 so now what we try to find out is what is the effect of temperature and pressure on these reactions okay first good ya so what do you think how this temperature and pressure is affecting the rates because again here we need rate of reaction right but unfortunately this time rate of reaction depends on temperature as well as concentration so now we have to find out what is the effect of the temperature on the rate right okay whether you have you know if it is equilibrium it is much worse the effect will be very very drastic so that is why we have to now discuss those things right so we just take this equilibrium composition, rate of reaction and product distribution are affected by changes in operating temperature that is one point okay what is this product distribution I think you understand equilibrium composition will it change with temperature, registry is thinking so it affects then what about rate of reaction I think that should be immediate louder answer I say yes ya like that okay that rate of reaction affected by temperature I think LKG kid will tell okay then what is the product distribution getting affected what do you mean by product distribution gain ya depending on activation energies then you will have some reaction preferred some reaction not preferred and all that so even your product distribution for multiple reactions is also affected by this temperature affected by temperature then what are other things that can get affected point number two product distribution will come in selectivity and all that ya product distribution is a general word any other thing which can affect temperature affects call call all files they are stored just call such the files activation energy is supposed to be independent of temperature ya something connected to that only you have to tell search search search all the fine sense fine rate constant first one rate of reaction affected means that is one you know no no no no no no no no concentration rate rate of reaction affected means concentration will come temperature will come yeah heat of reaction delta h or also will get will get affected by temperature so the next point is that heat affects during reaction which determine heat requirement and exchange exchange of heat okay also affected by temperature okay so these two are most important things and in fact the entire economics depend on these two the temperature how it is affecting the rate equilibrium conversion you see equilibrium conversion ya you know one case where equilibrium conversion falls with temperature which case is that equilibrium conversion falls or decreases with temperature which exothermic not all exothermic reactions yeah reversible exothermic reversible exothermic reactions will have lower and lower conversions when you have higher and higher temperatures now you see the economics will depend on that so if I take okay temperature is very good so I go to very high temperature then conversion I will get 1% right so I am not able to convert more so plant will it cannot produce more so that is why it may go into the losses so otherwise what you have to do is you have to put another distillation column separate this 1% remaining 99% you have to but not in the sense of recycle reactor that is why you are telling that to increase the conversions are we use recycle reactor so that is not recycle in fact you are only separating the reactants and products and reactants are again sent back to ya for the reaction to be carried out that is all but not as in the sense of recycle reactor recycle reactor you are mixing the recycle product with the fresh stream there you are making this one itself as fresh stream okay so that is why many of you get confused why recycle reactor you know more efficient than all other reactors because that is the question when I asked you most of you wrote that recycle reactor when it is used means when you need more conversions you will never get more conversions there you will get always less conversions than plug flow right okay good so that is the one then from thermodynamics we have to now calculate heat absorbed or heat released and also we have to now discuss equilibrium conversion these two and we have the equation that is why quickly very briefly we will give these equations that is heat liberated or consumed that means this is exothermic reaction this is endothermic reaction ya that is one case where let us take that I think you know a specific reaction a a going to r plus r plus s plus s this is the reaction okay so now I want to calculate delta h r for this what is the equation delta h r equal to delta h r not at some standard temperature then plus t 0 to t del c p into d t okay what are shinker close the not writing at all why you do not like the equations or what okay so this is the equation where del equal to ya r c p r plus s c p s minus a c p c where c p s are specific heats I think you know that right ya so then here also I have to say that delta h r oh delta h r negative means what delta h r positive means ya so this is exo this one is endo that is the conversion that means if I give minus delta h r equal to let us say 10000 minus delta h r equal to ya that is exothermic reaction and on the other hand if I give delta h r equal to 10000 that is endothermic reaction that is the convention okay different books may follow differently but that is the convention okay and also we know that c p a also is a function of ya c p s all these also functions of temperature alpha a plus beta