 ఏబరిమూమాంి సిసిం సిస్లిం లాస్నటత్ టారాస్లిని ంిదాచె దాస్కింి సిండికికారం last A in the bulk. So that will not contribute so that is why we have not written. Step 4 that is all, step 5, step 4 and step 5, right. So these are the 4 steps which you have to take into account and as I told you step 1, step 2, step 4, step 3 also are all mass transfer steps, right. And again you have to use only that simple convective mass transfer equation, right, okay. So that is why this, this, I am writing now for step 1, step 2, step 3 all equal to. So minus r A B bulk will be, we have k g A g, I will let you know what is A g C A C A B C A g B minus C A g I that is why this diagram will be very very good for you because you can identify what is the concentration gradients, right. So this is the first concentration gradient in the film. What film is this? Gas film. Then you have the liquid film. Through liquid film we will write here as k l A g. Now what are the concentrations now for this one? C A C A l I, so that means concentration of A in liquid, right but this earlier one is gas. You cannot write here liquid because the gas concentration is your, the way you calculate is different, liquid concentration is different that is why you have to be careful there. So that is why here C A C A l I, l I minus what is the C A l that is the concentration gradient here. Now through the film which is around the particle, around the catalyst particle we have, yeah. So this we call it as generally k C, this also we call A C, then we have C A l minus C A s, okay. This is again this concentration gradient. That is why this imagination is very, very important in all heterogeneous systems, okay. Why that imagination that will give me clear picture of what are the equations I have to write. And to get this level of imagining and then writing the diagrams, you know these pictures you need lot of information in your mind for the process. All these things are only in the mind and then that mind you translate this one, this one and afterwards this one on the paper. Then it is very easy for you to write mathematics, right. So that is why we started that. Now what is the next step? Next step is rate of reaction. But this rate of reaction step again imagination, you know it is not imagination. We have to find out separately without all these whether it is first order, second order or you know some orders, right. Or it need not be first order, second order. It can be even any crazy type of equation, right. But for simplicity we will now take this one as simply K reaction or simply we will write K only, A C C A S, that is where the reaction is taking place, okay on the surface, good. So if it is porous particle then you have another gradient here which is inside. So this gradient will be a function of R. That means if I take the particle and then look at the concentration how it is changing, right. So the A is diffusing through the pores and definitely it offers resistance and then you have the concentration gradient. You know how you can, beautifully you can take care of that by what is called effectiveness factor. So this is the rate of reaction, this multiplied by Eta. Eta is the effectiveness factor which you would have heard of, right. Because most of you have taken two courses. So catalytic reactions there is what is called an effectiveness factor where the rate, the actual rate divided by the rate at bulk conditions, at bulk conditions. If it is isothermal reaction then always inside the particle you will have less concentration and outside you have more concentration, okay, isothermal, right. So that is why the rate of reaction based on bulk will be more than rate of reaction based on the concentration profile that is inside the particle. So that is why you get effectiveness factor less than 1. This all these details again we have to discuss in the course, chemical and catalytic reaction in area, okay, good. So that is why that also can be taken by simply multiplying by Eta. Eta is a wonderful concept in chemical reaction engineering that also we can discuss in the next course. But right now we are assuming non-phoros particle. So that means there is no internal diffusion and all that coming. So simply it is this constant multiplied by C As, okay. Now this is the equation. So if I take this one as 1, this will be equation 2, yeah. So here I need a relationship at this point, at this point that means C Ag is coming to the interface. Now it is dissolving. After dissolving it shows C Al, C Al i. That is why at interface we have written C Ag i and also C Al i. So how you connect this one? Henry's law. So that is why we write here C Ag i equal to H into C Al i. This also that equation also you require, 3. So now using this equation that means, now what is the procedure? Approach. We have the universal approach in the heterogeneous system. So that is why I am telling now in all my course in heterogeneous system is very simple for many people because the approach is very clear. It is only mathematics which are more complicated depending on what kind of reactions you take, okay. What is the approach here? We started this one with catalytic reaction. We