissolution reaction. We don't really put mineral dissolution reaction. But as long as you put illite, then you need all the building blocks in aqueous phase, essentially.

So let's search in the database, how does illite-- what is the composition of illite of terms of different chemical species. So I do F for illite. So you have illite. Look at here. So this illite, imagine you will be writing illite as a solid phase dissolving at-- actually plus H plus, 8H plus, and then dissolving to become 0.25 magnesium, 0.6 potassium, 2.3 aluminum, 3.5 silica, and water. And then the rest of these are the eight equivalent constants in different temperature.

And then you have the molecular weight or whatever. And in any case, you can see is that in the illite block, illite is composed of these different cations. So although in the table, I only give you chromium, sodium, chloride, and other species, because illite as a mineral contains magnesium, silica, aluminum as additional species. So we do need to put in the input of five for this species as part of the primary species. So that's what you actually would do.

So these species are already given, essentially, right in the table. And these species are additional because of the inclusion of illite as a mineral. And you need all the building blocks for illite. Otherwise, the code is not going to recognize it.

So all these species are, for example, pH chromium, sodium, chloride according to the concentrations that are given to you in the table. And then SiO2 aluminum magnesium, let's assume that, for example, illite dissolution would be very slow. Let's say you have this. You are doing an absorption experiment. Usually, you want to look at how much does chromium absorb on the solid phase. Usually you do it using a very short period of time. And illite dissolution is relatively slow. So it wouldn't dissolve that much in the solution.

So let's imagine your solution doesn't have much of these species. I could put zero. But usually, I prefer to put this small number instead of zero. A lot of time, computers have some problem with zeros. Try to avoid zero if you can.

So these are the primary species. And then you have the site name. This is a name of site that you put in the database. Now, as I mentioned, if you use this three line equals sign in here, then when you put in database, you also need to put three line equal sign.

So here, this is a site density, which the unit is mole per liter squared. It's 1.0 times 10 to minus 6, which is given in the table. And then you have this illite. 0.003 with a specific surface area of 15.36 meters squared per gram.

So that's a condition block. You not only should put in all the species that are given to you in the table, but also the species that are part of building block of the illite, the mineral that the surface site is on. And then, actually, this probably should be in earlier. But anyway, the order doesn't really matter in the input file.

But just look at the secondary species. You have these. I put these secondary species. But some of them may not be important. We can buy it and go through it in the output file. So once you have this, let's look at this folder that we are going to run the simulation for this example 3.1.

So I click on this one, I get see our example 3.1 dot [INAUDIBLE]. So it went through. It just spit all the output file. But the key ones that you will be looking at would be-- so see our example output file. This one. Maybe this one. So let's look through this example.

Again, so at the early part of this, it'll be walking through your input file and database. Look for everything, for example, number of components, number of secondary species, number of kinetic minerals, and goes through all the K value matrix, essentially.

And if you want, some time when you debug, for example, if something went wrong and you don't know what was wrong with it, it's also hard to look through the early part of this. For example, you might be not putting the right log K values in these two problems when you do the calculations.

So again, these are the condition input, condition initial. We didn't really put a charge balance here. But right now it's a total charge of negative. So probably we should, if we want charge balance, it should be really, the sodium species would need to be put charge balanced.

Now, here. Let's look through. So this, essentially, is a table that is giving you all the concentration of different species, log molality, log activity, and everything. Let's look in log molalities concentration you get.

So the first several line for all the surface species. And then you have H plus, sodium, all the aqueous species here. So let's look at chromium. We are looking at chromium absorption. So it'll be interesting to see what are the dominant species. In the table, you're given a total concentration of chromium 9.6 times 10 to minus 5 mole per liter.

When you look at this, it's H chromium O4 minus H2 chromium O4 and then chromium O4 These are in orders 10 to minus 4, 10 to the minus 5, 10 to the minus 15. And then on the surface, we are supposed to have the surface species of this. But it's very, very small. It's 10 to minus 10, essentially. Very small numbers.

