 in the last class we have developed two surface reaction models one is kinetic control the other one is adsorption control, okay. So let me write those and then try to identify something in that and also let us I will not give the solution but I will simply give the equation and in between steps and finally the rate expression where adsorption, surface reaction, desorption all three are there not one controlling all are controlling, okay it is only mathematics so then I think you will have some nice things in your room to do things, okay. So that is one problem and before that we will write the same equations what we have written earlier the last equation, final equation just to discuss some more things this is L H W models continued, yeah the equation for surface control and when I have A gas, B gas, C gas plus D gas catalytic reaction this one you have already solved if it is surface reaction control the rate in general form is given as some k C A C B minus C C C D by capital K right or K naught whole thing divided by we have all those terms 1 plus k A C A k B C B k C C C k D C D plus k I C I if you have units if you do not have units that term will not be there so this is one equation and for the other one I have simply A gas going to R gas this is surface reaction control right reaction control and when I have here adsorption control what is the equation again rate equal to yeah again in the form some k C A minus C R by similar k naught divided by 1 plus k 3 by k 2 A plus k 3 C R plus k I C I if you do not have again I units then you will have this term will vanish you will have only this one can you see any commonality in this equation and the next equation see generalizations are very important in engineering after 2 3 problems you can say that you know there is some general things there around that anything numerator what yeah what do you call this term or this term driving force term so in any equation what you when you take you will have a driving force term you will have a kinetic term constant and you will have resistance or adsorption terms okay I mean they generally called adsorption terms okay so that is why whatever equations you try to derive with whatever mechanism for example here we said adsorption control you can also have here surface reaction control here also you can have adsorption of A control or desorption of C control or desorption of D control in all these things you will have this general format so all langmuir Hinshelwood kinetics will have a kinetic term a driving force term and a resistance term or we call normally it is an adsorption term okay so those 3 terms and if the reaction is not reversible this term will not be there you have the magazine driving force it is 0 okay good so now the other problem which I want to tell you is similar A going to R only similar problem A going to R but all the steps are controlling right okay another example is A gas going to R gas of course cat here also cat you have and you know in this the steps already we have written A step 1 is A plus S A S step 2 A S giving R S and step 3 R S giving R dot okay R plus S so this is you know adsorption step surface reaction step and desorption step and when you use this one similar notation as we have done earlier K 2 K 2 dashed K 3 K 3 dashed now in this the problem is that all steps are right controlling so let me also write that when I have R adsorption I will call A as treat all these steps okay let me also write the equation numbers these 2 have already been given right yeah so then I will have here 1 2 3 4 good so our general thumb rule is that every reaction is an elementary reaction I am again repeating I know I know you may not be interested you know but still if I tell 100 times then you cannot come out of that may be somewhere it will be there in the brain when you want to recall you can recall it otherwise just once only if I tell it goes evaporates very quickly the upper pressure is very high okay yeah so then we have R A as this one K 1 I am writing slightly advanced stage C S by K 1 this is one equation so this is equation 6 right that means the small K 1 you know meaning of capital K 1 it is K 1 by K 1 dashed that is why I said slight advanced stage and reaction step is K 2 small because the reversible reaction K 2 then I have C A S C A S is the surface concentration after joining with A and active site okay that is what C A S so C A S this will be C R S by K 2 this is equation 7 and R desorption will be K 3 this will be C R S so C R S minus C R dot S S is again separated divided by K 3 where K 3 is defined as reverse of normal equilibrium constant this is 8 okay yeah what a very happy androg I mean that shows your interest I say that is what is the said yeah because I also got because I think some Korean people came and started giving presentation I also did the same thing okay but I think it is not allowed in the class I am allowed there okay good so if I take all these 3 steps controlling what is the procedure now unknown concentrations procedure is same universal okay so this one all unknown concentrations have to be eliminated and we know that at steady state conditions this must be equal to this must be equal to this R A equal to R X N equal to R D under steady state conditions so we have to equate all of them and then remove all intermediate concentrations which you cannot see which you cannot measure and