started with non-catalytic. We now starting writing that one for salary reactor. What is the approach now? Yeah, so now I have to express this rate in terms of measurable quantities. That is called observed rate, global rate, even bulk rate, measured rate, all these things, okay. So this is also one of the questions I gave out of that 30 questions. Now if you remember, you would not remember now anything, okay. But I know you are all excellent deletors and I told you, most of you, all of you have Phd in forgetting how to forget, okay. Not how to remember. Very quickly you forget. But anyway. So now you first take these two, eliminate CIS. Then these two, eliminate CIL. Then these two, eliminate CIL, you know, CIL and CIG using this equation, using this equation and finally you express in terms of CIG bulk. That is how. That I will leave it to you. I may give in examination, okay. Unless you practice that at least in your room, it is not that easy for you to solve this in the examination hall, okay. You will take a lot of time, right? So that is why you try on your own and the final expression I will give you as minus RAB equal to, yeah, you see, this is the kind of equation what you will get, CAGB bulk. So then I have here AC by AG, 1 by KG plus AC by AG, AG 1, okay, AG, then H by, sorry, KL plus I have H into 1 by KC plus 1 by K. So this is the equation where still I have not mentioned what is AC and what is, yeah, AG and AC, okay. AC and AG are the surface area, you know, this is the, AG is interfacial area per unit volume of bubble slurry, bubble-free slurry. AG is interfacial area, okay. Interfacial area means it is gas liquid, right? Interfacial area of gas liquid per unit volume of bubble free slurry, yeah, okay bubble-free slurry and AC is surface area of catalyst, yeah, per unit bubble-free, per unit volume of bubble-free slurry, yeah, bubble-free slurry. Why we have to do that is, I will give you a clue, this is equation number 4. Now can you tell me what should be the units of minus RAB? If you take simply KG into CAB minus CAS, general expression I am telling, okay, KG into CAB minus CA, see I think that is the concentration. What are the units? Just tell me. That means I am talking about minus RAB, simply KG into CAB minus CAS, mass transfer equation. What are the units? Quickly, moles per, see you know, what are the units of CA moles per liter? What is K? I am talking about mass transfer equation. See mass transfer, convective equation, convective mass transfer equation. How much? Srishmitha, time inverse you get in mass transfer equation? Over N A, J A and N A. Mass transfer equation, convection. Moles per meter-scores, right? For surface area only you express there, usually. Then if you write concentrations in terms of partial pressures, so then you have many, many, you know, dimensions for the K, K value, okay. But usually we express as a flux, either convective flux or diffusion flux. What are the units of diffusion flux? Yeah, what are the units of flux? Rate per unit area, rate is so many moles per, need not be mass flux also, so many KGs per time per meter square, okay, mass flux. Like that, you know, mole flux and all that, you know, rate. So that is what. So now, now tell me with this clue, what are the units of minus area? Moles per liter, later? What liter? Later of what? Metricubed of what? Metricubed of Krishnaya. Yeah, what is metricubed? What metricubed? Because in heterogeneous system there are many metricubes. Yeah, that is what, usually that is way, that is the way in slurry reactor the rate is expressed, okay. Moles converted per unit time per unit volume of bubble-free slurry, bubble-free slurry. So that means what? Yeah, slurry contains what? Yeah, liquid and so on. Why we have not taken bubble? Because in the presence of bubbles, volume measurement is very difficult. So something solid which I can tell, okay. And also the original rate was that it is moles per meter square, you know, I mean surface area wise if you take, which surface area you can take, you can take surface area of solid, surface area of gas and both are difficult to measure, surface area of solid is slightly better. But surface area of bubbles is very, very, I mean difficult to measure because you do not have, first of all uniform bubbles, right? You have various kinds of bubbles, small bubble, large bubble and all that. So how do you find out what is the total interfacial area? So that is why safest bet is, that is why for heterogeneous systems defining rate itself is a difficult problem, okay. Defining rate itself is a difficult problem. So that is why these things are given there, okay. So these are the constants, will not change for a given system. So now you can simplify this K g and you know when I have very, very fast reaction again, so that means mathematically speaking K will be very, very large. So 1 by K will be 0. So similarly here this K g, this film, this film no one asked me, sir why there is a film inside the bubble? So that is why I am asking, you know, you are asking no? What is this? Why there is a film inside the bubble? What is there inside the bubble? Gas, okay. Can I have a film