 So, I think this is very important for you, you know, to solve all those problems, okay. I told you now, I have to give one derivation, that is very nice derivation, that is for till now we have talked about only liquid phase reactions. If you have gas phase reactions, what do you do? Because even taking sample of a gas phase reaction, whatever reactor you use, you may use batch reactor, even for gas phase, but taking sample is very difficult. Normally how do they analyze gases? Gas chromatograph, yeah, that is one, where did you use this, anytime you use, gas chromatograph is one, but gas chromatographs are very, very costly normally, so then you also cannot take the sample, of course you can take sample and then again inject, but nowadays if you want online gas chromatographs, I think they are 50 lakhs, 40 lakhs, so like that you have the cost. So as engineer, I told you, you know, without anything, how do you measure, that is the greatness of an engineer, if he is able to really measure it, without anything how do you measure things? So that is what your ultimate motto, right? So when you have gas phase, how do you really find out, the kinetics and how do you first of all take the samples or analyze the concentration or measure the concentrations? So gas phase reactions, gas phase, okay, homogeneous again, okay. So how do you get the rate for gas phase homogeneous reactions, the question is minus R A, how do you get, right? So that is why those who are familiar with Levenspiel book, I think Levenspiel is one of the greatest engineers I can appreciate anytime, because his concepts are simple, his explanations are extraordinary and his clarity is fantastic, okay. So that is the reason why many, many complicated things he makes it very, very simple. That is why the complicated chemical engineers won't like him, because some people deliberately want to, you know, make things complicated, right, starting for, for example starting with a tensor and vector, okay, Marga, I think, you know, the moment we say that tensor and vector, 90 percent of our brain is closed, okay. Then when you put that dell, then the remaining 10 percent also closed, I mean you see that experience, okay. So now mathematics is a beautiful language provided you are thorough with the concepts. That is a beautiful language. I mean representing in the form of, you know, the dell is a wonderful form, simplest form. Any complicated equation can be written in one or two words, that is all. I think when you expand only you will know what are the complications there. But that has to come when you are really thorough with the phenomena that is going on. So in the moment we say that dell X, so you should know what is dell X and then how it is representing, what kind of physical phenomena that is representing in your process. Then it is fantastic, okay. So that is why as engineers if you write only mathematics I think nothing will happen, right, that, those things are also required, because again don't use your subroutine thinking that, okay, Krishna doesn't have to mathematics, that is why he is telling that, okay. And always our subroutines work very fast in the brain, okay. So I am not telling that, you know, as engineers how do you make things very, very simple. For example gas phase reactions, how do you measure the gas concentration, okay, you know, how do you measure partial pressure, see always questions, always questions, you see it is very simple to say, you know, partial pressure, how do you measure partial pressure, have you thought anytime about that, okay, how do you measure total pressure. So I have taken a batch reactor where, okay, I may put a stirrer also, still I mean gases will move easily but still I will put a stirrer, then close this entire thing, okay, gas, this gas flow is highly movable, so that is why it will easily try to escape. So that is why you have to have perfect seals and all that and then put inside the closed vessel that we call as reactor and then you start stirring, if you want to maintain temperature and all that, again you should have a jacket and all that, okay, this is coolant in, coolant out, okay, C in, C out, coolant only, that is, okay, C means not concentration. So how do you measure here, the pressure first of all, how do you measure temperature? That is very easy, thermocouple or thermometer, okay, yeah, thermometers cannot be, you know, 2 meters, 3 meters long, so that is why we put the thermocouple very easily. So I should have a temperature sensor here, so may be somewhere here, so this will be give me temperature and here I should have a hole and then that inside pressure should reflect there, there is a pressure gauge, that is why I do not know whether you have read course on instrumentation where pressure gauges and all that are taught, okay, so those things are very important, those things are required, right, so this is the pressure what you can get, now if you get total pressure how do you get the partial pressure? Mole fraction How do you get mole fraction? Conversion, yeah, right, I mean if you know the conversions then you know each and every composition of each and every reactant and also, because again mole balance, simply mole fraction, mole balance, right, total number of moles and also that particular component what are the number of moles that divided by total number will give you mole fraction, okay, so like that, so that is the reason why gas phase reactions, the moment we started thinking about how do you measure gas phase reactions is not that easy, right, so that is why Levenspiel has beautifully used these two concepts, if I have a variable volume or constant volume, so that means variable volume if I have what will change, variable volume, variable volume answer itself in the question, what will change, volume change, so now if I have a reactor where the volume is expanding or