 So we have discussed I think what is multiple reaction, what is single reaction, I have just given some notes there and also various kinds of reactions, multiple reactions, series parallel, parallel series, that denby reaction is very famous reaction and also that van de Fussier, van de Fussier reaction also is very famous reaction, famous reaction in the sense that you have the conflict, I think those conflicts we will see now I mean what is the real conflict in those equations, right. There are some more also, some more reactions I will also let you know but before that we should understand the basics like we have what is conversion that all of us know, okay. Example if I have A going to R, R going to S, right, yeah. So conversion always defined as moles of a reactant, C reactant reacted per, yeah, reactant concentration fed, okay. So that we will write here, conversion moles of reactant reacted or consumed by initial moles of initial reactant, that means you know C A not for example, right, that is 1. Then we have yield, we have actually yield 1, where it is moles of, moles of desired product divided by initial moles of key reactant, that is 1 and also you have yield 2 because you know different books will give different things, so that is why we have to just also note down this, again this is moles of desired product divided by moles of key reactant reacted. Then we also have selectivity, again selectivity 1 moles of desired product divided by, yeah, moles of undesired, okay, yeah. So this is one way, that means you have to choose one of them, right, that means you know I may have another here, desired may be this, but I may have A again going to T for example. So you have to specify that, you are defining either based on S or based on T. That is why another definition is selectivity 2 is again this moles of desired, moles of desired product divided by moles of all the products, that is another way of defining. So that is why you know like heterogeneous reactions where you have various possibilities for defining rate itself, right, you can base it on volume of the particles, weight of the particles, surface area of the particles, voidage of the bed, volume of the bed, there are so many. Like salary reactor also you take, you can express so many ways. Similarly here also you have to choose which one is the suitable for you, which will minimize your mathematical representations, okay. So that is what, good. So this is what are the definitions generally used, okay, good. So now once we have this, normally we try to use this one as phi 1, this as phi 2, these are the two things which generally we try to use and of course conversion will be there anyway. Conversion you know, conversion is XA only, okay. If you see for example Carberry book which I have been telling you, he uses phi 1, that means always this will be in fact in this case, what is the equation for this, in this case, desired product as usual I told you R, okay, this is C R by, what? C A naught, C R by C A naught, okay. So like that and whereas this one, next one, C R by C A naught minus C A, C A naught minus C A, okay. So I think anyway maybe you are getting confused, let me write here, this is C A by C R by, C R by C A naught and this one is C R by C A naught minus C A, okay, that is final, corresponding to this. If I write here C RF, C RF, C AF, okay, so those are the things. So this is what we use and Levenspiel uses most of the time this and Carberry uses this, right, okay. So then what is the method of finding out this yields and selectivity because these are all in terms of now moles or in terms of the concentrations. Now we have to find out what is C R by C A naught if I ask you what is the yield 1, right. So if I ask you what is yield 2, C RF by C A naught minus C AF. So the why I am telling this one is I am trying to give you the connection. In the third chapter itself you have derived an equation for this A going to R or going to S, okay. So you could have derived what is C R by C A naught, correct you have done that. So that is what, that is what is yield 1, right. So one way of going with all this is straight away going to the equations like you know first order reaction if I have this is first order, this is first order and also yeah these two are first order reactions then I write the rate equations if it is elementary I know how to write the equations if it is non-elementary then I have to tell you what is the rate equation then go to corresponding reactor I am just trying to give you the overall picture what is the reactor I may use batch reactor or I may use continuous reactors plug flow reactor or mixed flow reactor or I may use recycle reactor sometimes, okay or I may use semi-batch reactor also sometimes, right. So you just you know the equations for at least recycle reactor and the other three reactors batch, plug flow, mixed flow, recycle reactor and semi-batch we have not discussed here but again that is only writing the material balance like we have written for all other reactors, right. So you have to find out now then which reactor you have to take one rate expression one way of doing and then use first batch reactor or mixed flow reactor or plug flow reactor or recycle reactor and then try to find out which one will give you maximum of yield to if you are using this equation or maximum of CR by CA0 that means for every reactor you will get for some given production rates you will get one value for CR, CR by CA0 that is fine. So then try to find out which one will be the most you know better suited reactor that is why I told you sometimes recycle reactors are better than even plug flow reactor depending on what kind of scheme you have here this is one scheme A going to R R going to T S there is another denby scheme what is denby scheme