there? Yes, okay. Yeah, made it Y S. I will also tell them why no? Why it is less? Yeah, so that means if I have, suppose I have pure gas, yeah. So whenever you have that gas inside and you have more than one gas, what you said is right, the molecules, what we are interested in the reactant molecule, that fellow has to diffuse from the centre to interface. So what is our imagination? All that diffusion, even though it is moving from centre to the interface but film theory tells me all that is okay but all the resistance inside the bubble, I can now imagine as a resistance only through the small film. That is why we can never measure those films, okay. Liquid film and all that you can find out from outside. Gas film also, if I have a solid particle, I can. I have the solid particle and gas is moving around that. I think people can measure and they can also predict with equations, all that is there. So inside the bubble when I have two gases, one gas has to definitely diffuse through the other gas so that it can reach the surface. Why it should reach the surface? Once the reaction starts, some of the gas that is here is already leaving and then reacting. Reacting means it is in the bulk, it is dissolving. So there is a concentration gradient. That is why that fellow moves. The other fellow like for example oxygen and nitrogen both you send, air bubble, oxygen will dissolve. Nitrogen solubility is almost negligible, no? So that is why now oxygen has to dissolve because of the concentration, has to move because of the concentration gradient. So from our film theory we say that, yeah, so it is encountering you know many molecules when it is going through but all that I will imagine that the entire resistance is only through a small film. That is a wonderful concept given by who? Lightfoot. Yes, lightfoot was Bachcha at that time, okay. When the theories have come, lightfoot may not be there at all. Boundary layer theory, what you learnt in fluid mechanics by who? Yeah, Prandtl later used it before him. Reynolds, Reynolds not talked about boundary. What is that? Who? Rally. No, not heard this name, Schlichting. Boundary layer theory by Schlichting, there is a big book in the library. Schlichting, name is S-C-H, L-I-C-H-T-I, Schlichting, okay. What is the Smith? Not able to S-C-H-L-I-C-H-T-I-N-G, that is German words are very difficult to pronounce. You have to say Schlichting, Schlichting. So that is what, Schlichting. So is the person originally boundary layer theory, then Prandtl beautifully used theory. Then of course, for application of absorption and all that, Lewis and Whitman proposed that two film theory, okay. So that means one side we have gas film, another side we have liquid film. In absorption same thing happens, okay. Good. So that is why most of the time, gas-gas diffusion is easy. So that is why again you will have K g values, normally large or small. When diffusion is easy, K g will be large or small, large. So this also can be neglected. Then you will have only these two terms, correct? No, K, normally we use in slurry reactor, what are the characteristics used? At least one example, which everyday you eat in your hostel, Dalda, hydrogenation of vegetable oil, that is one of the examples of slurry reactor. What is the catalyst they use? Nickel. So most of these catalysts are very, very active. When the catalyst is very active, what will happen to rate of reaction? Very high. So what will happen to K? Very large. So 1 by K is, can be neglected. And that, the other side you have the gas diffusing within the gas which is much faster than gas diffusing in the liquid, okay. And gas diffusing through the particle where the pores are very, very small. You see diffusion, I am teaching the entire chemical engineering, I say, that is why I am not able to complete quickly theory, okay. So that is why we should know that which are the terms here important, which are the terms unimportant, right? So when I have K g value very large, 1 by K g is 0, this fellow will go out. When I have very large catalyst, I mean very active catalyst, then this fellow will go out. Then you have again these two equations, I mean these two terms. Then again, what is that we are left with? Two mass transfer coefficients. Reaction disappears. Now that is the equation which you have to use, minus R A, oh no, sorry, V by F A naught equal to 0 to X A d X A by minus R A B, okay. So this B 4 is here. That is the equation what you have to use. Now I think definitely you can never forget about that diagram, contacting, kinetics, physical, chemical. Now you know all the terms in that equation, in that diagram. Now I do not draw. You have to only draw in your mind. Just close, like this, like this. Yeah, what are the terms? Input, output, two arrows, kinetics and contacting, physical and chemical. Now you have the meaning of what is physical and what is chemical? Yes, okay. So that is why in heterogeneous systems only that comes because mass transfer plays a role in heterogeneous system. Next time when someone asks what is the difference between heterogeneous and homogenous, do not tell single phase, multi phase. In homogenous all the molecules are available