 I think you have seen the assignment and all those rates that you have to develop using that assignment I think I told you last class also last minute when I was about to leave I said all those classes are called I mean all those reactions are called intensive rate of reaction okay so the meaning of intensive rate of reaction is no mass transfer coming but in reality you will have definitely some mass transfer all the time okay so that is why now we will take the other two steps in the beginning that is mass transfer through the film and also diffusion through the pores and of course same mass transfer steps even at the end also for the products so same analysis is also valid there why should we do this you know mass transfer steps mass transfer steps we have to do because if the mass transfer is rate controlling the entire surface area the way we imagine in LHHW models may not be covered with the molecules because you do not have sufficient amount of reactant A or reactant B which is going through the surface I mean which is going through the pores and then just sitting on the surface so that is why all the surface area that is there inside the catalyst particles might have not been used for reaction and that is really very bad particularly when I have noble metals noble metal catalyst noble metal catalysts are very very costly platinum is used for as a catalyst okay in many reactions so if platinum surface only 10 percent covered or 50 percent covered the remaining 50 percent of the platinum is waste so that is why it is always better to have an idea how how can we say that my catalyst is 100 percent effectiveness factor equal to 1 or 100 percent it is useful or only 50 percent is useful or only 80 percent is useful that is why we define a term called effectiveness factor okay effectiveness factor I think in your understanding can it be more than 1 or less than 1 or just always 1 or any what is your understanding till now always there is no other condition less than 1 under what conditions or you say for anything is less than 1 mass transfer only mass transfer is not coming into picture then you have intrinsic rate where the entire surface area is useful effectiveness factor equal to 1 okay but I am saying this 1 is it same I mean the definition wise is it valid for under any conditions or there are some conditions where it is not valid how do you define effectiveness factor yeah excellent actual rate of reaction divided by intrinsic rate of reaction okay or reaction evaluated at bulk conditions that means all the bulk gas whatever concentration you have in the bulk that is also there on the surface which means absolutely there is no mass transfer resistance otherwise same concentration will not have within the force right okay that is how but these it is restricted to a particular thing or generally we can define like that this definition this intrinsic rate is evaluated at what conditions single particle only that is okay but what other conditions because I told you also that the denominator intrinsic rate is always evaluated at yeah only for isothermal case it is eta equal to 1 or eta equal to 1 if you do not have mass transfer coming into picture but less than that if you have then you will have eta less than 1 but if you have exothermic reaction for example non-isothermal okay exothermic reaction then the reaction is taking place on the surface it might have not completely occupied by these molecules of reactants the surface but still it is an exothermic reaction and when the reaction is taking place even with 50 percent of area covered the temperature will increase and we know this temperature always has the effect of increasing the rate of reaction because of Arrhenius equation so under those conditions many times effectiveness factor can go to even 1000 times okay that means the rate of reaction inside the particle you know when it is highly exothermic the temperature is so high the rate of reaction within the particle will be very very high when compared to bulk rate right so bulk that means when you are talking about non-isothermal effectiveness factor we are talking about the actual rate of reaction divided by the rate evaluated at bulk temperature and bulk concentration okay so that is what you know next few classes we will focus on how do you evaluate the effectiveness factor so that I will find out for my catalyst what is the effectiveness particularly all these catalysts are very very costly that is why we should have an idea of how the catalyst is performing like same thing you know people say that we are not even using our 1 percent of our brain so what will be effectiveness factor 0.1 okay most of the time that happens 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 10 percent is larger 10 percent means all of you should have done each these and all that already yeah so we are not doing that yeah so 0.01 percent 0.01 is the effectiveness factor so like that it is better to have some idea about our catalyst other than that the another advantage you know because many people do not know what is the use of effectiveness factor we will simply derive the equations nicely but where are you going to use we do not know that is why now I am trying to tell in the beginning itself what is the use of these effectiveness factors one needs to find out whether we have a very good catalyst or not the other one is if someone has