 So let's get started. This is lesson five, so we'll be talking about microwave-mediated reactions. I put in the reading materials that in terms of importance of microwave-mediated reactions, how ubiquitous they are in different natural environment, and we also talk about the biogeochemical redox ladder in the reading materials. So things happen in sequence. And then we have this example of, I was talking about in this, so I grab some soil in the backyard putting a water bottle in the kitchen. So this is not real, this is a cup I would say. So that's the system we have, right? In that example, we put some soil there. Let's close it. We have some water there. So we have some soil. Let's just put these, let's say these are the grains, right? And the water originally have some oxygen in it. And I told you there's a soil that I have we just recently fertilized. I mean, you will have nitrate in the system. So essentially in the system you have oxygen and nitrate as electron acceptors, right? And typically, for example, the soils usually have bacteria already there. Mycobase everywhere, they do a lot of work. So and also usually you would expect the soil carbon, the soil have some organic material. So essentially it also have organic carbon which we use acetate to represent that, right? So essentially we're talking about the system that has water in it, it's well mixed, it has bacteria in it, right? Let's use that to represent bacteria. And it have two electron acceptors, oxygen and nitrate, perfect. We have system and we know it's going to have something going on, right? And again, it's well mixed. We are not talking about a vacuum transport dispersion diffusion yet. So this is a well mixed system, meaning there's no concentration gradient in the system. Now that's just the system you have. So you have bugs. We use bugs. The formula for bugs is Hc5H7ON, something like that, right? And depends on what type of bacteria it is. If it's using oxygen, then we put oxygen on the, at the side just to indicate this is oxygen reducing bacteria. If it's nitrate reducing bacteria, we put nitrate there just to distinguish between the two different bacteria. So essentially you have two type of bacteria there in the system. That's the system you have and what's there, all the players, right? Now if we think about the reactions, what are the reactions, right? So first of all we talk about in the, but you can read us later, oxygen is the one that is going to be used first because usually it has fast reaction rate. It also gets, the bacteria, the microbes also get more energy out of it. So that means it has gross advantage because it can grow more with the same amount of organic carbon they have. So the first one is we call aerobic oxidation, meaning you will have the transformation from CH3, we use acetate to represent organic carbon. I'm not putting all these numbers in terms of stoichiometry of the company, but essentially just writing what are the major products, right? So organic carbon will become oxidized to become bicarbonate or other forms of carbon. If it's very relatively acidic condition, you might have CO2 gas coming out and you have water or hydrogen or whatever condition it allows. And then you will grow bacteria. So bacteria is also one of the products that we talk about, right? And then producing the oxygen reducing aerobic bacteria or microbe. So that's the oxygen related reaction. So we talk about, okay, that reaction will happen first. And remember this is a closed system, meaning we have certain amount of oxygen dissolved at the first. And then it's going to be depleted over time because it's a reactant. So the microbe will be using this up. And then the next step, the next reaction that's going to happen will be denitrification, right? So you will have, again, let's assume we would have plenty of organic carbon there. So then you will have nitrate. Again, the will be inorganic carbon become produced. It's the same process if you think about the human system, right? We breathe oxygen, we eat food like grains, bread, rice, different type of essentially organic carbon. And then we breathe out CO2, which essentially is another form of bicarbonate, right? And then water, let's not write that. And then you have another type of bacteria coming, microbe coming out, which will be the denitrification microbe. So these are the two driver of the system. But then, typically you would also have, I'm just writing, very at the side, there should be the convert somewhat fast reaction compared to this microbe mid-direction will be the transition between CO2, AQ, bicarbonate, and carbonate. These are the inorganic carbon species that we know is going to happen. We talk about that in aqueous speciation, or aqueous speciation reaction that we discussed before. So these are very fast reactions. So the major driver are really these. And if you have other species, for example, calcium or magnesium, if there's plenty of them, there might be precipitation come because these reactions will produce a lot of bicarbonate. And bicarbonate can, when the condition allows, it could precipitate a calcite, for example. Now these, we're not going to focus on these. Our major goal right here, right now, is talking about