again A going to something else R going to something else if this is the desired product then we have real optimization problem in our hands. So you have to take one particular reactor for example mixed flow reactor as an example and then try to maximize by writing all the equations where do you get that maximum CR by CA0, okay CR by CA0 that is this if I am talking about yield 1 and yield 2 once you know CR by CA0 we can also easily calculate what is CR by CA0 into CA because CA by CA0 already I know, okay I mean in the derivations you will automatically get it. So the overall picture is that going to each individual reactor and then try to find out that is the approach taken by Carberry and Smith all these papers, okay all the books you may have around 2025 books they can be divided into two parts followers of Levenspiel followers of Smith, okay in Smith and all that you know you will never get epsilon and all that I do not know whether those people who have used Smith book there is no epsilon there epsilon A, okay whereas the followers of all Levenspiel in all those books you will have epsilon A that means I mean what is the difference both should give you same answer you cannot get for Smith one answer and Levenspiel another answer you should get the same answer, okay but what is the advantage or disadvantage in these two processes? Delta X improvement brain expanding the brain what is the advantage or what is the disadvantage particularly for gas phase reactions and all that so that means you have not used any other book than Levenspiel, Fogler, Fogler is cousin brother of Levenspiel you also used epsilon, okay ya so you have not gone to some other family you see Duryodhanand Pardha was family, okay ya so I think I do not know most of you have gone to only that approach actually both are right but mathematically you will have more complications in the other approach where you know Smith approach where every time you have to write mole fraction multiplied by you know concentrations all that will thing will come that means every time you have to write what are the total number of moles then you find out mole fraction then you calculate total pressure multiplied by mole fraction what you get partial pressure so most gas phase reactions in these books Smith and other party you know their party books only solve the problems gas phase reactions in terms of partial pressure, okay ya whereas Levenspiel you know this epsilon you can still use partial pressure and all that but his thing is directly using that equation y i into delta ya so that is all that means you do not have to remember any other thing this is simplifying so you are trying to generalize things so that it is easy for you to remember and also just proceed but I think you are trying to proceed so mechanically you do not know why this has come why that has not come so that is why I am trying to tell you atleast this point of time you have two approaches one is by using epsilon directly the other one is writing only the number of moles okay total number of moles mole fractions and then calculating partial pressures and then trying to integrate but that is strictly for which reactions gas phase reactions that too changing moles okay that is the restriction that you have to remember so that is why again here Carberry and also Carberry and Smith they belong to one school he always writes in fact Carberry book is the excellent book for yield and selectivity really excellent book so many problems he has dealt with and all of them are mathematical he takes a particular reaction scheme like for example that Fander Fussier equation or Denby I think he has not done that well so Fander Fussier equation he takes and then he will try to solve for mixed flow reactor plug flow reactor plug and batch reactor both give you the same equations only one is T and another one is tau that is all the difference because we are talking about constant density systems most of the time when you are talking about multiple reaction again the reason being that let us first understand what is happening in multiple reactions rather than complicating the problem with mathematics I told you know if you have too much mathematics beyond certain point of time you will forget what is the actual problem and you will only remember how to solve this problem using some mathematical technique so it becomes mathematical course that is why we call dy by dx we do not know which problem you are solving right or d square y by dx square which problem you are solving you do not know because y can be anything x can be anything that is what you are going to do exactly if we maximize the mathematics when you are talking about any subject so that is why physics is important for us as engineers what problem I am solving because this mathematics is a tool for me to finally get some relationship between concentration versus time okay or versus length if it is continuous flow reactor or if it if there is a change in distillation column I would like to find out what the concentration change along along the height of the column right or absorption also same thing so that is why you know that is the actual problem but to solve that probably you have to use very very difficult or different mathematical techniques to get that particular solution right so that is the approach what they take and now I am trying to justify Levenspiel so that is why I am telling all these so that is why if you see those who have used Levenspiel and also those who have done multiple reactions he gives some rules for parallel reactions what are the rules anyone remember you do not have to tell me the rules but at least do you remember that there are some rules for parallel reactions what kind of reactor I mean reactors will be better for series