already given an intrinsic rate that means there is no without any mass transfer controlling the rate and entire surface area is used but the catalyst manufacturer will say that you know depending on the force because he has to manufacture the catalyst normally he takes the powder and then compresses it and where is he compressing if he use too much pressure then the force the force will be very very small and then mass transfer automatically may come into picture if he does not pressurize much then particles will fall the strength of the catalyst will not be there then when tons and tons of this catalyst is put inside the reactor particularly packed bed and all that so they will be crushed that is why mechanical strength also is required at least for that sake you have to pressurize to certain pressure and then you have to also sinter and when you are sintering the particles that is you know to for mechanical strength for sintering the particles again the force may close some of the force may close so that is the reason why always there will be some mass transfer effect in the actual particles right so what the catalyst manufacturer tells is that my effectiveness factor for this catalyst is 0.5 okay but you have for the same reaction the intrinsic rate of reaction so then what is the actual rate of reaction now 0.5 so that is the actual 0.5 that rate you know 0.5 into that rate equation that is what what you have to use in the design expression that is also another advantage of or another use of effectiveness factor okay so this is what what we do now and the first thing what we do is we take independently the first step that means only film controlling okay if I have film alone controls what will be the effectiveness factors then we will go inside we will forget film and then you take only the force and if there is only mass transfer resistance in the force then how do you develop effectiveness factor now there are two steps pore diffusion and also film diffusion now combining what will be the overall effectiveness factor so that means when you have some film control some diffusion control through the pores then how do you calculate the overall effectiveness factor for the particle okay this is what what we do in the next few classes so to start with now we will have the first film control alone so we will call this one inter and intra intra phase effectiveness factors effectiveness okay good so what we do is we have the particle we have the film surrounding this this we have done many times like for example if I have if I have only porous particle sorry non porous particle okay there is no diffusion you know the second mass transfer step will not be there and we also have some catalysts you know non porous catalyst which reaction is occurring only on the outside surface so when you have that kind of catalysts non porous particles then we know this I do not have to ask you many times we have discussed this this may be CB bulk concentration then this will be CS that is surface concentration this is the catalyst this is film so we can also have here temperature profiles okay how do you draw temperature profile here yeah that is the question you have to ask is the reaction exothermic or endothermic first I will say exothermic you have to start only from here first no TB yeah so it may increase like this exactly how the function increases depends on the equation okay yeah like this only reaction is taking place there okay this is exothermic if I have endothermic decreases correct on the surface we should develop an equation for effectiveness factors taking these two into account first let us take isothermal particle okay then we can go for non isothermal particle the analysis you have done already that under steady state conditions the rate of mass transfer must be equal to rate of reaction at steady state okay at steady state rate of mass transfer I do not write the words but straight away I will write the equation because already we have done so many times yeah this is CB minus CS as usual I will take first order reaction this is KCS this A is centimeter square per centimeter cubed of the particle that means surface area per unit volume of the particle okay so then with this there will be lot of confusion so that is why I am just pointing out this even though it is very simple but I think you will make a lot of mistakes yeah then now tell me what will be the units of this K without A with A yeah without A and with A quickly time is going you cannot say simply because you have to write there and tell me without A it is per second why it is per second what is this what are the units of this concentration is most permittative yeah but who told you that yeah what is the overall dimension here for the rate this is rate this is ROB observed yeah now we understood now what is the problem it depends on first of all how do you define the rate and for catalytic reactions what is the logical way of defining the root yeah may be area is more difficult to use in the sense that you have to measure that weight is the simplest one so now if I have rate as moles per second okay second per KG catalyst now depending on this you will have the corresponding you know dimensions for KGA and K please remember that please remember that but the moment I also express this KG catalyst okay the moment I also express this moles per second per centimeter square okay imagine