contracting then if I am able to measure that, total volume change, so then I have to find out how the individual molecules you know contributing for this total volume change, you can convert that into concentrations or partial pressure, how do you get concentration from partial pressure? A by RT, A by RT, okay, that also we know, so that is why either this or that if you have you can convert one from the other particularly for gas phase but liquid phase there is no meaning of converting one from the other, okay, there is no meaning in that, if you want you can do it but there is no meaning, okay, so variable volume is one method, the other method is constant volume, this is constant volume batch reactor, V constant, okay, so now if I have a reaction here, right, so then let me say simply A going to R, okay, so now if I want to use constant volume means pressure should increase, right, volume is constant, PV equal to RT, I am keeping only one temperature, temperature is constant or anyway we know it is a constant, constant will you know, R, okay, so then if all that constant then only pressure should change but unfortunately when I have A going to R there is no pressure change, so then how do you find out again concentration? This why gas phase reactions are very very difficult, what we will do in this case when we have one mole going to one mole or when there is no volume change, okay, then you have to use what she suggested as gas chromatograph, okay, you have to take samples or you have to analyze continuously if you are very rich person you can buy very costly online gas chromatograph and then allow the samples to go continuously and then again return, so somewhere here you put a small port and put the gas chromatograph and again return back, okay, so it draws some sample, now everything is computer controlled, so one second, two seconds, three seconds, four seconds you can program on the computer and it sucks at one second, one sample, quickly analyzes and afterwards because you know you cannot throw it out all the time, if you throw it out all the time nothing will be there inside, inside the reactor after some time, so that is why again you have to send it back but now you see the response time and analysis time all these things should be very very fast, right, otherwise you cannot have another reactor somewhere here, that is you know gas chromatograph, so this is what is the thinking you have to do before starting the experiment, okay, now I have gas phase reaction, how do I analyze the samples, what kind of reactor use, what temperatures, what pressures you use and all that from thermodynamics you know you will get it, whether reaction is reversible, irreversible and all that, okay, good, so under these conditions we do not have a choice, we have to use sophisticated instrumentation, right, otherwise for simple cases if I have volume change how do we solve that problem, that is what we discuss now, how do you solve the problem, when I have actual changes in the moles during the reaction, we will take a very general reaction where I have A A gas plus B B gas giving me, it can be reversible also but anyway let me take first R R gas plus S S gas, okay, it is a gas phase reaction, so I think I know definitely this A plus B and R plus S must be different otherwise both are same means again there is no volume change, okay, good, so now initially at time t equal to zero I will have here N A naught, N B naught, N R naught, N S naught, okay, those are the initial number of moles which you fed into the system, so after time t equal to t I have here some reaction has already taken place and from your process calculations you know that that number of moles that are there at a particular time t is N A naught minus A, I use another word A into xi where xi is extent of reaction, please write that where xi is extent of, it is not conversion, it is not conversion, okay, I think I will just come back to that, so N B also equal to N B naught minus B xi and N R naught, sorry N R equal to N R naught plus, this is plus because it is product, so xi and N S equal to N S naught plus S into xi, okay, why we are using xi is xi is more a better parameter because that is universal parameter, if x is if I am using x I have to use only for A, one of the components but xi is general one, what are the units of xi, does xi has units? xi, you can take this, see you take this, so anything we say xi or x you cannot say it is unit less, you know not dimensionless because you have to see, now you can define xi in fact, xi equal to N A naught minus N A by A and also N B naught minus N B by B and like that, you know here also, right, that is N A minus N R naught by R, okay, N A minus N R naught, so all these things are there, you know for xi, xi definition you know already, these what is the parameter which used by that air is I told you know air is book, that is the parameter what is used, there are some advantages with that, there are nice advantages with that, so this is the xi where it is extent of reaction equal to extent of reaction, yah, so I would like to have you know the total number N T naught, N T naught is total number of moles at time T equal to zero, so all that will be N A naught plus N B naught, N R naught plus N S naught, okay, so equations if I start giving, yah, I think I can start from here only, one, yah, so N T, N T is N A plus N B, N R plus N S, so that I can also write, okay, so this one, I have already these things, right, I have already all these things there, so it is N A naught, let me write patiently all these, plus N B naught minus B xi plus N R naught plus R into xi plus N S naught plus S into xi, this is equation number 2, so now can I write this N T equal to N T naught plus delta N xi, this is equation 3, where delta N equal to, excellent, minus B, so that is the stoichiometric coefficient, you know, coefficients, the