then finally express only in terms of C A C R okay what kind of equation you will get I will write now that and I will ask you to do that okay yeah in the examination also I can give and I tell you if you have not done this in your room at least once and if you start this doing in the class without doing once in the examination all okay even 3 hours will not be sufficient okay do not blame me at that time that you know he gives very lengthy question paper as I told you if you are writing speed is 0 you will take infinite time and who will wait till infinite time no one can wait there okay so this one the overall rate R is given by some constant K which will be here S 0 and all that okay C A minus C R by capital K I will just okay K naught bracket is here so I have to write the whole thing there then I will have here please carefully note down this one it is capital K 1 small K 2 plus 1 by small K 1 my small K 1 will be something like this plus 1 by K 0 small K 3 this is a constant plus 1 by capital K 1 capital K 2 plus 1 plus capital K 2 capital K naught small K 3 K 3 into K 1 C A small K 1 C A some more oh my god I have to go further yeah plus I also have 1 by capital K 1 K 2 1 plus K 2 capital K 2 K 1 so I have to extend C further into K 3 capital K 3 C R very simple expression so this is equation number 9 okay by handwriting you have to identify small case will have this kind of thing okay these are all small see I made a mistake here K 1 C A this is capital let me check once more 1 by K 1 K 2 plus small K 1 plus K naught K 3 small 1 capital small capital small K 3 then K 1 capital C A K 1 K 2 small K 2 capital K 2 capital K 1 small this is capital K 3 and C R okay good yeah where we will write that K 1 equal to small K 1 by K 1 dashed K 2 also equal to K 2 dashed and K 3 small K 3 is the reverse K 3 dashed by K 3 this is capital K 3 yeah this also capital K now next one is K naught K naught equal to capital K 1 capital K 2 by capital K 3 even here you have the same format what is the format first is kinetic term that kinetic term will be changing on changing depending on the what are the other constant that will come okay yeah and the other things of course you are all you know this one is of course all these things are adsorption terms are resistance terms where the total rate of reaction will be decreasing with these things I do not know the physics of this problem you have understood or not if I do not have a catalytic reaction what will be the rate rate only this this will not be there then why for catalytic reaction this is concepts concepts phenomena the whole diffusion we are not taking whole diffusion and external mass transfer we thought that you know it is attraction attraction between what so if there is more attraction happy you know why you should decrease yeah Kavya you are trying to say something inside the force it happens but I think you know the mass transfer through the force is very very fast that is assumption only three steps we have taken the remaining four steps are very very fast the three steps are adsorption desorption surface reaction right okay how does that decrease the rate number of effective collisions decrease effective correlations decrease collisions yeah where on the surface or if there is no surface so yeah there is no no surface of the reaction and what will happen the reaction can take place anyway in the space molecules can easily react and collide so then if the moment you have the surface then adsorption takes slow it is a slow step when compared to random collision of the molecules okay desorption also slow step right you know it is like you know when you are writing only that J E entrance or any state entrance you are very very active free molecules after coming here year by year adsorption nothing comes out starts there then afterwards surface reaction second year third year and fourth year desorption the rate is the tremendously decrease because this will be infinity that term so then your rate of doing anything will be 0 okay exorgerating but still that is true right so that is why the physics of that is that in a catalytic reaction you have the other two steps which are really controlling even though we do not say it is controlling they are not first steps because first of all the molecule has to search for active site okay I mean in that terms it may be very very small but still that is comparably very very large when compared to free molecules moving in the free stream okay so that is why even non-elementary reactors also non-elementary reactions homogeneous also same problem because in between you have some other intermediate forming that intermediates have to decompose in fact this is nothing but the intermediate reactions here correct no this is a reaction this is a reaction this is a reaction but if you do not have all these if you have simply homogeneous reaction then all these things you do not see collision product collision product collision product okay so that is why atleast remember this as a story like you know what happens in a catalytic reaction and what happens in a homogeneous reaction okay so that is why always you have the catalytic rate is little bit less than okay the homogeneous rate of course if you then there is a big assumption if the activation energies are same that is very important otherwise the point of using catalyst will not come into picture at all