that we have moles second centimeter square what will be the units of this what will be the units of this centimeter square of catalyst surface I can always know what you are not able to follow follow the question see rate in heterogeneous system can be written in many forms one way of writing is moles of A reacted per unit time per unit weight of the catalyst we can also write moles reacted per unit time per unit area of catalyst that is why I said that is moles second meter square a centimeter square okay so now what will be the units of this KG and KGA or KGA and K meter per second meter per second and meter per second under those conditions this is not required okay and particularly when you are solving the problems you will make these mistakes and then you think that you correctly did it but you basically you made a mistake dimensionally also okay so that is the reason why I am just pointing out this okay anyway so these are the simple things but number of times I have to point out because you know otherwise you may not remember things okay so solving this CS we know already this is KGA CB by KGA plus K this already we have done I think even this is equation one one two yeah so then our OB is given by K CB by 1 by K by KGA okay this is what you get now after substitution and then just divide correct Anila you got it yeah so this is the equation where this also can be written as K CB by 1 plus dA where dA equal to damp collar number defined here as K CB to the power of n minus 1 by KGA okay this is another form of damp collar number okay what does that tell me I mean if I say that I have damp collar number equal to 1,000 large number which one is controlling okay if damp collar number is small 0.01 reaction is controlled okay so that is the meaning of that right so you also had another damp collar number K tau CA CA0 to the power of n minus 1 that is another form of damp collar number what does that tell you if I say that I have K tau CA0 to the power of n minus 1 is very large what is the meaning that is straight used only for homogeneous reactions for first order it is K tau okay for second order it is K tau CA0 what is the meaning of that if K tau CA0 is very large what is the meaning and K tau small means conversion is small okay so that gives an indication okay this reactor has very high damp collar number homogeneous system so that means you are getting very large conversions okay but the second form of damp collar number is for heterogeneous system that is for homogeneous heterogeneous systems where this will give us an idea of how the reaction you know which one is controlling whether mass transfer is controlling or reaction is controlling you know generally in an academic institution we never bother about these numbers but in industry it is generally lot of thumb rules there for them okay bio number so much bio number also will come sometime later okay that gives an indication bio number so much means okay 1000 okay you do not have to worry the things are going on very well like for example K tau CA0 is very large for homogeneous reaction means conversion is very high we do not have to worry very nice so that kind of things good okay so now this is the one damp collar number definition and now we will define Eta bar is the effectiveness factor Eta bar effectiveness factor as actual rate of reaction you have the all the names actual rate of reaction global rate of reaction observed rate of reaction anything you can write actual rate of reaction short form alright divided by rate without mass transfer without mass transfer limitation okay of course we can also write Eta bar as actual rate of reaction limitation divided by rate without any limitation means the concentration must be same throughout the particle okay must be same that is what what we expect but in reality that may not happen so that is why this effectiveness factor less than one means if it is isothermal system then we will know how much less okay yeah so this is rate of or rate with or rate or based on rate based on bulk conditions based on bulk conditions because some books are like this some books are like this yeah so that is the one this is equation I am equation this is 3 this is 4 this is 5 good so now this I have taken first order reaction okay I can also take second order reaction and then we have to solve correspondingly now for this example what is the effectiveness factor what is the actual rate of reaction or observed correct no actual rate of reaction is r observed so r observed is written as kcb divided by one plus dA correct no good so the other one kcs why yes kcb because evaluated under bulk conditions at bulk condition so kcb this this we can get cancelled out then we will have one plus dA so effectiveness factor for first order reaction is this equation okay so this is equation number 6 that is equation number 6 okay good yeah Swami are you telling okay yeah so now what normally can happen is that if I know damkohler number this is the damkohler number and for first order this simplifies only k by kga yeah kga then kg is the mass transfer correlation which I can get and k must be yeah the intrinsic rate constant please remember that is intrinsic rate constant this k that means what is the meaning without any mass transfer effect coming into picture like we have imagined our langmuir initial wood kinetics langmuir initial wood kinetics we never thought