reactions what kind of reactors are better for series and parallel combination also what kind of reactors are better so that means by looking at A going to R R going to S you have something in your mind that okay this reaction is this reactor is good so that way I think it may be spoon feeding but still that gives you some kind of remembrance where okay by looking at A going to R R going to S you are going to feel that okay in fact plug flow reactor is better for this mixed flow reactor will not give you that much yield when compared to plug flow reactor when strictly when you have A going to R R going to S but that is again for simple simple A going to R going to S or simple A going to R R going to A going to S this for simple parallel reactions and simple series reactions but when you have again too much complicated things for example didnít be reaction you cannot tell because you have parallel as well as series reactions okay so that is why first let us see this kind of rules first and then afterwards we will try to solve the problems and it is now you donít have to learn any new conceptual techniques but it is only the mathematical techniques you have to learn I am repeating thousands of times this mathematical techniques and I know tomorrow morning you first had a differential equation you cannot solve if I give you a problem and then you blame that you know the question paper is very lengthy okay if you donít know anything I mean it can be lengthy I say what do you mean lengthy I am not giving 10 kilometers length question paper only A for sheet I am giving correct no what else I am giving I am not giving anything else but because as I told you if your writing speed is 0 you will take infinite time who can wait till infinite time even this universe cannot be there till infinite time at some point it has to go right so that is the reason why those mathematical techniques are very very important for you and you have to work you have to work you have to work to get marks also in the examination okay good please take this for analyzing multiple reactions let us assume density in the bracket epsilon i equal to 0 and the reactions are elementary to understand the concepts in real world the concepts learnt here are still valid but the algebra will be messy that means you know you will have more complicated algebra equations so now of course we have derived what is conversion and what is yield then yield again and most of the time we will try to express our things in terms of yield rather than selectivity but some books strictly I think someone was telling me that engineering of there is a beautiful name engineering of chemical reactions which book is that who has written that book then be is beautiful chemical reactor theory course name Schmidt yeah smith and smith there are two people okay yeah so he has used again I think it is only selectivity what he talks if I remember correctly I just look for some time by a long time back only selectivities he will use so that is why it is only our personal choice and also mathematics here there and here also it will be equally same right so yields only we will take and yield has again instantaneous yield instantaneous and overall yield and overall yield okay yeah this is overall yield in fact what we have discussed here phi 1 is the overall yield okay and I can also write phi 1 and phi 2 are overall yield okay why because at the end only we are writing this at the end of the reactor what we have CRF divided by CA not and for phi 2 it is CRF divided by CA not minus CAF okay because we came again already outside the reactor so what happened in the entire reactor only we are taking that is why it is called overall yield but in this time inside the reactor when I look I may have the instantaneous yield defined as this is small phi equal to moles of product let me say it is R formed okay by moles of moles of reactant again A reacted so this is written as DCR minus DCA okay why that minus yeah definition of that derivative is you know always CA2 minus CA1 okay but normally here you have written CA not minus CA not is larger actually it is supposed to be CAF minus CA not okay so that is why that minus is given okay so that you will get a number here positive right positive quantity good so this is the instantaneous yield and now in this instantaneous yield we have to find out depending on the reactor whether you have plug flow reactor what kind of instantaneous yield equation you get or mixed flow what kind of equation or batch reactor what kind of equation right okay so that quantification we will go a little bit later but right now what we have to discuss is to find out I know this yield I told you instantaneous yield what contacting pattern will give us the best yield that is the question okay what is the question question is what contacting pattern I hope you remember what is you know it is a long time I have drawn my diagram long time back okay so don't forget that what contacting pattern gives the best yield okay that is the question okay what contacting pattern means in other words what you are asking is yeah so let us do that for parallel reactions first parallel reactions in parallel reactions we let us take the simplest scheme it is only just to get the rules first yes this is let us say K 1, K 2 okay this is the scheme and as we told that these are elementary reactions so it is first order only right so when I write R R what is the equation yeah DC R by DT if I take you know with respect to this rate then K 1 CA here okay just for discussion sake I am not taking initially n equal to 1 but some value n1 okay yeah so then RS equal to DCS by DT which is K 2 CA this is n2 okay yeah even though we have told about yield and all that to discuss what kind of contacting pattern you get okay