so mass transfer will not be a problem there whereas in heterogeneous mass transfer step comes in between, including heat transfer step also will come in between. So that is the meaning there. So that is why you need physical and chemical. The other side you have contacting, okay. What are the things we have there? You know when you have to use batch. Yeah, yeah. So all this CRT do not save in temporary files. It should be in permanent hot disk, okay. No one should delete that, Abdul. No one should be able to delete, okay. So that is why, yeah, that is right. So batch you know when to choose and continuous you know when to choose and do you still remember when do you choose mixed flow, when do you choose plug flow? Very good. Atleast that part you remember. Atleast that part you remember I think you know with the first 5 questions which I have given with that then you know that what is going to happen or what is happening in CRT. And CRT is the basis for the entire chemical engineering because if there is no reactor there is no chemical engineering. Because there is no chemical engineering plant. Because our idea of chemical engineering is converting some product, some reactants into products. That is what is the main thing. In between all these things you have, you have to heat it so heat exchanger will come, you have to pump it, pump it will come, you have to store it, storage tank will come, you have to separate, unconverted and converted, you know that mixture from the reactor. So you use distillation or you use absorption tank, you know something like that only all the time, okay. All those things are only outside things. That is why we say real heart is CRT. Reactor is the real heart of any process. Now I think you know what is the meaning. Earlier you know only heart and process. But now you know you have the feel, okay. That feeling is very important in subject. If you do not have feel you will forget very quickly, okay. Yeah. So that is why you know when you are walking on the road you see so many people, you do not have any feel but you will forget. But by looking if you start having some feeling then you do not forget that figure so easily. So this is the equation what we have to use and now with this I think you know by solving an equation for slurry reactor you got I think fairly good overview of what is heterogeneous system, okay. So now this fellow will not change. What is this fellow, this equation corresponding to which contacting pattern? Plug flow. If it is mixture flow I will write V by F not equal to XA by minus rA, right. If it is batch corresponding equation. So that is why actually it is very easy to remember contacting only three ideal. Non-ideal we rarely go. Non-ideal we very very rarely go, right. So that is why contacting is much easier to remember and the other part heterogeneous part is the kinetic part in the terrible headache. So now after seeing this now we will go for homogeneous kinetics how do we actually find out, right. So now we will start homogeneous kinetics, homogeneous kinetic equations, okay. So what do you get from that? Homogeneous kinetic equations means, yeah I think I can also write here kinetic rate equation so that you will remember what is that, what meaning of rate equations, yeah. What we have discussed earlier was that you may have either heterogeneous or homogeneous the stoichiometry can be anything, simply A going to R, simply otherwise A going to R plus S, A going to R plus S plus T. Similarly you can also add here A plus B going to R plus S or A plus B going to only R. So how many combinations you have? And particularly you will have hell if I simply change, you know I may give there A plus A going to R but the moment I ask you A plus B going to R, then entire kinetic equation will change. So that is why most headache part is this kinetic rate equation and also we have unfortunately so many kinds of stoichiometric equations that A plus B and all that and in heterogeneous system also you have the same equations. Now what you have to write there is, okay A solid or okay A gas plus B solid giving me some other product. I think fortunately most of the time there, you know heterogeneous system I am talking, if I am talking gas solid system I have A gas plus B solid, example coal, okay. So coal is solid and oxygen, so this A is oxygen, B is solid giving me CO2 gas and same thing again I have A solid, sorry A gas and B solid, iron ore is the solid, B and hydrogen is gas, I am talking about reduction of iron ore to iron. So then the other side what do you get? Solid plus gas also, H2O you get and also you get solid. So like that you have real headache with these kinetic equations. For homogeneous systems how do you really solve it, right? But fortunately before starting any process we know what is kinetic equation, right? That is assumption in the beginning itself, right? Otherwise you cannot even calculate what is minus R A, sorry what is F A naught, right? So you go to market and then find out so much product you have to produce. Now you go to stoichiometric equation and come back to reactants, so so much reactants you have to feed. But again you have to