these drivers. And if there's applications that you would need to consider, these are some things that would be specific about particular applications. Now, so we have these reactions. These are the processes we could focus on. And then we'll be thinking about the species species. Like, what are the species out there? If we have, so for sure, we would have all the electron acceptor there, which is oxygen. It dissolved oxygen. You have nitrate. You have CH3COO. These are the variables that we are solving for in these equations, right? And then we also have, let's put bicarbonate. But we know these sets going to be also carbonate, CO2, AQ, right, or H2CO3. Yeah, the same. These three are almost like equivalent with each other. Hydrogen ion, for sure. And then it goes with H minus, right? Electron, acceptor electron donor products. Nitrogen is, did I, right? Okay. I should, here I should add another, which is the product of denitrification. One product denitrification would be N2. There could be a lot of, like, a few other intermediate reaction products like NO2 minus. People have seen that, or ammonia even. This could happen too. We are just using this as an example. So N2, right? So these are the major species. But also when we solve for this, when we are writing these four reactions in terms of this reaction, mycubi as a product, we also should have C5H7ON and then O2, right? And then C5, these are the two major products too. It's not just as a abiotic species. These are the, we consider the, mycubi are the products of this reaction too, right? So these are the species that you are solving. And then, okay, so you, we are not talking about other complexation reactions. So really, we are focusing on this species and you probably quickly know by this time, these are the, it could be the second species, second species, second species, right? These are the things that we consider. And then the primary species would be oxygen, nitrate, this, this, hydrogen, N2, N2, and these, right? These are the primary species. Let me just write it as primary to indicate the color. So that's what you have for in terms of variables we are solving for. Now, again, we are talking about the well-mixed system. So when we think about the reactions, the equations would be really the reaction in term, for example, oxygen, you would have something like this, right? It would be DC DT for oxygen, for example. Oxygen is being consumed, right? So volume. So it's really volume of the bottle, the mass, and then times this DC DT, but then you also have, essentially would be the mu, right? The mu is just, let's call this mu is a stoichiometric coefficient. It's consuming, right? It's in the left-hand side of the, of the equation, the reaction, because meaning it's being consumed. So this is stoichiometric. If, for example, in Francis, this is 0.5, this value would be 0.5. And then we will be, we think about the consumption. So the rate of this will follow monod, dual monod kinetics, right? So you would have this mu max for oxygen term, and then we have this, how much bacteria are there? So it would be the C5H7O2, and I should have O2 here. That's why I feel something is, something is weird. O2, it should be, I'll have O2 there. All right. So you have this species, O2, and this is oxygen reducing bacteria. So mu max concentration of biomass, and then you should have the two monod term, right? One is for concentration of oxygen, and then Km oxygen, plus concentration of O2. That's electron acceptor. And then you have the CCH3CO minus, sorry, I'm writing a bit of, this will be time, right? So Km, and then the plus C acetate, CH3, and I can't write anymore. But you know what I mean. So this is electron donor term, electron acceptor term, biomass, maximum reaction rates. So that's for oxygen. Similarly, you will write this for VDC. It's also being consumed. So essentially you will have the same, but you will have mu of CH3CO minus and the same expression, right? It's the same reaction going on. Just consume different chemical species in different proportions. And you would write again also for bicarbonate. So let's say one of the products, so you really should have positive sign before this, right? So you have write VDCDT. This will be like total carbon, right? And then mu of, right? So all these goes on. So you will be writing for all these. Now when you write for, so if you only have oxygen, you would have oxygen this acetate bicarbonate and other species. That's good enough. But if you have nitrogen, then your equation for nitrogen will be a little bit different in the sense that you would have the same, but it would be replaced by nitrate acetate. But you will have the inhibition term by oxygen because oxygen will act as inhibitor for denitrification to carbon. When you have plenty of nitrogen, oxygen in the system, denitrification is not going to happen. Only after this concentration of oxygen has been decreased to levels that this term is more or less much higher than this, then this value will be close to one, then denitrification really kicks in. So that's for nitrate. But also notice when you have nitrate, when you have both electron acceptors, these reactions will be happening at the same time. Just at the