a t plus gamma a t square we are stopping only with square okay so then this one is alpha r plus beta r t plus gamma r t square this is 4 then this will be alpha s beta s t plus gamma s t square this is 5 right this is from thermodynamics we know this so then actually I have to substitute all this in this and then calculate what is delta h r at the required temperature at which I am conducting the reaction so I may give you delta h r not at 25 degrees is so much and I can give the temperature is happening may be around 500 degrees centigrade then if I give all these values you have to substitute here and then integrate and then finally calculate delta h r at 500 degrees centigrade okay that is what is the actual heat that is released okay good so I will also give this integral integrated expression so if I have okay ya delta h r equal to delta h r not plus okay t not to t we have delta alpha plus delta beta t plus del gamma t square d t which after integration gives me delta h r not sorry del t minus t not plus beta by 2 t minus square t 0 square plus del gamma by 3 t cube minus t 0 cube ya this is equation number 6 this is equation number 7 okay so this is delta h r where again I have to write del alpha what is del alpha equal to okay r alpha r plus s alpha s minus a alpha a del beta equal to I am sure most of you switched off your brains s beta s minus a beta a sorry capital A del gamma equal to r gamma r plus s gamma s minus a gamma a so this is 8 9 10 I am not giving any explanation how you got and all that but anyway it is straight forward you have to substitute there integrate and then group out all those things like this then you will get the simple form of equation dels are normally used only to minimize the space and minimize the rating okay so that is why this is the one good so now the next one what we have to also think is the equilibrium conversions okay so this is one and second one is equilibrium conversion conversion ya equilibrium conversion so what is the equation normally we use d t equal to delta h r by r t square what is this equation ya pent up equation and once you integrate this what you get ln k 1 by k 2 because this is equilibrium k so k 1 by k 2 if I have forward reaction and backward reaction equal to minus delta h r by r 1 by t minus 1 by t not in our sense ya okay this is equation 12 good how is this equilibrium conversion how do you get here I have not told anything about equilibrium conversion but I gave this equation k 1 by k 2 is related to because this is nothing but forward reaction by backward reaction so in a simplest sense when you have a going to r reversibly so then what is equilibrium conversion in terms of x a x a e by 1 minus I think all that you remember hopefully okay capital k equal to x a e by 1 minus x a e and you should know how you got it okay very good so there is a reversible reaction also so in like how can we write del c p as a product minus reactor there will be some equilibrium conversion also what is that you are talking this is different that is different but h r you have taken from there ya this h r okay ya your problem of this one ya here when you are doing it we take delta h r as constant is a function of temperature right 100 percent conversion we have not that is the total delta h r okay so this is the ya that is that is true at the end I think this is only 100 percent conversion right so you write for that but in the actual one how do you calculate how much heat released that maximum delta h r minus or not minus into minus r a present at any time stoichiometric coefficients final stop any time when you are will it be valid if the reaction is not going to be completed whatever ya definitely because whatever conversions you get at any point of time it is only stoichiometric proportions only you cannot have any other that is the beauty in stoichiometric you know it is only the stoichiometric proportions only we will react we will result finally the products okay ya so that is why that is not a problem but in this equation what we have assumed is that delta h r is not a function of temperature not only in this in most of the chemical engineering calculations we assume that delta h r is not a function of temperature that is justified ya yes mathematically it will be very very complicated but normally in engineering we do not do that at all because our reactions in any reactor happening over a small range even if you have a non isothermal from inlet to the outlet maximum you may have some 100 degree centigrade or 50 degree centigrade okay over that whether how much it is affecting that is what what you have to check that means at inlet temperature what is the delta h r at outlet temperature what is the delta h r if that variation is not much then you assume that delta h r is constant but as an engineer what we also do is even if there is not very very substantial change but reasonable change then what do I do I will take the arithmetic average of these two and then say that my temperature my delta h r is reasonable over this and constant over this range of operation otherwise it is only mathematically complicated if you want to do you can do it right but only thing is mathematically complicated so that is why okay abhishek ya so that is why delta h r is calculated for final one only right and then delta h r multiplied by you know minus r a what are the units of delta h r kilo calories or kilo joules per mole then I have to find out you know what is the rate of release