మాభావారడినం మారారడూచ౰ిల్ల్ మాసివారన మాచాయెమానం మనోమాసిలం మా�one నిల్టైలులూ మారిటుమాటెపె మారనాలఱలకమాల్రనినమారనాస్లడడిరా a develop a rate equation for heterogeneous reaction if it is a catalytic reaction and also non-catalytic reaction I mean the rate how do you develop for non-catalytic reaction so that is the idea so we have taken catalytic example as ammonia right catalytic reaction ammonia synthesis that is what is the example what we have taken and this ammonia synthesis as we know already there is not a new process that is old process so we have taken a packed bed okay so then this is coming out this is entering somewhere here I have taken for my kinetic equations okay I have to take a single particle this is true you know even if I conduct this ammonia synthesis catalyst as iron right fluidized bed also I can take in fluidized bed these particles will not be stationary not like packed they will be moving yesterday also I have demonstrated now with people particles move so they will be moving so even when they are moving I can pull out one particle what is happening around that particle you know this is the original system for all heterogeneous systems you should have that thinking of you know some thinking about the process if it is fluidized bed okay so what is happening particles are constant around that you have the flow of reactants okay so then what are the steps that are required right that we understand fluidized bed also now we understand fluidized bed will be something like this where gases are entering gas gas liquid also can be same so here are the particles this is the catalyst and then it comes out this is fluidized bed so when we are making these particles float with the support of you know the liquid or gas you are able to follow me know fluidized bed because most of the chemical engineers must know what is a fluidized bed right I think Arya in your wastewater treatment also fluidized beds are widely used right so I think in chemistry they may not be 100% knowing that I think someone has to help them so you take this for example sand because it is easy to imagine sand all of you would have seen I think don't tell me that you have never seen sand okay ya you have seen sand no ya okay so sand you just take in a cylindrical column where you have a distributor plate at the bottom okay and now send the air for example air you cannot see but we know we can feel right when you put fan starting you know air is touching you but you cannot see it right ya so then you are sending air or some other fluid also but air is easy for us to imagination this air when it is going through the perforations it will push the particles and then it also moves through the particles to go right if I am using very very small flow rates then air has just the capacity to move through the particles and now slowly increase that velocity I am just telling particularly for this chemistry people and those who have not been exposed to that so slowly I am increasing that flow rate here through this before that you have sand just filled up in that that is theoretically a packet bed why packet bed that is a packet bed because particles are not moving then slowly introduce the air then at very low velocities those you know the gas will go through the perforations and also through the particles between the particles not through the particles means not inside the particle okay around the particle and we have in a packet bed the what is called voidage porosity of the particle of the bed so through that it goes so you keep on increasing you keep on increase the flow rate a little bit little bit by little bit so initially when it is very very small then it will only move through the particles but when it has sufficient velocity then it starts moving the particles that is the first time okay so that means the particles will try to get adjusted on its own when the when there is a such a velocity where it is able to move the particles a little bit you slightly increase even above that then the entire particles also will be floating and when I look at one particular particle then this gas is sufficient the gas velocity is sufficient to keep that particle under suspension okay theoretically you can also be fluidized if you are going by a motorbike very very high speed correct no because what is happening is the drag force of the air which is acting on your body right if you have not properly hold it and then you know legs are not firmly on the pedals then you may be fluidizing that is what I am telling or afterwards you may be pneumatically conveying that means you will travel with you will travel with the air okay that is also same thing happens here sometimes you float and afterwards you will be traveled so here also all these particles are just suspended in air stream okay that you know we have many lot of dust is there now in the air you can see that on your cycle or if you have car or if you have your furniture and all that and if your room is open the windows are open then you can see after one day you go and touch it there is a lot of dust so those particles also practically fluidizing right if they are not moving from place to place when it is moving from place to place then they are also pneumatically conveyed and finally it will go and then it unfortunate that it will enter your room because there is no sufficient amount of breeze there to go away so then they settle okay so that is what what you are talking and even this catalytic reaction the solid particles are catalyst and the gas which I am telling here is ammonia plus or not ammonia hydrogen plus nitrogen together mixture okay you may send it in stoichiometric quantities or whatever okay so that is the one what you are talking even here I can simply pull out a particle not only this we also have what are called rotary kiln have you heard of them it is a kiln big tube cylindrical tube it will be slowly moving you put now this side the solid particles right and posit side you can also put hydrogen and hydrogen the particles may be slowly coming and you are taking back again introducing them you take back and again introducing them there is also a possibility no one does that okay but there is also a possibility why all these things are possibilities but these are difficult possibilities than packed back pack bag is the simplest this also can be used there is another reactor also called moving bed reactor you take the packed bed and put a hole here not distributor distributor has small holes where the particles cannot fall only air can enter or or nitrogen and hydrogen can enter so now you can put big holes there where the solids can slowly come down so then you are also sending in the opposite direction the gas now the entire bed is moving that is why it is called moving bed okay understood no these are not generally difficult okay so that moving bed also when I want to develop a rate expression for catalytic reactions I will pull out one particle again right see the chemical reaction rate will not change in all these systems what will change is the physical rates that means how mass is transferred to the surface but in all these things what is our imagination we have a particle okay yesterday I have drawn horizontally but now I will show more truly I will just draw this so this is how if I pulled because I pulled out one particle why I should pull out one particle because let me imagine that what is happening in this one particle same thing must be happening to all the particles so if I develop this equation and this equation is valid at any point where you pulled out and because it is a packed bed there is a change of