assume there either 90 percent or 50 percent, 30 percent, you have already burnt your fingers in that problem, right? When you are back calculating in batch reactor, all of you took 100 percent of that. So actually that is only 30 percent. That is why you get, you know you can see, you choose between 0.7 meter cubed or 7 meter cubed. So if it is actually 7 meter cubed and if you tell your boss in the company that sir it is only 700 liters, you will be happy in the beginning, you start construction and then you know you produce, what do you produce? You will not have sufficient production rate. So then you will, what you will do? Fire, okay. Yeah, you will not get job, right? You will be thrown out of that company. So that is what happens, so that is why we have to be careful with the stoichiometric equation, good. So now what is the, what is the, how do you find out rate equation? How do you find rate equation? What is the first step? So that means I know the stoichiometric equation, may be I have, simple thing is A going to R, let us start with simple thing. How do you find out rate equation? What is the starting point? Yeah, so okay, so then what is that you are trying to do? You are trying to do the experiment first, correct no? Yeah, so now when I have this A going to R, now I have to choose may be A is liquid to easy imagination, gas is slightly difficult to imagination. So this now, that is why always, nowadays, now onwards if you write always, you know the phase that is very good for you, now onwards earlier I think you never thought of that. So if you are able to write that always, then that will clearly tell you whether you have homogeneous reaction or heterogeneous reaction. Here I have homogeneous reaction, A L going to R L. Now I want to find out kinetics, what is the starting point experiment, right? How do you do the experiment? Because I do, even now we do not have a theory to predict what kind of rate you will get when you have this kind of equation, otherwise theory is the best, because you do not have to do experiment. Experiment may be time waste. If you know the theory, you can always calculate, okay, for this stoichiometry, this is the order or this kind of rate equation you get, order you remove. What we are trying to find out here is, how do you find out, okay, question mark, how do you find rate equation means what is this minus R A, minus R A is a function of C A and T, that is what only what we know. But what is the format only we are trying to find out, good, okay. So experiment is a must. So how do you do experiment depends on individuals, I think what kind of tactics you have, your intuition and also your hands how they work, because for some people I think hands are very bad, whatever they touch it will break. So I think, you know there are many people like that. So like that some of you also are really allergic to the experiments. But I think as engineers you cannot survive like that, you have to do the experiment, right. How do you do the experiment? If it is liquid, you think most of you would have done kinetics, you know, kinetic experiment in B Tech, reaction engineering lab, what did you do? Abdull, what did you do? Take reaction, you cannot take reaction, okay. First of all you cannot take reaction, what do you take now? Take reactor. We let the reaction proceed and we collect the concentration of the product. Is it so simple? I mean how do you do the thing means, okay, well let us allow the reaction to proceed. What reaction, where you have to proceed? I am asking you to describe step by step. I ask you, okay, I will give, you know same thing what you have done in the, in your B Tech, what is the thing you have done? Sodium hydroxide and? Ethyl acetyl acetyl acetyl acetyl acetyl acetyl acetyl acetyl acetyl acetyl acetyl Very famous reaction, I give you now and then ask you to proceed, you get me the kinetics of that. 어, и вот That is what we gave now, what do you call that, lab manual. Lab manual, yeah, lab manual.ー Now you do not have lab manual, you have to imagine, because there is a new reaction, I told, වරබුගි, වරබි, වරබිරකරා kav. Because, you know those things. But you don't have a manual now. How do you start? Prepare solutions. Reactance only, yeah, correct. Prepare solutions. You know now that is the first step. And what concentration? Yeah, it is not that easy, you know. The way we're discussing here, it is not that easy when you're actually starting. That is why doing experiment is much, much, much, much difficult than solving an equation on the computer because there all the things are available if you go to matlab solutions are available for most of the things if you go to excel many things you do not have to do draw the line drag you get the answer but here I think if you drag nothing will come only I think reactor may break okay so that is why it is not that easy please appreciate experimentalist who are doing that process control needs theory and experiment both so that is why many people may be happy in doing theory but I know I think Shankar will be very happy to do experiment even though he started with theory so that is why doing experiment you know the first