 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 this complexity that's being formed between aqueous species and this 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 example, if we think about a system, that you have a 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 E-line greens, which is a very common type of clay. And then we have the water that has this chromium 6 on it. And we know that this species will sob or sulfate complexes with species on E-line. So what we have here is these greens and then these water. But also there's some background species, like sodium chloride, that providing some salinity. And E-line itself will be slowly dissolving out. So there are some other species, for example, magnesium, silica, we'll talk about that later. So in order for a sulfur system, we think about this system again. Sulfate complexation is usually considered also as very fast reactions, similar to aqueous complexation. So we usually think about the super dynamics 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 there's both actually happen 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 association dissociation to become hydrogen ion and hydroxide. This is a reaction that must be there. But also we include the chromium-related reactions. So it can, chromium 6 can have three different forms, right? You have H2Cl04 can become H-press and then this species. And this can further dissociate to have hydrogen ion and this chromium O4 in 2 minus form. So in the water phase, we are actually, there could be a lot of other reaction happening. But for simplicity, it would only include these three. So that's for the water phase reactions. And also, we are at the water and solid interface. We're really talking about that water and inline interfaces. We have these solid phase, solid species, like a 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 species can react with hydrogen ion to form this and also dissociate hydrogen ion in coming out to become this. But also, 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 reaction here, these reactions, we write, for example, the same type of loss of mass action, like in aqueous complexation. So we have these active hydrogen ion, activity OH minus is times together equal to Kw, and similar for chromium A1, A2, right? So 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 all these k's are constants. So again, we have these three reactions, but also then we have four, five, six, seven. So we have three aqueous phase reactions and another four reactions that are quite a lot in solid interface. And each of them, you can have these expressions of loss of mass action, which I'm not detailing out. But also, as I mentioned, is that ilite itself were dissolving slowly. So in crunchy flow, 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 crunchy flow, the input file, we do need to have these reactions, or these chemical species there. That is actually part of the ilite. But it's not really explicitly talked about in this aqueous phase. So these are the chemical kind of components of ilite that we have to put these there as the primary species. Now, if we think about this 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'll have H, of course, hydrogen ion, OH minus. And then you have three chromium-related species, which with different hydrogen ion there, CO4 2 minus. And then you have these solid. We also need to solve the concentration for the solid species as well, right? So you have this SiOH 2 plus, SiOH self, SiO minus. And then this form complexity to have SiO Na, SiO. And then you also have these OH 2, SiO 4. 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, and then the chemical composition of these ilites. So you have Mg2, potassium, aluminum, SiO 2, equips. OK, so 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 six. So in total, we have 16 species, including all the possible equate species and solid species, right? Or surface species. So we have 16 species. That means 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 reactions we specify. And we know every time we specify one reaction, there's an algebraic relationship related to that. So we have 16 minus 7 equal to 9, right? So we have 16 unknowns. 7, we know the relationship. Meaning these conditions are all activity dependent on each other's relationship. That means we need to specify nine additional conditions for completely solving these reactions. So what we can do here is, for example, a lot of time we know pH. So these conditions should be already given to you. And what do 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 you the total concentration of chromium, 6. And this should be equal to, for example, concentration of CRO4 plus concentration of HCRO4 minus plus concentration of H2CRO4 equals, right? And this together should be equal to whatever constant it give to you, which I'm not writing. And you also should know it should also give you a concentration of sodium, give you a concentration of chloride, and give you a concentration of potassium, aluminum, magnesium, and SiO2AQ. Another condition it should give you is also how much total site you have. So this would be something like, so the 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 will be adding all the surface complex species. For example, SiOH2 plus plus C SiOH plus C SiO minus. And then the CSIO sodium plus CSIOH2CRO4, right? So these are the five different surface complexes that can be formed. And this should be equal to a constant total number of, a total concentration of sites in the water, on the E like grain. And the total contribution of sites should be equal to, for example, how much E like grain you have, how many grams. And also the site density, time the site density, time the surface area. So these should be conditions that you should have. So if we look at this, you have seven and then eight, 9, 10, 11, 12, 13, 14, 15, 16. So this is a closed form, right? You have all these, you have 16 unknown, 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 will end up with is a concentration of each species, both aqueous and solid, at equilibrium because the system reaches equilibrium very quickly. So essentially you have seven relationships and then nine conditions to complete a very soft concentration of all species involved in the system.