the arguments will be same so now what I want to do is that I will take DCR by DCS T T that means I can take the ratio of R R RS so which means that this ratio should be maximum that means RS should be minimum that is all I think you know that same argument even if you write in terms of yield also you will get the same conditions only that will not change but this will give direct straightforward answer so that is why we are taking only for explanation good so now let us say 1, 2 then if I write R R by RS which is nothing but DCR by DCS again which is nothing but K 1 by K 2 CA to the power of n2 okay this is equation 3 now let us discuss this equation our idea is to maximize this so that I will get the maximum R okay so what are the variables with me to do this but you know we do not have luckily unfortunately we are not the dictators of what is n1 what is n2 right that is the nature of those reactions so we cannot do anything so that is the reason why what we will try to do is that let us take in the first case case 1 if n1 is greater than n2 right case 1 okay what will happen because I want to maximize that if n1 is greater than n2 for the present let us assume that we have isothermal system okay temperature that means K value I do not have again choice okay because let us understand each at one time okay so now when K1 that means K1 K2 constant there under these conditions and then you have n1 greater than n2 means CA should be n1 is that but I think you know that means the concentration of A if as much as possible high then you will get more okay more R so that is the condition right so that means yeah exactly so now we have to think which reactor will give me that kind of high concentrations when the reactants are introduced into the reactor why only PFR that is also exactly same thing so that is why but the general condition is CA should be for this CA should be as high as possible that is the one okay so then if 2 if n1 is less than n2 the reverse of that definitely so CA should be as small as possible okay then the other alternative is if n1 equal to n2 then yeah no what you have to say in terms of concentration okay yeah CA does not influence influence the yield okay good then what influences now in K1 and K2 right so in general okay K1 and K2 only what we have that means when you are talking about K1 K2 changing so you have now temperature coming into picture right that is the second alternative so that means of course even even here also I should be able to say now n1 greater than n2 and I have two constants what is the parameter which can characterize the reaction temperature is one but other than that what are the variables you have in this equation K1 okay so that means you also learnt this if I have high activation energy will it favor reactions at high temperature? my question is if you have high activation energy will it favor reactions at high temperature? you have to answer that also please remember the diagram what diagram lawn K versus lawn K right yeah so now if I have high activation energy what kind of slope I get so if I have low activation energy so that means this is K value so if I talk about the temperatures over a small change I have tremendous change there with the temperature whereas here over a small change I do not have that kind of you know this is T1 corresponding to 1 by T1 okay T2 this is also T1 T2 no please do not get confused this is corresponding to 1 by T1 T2 right that scale right so that is why this if you remember you do not make the mistake when it is too steep a slope then a small change in the temperature will increase will increase the rate of reaction why K is increasing when K increases it is minus or equal to K into CA the power of n or CA square or something so when K is very very large with slight temperature so that is why now you have to also add that other term E1 and E2 so depending on what is E1 and E2 we have to also discuss whether the temperatures depending on the what kind of temperatures you maintain you would have chosen for this case n greater than n2 plug flow reactor or batch reactor right so once you have that system now you are not satisfied with that you want to increase further the yield what do you do you look at the activation energies so depending on activation energies now if the activation energy of first reaction is let us say greater than second reaction then maintain high temperatures you see the rules these are the beautiful rules and these rules are same for almost all the cases generally n greater than 0 okay we are talking about only generally greater than 0 so that is how you now bring the temperature and also concentration and then try to choose the best reactor one is concentration choosing will depend on what kind of reactor you are choosing high concentration means normally it is plug flow but the change in S is smaller than the change in R why activation energy again the same thing the rate of formation of R is much higher than the rate of formation of S definitely it will increase okay but how much it is increasing and whether you are desired product is getting increased much more than the other product right so that is why there is a beautiful site I do not remember exactly now attainable regions if you go to Google always you are in Google only so I think now next time when you are in the Google you just type attainable regions A T T A I N A B L E attainable region this site was started by some South African University I think you know they are doing wonderful work particularly for multiple reactions attainable regions means what is the maximum yield I can get by using various kinds of reactors for the same reaction you know till some value of concentration one reactor beyond that another reactor I may add this parallely or I may