difference of stoichiometric coefficients between products and reactants, okay, so that is the one, delta N, so now N T by N T naught, okay, that is total moles, at any time divided by total moles at time T equal to zero is now one plus, I am just dividing this by N T naught, so I have delta N by N T naught into, N T naught into xi, okay, so this is equation number, this is 4, this is 5, xi definition you know, why, I know number of moles how much is converted that is best parameter for me, number of moles is much more important than me for the concentration, sorry, sorry, we are for each thing here using the same conversion, yes, does not matter, actually that is what I require, because if I am able to use that, that is very good for me, because now I do not differentiate whether I have N A or N B or N S or N, because everything is same, that is what, always university or any academic institution wants this unification, always industry wants differentiation, really that is why periodic table has come because that is unification of all the properties in one place, why should you remember 103, how many are there 103, 104, 105, 189, 180, 109, that is what you are telling, 118, so many no is not there, 109. , yeah, I think so, I remember till 104. afterwards I do not think, I do not want to remember. So why should I remember this 104, 105, 160, 107, independently all the properties, okay, instead of that I put in the periodic table, that means horizontal roast and vertical because now i can unify all these elements in this row will have or in this column will have some properties or in this row will have some properties beautiful unification who did it all of you jyothi where is he from or where was he from that is what is the one whereas industry they want differentiation why because if they want to produce hydro hydrogen all of them are interested only in the properties of hydrogen they do not want to look at any other element that is why it is a wonderful statement when i said that you know industry always lives or thrives on differentiation and academic institution always thrives on unification because for anything even if you do PHD definitely one of the examiners at any point of time or in your interviews also they may ask that okay what is the generality you have done only on the system how do you generalize they ask okay so that means your work which you have done in this laboratory is it valid only for that specific purpose can you extend also for other systems okay i mean in terms of temperatures pressures or flow rates and can you extend further so that is the kind of thing so that is why please remember industry always thrives on differentiation and academic institution thrives on only unification so that is why you have to really appreciate you should question me sir why are you using XA conversion okay conversion because you know these things when you learn first time that is why you say you know love it first right you know and the first time love all these things we say because first thing anytime you do first time you remember always that is why whatever you learnt in high school only you remember because that is the first time you have started writing you know alpha beta and all that so beyond that i do not know how much really we learnt when you come to the graduate school like btech and all that i think we are not learning much you check yourself you check yourself in the school how much knowledge you have retained here knowledge means not degrees okay how much is retained at any time what you can recall what you learnt in school only you can recall so now this is the equation what we have where xi definition i think okay let me write xi equal to NA0 minus NA by A which is also equal to NB0 minus NB by B which is also equal to NR minus NR NR nata by R also equal to NS minus NS0 by S okay good so this is the general definition of xi that is no problem i think this equation i can call it as 6 good so now we take this equation and we will try to just try to manipulate that equation so this NT by NT0 what is our ultimate aim to measure the pressure or volume okay yeah so NT by NT0 equal to 1 plus this one what i do here is delta N by NT0 NT0 and this one for xi i will take you know for xi next is xi i have right for xi i will substitute here NA0 minus NA by A okay i will further simplify this one i think i will come to merit i want to satisfy merit by writing that so this is delta N by NT0 NA0 NA0 minus NA by NA0 what do you get correct no NA0 NA0 i can cancel out so then i will get only this so why i have written this one is to satisfy merit okay so delta N by A this is NA by NA0 correct no sorry NT0 NA by NA by NT0 then what i have into okay merit are you happy NA0 minus NA by NA0 where is NA0 this one no this one this one this one okay delta N i have given here oh this one thank you thank you NA0 good so NA0 yeah NT by NA0 okay into XA very good thank you i think you have not stopped you have not started sleeping so yeah this one now NT by NT by NT0 i can now write as this one as delta A into Y0 by the by NA0 by NT0 what is that mole fraction correct no initial mole fraction at time t equal to zero mole fraction of A mole fraction of A so YA0 this is the one okay so these two into XA where this equation equal to seven where delta A equal to what is that delta N by A and YA0 equal to NA0 by NT0 okay good you know you may not remember now this delta A into YA0 is infact epsilon Levenspiel epsilon okay yeah so this also can be written as NT by NT0 equal to one plus epsilon A XA where epsilon A this equation is A8 where epsilon A equal to delta A into YA delta A into YA0 okay so now normally we define epsilon A as volume at yeah volume at 100 percent conversion minus volume at 0 point by okay yeah i mean you know that mug up is there in your mind you know there is no problem that is the definition