it is first order reaction by the way what is the order of reaction in those cases in langmuir langmuir initial wood kinetics what will be the order of reaction for LHHW kinetics one why one what is the meaning of one when you say order yeah but then what is the order with respect to you know the equations which we have derived for example first equation A plus B going to R plus S you have developed a big equation order of the rate determining system yeah the order of rate determining step only surface reaction if we have taken first case you see what is the equation you got you have the notes you know this is very important I think I have to connect you every time I have to connect you every time you know because order of reaction there is very interesting point here that is why I am trying to tell you yeah what is the equation on rock final rate only no yeah that is what what we are asking that is intermediate rate where I do not know anything yeah Bihla you have yeah rate equal to CACB minus yeah but then all that then what is the order of reaction you said one now it got to 2 after I ask another five minutes it will go to 3 okay yeah why why it is 2 why it is 1 so it should be 1 yeah so what it should be you cannot say any order for that kind of equations it is purely for the power law model where rate is defined as minus R equal to K into CA to the power of something CB to the power of something okay of course even if you are reversible reaction also we can say it but for heterogeneous systems you cannot unless you take out all the terms neglect one term you know in the denominator except one all other terms are neglected okay I mean just trying to tell that so then you will have only one at the bottom right then you remove also the backward reaction then what is the order you can say it is the second order because CA to the power of 1 CB to the power of 1 so that is why you cannot say for any rate equation what is the order of reaction unless you have power law model highly restricted this is one of the basic things even when I sit in a PhD interviews when I ask also why I am PhD interviews means 2 degrees already they got okay that is why I am telling so after getting 2 degrees also this clarity is not there for many people in the mind that is why I try to tell all these simple things complicated things anyway you can learn later if you know simple things so that is why order of reaction means immediate you know what we say is first order or second order okay you cannot say anything for heterogeneous particularly NHHW kinetics what is the order of reaction right and I told you also there are some negative orders it is very funny negative orders are really very good if everything is negative orders it is very good why as the concentration is decreasing rate of reaction will be increasing that is excellent no so you maintain zero concentration you will get infinite rate theoretically so infinite rate means you do not need any reactor at all rate infinity means if before you start the reaction convert it so nice but you know in the nature I think we do not have any negative order reactions except in Langmuir Institute kinetics when you take I think you are going to solve those problems in the assignment so when you are solving those problems so sometimes you get in the denominator some terms very important dominating terms sometimes can be neglected so under certain some conditions you will have at the in the denominator you will have some terms and in the numerator you will have less number of terms for example C A C B or simply only C A C B here in the bottom you will have may be C A square and C B some conditions it depends on you know how the actual reaction is taking place we have taken very simple cases like one active site and one molecule absorbing but if you take the hydrogen example you see these books you know I mentioned kinetics Smith book I do not know Fogler has given this sometimes you will get square root also in the in the denominator you would have seen in the table which I have given sometimes you will get square so that depends how that depends how that depends on how the molecules are getting adsorbed on the active site and then getting dissociated or getting associated all these kinds of situations will come into picture under those conditions you may get sometimes negative orders and one reaction what I can mention Carberry given that one is I think C O going to C O 2 on platinum catalyst under certain conditions you will get some negative orders okay it is given in Carberry book also okay that is only one example which I can give but that is not straight getting but after finding out the kinetics finally you will end up some terms and that will result into negative order that means it will be again it will become a power law model type where minus r A equal to K by C A or C A square or C A to the power of N in general okay so that is what that is the kind of thing okay good so I think we have to stop here okay we will stop here and then I will give you the assignment for you to you are not submitting anyway for second order reaction and half order reaction in the same case here start second order here that means square and then you solve same procedure and half order you solve for C S and again same procedure so this will be the exercises you have to do in your room okay good I think tomorrow we will meet anyway