okay I mean always we say that go for catalyst go for catalyst right but the activation energy here is tremendously reduced then so that you will have more number of collisions and all that overall rate will be more but the term will not be there if you have homogeneous reaction if you are comparing at the same energy levels okay so that is the one so now you have in general what you have here is the rate is rate can be written as a yeah rate of reaction in all LHHW models can be written as this also you just remember because I think this is interview question people may ask again decent interview if you have kinetic term driving force term driving force divided by resistance term these are the three terms good so now let me give you something can pass it on see I think yeah so what do you see from that tables you have table 7.3 7.4 anyway that doesn't mean anything to you number but only matter in the table what table shall we take first 7.3 yeah by looking at the first one can you say anything yeah not reversible that is one thing yeah which one which one will be rate controlling where do you say adsorption that is what I was thinking at least someone will see the top the title yeah there itself it is written surface reaction control without seeing always it happens you know you don't read which question paper you have taken you know the moment we distribute the question paper you first go to only question number one to read okay general case sparsely covered surface fully covered per se you know I just want to tell you that there are so many possibilities in these models okay yeah and the second one is like this one a going to R but here it is adsorption control but if you have reaction control you can easily write that equation without even deriving it okay of course there is no units involved there but it is given in partial pressures and also theta coverage you see that theta is nothing but your A S theta A A S theta B if I have their B S like that I told you know there are two schools of thoughts about derivations one is the langmuir not langmuir hinshelwood the other one is auger and watson auger and watson will write A S active sites okay and langmuir hinshelwood will write in terms of fractional theta coverage theta is the fractional coverage both are same at the end you will get the same thing so I can ask any of these derivations in the examination or including separators okay good again you know below you have got the general expression given as kinetic term and then driving force and adsorption term and also it is called resistance terms good very good excellent so just keep that with you don't throw them away try to yeah the other side you have adsorption control good so some more things about these equations I have to tell you that I have so many constants here too many K K S here K K K K K K always K K right yeah K 1 K 2 K 3 K 4 and all that okay too many K K S so that is why you have problem always how do you evaluate them all these constants experiment only but after doing the experiment you should use many many techniques to do that see one simplest thing is let us say that rate is increasing with one simplest example I will tell you when you plot let us say rate versus PA or CA okay concentration of A and then this is about rate concentration only not in the bulk concentration only otherwise overall rate this is overall rate so then how do you expect I mean what kind of curve you may get here question is not clear it will depend upon that it will depend upon it will depend on the reaction yeah only I have given A but let us say of course any reaction even this also A plus B also because stoichiometrically A and B you know one now okay for the simplest one you take A going to products A going to all product for any you can take reversible yeah I mean you know you are drawing somewhere like this like what initially it will increase at an optimum or a maximum point and then decrease because because PA is CA is still increasing CA when you say decreasing why you should decrease because CA is increasing see this is what I think is beautiful I say really the imagination of something happening trying to first imagine in the brain and then try to draw the curves I told you know as a hobby you can develop that that means when you are free just take you know a pump how does that work and then if you are increasing the input for example HP how the outlet the delivery how much you have to pump out so how it increases distillation columns for example change the temperature how the concentrations change absorption okay again change the flow rates how the concentration changes just sit down and then draw and it is not that easy I told you know I have the simplest example you can try in your room that is taking an iron ball of maybe 6 inch diameter big ball put it in a furnace at 500 degree centigrade allow it to come to thermal equilibrium okay 500 500 just take it out imagine that it is hanging draw the temperature profiles there because it has to cool know you brought it out hang it there imaginary and then after you wait sufficiently then the temperature throughout the particle also should come to room temperature how the change occurs same thing when I think you are eating bonda in your Himalaya I do not know whether they are giving you bondas bonda are spherical particles beautiful particles vada is flat plate circular okay