first, oxygen will be the dominant one because this term will be, have very small value will be inhibited denitrification to happen. But then this, this rate of this will become smaller and smaller because oxygen becomes smaller concentration while this term become bigger and bigger. So there is a switch between different electron acceptors. The other thing is when you have multiple electron acceptors, when you write these acetate equations or when you write these, for example, produced in organic carbon, you will need multiple term too. Because nitrate, denitrification process also contribute to the consumption of acetate and production of biochem. These are like common products or common reactants. So you will have multiple term if you have the nitrate related term. I'm not going to detail everything, but essentially that's what you think would have. So solving these equations, let's say you have all these species, you'll be writing how many independent equations for primary species. Then you have three fast reactions that you can form algebraic relationship to solve for these other secondary species. You solve everything as a function of time. So this is dt. This is not partial t. Now in that case, what do you think will happen when we have these products? So I talk about we have some magic power, magic powder putting in the bottle. We help us, we read our numbers. What do you think will be the chant, for example, oxygen? And what's going to be the chant of temporal evolution of nitrate that's using nitrate for this one? How do you think they're going to look like in term of curve? And so that will be actually the output of the model, right? You can look at, you can think about what's going to happen. So aerobic oxidation going to happen. First oxygen concentration is going to be consumed first and decreased, right? So let's say it's maybe oxygen start from here. You will see a decreasing chant of oxygen. Let's say just something like that. And then what about nitrate? So nitrate is, at first it's because of where there was a presence of oxygen. You wouldn't see much of nitrate decreasing. So probably at the beginning it's going to, let's say, start from somewhere here. It will be relatively flat, right? But it's also when the nitrogen, when the, I'm sorry, when the oxygen starts to decrease, it's just start to show the sign of, and depends on rates, right? How fast, how long it will take, it will depend on. So when it's like almost completely depleted, then you would have nitrate kind of going full swing and then it's going to decrease really fast. But then when you think about the products, right? So this produce N2. So it's probably N2, let's say at the beginning it's not much, it's almost zero. Now when nitrate is start to be denitrified, then N2 start to increase, increase, right? It's almost like in the, it almost mirrors the nitrate. So this would be N2. That's the product of denitrification, right? Oxygen decrease followed by nitrate decrease and oxygen increasing. What if you also have sulfate? Let's use another color. Let's use blue again. What if you have nitrate? So nitrate, so let's assume there's no ion there. So when you have sulfate, so there's another electron acceptor, which is sulfate, which is also pretty active in subsulfate environment. Probably not in very shallow soil, but in a bit of deeper, when you don't have a lot of oxygen, you tend to have sulfate. So sulfate will be probably, let's say, something like, let's just start here. It would start to become decreased when this denitrification happens and the concentration decreases. But then it will also follow, right? Maybe it won't decrease, depends on how much electron donors you have in sceptra. So this, let's say this is representing sulfate. And the product of that is sulfides, right? So sulfides are probably with this small at the beginning, but then it'll be increasing over time. Something like that. Let's call it HS minus. Just this is like randomly ending another electron, except it's not easy equation. But if you need to write for sulfate too, then you would have three major micro immediate reactions. And in addition to this, you would also have equation related to sulfate and sulfide production. And notice also, sulfate reduction will be inhibited by both oxygen and nitrate. So then you have two inhibition terms. So in that case, when only when oxygen and nitrate is depleted to pretty small amount, then it is sulfate reduction can start to kick in. So these inhibition terms really would ensure the biochemical reduction later in the system. Okay, so that's what we have for this unit, for this lesson. And you can use this or set up state for you to do the homework, think about different reactions that are going to happen in sequence in natural systems, in soil, aquifers, and then how mycubee evolve and the different concentration of our time. Actually, we didn't talk about mycubee, but the mycubee concentration will increase over time, following where these different types will be following their own electron acceptor, electron acceptor evolution, right? Oxygen decrease and aerobic mycubee will be increased, things like that. Okay, so let me stop here and you are ready to do the homework. Thank you.