concentration from this place to this place then I can integrate because this is a distributed parameter system that means the concentration is changing from this end to this end whereas here it may not I mean that better not talk now about fluidized bed fluidized bed is one of the most difficult reactors to be modeled to be constructed to be to operate it is not that easy but still very very efficient one but why it is efficient also I will discuss if you take the course next semester but right now I think we will just only mention the name okay good so that is why in all these systems whatever reactor you choose whatever system you know because we have many many possibilities for the reactor it was in a system so now if you see this particular bed right there are two phases and in our diagram we have contacting pattern right so now we have to talk about for each phase what is the contacting pattern when you are talking about homogeneous reaction there is a single phase so you are only talking about contacting pattern of that particular phase whether it is in perfect mixing or whether it is perfect plug flow or whether it is in third one perfect mixing is mixed flow who is that plug flow already we told or do not forget batch I say may be LKZ information but still because that is what first we learn batch so we have only three contacting patterns whether it is batch or plug flow or mixed flow plug flow mixed flow are continuous okay and whereas batch but you have to now identify for each phase here how they are moving that is very important again for us so when I talk about this packet bed I have solid phase and gas phase these two non catalytic gas solid reaction so now I have to tell what is the contacting pattern for solid in packet bed now only three just imagine I say we have only three batch plug flow mixed flow batch why because solids are not moving they are there okay so that is why so this is batch and what about gas how it is moving it is plug flow why I can tell I mean when you look at the packet bed fluid mechanically also you can prove that most of the time your plug flow the velocity profile will be flat if you are operating properly in the Reynolds number no book gives about the connection between Reynolds number and plug flow only KKG okay that connection that is why please remember when you are operating packet bed it should be in the turbulent Reynolds numbers what is the turbulent where that Reynolds number for turbulence in a packet bed greater than 500 do not tell for 40,000 and all that 40,000 also will be but I think starts from 500 onwards okay good excellent you remember that yeah so that is why here you have plug flow PM now my design expression will depend on whether I am choosing solids or whether I am choosing gas and here I cannot choose solids because they are not that is not the phase where the catalyst is converted from one to the other we are only talking about in the reactor conversion from reactant to products only gas is converted from reactants to products whereas catalyst here only helps me in increasing that rate of reaction right so that is why that even though it is batch I cannot write any equation for a catalyst particle because as far as conversion is concerned because reaction is taking place only within the it is taking place on the surface of the catalyst and inside the catalyst but what I am converting is my entering reactants and then the products will come out so that is why yeah yeah any any answer for that I think let make you fight I will be afraid yes sir possible no that is actually wrong why yeah so okay he says that you also take that as one face yeah we said that I should yeah okay yeah so important thing is there is extra whereas when you talk about homogenous I think this is a good question what he has asked others also may have this confusion over the number of times when we talk about homogenous system there is no external mass transfer coming in actually that is the definition of homogenous and heterogeneous in heterogeneous system you need mass to be moved from one face to the other face here the mass is moving from gas face to the solid face if there is no solid there is no reaction correct no it is not reacting with solid it is reacting in the presence of solid because that is a catalyst right so that is why you cannot now say that you have an heterogeneous homogenous system it is heterogeneous because the necessarily here this is what next one I was trying to tell you know yeah so this one I have a film around this and the yeah here I have nitrogen and hydrogen going and here I have N2 H2 and also NH3 because it is reacted after this particle contacted there and then it is coming out so now this N2 and H2 without contacting this if it is going out then there is no reaction so for the reaction to take place this N2 and H2 have to diffuse through the film then it has to go to the surface if it is only non porous iron non porous iron then the reaction is occurring only on the surface but this mass transfer step is must then the reaction rate that is happening on the particle so the reaction that is taking place on the particle we call it as chemical reaction chemical reaction right and then this mass transfer step we call it as physical rate step that is why you have in the diagram under kinetics physical and chemical both together so now for heterogeneous both are required so that is why now when I write this simple equation later you will know what kind of rate expression you get because I do not want to complicate it because so that first we have to understand the basic things and then we can extend you know next one is only algebra that is all if you understand this concept next thing is only algebra that means equation will be more complicated so you have to spend more time for actually finding out the rate that is all the difference so that is why we have now you understood now why we cannot call it as homogeneous I mean but actually again when you take next semester this course on chemical and catalytic reaction engineering there what actually he said was also right under some conditions we will take the entire system as pseudo homogeneous packet back pseudo homogeneous packet back there are particles but I do not feel the particles under certain conditions that conditions I cannot discuss because I think we have to talk about homogeneous systems more for understanding so that is why you have that information also and most of the time the models we are using for packet back is what he suggested it is homogeneous system pseudo homogeneous models there are class of models where models means writing trying to write equations okay trying to write the phenomena in terms of equations that is all modeling that is why phenomena is important that is why I am telling you so many times take the particle out and then imagine that there is a flow around that then you have the step one as mass transfer through the film to the surface and if it is non forest then I have only one step that is reaction occurring on the surface and after reaction there is no use of that reaction if NH3 N2 H2 all are there on the surface without coming out correct no I do not get any product it is sticking only to the surface but that cannot happen by nature because ammonia reaction is taking place reaction is taking place on the surface ammonia is produced there at the point of production you have the concentration of hydrogen more ammonia more so at the outlet you have not outside in the bulk concentration of ammonia is less so it is natural phenomena you cannot stop it right so whether you have a good smell or