of epsilon but the real meaning of epsilon A is it is the stoichiometric ratio delta N by A okay delta N by A that is why you are writing epsilon A one can write also for epsilon B and all that with this derivation whatever you want epsilon B also one can write right and this equation can also be written in terms of XB only thing is correspondingly wherever you have to substitute for that xi you have to substitute here okay so this is more general expression yeah so do you know this delta delta is delta N by A do you know that in the beginning itself before starting the reaction yeah how do you know stoichiometry you should sometime tell me sir you are asking stupid questions we already know this but you have to tell me that then i stop asking that kind of questions okay because i think you know this delta N i have written here clearly but those people who are sleeping i want to wake them up that is why i am asking i in that question okay so delta N i know in the beginning itself because stoichiometry is one of the requirements for me to start with my entire reactor design okay that is the first requirement stoichiometry so i know what are the stoichiometry coefficients so that is why i know delta A and why not do you know you definitely know what is why not if i have pure reactants i mean pure reactants means if i have only A if i have A plus B just A plus B only we have point 5 so that is why you know that information so you do not have to go and write volume at 100 volume at 0 divided by volume at 100 all that you do not have to write because from stoichiometry equation itself you know all that information epsilon A you can calculate and by the by this is the definition given by Levenspiel and he has propagated this way of thinking so that he can formalize this epsilon A that volume change whether it is increasing or decreasing in terms of an equation that also i will just derive but there is another school of thought by you know Carberry you heard of name Carberry James Carberry James Carberry he has also chemical and catalytic reaction engineering in fact the next course is based on only his own book title he wrote a book called chemical and catalytic reaction engineering Carberry in fact it is J J James J Carberry chemical and catalytic catalytic reaction engineering that is the title i think this is Megrahill Megrahill New York N Y we write i think it is may be 77 but anyway i think i just put question mark you will tell me afterwards okay so that is how you write the text books whenever you are writing okay so J J Carberry and yeah Carberry and Smith James Smith also James Smith chemical engineering kinetics and he is also Megrahill publication New York is the place and here okay i think his first book was in 1951 or 1952 James Smith book so then whatever you see the current book is actually third edition i think 1983 or so okay so three volumes i think he contributed a lot for example his Smith and Van Ness thermodynamics book so even now it is a wonderful book and i think when it completed 50 years there was a big celebration also for that book because really it was one of the books that are available for chemical engineering thermodynamics title also is wonderful chemical engineering thermodynamics even though the best book is Denby chemical equilibrium okay but this one is straight for the student that is for philosophers you know chemical equilibrium right huh what is that tell me sir why we see long i think that is the latest generation because i think ipad is 5 or ipad is 6 or 3 or so this generation is latter that is 0 i think this is another problem i think most of the people now they are following in our time we don't have any Indian books it is good to have some Indian books also but it is not only Indian books you have to read because you don't get the other exposure all our books are foreign books and we were proud when we were doing our b-tech because only chemical engineering people were using all imported books civil engineering, mechanical engineering like a theraja, theraja okay, Bharati, Bharati okay I think you know that kind of things are heat engines by some shokla shokla so that kind of books only are there for them but for us you know 11 speed right, Smith James Smith also you know thermodynamics and fluid mechanics by I think mechanical engineering not mechanical engineering Smith all our books are only foreign books okay, a tri-ball right, ya ya, a fogler was not there he was not born when I was studying okay so those are the books what we had you know at that time we were really proud but now you don't know all those books you know only why we are here and who is that person who writes many books panda what is that gawani gawani is expert on all subjects okay ya so I think you should be given noble prizes it is not possible to be expert in all subjects right I think we don't have noble prize in India so we should have given that so that is the kind of things what we have okay and you should also remember you should definitely see this is the time to see all these books are there in our library at least for the sake of seeing but you know you have satisfaction of I have seen this book okay so I think you have seen or the Indian book is there gawani hand book of chemical engineering by gawani is there not there I have never seen that book I don't know somehow I think many people I think my students used to tell me okay good so this is the equation that is why this epsilon that is the blind definition what he has given for some time and we not time conversion ya 100 percent conversion and all that good so this is the equation now this equation we can write also in terms of volumes and pressures because n t by n t not so I will go to now my ideal gas equation p v equal to n r t okay n n, n is the number of moles that is this will come there so I will have this equation equal