but bonda bonda you know abhinav bonda you know samosa is a peculiar structure so you cannot imagine draw but I think spherical particles are always better okay why bonda I think you can also imagine your golaab jam that is beautiful spherical mtr golaab jam much more spherical or much more smoother okay yeah then very hot thing they have given to you and then now you sit down in the mess still it cools to room temperature how the temperature decreases just try to draw that yeah he has already done once like this it is not that easy if you get just go deeper and deeper and try to observe what is happening so like that I think this is very good I think of course here coming to this it has to increase with CA know as the concentration of A is increasing rate has to increase so you may have something like that okay good so why I told this is this is experimental curve this is experimental curve right once you have this experimental curve theoretically speaking how I can find out k1 k2 k3 k4 and all that I will go to my model for example this one or maybe this one now I go to matlab right and then give initial guess values of k1 k2 k3 all this how many I have here 1 2 3 4 constants and if you remove this you will have only 3 constants give these 3 constants the guess values and then ask matlab fellow who is inside that okay to calculate yeah to calculate for different CA's because this equation has CA and once you know CA's here is all you know because 1 mole 1 mole there is a relationship you now calculate this and then try to plot okay so this matlab fellow inside that you know program will you would also give some kind of difference between your calculated value and experimental value at every point it calculates at every point it calculates here here here here and how many points you choose depending on your patients okay so at every point at every concentration you allow the matlab to calculate R and then the difference between R experimental and R calculated should be minimal theoretically it is 0 but the moment you put 0 and infinity computer broke it breaks you know I mean it cannot say anything I think whenever you want to spoil computer put infinity or 0 I think divide divide double you know explanatory marks all that things will come right so anyway that is why you have to have at least 10 to the power of minus 10 10 to the power of minus if you want to go to 0 almost that is the difference between those two and then you allow it to calculate and finally put that point here point here point here point here point here if both of them are matching then your k values you will know because that will have k1 value k2 value k3 value there is a lot of things that is required again like a story okay once you have k1 it will take you give the initial guess values k1 k2 k3 let us say 1 2 3 right so then it calculates if it is less then it will try to increase if experimental value is higher than the calculated value right then again computer will take now k1 increase calculates k2 increase calculates k3 increase calculates so there is lot of programming going on there but if it is moving towards this then it will go I think prasashankandar simon beautifully tells that in optimization is course okay how do you match this this match between that optimization also here is matching between experimental values and and model value so finally when all of these things when you have 10 to the power of minus 10 matching then that will give you that k1 k2 k3 values it prints out but unfortunately if I do separately if you do separately if shokumar does separately all three will be different but beautifully it fits it fits much more beautifully if you have more number of constants not points constants okay so that is why Levenspiel always says that do not use your parameters more than each one is a parameter here k1 k2 k3 and all that more than 2 3 also is very difficult because that uniqueness will not be there see the physical system is only one right we have done only one experimental run and as far as physics is concerned that is not changing but how can it change depending on who gives the guess values so it is the mathematical technique problem so that is why when you have more number of k1 k2 k3 uniqueness in parameters uniqueness uniqueness in those constants is questionable but it fits the data if you are only trying to fit the data without thinking about what is k1 k2 k3 it is fine but if you also want to get some physical meaning for kA kC kD kB and all that then you have to use some optimization programs where you have unique optimization where anyone does it will give the same constants whoever does it that is the best method if you are able to do that otherwise divide and rule we are excellent in that okay because our British people have told us so we still follow that so that means divide this equation into 2 this you remove this fellow only forward reaction okay and forward reaction means only this term will be there even CR term also will not be there okay and then you now this equation is simplified this is all this is one constant this is another constant right so that is how you do you heard of what is called initial rates yeah here only very very I mean profusely used these methods you know initial rates particularly for catalytic reactions because forward reaction you take conduct the reaction such that it is not going towards