bad smell if it is released from your body you cannot stop it because that is nature God will take care of it he will spread it uniformly okay so that is why when I have sent and all that I think everyone will enjoy not only me why it is not my greatness it is the greatness of the nature because whatever scent I have that concentration is not there with Gopinath equal concentration so if there is exactly same concentration no I will keep my smell with him and he keeps his smell with him because his concentration there is no gradient it cannot move so that is the reason why ammonia after formed here it will come out that is what you are seeing at the outlet here okay so that is what is the entire phenomena that is taking place now to write the equations let us list now for non porous particle non porous particle what is step 1 step 1 is mass transfer M T from bulk to this is bulk this is bulk and this is film okay that is film and this one is FE catalyst non porous catalyst so now all these three we have now M T of whenever you are writing mass transfer I have been telling you this is the difficult thing in mass transfer when you go to fluid mechanics also everything put together you will write momentum transfer and in the heat transfer also entire whatever number of phase you have the entire thing you talk about so what is the total heat that is contained but when you come to mass transfer only you have to identify each and every species so that is why when you are writing here if I am calling my hydrogen is the limiting reactant because normally that is what is the limiting reactant so that is my A N 2 plus okay sorry let me also write this H 2 gas better write N 2 gas giving me in the presence of FE 2 NH 3 correct 2 NH 3 gas this is 3 ya 3 H 2 that is balanced okay and in the presence of FE this is the reaction so my A is this limiting reactant you can also choose N 2 I mean that is not a problem for us but that is my A so that is why if I write here I think I better write here then 1 is MT of A A you can write here this is B giving R okay corresponding numbers and all that you can take MT of A from bulk to surface through filling that is step 1 correct no mass transfer of A from bulk to surface through the filling then second step because it is non porous particle that is what we have taken non porous particle right reaction now you see I am simplifying things here next semester it will be more complicated so whatever is happening I am not but actually if you look at the molecular level hydrogen will go and get adsorbed on the surface then N 2 also is coming because it is the gas phase it is stoichiometrically mixed and then you are sending it right so N 2 also will get adsorbed and again you know how deep you go depends on our mind only but as engineers we are not going that deep so what we just imagine is hydrogen got adsorbed there nitrogen is also getting adsorbed there they somehow decompose to the intermediates and those things will come together and then you have NH3 formed and because of the concentration gradient NH3 leaves that is desorption of the product it comes out through the film and then finally joins the bulk okay that is what but in fact if you go to the mechanism for which that Airtel I told you Airtel Nobel prize he got Nobel prize for sending for exactly proving this mechanism experimentally it is not that easy the way I told you hydrogen something it will happen nitrogen something will happen I think energy there are so many beautiful things what he has explained in his actual mechanism what is the surface how the molecules are behaving for the reaction to take place he has mathematically proved and also experimentally found out the same thing what is happening what he has proved mathematically that is why he got Nobel prize but as engineers we are not doing that our thing is okay I need hydrogen I need nitrogen both of them went to the surface something happened between them got the product and then I am happy to have that product but if you are a scientific engineer okay engineer also can be scientific then you will go deeper and deeper and then look at the molecules what is happening that is why you have the nanotechnology and all that because we think that we have understood all chemical engineering then now engineering is you know macroscopic and science is microscopic or nanoscopic you can go to even nanoscopic level and then try to find out what is happening and this nanotechnology entire thing started with that because it is exactly you know one simplest example is how on this planet life is coming out if you take any mammals sperm and egg what is the shape you do not know shapes we know but inside that cells and all that also you know shapeless only cell so with time with reactions with conditions changing slowly it can be a bull or it can be a man or it can be a woman or it can be a monkey all these things but what is the starting point only that very very small minute things what a wonderful creation that is why you know humans of course we can when they get pregnant and also you know how the body the baby is growing all that nowadays you can also see in the youtube and all that at various 3 weeks 5 weeks 10 weeks like that you know what is that nature is trying to do it is using the nanotechnology to build up by adding more and more and more finally to bring to a shape that is what exactly we are trying to do in nanotechnology we go to the atomic level and then now try to arrange those atomic levels and to a particular shape to a particular product nature has already done that otherwise you and me would have not been here discussing CRE if nature has not done that so that is what is the meaning of nanotechnology please remember I do not know nanotechnology happy to do research in nanotechnology may be without understanding the basics okay so what we thought was I gave you the example you know in Malaysia when I went that girl beautifully told me that sorry you bring hydrogen you bring sulphur you bring O4 that is what is wanted you know in nanotechnology level I will simply pull out one hydrogen molecule simply pull out some O4 some you know sulphur and then put them together okay Abdul take it this may come after may be 200 years 300 years later in in you know hospital when you go for a particular disease I can guarantee you will have much more diseases at that time okay because we are not following the nature here we are only following ourselves okay so then you know the doctor will go and then he will not write any prescription he has a lab you know now you already seen in some movies where now this dragging has come in cell phone and all that pull like this you will get all the messages earlier there was movie called minority report so there if you see the computer like this all structures you put this way and then finally you will get a structure that is what it may be happening in every doctor's room he may be taking all molecules stored entire periodic table pull this this is the medicine take finish over that is what is nanotechnology so when we are talking now at present as chemical engineers we are not talking about that particular thing that is adsorption then we have the decomposition after adsorption and all that molecules decomposing then you have surface reaction that means the molecules the intermediates coming together and then reacting and then of course producing the product then you have the product coming out right so those steps we are not talking to make the simple things to make the point what is the difference between homogeneous and homogenous that is the main thing now so that is why step 