 So we'll be talking about aqueous complexation today. What is particular about this? Usually we use aqueous speciation and aqueous complexation almost interchangeably. What is particular about this type of reaction is that it occurs really fast, usually in the order of, for example, seconds or milliseconds. So because these reactions are very fast, it usually we consider only reaction thermodynamics, not thinking about reaction kinetics of this type of reaction. And these reactions are really important in the sense that it occurs everywhere. As long as you have water, you have different species involved, they tend to have this fast record very quickly. So it's a very important type of reaction. Now what I'm going to cover in this video is, first of all, I'm going to use essentially one example, which is our system. It's a carbon water in closed batch reactors to think about the different type of reaction it has. It's a relatively simple system, but it illustrates the general principles. And then we'll be covering the important concepts in rectal transfer modeling, which is primary and secondary species. And then I'm going to cover, talk about the equations that the code actually solves. Because usually we use models, but I don't think it's a good practice to use a model as like a black box that you don't know what's going on inside the code. So I'm going to cover what type of, which equation for this particular system the code actually solves and then what do you expect from solving these equations. So first of all is the system. So what I have in mind is I call it carbonate water in a closed system. So you think about that like for example a bottle and it has some carbonate dissolving like for example CO2 gas dissolving towards it. It essentially have certain different carbonate species there. So what I hear list is essentially three different reactions. You think about this kind of system you would have first of all water will be dissociated to become hydrogen ion and OH-hydroxide. And then this would be the combination of carbonic acid and CO2AQ. This we still call carbonic acid can dissociate to become hydrogen ion and bicarbonate. And then bicarbonate can dissociate further to become hydrogen ion and carbonate. So these are three different reactions and each of these reactions have its own we call equilibrium constant under certain temperature and pressure conditions. Here we are more focusing on ambient temperature pressure. So the Kw would be equal to 10 to the minus 14 and this should be equals to activity of hydrogen ion times activity of OH- that's the first reaction. And then the second reaction you have carbonic acid to dissociate to become hydrogen ion and bicarbonate. This will be the value of Ka1 because it's 10 to the minus 6.35. And the expression of that will be activity of hydrogen ion activity of bicarbonate over activity of H2CO3. And then the last reaction you have Ka2 which would be equal to 10 to the minus 10.33. This would be again these numbers are for the ambient temperature and pressure conditions. So if your temperature and pressure changes they see the value would also change. So again H plus a activity of carbonate over activity of HCO3. So we have these three reactions and three constants associated with. So you notice that for these reactions these expressions essentially relate the activity or concentration of different chemical species into one algebraic relationship. So each reaction has this one algebraic relationship. So now when we think about the different species I mentioned in the first lesson that we typically in reaction transfer equations we tend to differentiate different type of species into primary species, second species. But first of all let's think about what other species we have. If you think about this you have water which is everywhere and it's abundant and we don't really calculate its concentration. So it's water is all in expresses there. But then you also have if you look at these different reactions you have hydrogen ion and OH minus is associated with water. And then you have these three carbonate species right. You have the bicarbonate acid bicarbonate and carbonate. So you have these three. And so in total you would have not including water you would have five species. And then thinking about how to differentiate them to become primary species and second species later is more important. But right now I think about the primary species as a building block of the chemical system. So you need to look at what the elements are there. And then the second species should be able to be written as a formation like as a different combination of primary species. So if you think about the different chemical elements that you have hydrogen ion almost you have to have that there almost every species have hydrogen ion. But you also have carbon and oxygen right. So it would be wise to think about putting at least hydrogen ion in the primary species and one of these species that have carbon and oxygen which you probably can pick bicarbonate which is kind of in the middle it's easier to manipulate. The other question is like how many primary species we have. If you think about the system we have five species and we have three relationships right. This algebraic relationship we have three. So essentially the number of primary species will be equals to the total number of the species which is five and then how many relationships we have which is three. So you will have two primary species and then the rest of it will be secondary species. So this should be the total number of species minus the number of primary species which is this is two so you actually have three secondary species. Now what are they if we think about the different combinations. So I mentioned we could put hydrogen ion maybe I'll write here. Hydrogen ion as one of the primary species and we put bicarbonate as one of the another primary species right. And we should think about it we need to be able to form right to be able to write all the secondary species in terms of primary species. So if