you I am talking about reactors okay I have the given scheme of one reaction right given scheme of reaction may be din bee scheme for example right so that means that is A going to R R going to S and also A going to something else and also R going to something else so now my desired product is R so by using any combination of reactors that scheme is given to me I am not talking about any more multiple reaction I have one multiple reaction complicated one now by using any combination of reactors either parallel series may be till concentration 10 percent one reactor 10 to 20 percent another reactor I am just telling you know all possibilities and may be 30 to 40 another reactor different combinations all these combinations maximum R how can you get you will see that if you have this kind of you know in the site if you go through you will see many many rules there also that is why in industry it most of the time it is multiple reaction in fact all academicians are cheating you by giving only simple examples right most of the time because otherwise if I give you din bee reaction and ask you to solve inquis you need 10 days okay but 10 days quiz I cannot have no so that is why I think you know this open problems and all that sometimes we give assignments and all that we give but what we teach here is the concepts where whether you use din bee reaction or get in this grand father reaction no problem the rules are same okay so that is absolutely there is no problem that is the reason I know why all academic I told you also know academic institutions always try to unify the knowledge I told you I think already I do not expect that whatever I tell you remember also okay so that is why I am repeating many times so what did I tell about university always would like to have that is why name of the academic institution you know university name itself is that you are unifying many things okay whereas industry always thrives on diversity differences okay so you know see if I industry list sits before periodic table you will get confused it is he does not know what to do but if you tell in one column let us say okay between maybe chlorine and you have no what are those things chlorine yeah so then someone says that I didn't have excellent market then you will never look any other element only at I to I have I didn't because that gives him more money okay but if you ask a professor to sit before the periodic table oh 103 elements how can you make all 103 look like as one element you know by by unifying the properties of all this in terms of only one quality that means I don't have to remember 103 wonderful no so that is why you choose whether you want to become an industrialist or an academician academician means 103 one and there 103 means 103 you have to remember and then see okay I didn't best tomorrow morning someone tells you no no don't go to I didn't go to some other I know tell me some other compound a chlorine is same thing I think some other element why I say hydrogen everyone hydrogen production hydrogen production on this planet so much so much research is going on in terms of hydrogen production and how do you produce how do you store how do you transport all these things are big problems because we think that by producing more amount of hydrogen we can solve the environmental problem because when you burn it you don't get his CO2 you get only water it is very good for us we don't have any way water you produce water you produce water collect somehow so that means each car will have a water tank right hydrogen tank and then water tank so you can use hydrogen go in the car at the end you take water drink again come back so that is the kind of thing hydrogen tremendous amount of research is going on so that is why industrialist always think that okay now let me concentrate only on hydrogen and whereas this fellow professor always think that okay hydrogen has only one element one what that yeah electron and you know some other thing has got 23 electrons I have interested more in 23 not in one what is there one in one so like that you know again you will try to bring that 23 into one and then say that what is the commonality in these two right so that is the reason why these rules are important for us to remember right so these two things please remember when if you have parallel reactions when n is large try to maintain the concentrations as high as possible for the desired product and when the activation energy is very high please remember that activation energy more means the rate of reaction will be very sensitive the rate will be very sensitive if it is desired product what you want and the activation energy in the desired rate is more okay then use high temperatures otherwise in the same example I have K2 all these things are not our choices okay you have to find out sincerely the kinetics kinetics means you should find out order of reaction and also the activation you know the activation energy here then that is the property of that reaction only because we do not have any choice there you I may like this reaction this is our my desired product but this will have more activation energy then what do you do you have to use low temperatures then again I think Abhishek will ask that sir the temperature low means you do not ask the converse is not true means you know you may say that it is not the rate high okay you may say that sir the rate is falling what do you do yeah again there when you compare you know the the production of r and then production of s still production of r will be more so that is how you have to manage that is all the simple rules and the remaining is only mathematics tomorrow we have on Saturday I mean I thought I will complete this battle reactions so tomorrow morning and Saturday this time we are meeting