2 is surface reaction the surface reaction contains adsorption desorption and surface reaction again you know surface reaction is between the intermediates and all that all that we are not talking good then what is the third step actually before this there is another step if it is a porous particle if it is a porous particle other thing is something will get go to the surface external surface but there is a lot of internal surface that is available as pores so it will diffuse into the pores that is another mass transfer step diffusion is a mass transfer right so that step also we are not taking that is why simplify to have non porous particle where non porous particle this is one what is the third step now now mass transfer of product if I say R, R is the product mass transfer of R from surface to bulk through again film simplest assumption is one molecule is going through the film to the surface getting reacted another molecule is coming out then we have some kind of adjustment between these two then you will have a rate expression for mass transfer that is what you have studied in your film theory that is what I think something is coming in this direction something is coming equimbal or counter diffusion we will say we know what is the equation what we have to use simplest one and we are not using here diffusion equation even though there is a connection between diffusion and mass transfer I do not know whether that connection is known to you or not so that is why now I have to write these three steps but right now I am imagining that my reaction this one is not even because I am simplifying many things just to make the point now even this reaction is not reversible okay it is not reversible reaction I mean do not think that ammonia is not reversible I am just simplifying that this A plus B going to R is not a reversible reaction so what are the steps that will eliminate if I say that the reaction is not reversible because at steady state all these three steps must be equal for the reaction to happen and also for the product to come out right but even these three steps I can still further simplify if I say that the reaction is not reversible reaction where is mass transfer of unreacted A and B coming in these three steps I am talking about these three steps product is coming out from the surface after reaction second step is reaction first step is reactant transfer through the which step you can eliminate one of these steps can be eliminated if I say reversible reaction what is the meaning of that that means the product is yeah so that means the product is also affecting the rate the moment I say irreversible reaction then product does not have any effect on rate then which step you can eliminate now excellent how do that so that is why the thinking I say expanding your brain a little bit delta x delta x delta x so by the time course is over that will become this much that is good that is what we want it is not the physical increase the knowledge increase that means what we are able to think beyond what the teacher tells so that is very simple only now we see reversible reaction what is the effect now definitely the product also will affect the rate of reaction so I want to simplify mathematics so that is why I say that now let us assume now we have reversible irreversible reaction so that means the product does not have any effect so that means this step also can be ignored now under steady state steady state correct no the other one also is there but that is not participating in the reaction and when I want to develop an equation this is the mass transfer step so many moles are going under steady state conditions so many moles per unit time must react correct no and they have to come out but they are coming out in third step but it is not changing rate then why are you not considering the third equation because what is the idea of writing all these three steps how to develop a rate expression how to develop a rate expression now by assuming irreversible reaction my rate expression is not affected with the third step why because rate is not changed by the product it formed but again in the reversible direction that will again decompose to some reactant that is what the reversible nothing you know that is not there that possibility is not there so that is why first two steps itself is enough for me so now steady state rate of mass transfer okay let me also write rate of mass transfer of A must be equal to rate of reaction of A on the surface rate of reaction because these two I can now say that it is minus r A this is minus r A what is the equation for rate of mass transfer of A it is simple film theory film is there through the film the mass is going to reach the surface so then what is the equation we use mass transfer equation so that can be K G into so now more step I have forgotten to tell you this can be now imagined as like this this is the surface of the catalyst surface of the catalyst so then this is the film correct this is the film now outside I have bulk right so if I want to draw the concentration profile this will be C A B or okay C A B that is C A B okay now definitely there is some concentration gradient inside the film so now if I show that that will be something like this what is this one C A yes so drawing this concentration profile will make me the things will become very easy to write the equation I know now I have to write an equation through the film and I also know the concentration on the surface and also concentration in the bulk so that is why and I know that this mass transfer rate also equal to reaction rate that is why I am interested in reaction rate that is why I have written minus r A I can also write that one equal to N A I am interested in rate of reaction so that is why we write here minus N A K G that is the proportionality constant mass transfer coefficient then C A B minus C A S right okay now this must be equal to rate of reaction rate of reaction means you should have an equation for rate of reaction that is the pure chemical step this is pure mass transfer step taking both of them into account that is why in heterogeneous system that is the extra step this physical step this mass transfer step you will not see this in homogenous why because mass is available all through without again transferring from one place to the other place it is there if you have A molecule there may be 10 B molecule if there is B molecule there may be 10 A molecule so that is why for any time for the reaction to take place sufficient number of A sufficient number of B is there it is not there unless it is transported to the surface there is no reaction even though catalyst is capable of converting anything that comes there there is no reaction so that is the reason why this extra step that is coming because there must be some transfer from one phase to the other phase in any heterogeneous system where mass transfer also plays a role right and I have the film thickness so big no mass is going inside the surface so then what will be the rate of reaction it will be very very less that means it is affecting you know what is that affecting mass transfer is affecting physical step is affecting that is why in that diagram we write chemical and physical that is what is the exact difference between heterogeneous system and homogenous system where mass transfer will not come into picture good so now what again I have tremendous assumptions here is for easy mathematics I will assume that I have first order this is rate constant K and CAS please remember the reaction is occurring on the surface here reaction is taking place on the surface that