question what kind of concentrations you take before making that how much you make 1 liter 10 liters 100 liters so all these are the questions which you have to answer then once you have that information okay now I make the solution let us say 1 normal or 0.1 normal right so then you bring these reactants together that means you take the reactor put these reactants if there are 2 or only 1 and now you have to heat to that temperature and what temperature that is also question mark what pressure question mark what kind of reactor is it open or closed because in laboratory we only take open cylinder why open cylinder because sometimes if it is dangerous you know liquid where slowly it is vaporizing also right vapor pressure so then you have you know poisonous gases coming and that may affect your health then what do you do you have to close so that is why if I give actually that is what I told you know we are only filling up the bucket but we are not opening the tap okay so what I am trying to tell there is experiment is not that easy so you have to think a lot before doing the experiment why are you doing experiment finally no kinetics okay but what do you get from the experiment yeah to get the data okay yeah so in kinetics what do you get concentration versus okay so again there is a big assumption LKG assumption already that is why you all of you told that concentration versus time why concentration versus time if I take a CSTR will I get concentration versus time CSTR also I can take the same reactant I can send through so here I will put yeah so reactant is continuously added reactant is removed that is A C A not coming C A CSTR also I can use as a reactor why should we use only batch reactor we do not have to use okay but yeah so that is why that is much easier for me yeah product or concentrate I mean reactant that is not the problem CSTR I can simply collect here sample and then find out what is the concentration also I can find out okay yeah so you can also use this but it is not that easy to conduct this rate for plug flow reactor because along the height also you have the change in concentration or along the length or height okay yeah but this CSTR is one of the excellent reactors why I tell you later right I will tell you that one later but okay I will go to batch reactor as you said what do you get in batch reactor concentration versus time okay so I will give an example here concentration versus time which I have taken from Levenspiel the data which you get is I will write it horizontally T seconds and then I have C A in moles per later C A moles per later moles per later so then I have here zero then I have ten eight no sorry twenty seconds I have eight forty seconds I have six and sixty seconds I have five one twenty seconds I have three and one eighty seconds I have two then three hundreds three hundred seconds I have one this is the data what I got okay there are lot of things here which you can see even from the data C A not a time T equal to zero that is equal to C A not there is no problem you see now first I collected zero time is C A not the moment I started the reaction then what is the time twenty seconds afterwards forty afterwards sixty then what did I do hundred and twenty then one eighty then three hundred even choosing this interval is a big problem for you when you are doing first time even choosing that no timings otherwise what you do is you know you will miss actually some concentrations where you will not get correct rate so initially you have to take as many samples as possible within short interval and at the end you do not have to take so many samples so time can be large why our imagination what is our imagination imagination is concentration versus time if I have batch reactor it will be so here it is a slow change not much change whereas here quick change and sometimes this also may go like this so that is why when you are taking samples also on your own it is trial and error first few runs you will spoil it definitely you will spoil it okay good so then once I have this data what do you do I have given this data now I ask you to find out rate equation plot the graph what what graph you plot but first of all why are you plotting that graph there must be some some aim you know some objective to plot the graph why should I get this low to get the rate okay so what method you are following now for this is your integral you why do you say it is integral where is integration coming there concentration decreasing does not mean integration so that is why again my question is you have to choose whether you are following a differential method or integral method we told you in the CREL app that okay plot the graph first and then you take the slope so you are repeating the same thing you know like parrots okay but why we are plotting I mean drawing the slopes that means what method you are following all that we are not telling you right we have now you know the differential method and also integral method which method you have to follow which method is best which method is bad differential is bad or good why so what if you give slope you like it okay good what you do in integral yeah