to n t r t that is one equation and another equation is p not v not n t not by r t this is t t not right now you divide n t by n t not equal to n t by n t not equal to p p by p not correct n t not what about v v by v not into t not by t r will get cancelled no ya so now this is equal to I have 1 plus this is equal to 1 plus epsilon a xa ya okay now now I can write this equation as p by p not okay first I think I will write the familiar form so v by v not equal to 1 plus epsilon a xa into p not by p if I write wrongly please tell me t by t not correct if I have a constant density system that means variable volume variable volume and if I have isothermal case what is the equation what is the condition I have constant constant temperature constant temperature and also variable volume that means pressure is constant okay that means p equal to p not variable volume when you have variable volume pressure must be constant right so that means p equal to p not so for variable volume variable volume p not equal to p variable volume and isothermal isothermal and t equal to t not okay what is the equation you get v by v not equal to ya now now at least you remember what is this equation this is 10 this is 11 this is what is the definition of Levenspiel strategic condition like variable volume that means pressure is constant temperature is isothermal condition so temperature is same therefore you get this equation okay good so now you have to use this equation to define conversion and all that let me write that pressure equation then we can decide tomorrow you cannot run immediately so then the other equation in terms of constant constant value and isothermal case what do you do whereas I show thermal, constant volume means, V equal to V0, and T equal to T0, now tell me the equation, P by P0 equal to one plus X1. Correct? P by P0 equal to one plus, yes, good, so now, this equation you are familiar, but from this equation you have to get the partial pressure okay so from one equation we are able to get two of the allowance fields you know derivations two derivations he has done I mean he has not derived that actually he gave the definition that is all no derivation there right so what we have to get is you have an equation which you have seen in third chapter p a equal to p a not minus a by delta n p minus p not see this one p when I write like this this is the total pressure when I write in somewhere here it is partial pressure okay so this is the equation which you are familiar with you know when you see allowance field book third chapter in fact third chapter first derivation is this right so can you get this this from this so that is equation number 12 this is 13 and I will put question mark how do you get this in fact from this you can also get this I will just leave it to you that one how do you get in fact you can get this one for not only p a p r you can get p b you can get p s you can get all that can you get this from this okay you have all the derivations you have what is a right and you know what is x a here in this equation there is no x a x a is nothing but that is okay but in terms of partial pressures how do you write because it is constant value constant value in terms of partial pressures how do you define x a that is all p a not minus p a by p a not so you substitute for x a that and epsilon a you know right and then you arrange that equation you will get because you have mole fraction and all that know why not is mole fraction right yeah so that is why I tell you leave it to you that you derive on that so that I have at least one for separate test okay I will tell that okay derive this equation right I think it is not difficult know all of you are okay or what you can done okay no problem yeah this is very simple derivation only it is not that difficult provided if you use these equations you can easily derive this from this okay this from this okay this is nice one because I think from the same equation we are able to get the two things now you have a lot of work to do because now third chapter is over and fifth chapter is over okay that fifth chapter is reactor design that equations we have actually second chapter is t and all that you know Arrhenius equation mechanism of reactions and all that that also we have discussed so first chapter is introduction anyway so third chapter is now what we have discussed now I cannot derive each and every equation now it is for you at this point of time you derive all the equations now our idea is to go to that final diagram what is that input output contacting cantics now you have the contacting contacting means any reactor when you have to choose what is the design expression that part you know and in that design expression you have minus r a right minus r a that minus r a now you know how to get right so what you do is once you get this P a P b P b also you can have another equation P r P s those are the concentrations for us now that verses time will be given right otherwise you can also convert this into concentrations by dividing by r t r t r t then you have now what do you have concentration verses time or partial pressure verses time in fact I would have given also Sushmita you have seen all the problems in the assignments I think if I remember correctly I also gave in terms of partial pressures one or two problems okay so that is why unless you also move with me by spending time in your room you will be lost and otherwise you will not be comfortable in the subject in the class you feel that everything will be clear but the moment you start solving problems you will have many doubts so at that time you have to discuss with your friends if they are not able to clear you have to come here we will discuss and then we will completely try to learn the subject as deep as possible okay we will stop here and tomorrow morning 9 o clock we will start the class thank you