is why it is CAS it is not CAB and the assumption here is that I have first order rate this is first order K into CS I can also have second order I have any complicated order this may be again M plus CAS but this concept is same equating that is same good now that I do not want to complicate right now so now this is the equation what I have as engineer again I tell you that you know we should know how easily one can do things for me which composition measuring is easy which concentration measurement is easy CAB I do not have to go to on the surface I can find out what is the concentration of CAS that is why from this I can now eliminate CAS I can now eliminate CAS so at steady state when these two are same then now we can you can eliminate so minus R A first let me do this KG CAB minus CAS equal to K CAS so I am writing all spoon feeding steps CAB minus KG CAS equal to KCS CAS somewhere I think I have not started putting them okay from here I think this is 1 this is 2 this is 3 4 5 from 5 can I say that I have an equation CAS equal to KG CAB by KG plus K so this is equation number 6 so now still my problem is not over that means I should now find out what is minus R A right how do I find out I can either substitute that idea is that CAS I should not have in my equation why if CAS is there I have to go to surface and then measure the concentration but without that I have to express the rate in terms of only CAB bulk concentration where simply I can take the bulk gas and then now try to find out what is the conversion there or what is the concentration there so that is why so I can use either this equation or this equation because this is also equal to this or that now substitute easy one always humans go for easy resistance so this is the one I can take for this CAS equation 6 so then what do you have you will have minus R A equal to K KG CAB divided by KG plus K so this is the rate expression for you and this also can be nicely written as minus R A equal to why nicely means just to get 1 by KG by 1 by K so this is the rate expression now I also ask you this question in zero test what is the bulk rate of reaction or overall rate of reaction okay in retrogene system that will come this is called bulk rate why because now this rate expression is only based on bulk concentration bulk condition okay so the name of this is either bulk rate bulk slash overall slash observed any other name Rahul remember global so many names global rate of reaction so that is the name given to heterogeneous reactions because all heterogeneous reactions the method is same all heterogeneous reactions now I can just tell you now that if I have a complicated equation then I will have here M plus do not write that I am just telling you this is the equation this side it will not change but I told you mathematically it will be more complicated so whatever form you can also have simply quadratic equation C A square C A square then you have the quadratic equation C A square C A C A B these are constants anyway then you have to solve a quadratic equation and get what is C A S and substitute C A S in in any equation either this equation or this equation that is what is the overall picture and approach to approach to all heterogeneous system one more thing also I have to tell you here is this equation is a wonderful equation for discussion so I think you know in heat transfer you should have heard what are resistances right here also 1 by K G is a resistance 1 by K is a resistance that means so if I say that I have at very high temperature at very high temperature I want to simplify that equation special cases special cases when mathematically telling K tends to infinity that means I have very high temperature and we know that when we have very high temperature okay K will be very very large because exponential increase so then what will happen to that equation this is 7 8 okay so now minus R A equal to minus R A B equal to 1 by C A B by K G into C A B this is what is very very important thing in heterogeneous system okay now do I have any rate constant there now it is controlled by which phenomena mass transfer why because that is the slowest okay I told you know sometime back you have one example I may have I told you also which is the costliest car which can go to 500 600 kilometers per hour but in mount road if I go if there are 10 buffaloes walking very slowly what is the use of my 500 kilometers per hour no use it is controlled by only buffaloes and what is the buffalo walking speed huh that is all 5 kilometers per hour you see 500 to 5 kilometers so who is controlling now buffaloes okay so that is what is rate controlling step right and also I think when time comes I will tell another example also I have you are hungry when you are very very hungry mess all of you are very hungry after the class and then go to the mess imagine that they are only serving idlis idlis are coming over the conveyor belt okay so you all of you stand this side and that side idlis are coming when you are very hungry practically can you see any idlis on the conveyor belt because the moment idli comes over so the on surface it is almost clean but may be how much time you can eat may be half an hour you wait idlis okay continuously after eating half an hour what will happen to your hunger so once you have that saturation what will be now concentration of idlis on the conveyor belt nothing will happen everything will be going on so that is what is the profiles now we are going to draw with these 2 examples because now your hunger was so fast right and you will scold the cooks if they are not quickly supplying the idlis so what is rate controlling step at that time not hunger hunger you have mass transfer mass cook because he is not able to produce there is no sufficient mass of idlis on the conveyor you have the reaction you know hunger tremendous reaction is going on inside okay capable of eating anything but you are not able to eat because there is no mass transfer okay no idlis that is the same thing that is happening particle may be at very high temperature capable of converting any molecule coming on to the surface but where are the molecules cook is not supplying so mass transfer controlling that is what is this mass transfer control and when you have the other thing that is k g tending to infinity that means when do you get this case this is empty control this is empty control yeah in the second case my k g is infinity yeah no resistance through the fillet when can you get that when do you get thin fillet very high flow you see there is a relationship as Reynolds number around the particle is increasing your film thickness also go on reducing reducing reducing but I know you do not have much use of that because by sending infinity velocity residence time will not be sufficient correct no so that is why but that is the case k g so you can also reduce the mass transfer increase mass transfer increase mass transfer by increasing the velocity particle velocity around the particle so then you have minus r a b bulk are observed is now k s k into c a b this is mass transfer equation where we can also write this is c a s which is 0 on the surface now when I plot this the profiles again that is the film thickness and this is c b right for this one when k equal to infinity how do I draw the profile extremes k equal to infinity that means the reaction is very very fast right so this is surface this is surface here what is the concentration on the surface 0 0 idlis remember idlis reaction very fast means you are very hungry so you can eat any number of idlis and on the conveyor belt you will not have any idlis left