this you know this equilibrium or this side and only initially and again start with R because you are doing experiments right you are not producing anything R you can start and then with R backward reaction this reaction both reactions will be there okay but again now when you take R CA will be removed from there and you will have only this reaction this reaction will be going on but most of the time this you know backward reaction that is the starting point initial rate so then finally you conduct one reaction completely taking A alone and then see that whether the constants which you have evaluated from this technique that is you know initial rates forward reaction backward direction whether it is also completely matching this is experimental that is experimental okay so if you are able to get your excellent match okay even here also excellent match that is why nowadays we are not doing this at all okay I mean first of all nowadays who is doing chemical engineering at that level in fact at industrial level where you have the catalytic reactions you have to model it and all that so that is why as engineers there is another technique okay that technique is you have this kind of equation do not worry about what kind of model you have model will give you more information for understanding what is happening right and if you are not able to spend that much time another easiest engineers way is assume that we have this rate as a is proportional to or the proportional constant is this C A to the power of A C B to the power of B minus C C C to the power of C yeah if it is reversible reaction that is all okay that means you are now trying to have some kind of empirical relationship which will satisfy your experimental data okay this is power law model understood no if it is only reversible irreversible reaction even this term will not be there if it is irreversible this term also will not be there you will have only C A C B so you have to evaluate A B and K and do not care whether some mechanism exist there or not purely empirical rates which break it down purely empirical rates thank you that is how we do most of the time we have minus r A equal to K C A to the power of A C B to the power of B and all that okay it is valid in chemical engineering because our idea is to develop a rate expression such that this rate expression I can use it in my reactor design expression okay that is one style of doing things the other style is the other method is other way of doing things is that okay let me now understand I think most of us will do that okay every subject when you start you think that you know it is interesting and then after some time you know you think that okay let me read everything let me read everything let me read everything but finally before the examination you cannot read anything but also you know you did not solve any problem so like empirical okay then try to remember something come warm it in the examination hall on the answer paper that we have to clean it so then I think some marks you will get and then you get the marks okay so that is another way I think you know to start with every student thinks that oh this subject is very good but after some time because he is not able to concentrate so many other things you know because he has to take care of things in the India how many things are going on and all that so that is why I think he may not have sufficient time to read that and finally before I think the other day we were talking you know Prabhu was telling that are night outs yeah night outs night outs when yeah before hardly may be 12 hours okay 12 hours also too much I think you know you start I think around 2 o clock in the night and next day 8 o clock class okay I mean these are the realities you know you do not have to get angry with me okay but these are the realities okay not only you I told you all Indians are brothers and sisters okay nothing will change okay all of us I have the same mentality so at the end the result is that we do not learn anything yeah so now you become you know these are another seniors one year you become senior to your junior then you feel that everything in the world you know and you advise also that fellow as if you know everything you solved all the problems of the world and now this fellow is very small okay let me give the advice and that fellow does the same thing you know for his juniors one year you know I mean even 20 years difference also I think you know that wisdom you do not have much difference I do not in one year how suddenly you become that kind of very intelligent fellow to advise all your juniors okay yeah and your advice I know do not take this course because that fellow will tell you all this okay that is the kind of advice and you know the other fellow is quite question papers he gives same question papers you do not have to read at all so take question papers and then solve H circle they do not know poor guys okay when time is there I will tell you what is H circle later okay H circle is hostel circle that is what okay yeah so that is how it is happening and unfortunately of course in engineering most of the time it is thrills it is really thrills engineers are the people who run the world and doctors are the people who protect the world because they should not die you know yeah and lawyers are the people who do not kill the world I think you know make the money they