So that means-- what does that mean? You have this 10 to minus 10. And then you also have chromium CrO4 2 minus is 10 to minus 4. 10 to minus 4. And then these are 10 to the minus 5, 10 to minus 15. So what does that mean?

Do you think chromium absorbed on a solid phase or not? If you think about it, comparing the different species, on the solid phase, you are supposed to have this surface species, you have very low concentration of 10 minus 10. And chromium is-- chromium O4 is 2 minus.

So then if you compare this, you know this is, essentially, actually most of chromium is still in the aqueous phase. It's not absorbing much at all at this pH. Solution pH is still 8.0. So it's not really reacting much. Because the absorption reaction doesn't at these high pH values.

All right. So you can pull out these numbers and answer the question, get a table, answer the question. What's the concentrations of different surface complexes on this and the pH value.

And then second question is pH is 4.0. So let's change a condition here. If I change this condition to 4.0, just change the pH to 4, what happens? So I changed it to 4.0. And let's rerun it.

So what happens, I might have mentioned this before, when you run this you can delete all the odd profiles if you want. But you can also just leave it there. Or you can build another folder, if you want, to keep all the odd profiles.

But if you run it in the same folder, the new simulation would overwrite the old file. So you will get the new file with pH at 4. So let's just try this. I need to save this so it will actually reflect. So let's run it again.

OK, because I changed the concentration. This is a solution that is relatively-- I guess it doesn't take-- you would still need to take mole per kilogram. It doesn't really matter when you have relatively dilute solution like we have here. So we have mole per kilogram. Let's re-write. It doesn't recognize mole per liter. Let's do it again.

It's done. Hopefully, it's giving me-- I'm just trying to update it like go to our folder and then we open, make sure all these files are the new updated files. You can look at the time to estimation. It needs to be the latest time.

Anyway, so you have things-- So the output file should be this one. Looks like it's still organizing. It's still not green yet. It's actually ready. So it's full. Every thing else is the same. We can just go down and look at the last block that lists all the concentrations. So now it's pH 4.0.

So we can look at the same, for example, different species for chromium. Chromium, so HCrO4 is still pretty high, minus 4. And then this is H2. It's minus 9. Now in chromium, CrO4 is 10 to minus-- so the aqueous species dominant one is HClO4 now because you have much more hydrogen now. It's a much acidic condition.

Now here you also observe that SiOH, this surface species, before it was in the order of 10 to the minus 10. Now it's 10 minus to minus 4.8 essentially. So increased by about five orders of magnitude, which means you absorbed much more chromium on solid than what do you had before. So pH has a huge impact on how much you can absorb on solid phase.

Let's see if I try pH equal to 3.0, what happens? Let's try it again. Let's close this. And change this to 3.0. So it's updating. Going back. Let's look at the output file.

It's here. Now here with pH 3, we increased more on the solid phase. So essentially, you would have absorbed species this much. So it's in the order of 10 to minus 4.5. So between pH 4 and 3, they all already have a lot of different hydrogen ions in the system. So it doesn't change much as when you change from pH 8 to 4.

Now the reason, here's why. Chromium 6 with a pH 8.0, the dominant species, it's an active charge species. So it tends to absorb when the system, when the surface site, has a lot of positive sites.

Now at high pH condition, the aqueous solution have a lot of OH minus instead of H plus. So the illite surface tend to be negative. And because it's negative, it wouldn't attract much of the negative chromium on the solid surface.

Now when you increase acidity or decrease pH to 3 or to 4, you have a lot of H plus in the system. And this H plus will go through these reactions with the surface site to form SiOH2 plus. So you would have a lot of positive charges on the surface. Now, in that case, chromium would be attracted to the positive charges surface. So that's why under low pH condition, you can absorb much more chromium than the situation of high pH.

So now imagine, this is for chromium and it's a negative charged species. What if you have, for example, cadmium or zinc or other species that these cations that are positively charged, they tend to be attracted by negative charged surfaces.