assume the order of reaction yeah okay so in integral you assume a particular order the simplest thing which we can assume here is the first order reaction for example so that means that equation I have to develop right that equation now we have integral method as well as differential method in fact if integral method works that is the best method for normal first order reaction second order if you are lucky if you are order is second order or first order you are really lucky so then you know you will get a beautiful fit beautiful values correct values for the constants also to determine okay why because I do not have to again plot graph and then plot you know the slope draw the slope that means I do not have to even evaluate what is minus r a why I am imagining a minus r a already and then integrating now that integral expression where it is only in terms of concentration and time if it is a batch reactor concentration and time so that is what now I will try to fit if it is exactly fitting then excellent right so that is why so now we have to talk about choose one method either differential or integral method integral method of analysis okay and before choosing this also by looking at the data you can understand a lot you can really understand a lot by looking at that can we say it is reversible reaction or irreversible reaction why irreversible reaction it increases sorry reversible reaction what how do I find out whether the reaction is reversible or irreversible optimum you are talking about concentration of a okay yeah continuously here also continuously decreasing again it increases cannot increase because you are plotting only C a yeah so every point what you are measuring there is the combination of this reversible only with time okay so then how do you really find out from experiment whether you have reversible equation or irreversible equation irreversible is easy because you conduct for one day you will get zero concentration of a at the end right so then this one day if you repeat the same thing for reversible reaction end of the day still you have some concentration of a so that is why Levenspiel also beautifully puts in some problems that you will write there infinite time still some concentration that means he has taken for long time infinite means okay so then that is a reversible reaction oh yeah infinity is given in Levenspiel book or not that infinity means very very long time you go still you have some concentration there so that means that is how you have to determine whether you have reversible or irreversible so because that determines which rate you are trying right if I am trying integral method and if I am assuming you are going to or that is the easy best easy bit so to start with the simplest reaction that is possible if you are lucky you are hitting the jackpot right so if you are not lucky then you know complications will increase so best thing is once the data given and ask if someone asked you to find out what is the rate equation if you are following integral method the best thing is imagine first order reaction okay now if I put infinity there and then still there are some concentrations then I should put reversible this I have to try that means it is definitely reversible reaction and also when you give infinity it is not only you know just telling you reversibility that is why I told you you know not only I am talking about reaction engineering to find out rate even tomorrow when you are doing project this thinking is required from data itself you can get lot of physics that is going on if you are able to collect data carefully so from the data even without using an equation you can tell many things why this data is coming and now using one or two points also you can again check what is happening in the process here for example when I told you I have infinite and still there is concentration what is that concentration is equivalent to infinite I have put there and then I have still five for example there I mean one well ya that is equilibrium concentration if it is first order reaction it is you know the stoichiometric equation you know if you know how much reactant is reacted can you also manikantan is expert always he says products because he came from industry you know he is interested only in products manikantan can you calculate how many moles of product has come you measured reactant ya back calculation ya you can calculate so that means I know concentration of reactant and also concentration of product at equilibrium once I know these two can I calculate what is equilibrium constant now I am imagining that I have simple first order now we have to imagine it is irreversible first order reaction what is the rate expression that we should know what is k c a minus r a equal to k c a right now it is a batch reactor what we have used so what is batch reactor equation c a not equal to 0 to x a d x a by minus r a right now minus r a equal to d x a by k into c a right but this I cannot integrate why ya because this is in concentration this is in conversion so now I have to have an equation for ya the relationship between conversion and concentration and that we know already most