we list all these different species you have hydrogen ion bicarbonate still there which is primary species but you also need to be able to express hydrogen ion and then carbonic acid and then carbonate right. So here if we think about that as a table and water is kind of in explicit that it helps but we don't need to explicitly write that up because we know water is abundant water. So hydrogen ion is equal to hydrogen ion so we put one here right. And we don't need carbonic acid to form hydrogen ion. But then for bicarbonate we don't need hydrogen ion but we need one carbonic acid. For OH- you would have think about the OH- as this reaction right. If you write OH- is equal to water minus hydrogen ion you would have essentially water is one. So this is zero zero and then you have hydrogen ion minus one because it's minus in front of and you don't need this one. So similarly you do it the same for example carbonic acid you need adding these two terms and the coefficient in front of that is one right. So you would have one one in front of you don't need water. But then for carbonate you have carbon if you move the hydrogen to the other side you have bicarbonate in front of is one and then move this minus hydrogen ion. So you have minus one. So essentially you have minus one and carbonic acid. So this will give you essentially the kind of combination. So these are secondary species and then these are primary species. So you can say you can see that we can express all this kind of secondary species as combination of primary species. So this system works. But this is not necessarily the only set of primary species. It could be different combinations. For example you actually can also use carbonate species as primary species to replace this but used by carbonate as secondary species. These are kind of exchangeable. Actually as long as you pick one of these species, one of the carbonate species as a primary species and either hydrogen ion or or minus as one primary species you should be good to go for the system. So these are the primary species and secondary species list. And then with that we also want to know for example when this carbon water let's say in a system we know how much is the total concentration of these three species and we want to solve under certain conditions for the concentration on the different conditions. So what are the equations that the code actually solved for? For this type of systems. I talk about the three different relationships. One is this equation is one relationship and then two relationships which is another equation and then the third relationship which is the third reaction, the K2 expression. But then we also have, in total we have five species. That means in total we have five unknowns. Which means we need to have five equations to solve for five unknowns. So we are essentially missing two more equations. So if for example I specify, I would need to have another relationship. Another two relationship let's say for example if I specify this carbon system is at pH 7 then it would give for example log activity hydrogen ion. So negative its logarithm would be equal to pH. That's equal to 7. That's another condition you can specify. And then for example if I'm saying okay in this system so total organic species, total inorganic carbon. The total inorganic carbon means the concentration of all these three add together. These are inorganic carbon. So if I say CT equals to concentration of H2CO3 plus concentration of carbonate and carbonate. If the total is for example 10 to the minus 3 more per liter then I essentially have five equations. So the system is fixed and we can solve for this. What it means is that we will need to solve for the, so all the unknowns are the concentrations. All the C's right, we have five of them. And notice here I'm writing A instead of C but this if we, so A activity is always equal to activity coefficient times concentration. So in a fixed system with certain salinity or this level of concentration chemical species these C's number are constant so we can only solve for C. And a lot of times in dilute systems this is close to one so it's in dilute system. So which means we can essentially almost assume activity is essentially approximate concentration. Okay so this will solve for the concentration of different chemical species of all these five concentration, five chemical species. Now the outcome of that would be, let's say we are solving them under different conditions. Right, so let's see what's the outcome of just a very small figure that illustrates what we are going to see under if we solve for this. So let's say we have this pH, right. So here I specify pH is about seven and then you have these chemical species solved under certain conditions but also it's important that we notice that this speciation of different conditions will change under different pH conditions. So here if I put in kind of different zones of pH typically when you have fixed the CT, let's say we have closed the system so the CT would be fixed. Right, so CT would be remained the same. But then I'm actually going to have very different distribution of chemical species under different pH conditions. So this would be pKa1 which is 6.35 and this is pKa2. It would be 10.33. And then if we look at the distribution of chemical species, for carbonic acid it's going to dominate under low pH condition when pH is below pKa1 so it would be something like this. So this would be H2CO3. So if you are looking at the pH condition below 6.35 it would be mostly carbonic acid. Then when you have pH between 6.35 pKa1 and pKa2 you would have bicarbonate as a dominant species. Something like that. So this would be bicarbonate. And then on the high pH conditions you would have carbonate dominant in the system so it would be looking like this. So under one pH higher than it would be mostly carbonic species. I mean it would be close to CT. So that's all I have today. These concepts are illustrated in the online materials. If you need to read more, think about it more, please feel free to do that.