So think about what condition, under what condition you tend to have more surface complexation for these cations. The answer would be opposite to what you have here. So for example, these heavy metal cations, you tend to see more absorption under high pH conditions.

I think we can end now, I believe. I talked about everything I need to discuss. And just as a reminder, if you're not clear about what you are going to do and you want a bit more detailed information from the manual or everything, I listed in the online materials that for surface complexation examples, the menu, CrunchFlow menu page 6-3, 6-4, and 6-9, they are going through different blocks in Crunch.

And we uploaded a set of exercises with input file and documents that explain what each exercise do. So these are good resources again, good example files for you if you need something to look up. So in that exercise folder, let me just pull it up so you can see it.

In CrunchFlow related, I added a CrunchFlow example exercises. So in that photo, we have photos for different exercises. And in Exercise 4 is for a surface complexation example, if you would like to look up.

Let's stop here. And I hope you had fun working on this and the rest of the homework. For question one homework, which is an extension of example 3.1, you have total chromium. This is essentially the same. But essentially, I added one more surface species, which is aluminum.

And with that, you would need to set up in your database with this species like the site density would be in the input file. And also, all the reactions that are associated with the database, you need these reactions. You also need to put in the beginning surface complexation block to define it. And then you can run the simulation.

So remember, you need to update database. You need to update that input file to run the whole suite of thing. All right. I will stop here and have fun.

Click here for the solution.

Solution 1: After the reaction, pH = 7.97
Species	Moles/BuldVolume(m³)	Mole Fraction (%)
SiOH₂⁺	6.335E-08	0.000179
SiOH	1.871E-02	52.9
SiO^-	1.265E-02	35.8
SiONa	4.000E-03	11.3
$\left(\equiv\mathrm{SiOH^0}-\mathrm{H}_2\mathrm{CrO}_4^0\right)^0$	4.099E-08	0.000116

Solution 2: After the reaction, pH = 4.92
Species	Moles/BuldVolume(m³)	Mole Fraction (%)
SiOH₂⁺	4.257E-06	0.101
SiOH	3.118E-05	0.740
SiO^-	5.201E-04	12.3
SiONa	5.808E-06	0.138
$\left(\equiv\mathrm{SiOH^0}-\mathrm{H}_2\mathrm{CrO}_4^0\right)^0$	3.653E-03	86.7

Credit: Li Li @ Penn State University is licensed under CC BY-NC-SA 4.0 [2]

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. [3]

3.5 Homework Assignment 2 (Optional)

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 AsO₄^3- 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 AsO₄^3-, PO₄^3- 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 AsO₄^3-, PO₄^3- 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 AsO₄^3-, PO₄^3- and Na⁺ by setting the LogK_app 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 LogK_app. 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	25^oC
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

3.6 Summary & Assignments

Summary

Surface complexation occurs ubiquitously in natural and engineered systems. Understanding surface complexation reaction is important to understand and predict reactive transport and fate of chemicals (such as Cr, As, Cd , Cu, Pb) in natural waters, soils, and sediments. Here we introduce the mechanisms and importance, and controlling parameters of surface complexation reactions, and how to set up the model for ion exchange reactions in CrunchFlow.

Other reference books

Competitive Sorption and Transport of Heavy Metals in Soils and Geological Media.by H. M. Selim, 2012. Chapter 2. Equilibrium and kinetic modeling of competitive heavy metals sorption and transport in soils.

Kinetics of Water-Rock Interaction. Brantley, Susan, Kubicki, James, White, Art. 2008. Chapter 4. Kinetics of sorption-desorption.

Aquatic surface chemistry: chemical processes at the particle-water interface. Stumm, Werner. New York : Wiley 1987.

Reminder - Complete all of the Lesson 3 tasks!

You have reached the end of Lesson 3! Double-check the to-do list on the Lesson 3 Overview page to make sure you have completed all of the activities listed there before you begin Lesson 4. [4]

References

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Appelo, C.A.J. and Pstma, D. (2005) Geochemistry, groundwater, and pollution, 2nd ed. CRC Press, Taylor and Francis group, Boca Raton, FL.