at all that is 0 so that is why it may go to almost 0 like this this is here approximately c a s equal to 0 on the surface this is the surface okay this is surface okay good so that means I may write this one as something shape also maybe like this okay it is not sudden through the film you will have some concentration but on the surface it is on the surface I know you are not understood why after reaction only very good question concentration is 0 there is no reaction correct or what you said on the surface what is the meaning of that what is the meaning of k equal to infinity surface is capable of converting any molecule whenever it just comes there does not mean that reaction is not there whatever molecule comes there and also what you are drawing for you are drawing for c a b reactant reactant so the moment it touches the surface then it is converted to product then what is the concentration of a that is the meaning of 0 it is not l k g 0 means reaction extend delta x mind right so that is what is the meaning okay good now this is the one my example is very easy to remember when you are very angry idlis are coming it is not that he is not supplying but he is continuously sending maybe 100 idlis per maybe per second or so but now immediately all of you are so angry the moment idli comes you are eating that means there is no rate of reaction there is you are eating idli right that is the rate of reaction but on the surface what is idli concentration 0 that means you do not find any idlis that is what is the meaning of that okay this is mass transfer control okay this is m t control ya the other one what is the other one reaction control it also right here reaction control ya in reaction control how do i draw when you are satisfied you are not able to eat anymore what is the concentration now all the idlis what you have are also simply coming so what is the concentration now almost same that means how do i draw that line strain excellent this is e a b everywhere this is which control reaction control reaction is very very slow the fellow is not able to convert right on the surface reaction is very very slow so that is why that entire surface is flooded with molecules because the surface is not able to convert those molecules into product so that is why everywhere you have c a b whereas in the other place it is able to convert so fast practically you will never see a molecules the reactant molecules on the surface but in reality you will have this kind of so this equation this is the equation equation 8 is this this is equation 8 this one is equation mass transfer control ya here i have to put now this is 9 this is 10 mass transfer control ya 9 so this is equation 9 and this is equation 10 see and now when you want to design a reactor for example you know the equation now i think i just take this example and then i will leave it to you now let us say that i have a packet bed where i am now i am trying to design to find out what is the volume of the reactor okay i am projecting to weight of the catalyst later volume and we know that packet bed is a plug flow reactor so which is design expression you take this is the rate now which we got from heterogeneous kinetics minus r a i have f a not i have m b a already people have given me and then minus r a i have so now if i know conversion i can calculate volume or if i know volume i can calculate conversion no matter where i do not have volume so that is why i will say that okay 90 percent conversion how much is the volume so what is the equation i have to use very good v by f a not equal to so v by f a not equal to 0 to x a d x a minus r a i so this minus r a i is if it is mass transfer control what is the equation you are using here this is d x a integral k g c a b 0 to x a you see now it is actually a reactor where nothing corrected with reactor is there that means reaction rate constant is not there it is only the mass transfer coefficient what you require mass transfer coefficient so this is what is the meaning of heterogeneous reaction system so under some conditions it is only the physical steps that are controlling but it is not the chemical step which is controlling chemical step is pure chemical reaction now that chemical reaction is influenced by mass transfer step if there is not sufficient amount of mass transfer to the surface reaction also is poor that is the difference between heterogeneous and homogenous whereas there is no this kind of mass transfer availability is not at all there in homogenous all the time you have sufficient mass volume by taking it as a batch reactor also batch reactor again because you told us that how to t by c a not how to relation between t and b same thing what you have done in that problem you have not done that problem so if you have a contacting pattern as batch then what you get is t by c a not equal to you know that integral that integral is same as this integral that will not change no no you are talking about again volume change and all that did I say any volume change and all that here heterogeneous reaction does not mean you have volume change if I have only a one mole going to one mole where is the volume change see again please do not get confused I think puja that question is good because we know all Indians are brothers and sisters okay so we do not know but definitely same confusion also you may have heterogeneous does not mean that volume changes volume change will come in the reaction only when you have mole change here I have taken simple first order a going to b or a going to r so that is why that problem you should not imagine at all okay so if there is real change in moles automatically this rate equation will change this is not the same rate equation what you get you know if you want to write that in terms of conversions and all that whenever you concentration is converted that equation is different for if you have volume change that volume change will come when I come to again the homogeneous reaction so the idea is now this where we can clearly say that what is the difference between heterogeneous and homogeneous and under certain conditions you do not have to worry about reaction rate constant what is the order of reaction but you have to worry about only mass transfer coefficient mass transfer coefficient you know can you give me an example where this can happen in heterogeneous system it is very all the time it happens everyday you see everyday when you go to kitchen and all that also you see in kitchen you can make tea but what is making tea flame what is the combustion in all combustion reactions it is mass transfer limitation it is the oxygen supply to to the flame why oxygen is required but oxygen oxygen is required I am saying that all the time it is that oxygen supply to the flame that is controlling rather than reaction oxygen also pure oxygen also you can supply but even then that controls control combustion that is the point that is the point you heard of him you have not heard of him he said something temperature in all combustion reactions the temperature is very very high you want to find out put your finger so if it is not burning not much combustion all combustion reactions you know the moment you see that red flame you know what is the temperature there is approximate estimate how much it will be at taste you know cigarette smokers don't smoke cigarettes very bad for health but unfortunately if you are smoking you should know the temperature okay what is the temperature when you are means you know that tip will be glowing you know what is the temperature at that time 85 65 600 degree centigrade 600 okay and you know what is