of you will be knowing that so c a equal to c a not into that I have to substitute here okay now substitute and tell me what is the equation integral equation minus ln 1 minus x a equal to excellent very good ya now I have to test that data I have no concentration and time there also have concentration and time so how I imagine this one is this is all I plot as y and this as because I think everything you have to convert into our y equal to m x plus c straight lines okay but where is c here for this equation there is no c no constant so that means if I plot this how we should go ya it should go through the origin and straight line with a slope of m so now what is m here for me k so that is why okay because now I am checking that data now I have to calculate that data in terms of this concentration you have to convert into conversion ya 1 minus x a and also ya correspondingly then what you have to do you have to also take logarithm of that so more systematic people will also do this minus 1 minus x a again all that right now that is why for you you plot here those things so beautiful straight line okay but you know do not expect lives to be so happy you know you cannot actually if you plot that you will not get a straight line actual data if you plot that okay so if this is the one then you have this slope measurement where many people okay this is t where many people do not know how to measure the slope also you know I can tell you many people do not know right how to calculate or how to measure so the slope will give you k so then what is the order of reaction for you it is first order if it is straight line confirmed and k value you know so as an example in this case this may be minus 0.05 c a that is all okay so this is what that means with respect to concentration it is order is first order and I have this k value but what I have done all the time without mentioning is that what one particular temperature now I have to also get in rate that Arrhenius equation that means few different temperatures also I can try so then if I try to different temperatures I may get like this like this okay like this another term so this slope is for high temperature or low temperature yeah slope is low so k is so this will increase temperature will increase in this direction this is t right so now once you have this again you have Arrhenius equation to calculate so Arrhenius equation is minus k equal to k0 e power minus e by RT right take logarithms and then you will plot this plot you know minus ln k versus 1 by 1 by t R is the constant okay yeah how the if it is correct how the straight line should come yeah because it is negative slope it should come like this so this slope will give me yeah because it is already negative so it is e by R decreasing e by R so then you have the complete equation as minus Ra equal to yeah then using this e by R you can now go to this equation and then calculate k0 activation is already known from this slope otherwise intercept you go and then find out what is k0 right so then I have all the information may be k0 may be 10 to the power of 5 is an example okay and this is e power minus this may be 20,000 by RT okay into CA so that is the expression that is the expression what you have that is the rate equation in terms of temperatures this is how you have to do we have taken the simplest example but life is not that easy every time it is very very difficult so that is why now you see if you go for integral method you need all integral expressions entire third chapter of 11 spiel is only integral expression that is why those who have not solved those integrals you know it is first order second order reversible irreversible and you know third order also and you have also autocatalytic reactions and parallel reactions the procedure is same okay series reactions all these things are there so those people particularly I think chemistry background and also you have 11 spiel book yeah so that third chapter please you know solve all those equations which has already given right you will not give each and every step but you have to solve on your own otherwise in this course most of the time it is you know in the even though I talk all words here in the examination I will only give problems okay I mean you cannot tell all the time I will give only problems I can give anything but most of the time you know engineering we will try to give you know this kind of if it is not numerical problem derivation okay so these things are otherwise simple concepts so that is why you have to practice others are supposed to have practiced earlier correct all third chapter derivations you are supposed to do it otherwise if you have not done that do it now otherwise it is very difficult for you in the examination because in this reactor theory course I am not allowing any formula sheets whereas in the next course you are matured enough then I will give you formula sheets there for C R E 2 okay that is a chemical and catalytic reaction good so that is why whenever I give you a problem you have to now derive that equation and then substitute the given values and then you have to find out what is what is asked we will stop here