Baeyens, B. and Bradbury, M.H. (1997) A mechanistic description of Ni and Zn sorption on Na-montmorillonite Part I: Titration and sorption measurements. Journal of Contaminant Hydrology 27, 199-222.

Bradbury, M.H. and Baeyens, B. (2005) Modelling the sorption of Mn(II), Co(II), Ni(II), Zn(II), Cd(II), Eu(III), Am(III), Sn(IV), Th(IV), Np(V) and U(VI) on montmorillonite: Linear free energy relationships and estimates of surface binding constants for some selected heavy metals and actinides. Geochimica et Cosmochimica Acta 69, 875-892.

Goldberg, S. (1991) Sensitivity of surface complexation modeling to the surface site density parameter. Journal of Colloid and Interface Science 145, 1-9.

Goldberg, S., Criscenti, L.J., Turner, D.R., Davis, J.A. and Cantrell, K.J. (2007) Adsorption - Desorption processes in subsurface reactive transport modeling. Vadose Zone Journal 6, 407-435.

Gu, X. and Evans, L.J. (2007) Modelling the adsorption of Cd(II), Cu(II), Ni(II), Pb(II), and Zn(II) onto Fithian illite. Journal of Colloid and Interface Science 307, 317-325.

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Hayes, K.F., Redden, G., Ela, W. and Leckie, J.O. (1991) SURFACE COMPLEXATION MODELS - AN EVALUATION OF MODEL PARAMETER-ESTIMATION USING FITEQL AND OXIDE MINERAL TITRATION DATA. Journal of Colloid and Interface Science 142, 448-469.

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Li, W., Tang, Y.K., Zeng, Y.T., Tong, Z.F., Liang, D.W. and Cui, W.W. (2012) Adsorption behavior of Cr(VI) ions on tannin-immobilized activated clay. Chemical Engineering Journal 193, 88-95.

Müller, B. and Sigg, L. (1992) Adsorption of lead(II) on the goethite surface: Voltammetric evaluation of surface complexation parameters. Journal of Colloid and Interface Science 148, 517-532.

Riese, A.C. (1982) Adsorption of Radium and Thorium onto Quartz and Kaolinite: A Comparison of Solution/Surface Equilibria Model. Ph.D. Dissertation, Colorado School of Mines 292p.

Serrano, S., O'Day, P.A., Vlassopoulos, D., Garcia-Gonzalez, M.T. and Garrido, F. (2009) A surface complexation and ion exchange model of Pb and Cd competitive sorption on natural soils. Geochimica Et Cosmochimica Acta 73, 543-558.

Sposito, G. (1981) THE OPERATIONAL DEFINITION OF THE ZERO-POINT OF CHARGE IN SOILS. Soil Sci Soc Am J 45, 292-297.

Um, W., Serne, R.J., Brown, C.F. and Rod, K.A. (2008) Uranium(VI) sorption on iron oxides in Hanford Site sediment: Application of a surface complexation model. Applied Geochemistry 23, 2649-2657.

Wang, L. and Li, L. (2015) Illite Spatial Distribution Patterns Dictate Cr(VI) Sorption Macrocapacity and Macrokinetics. Environmental Science & Technology 49, 1374-1383.

Webb, P.A. (2003 ) Introduction to Chemical Adsorption Analytical Techniques and their Applications to Catalysis. MIC Technical Publications.

Zachara, J.M., Cowan, C.E., Schmidt, R.L. and Ainsworth, C.C. (1988) Chromate adsorption by kaolinite. Clay Clay Miner 36, 317-326.

Zeng, H., Fisher, B. and Giammar, D.E. (2008) Individual and competitive adsorption of arsenate and phosphate to a high-surface-area iron oxide-based sorbent. Environmental Science & Technology 42, 147-152.

Zheng, Z.P., Tokunaga, T.K. and Wan, J.M. (2003) Influence of calcium carbonate on U(VI) sorption to soils. Environmental Science & Technology 37, 5603-5608.