that by doing like that what are you doing you know you are only supplying mass oxygen when you are doing like this it is a porous so it sucks oxygen from the not only oxygen air and all that from the surrounding air okay because it is porous you are able to like that you are able to do so that means it is now taking more and more oxygen the glow will be more and more red I don't know whether you know smokers now you start looking at the smokers and if they don't like that if they don't do what will happen you don't see the glow will not be there so mass is supplied there you see how beautiful even cigarette smoking there is lot of chemical engineering it is heterogeneous reaction oxygen has to be supplied okay this is a porous one that is why if you don't take porous one and then you cannot smoke cigarette at all if it is not porous oxygen because it is porous like that you do then oxygen is coming inside not only oxygen air and all that is coming inside so that is why you are able to smoke cigarette tell your friends because you are doing like that more stress on the lungs not only more stress high temperature because now air is getting heated through that flame going into your lungs so that is why 100 percent guaranteed damaged lungs after 10 years that is why you should not smoke cigarettes okay you see we started with heterogeneous reactions and stopped with cigarette smoking


So, first of all, happy new year to all of you and welcome. So, I just thought I would tell you that this is a this course is officially titled Quantum Chemistry CH 560 and the prerequisites are kind of CH 425, which was the first year MSC course. So, that is the kind of prerequisite. I hope all of you have done a similar course somewhere, somewhere in the country, you might have done a similar course to CH 425, which is basically the basic quantum mechanics, postulates and simple problems like hydrogen atom and so on. So, that is very important that we must realize that this is a prerequisite although I would do a revision, but the revision would be a very quick revision. Now, in case somebody has not done that prerequisite, please raise hands first, who has no exposure of quantum mechanics. What is your background? So, you are doing what we take now or PSD, PSD, classical simulation.  So, do you require it for your research, the quantum or you are doing one thing. What about you? Same, same, same group. You are also doing classical simulation. So, you have to excuse little bit in the same that you have to read on your own, the basics though I will revise. So, the topics that have been covered in 425 I will definitely mention. So, you must make a revision. The basic course will start with many electron problems. So, this will be the focus of this course. Many of the exactly solvable one particle problems we will skip except making a revision. So, the basic idea will be the many electron problem and that is what we need to learn in chemistry. One particle problems are model problems. They are exactly solvable, but model problems. So, many times they are useful, but of course, when you do actual chemistry, you have to learn how to deal with many electrons. So, that is something that I want to tell you. Rest of the people have some kind of exposure. I think many of you have done 425 here. So, at some point of time, some of your second year MSc students, most of your second year MSc students, those who are taking class, three of you and the rest are 5 year integrated, some of them. BS, BSMS, BS, just BS. So, third year of BS or fourth year and the rest are some of them are PhD students. So, let me first state that for those who are doing classical simulation, we actually discussed in the 425 three important experiments, three important experiments which highlighted the failure of classical mechanics in the atomic and molecular regime. That is the reason because you may first wonder why not classical mechanics for electrons. That is the first thing that you would think. So, the failures were actually highlighted more than 100 years back by one major experiment was, one of the major experiments was the Planck's blackbody radiation in which in the ultraviolet region, the radiation could not be explained. The change of the intensity with the wavelength could not be explained because Rayleigh-Jean's catenary tells that the intensity is proportional to 1 by lambda to the power 4. So, as lambda, so this is the classical Rayleigh-Jean's. So, if you use classical mechanics, the intensity of a radiation in a blackbody, so this was basically a blackbody, blackbody which perfectly absorbs and then radiates. So, the radiation intensity is proportional to lambda to the power 4 which means as lambda increases, intensity should decrease. However, in the actual experiment, it was not like that, it actually increased initially and then decreased whereas Rayleigh-Jean's would predict a completely different curve. So, this low wavelength, so this is the low wavelength, wavelength is increasing, is called the ultraviolet wavelength. So, this ultraviolet region could not be explained by classical mechanics because this region it fails and that is the reason this blackbody, so this is basically the blackbody radiation. So, this is why this is called the ultraviolet catastrophe. So, this was one of the experiments which actually signal the failure of classical mechanics in the quantum regime. Now, these bodies were of course quantum bodies which means they are very small. So, atomic and molecular length, so it is a length scale is very, very important. This was one of the experiments. The second one was the very famous experiments of the Einstein date of photoelectric effect. So, that was the second experiment. So, the photoelectric experiment essentially is that it signs a light on the metal of certain frequency and intensity and then you expect that the energy that is given on this metal would be sufficient at some point to eject the electrons, ionize the electrons. What was interesting is that it was shown that if nu is less than some cutoff frequency, no electrons were ejected. So, that was a very important experiment to see and this cutoff frequency depends on the metal. So, this is actually metal dependent. So, no electrons are ejected. So, that was the experiment A and the B it shows that if nu is greater than nu cutoff, then of course the energy of the electrons would increase and the kinetic energy of the emitted electrons is proportional to the frequency. So, these two experiments essentially showed that the energy and this is the first time it was shown that the energy is proportional to the frequency and this was actually later told by the Planck as energy of a single photon is energy as h which is the Planck's constant times the frequency. So, this was a very important experiment. What was the failure of classical mechanics is the following that once again if I increase the intensity, nothing happens if it is below the cutoff. So, once again it shows that the intensity is not proportional to energy. Both the experiments show the intensity is not proportional to energy which is what the classical mechanics essentially assume that if I have a high intense light, it has a more energy that is not true. Energy is dependent on the frequency even if the intensity is low. What happens when I increase the intensity, more number of electrons are emitted that is all but their kinetic energy of each electron is the same. So, this was one experiment that again showed that the classical mechanics failed and the final experiment that I would end with is of course the hydrogen atom spectra. So, that was