create teachers teachers are poor fellow I think you know do you remember your teacher okay you don't remember your teachers teachers are you know on the way expendable all these guys are expendable guys okay after my course is over don't care and if you don't care it is fine but tell everything opposite to him you know to other people I can esteem okay don't take this he will tell that he will tell this and all that I don't know that's why nowadays in every department we have angels faculty the angel faculties are preferably deaf and dumb okay even if you go and ask they will say only their head works that's all okay either horizontally or vertically you know horizontal means no vertically means yes and even if that angel also tells many times like this then he will also become devil they also won't go to the go to him because he is telling too many things like this so that is the kind of thing you know teachers respect nowadays good anyway so this is a wonderful thing really because it is very very complicated to develop a rate expression that's what finally I want to tell you I am not saying it is pessimistically I am the only trying to tell you the challenges that are involved in the design the challenges that are involved in reactor design okay why the first challenge is rate itself how do I get all these constants here or all these constants here and you need lots of knowledge for that you know to evaluate all these constants accurately otherwise imprecisive simple imprecisive and you know there is much more than this much simpler than imprecisive also imprecisive also you don't need any equation at all till you can design how what is that thumb rule no no thumb rule you still design you will find out weight of the catalyst what is the equation W by F not equal to if it is minus r a you collect minus r a data experimentally you know that is why you have to appreciate Levenspiel I say so what Levenspiel does he gives this equation wonderfully this graph wonderfully minus r a versus x a so you simply plot it may go like this so you are assuming you are designing a new reactor so you put 90 percent conversion and then area under the curve will give you W by F a not F a not is already you got it okay so W can be estimated that is much much simpler one if you want to really quickly design a reactor like war time and all that yeah war time designs are there you know during Second World War all these thrills were there you know one group will be theoretically working another group will be working like this very quickly to produce in fact during Second World War only denby has done wonderful work on you know denby you heard of his name Kavya denby his initials are I think Kg not mg milligram Kg okay yeah so he is from UK in fact he is the person who gave the name for the CSTR as mixed flow okay and he was using you know he was preparing explosives to throw on Germans you cannot yeah and in explosive reactions the reaction is liquid phase reaction and temperature control is very important so that is why he has chosen CSTR because the temperature can be controlled so there again intelligent fellow so he used three tanks four tanks to get in every tank you can control the temperature very well and three four tanks if you use almost you will get efficiencies the production rate will increase tremendously for a given conversion okay yeah so I think why I was telling his name okay during World War 2 only our CSTR definitions have come okay so anyway I think he has also used lot of empiricism but I don't know I think I sent you last semester some of his papers you know the way he writes with minimum mathematics and maximum insight beautiful really beautiful later he became philosopher yeah I think the last 10 years or 5 years of his life I think he just stopped chemical engineering and then start analyzing philosophy in terms of thermodynamics because he has also written a book chemical equilibrium okay I don't know whether you would have not seen no of course if you have seen you would have remembered the other's name which book you have used in your course thermodynamics Smith and Venice only no other book no other book okay yeah and the classical book is DINB sandal this is private engineering colleges stuff and why we say our book is not used no no he is from IIT but that is popular only in private engineering colleges IIT is no one will use that where you are using but I think teacher is not using that teacher follows that this is surprising to me but B Tech I think we never followed minimum is Smith and Venice that you reduce it to too much empiricism you reduce it to too much empiricism so it is only class notes it is also not your class notes other's class notes okay so I think in the next class what I tell you is based on this approach I I have I will write at least some 5 or 6 industrially used rates I am only trying to generate some kind of interest I say but in the on rocks it is there always as if he is not in this world physically yes mentally also okay next time I will ask you question okay to check whether you are mentally there or not so at least you know that kind of interest you are going abroad I say you should learn this okay anyway so tomorrow first hour I think you know it is long time I have done surprise test so I think you may have surprise test also tomorrow okay anyway I think thank you tomorrow morning we will see