important experiment which again showed that the energy spectra, the emission spectroscopy or emissions is discrete. Depending on where from where it emits, you have a different wavelengths but they are all discrete. So, you have only discrete at discrete frequencies or wavelength emission is observed and not proportional. So, this was again showed that essentially energy is quantized. So, this is the first time this concept came because of the atomic spectra that the energy is quantized that essentially means that the classical thinking that the energy can change continuously was again wrong. Like if you take a cricket ball, you can increase the energy continuously. There is no reason that energy is quantized. You can keep on pumping more and more energy and energy increases continuously but in this case energy is quantized. So, this was also a non classical explanation to this experiment and there are no way the classical mechanics could explain. So, some of these experiments gave birth to a new mechanics and the exact evolution of the quantum mechanics is of course there is a lot of history behind it and it is not very easy to kind of say that what brought the other but essentially there are a lot of thoughts that are going on and because of the people like Schrodinger, Heisenberg, Niels Bohr, Wolfgang Pauli, many of these people who actually in later Dirac, Feynman, many of these people actually kind of put quantum mechanics on a very hard footing. Ironically of course Einstein himself although he is experiment started photoelectric effect this experiment started quantum mechanics and it actually won the Nobel Prize also was not initially convinced about quantum mechanics. That is a very ironic thing that Einstein thought that the and we will say which are the parts which Einstein disagreed but eventually of course he could not disprove quantum mechanics. So, that is another part of the history that I always quote and particularly there is very nice exchange between Einstein versus Schrodinger, Einstein versus Heisenberg. So, it is a Schrodinger and Heisenberg who actually billered quantum mechanics in the early days. So, with that what we did was of course in the original in the basic quantum mechanics class was to tell the postulates of quantum mechanics. So, after that it is very hard to say the history of quantum mechanics in a sequential manner because a lot of things happened and sometimes they happened in a haphazard manner people started working in different directions. So, one of the important things that came up was actually an uncertainty principle at that time. So, these two were very very important one is the energy is proportional to frequency another is uncertainty principle which says that the uncertainty in position and momentum must be greater than some number like h cross over 2. So, that essentially means that if you have a finite energy system you cannot find the electron or an atom or a molecule at a specific place because if it has a specific place what will happen to delta x it will become 0 and if delta x becomes 0 according to this equation delta p will become infinity which means energy itself will become infinity. So, for any finite energy particle it is impossible to locate the quantum particle. So, the only issue is what is a quantum particle? So, that was very very important of course cricket ball you can locate where the cricket ball is. So, the quantum particles are of course defined as particles with very small size. So, which are basically atoms molecules electrons and there have been lots of exciting discussion how small is small how large is large all right because there are something between atoms and molecules clusters of atoms and molecules and the cricket ball. So, cricket ball contains Avogadro number of molecules all right a cluster can be 1000 10000. So, when do I stop using quantum mechanics and can use classical mechanics? So, that is an exciting discussion by itself which is basically the quantum classical transition and there again there is a very nice theory that it says that if I have if I can assume limit as h tends to 0 then the quantum principles move over to the classical mechanics. So, this also is another important principle and you can see that this actually follows the uncertainty principle because in the limit h cross tends to 0 the product of the uncertainties can become 0. I can make it 0 which means that means the particle can now be a classical. But when is this limit reached that is a question when do I reach this limit of h tending to 0 h is actually not 0 Planck's constant remember Planck's constant never changes. So, when I say in the limit h tends to 0 it means I can assume for all practical purposes of my measurements that the value of h is close to 0. So, when does that happen when the values are very large actual values are very large which again means if the particle size is larger and so on and so forth question again is exactly when. So, the point I am not trying to kind of satisfy you I am not trying to avoid but at the same time this point is a very important point when can I say that the quantum principles will become close to the classical. So, that is a very important question that we will answer and this question is still unresolved. So, the question are unresolved today people are using nano materials which are actually in the bridging length scales. So, is the nano material a length scale where I can stop using quantum mechanics is sufficiently big and if you look at the bulk from the bulk it is sufficiently small then you can argue that you have to use quantum mechanics. So, none of these are very clearly defined. So, that is a region that may be a gray region where many people use quantum mechanics many people use classical mechanics many use semi classical. In fact, there is a whole bunch of theory which is called semi classical. So, that can also be used in this region. So, this again was a very very important theory apart from the fact that E is H. At the same time the de Broglie actually postulated that every electron has a wave and particle such that the wavelength of the electron is related to the momentum of itself by the following relation of lambda equal to H by T. Now, many of these were actually the founding principles of quantum mechanics based on which essentially the full quantum mechanics was postulated. Remember while doing this Niels Bohr was already looking at the Bohr's atom 1913. In fact, Bohr's theory came many of you have read this in the schools these days or at least in class 11, 12 that is the Bohr's theory which made an ad hoc quantization. Bohr's theory was initially to explain the hydrogen atom spectrum remember the hydrogen atom spectrum. So, Bohr actually came up with a theory that the angular momentum is quantized. So, you remember this m v r equal to n H cross angular momentum is quantized and from this actually Bohr came up with the energy of the atom of a hydrogen atom which depends on a quantum number because this quantization brings in a quantum number. So, essentially m v r is multiple integer multiple of H cross. So, that brings in the multiple integer n and that n actually gives you the energy which essentially shows for hydrogen atom it was minus 1 by n square and hydrogen like atom Bohr essentially said that this would be minus z square by n square hydrogen like atom or atoms with one electron but charge z.  So, this came about independently in 1913 and remember the quantum mechanics has still not started. In fact, at some point of time I can show you the slides of history of quantum mechanics how the quantum mechanics started.