how do you calculate that multiplied by minus r a what do you what do you get kilo joules per or kilo calories per per second per meter so now that is why that volume element also will come let minus r a into d v small v if I take plug flow reactor or if I take mixture flow reactor it is total v okay so that will tell me how many calories or how many kilo joules per second released okay that is the rate of heat released right good so if it is exothermic reaction knowing that this much heat is released now my process requirement tell me how much I have to remove out of that okay if you completely remove the temperature will fall and then again conversions may be less depending on the reaction I am telling okay sometimes less sometimes more so that is the reason why I also told you in the beginning you know economics will depend on these how much you have to cool how much you have to heat and also delta h r also we need that information because that will also determine what is the temperature in the system correct no if there is too much delta h r definitely temperature is going to increase if it is exothermic reaction if it is too much endothermic also delta h r then temperature will fall very rapidly then you will have very very low conversion rate of reaction equal to almost zero okay so this is additional parameter which automatically comes into picture when you are talking about temperature effects okay good so that is the one and now we will just summarize few points about the thermodynamic information that is required for reactor design thermodynamic information required for please write the thermodynamic information required for reactor design in terms of points we will go one by one Levenspiel beautifully summarized all these okay yeah now let me take let us take those points and discuss point number one thermodynamic equilibrium constant is unaffected by the pressure of the system comma by the presence or absence of innards comma or by the kinetics of the reaction comma but is affected by the temperature of the system how it is affected also we will draw here so this is XAE saying that that means A is our key component okay so this is temperature this is maximum conversion that is one so now if it is exothermic you will have like this if it is endothermic now like this okay this is exothermic and this is endothermic okay point number two though the thermodynamic equilibrium constant is unaffected by pressure or innards comma the equilibrium concentration of materials and equilibrium conversion of reactants can be influenced by these variables point number three we will discuss you know once you note down one by one we will discuss later okay point number three K for greater than one indicates that practically complete conversion may be possible and that the reaction can be considered to be reversible excellent we stop there okay K for less than one next next sentence K for less than one indicates that reaction will not proceed to any appreciable extent that is in the direction what we want okay number four for an increase in temperature equilibrium conversion raises for endothermic reactions and drops for exothermic reactions I am telling all this because this can be one of my separators yeah all these six points you have to write you know two more will come yeah next one number five for an increase in pressure in gas phase reactions conversion raises when number of moles decreases with reaction semicolon conversion drops when the number of moles increases with reaction okay good number six is a decrease in innards for all reactions acts in the way that an increase in pressure acts for gas phase reactions now what are the meaning of number one point number one because in fact all these things is beautiful summary of thermodynamics that is required for reactions there are many other things you know for energy and all that there but for reactions wonderful points wonderful summary the thermodynamic equilibrium constant is unaffected by the pressure innards okay and also the kinetics kinetics also but only thing is it is a function of temperature okay that we should know that is number one number two is though the though the thermodynamic constant is unaffected by pressure and innards but the equilibrium compositions will change that is why we add sometimes you know diluents and all that to shift the reaction for conversion from one side to the other side right so temperature affects only thermodynamic equilibrium but compositions that means the conversions okay yeah actual composition that is C A C B C R C S those things will be affected by again innards okay yeah that is point number two good what is point number three very simple K is far greater than one it is almost irreversible reaction that means yeah so almost here K you may get almost 100 percent reaction okay this is K far greater than one okay depending on you know how do you know that what of all the reaction is occurring depending on Gibbs free energy you can because Gibbs free energy again is connected with K so if K is very large you know you calculate exactly that is what I think you know the first few questions what we have discussed there how does a chemical process start in that the first step is to find out whether the reaction is feasible or not how go to delta G Gibbs free energy calculate delta G from you know how to calculate but you should know the stoichiometric equation if you have stoichiometric equation like that you have the tables where for the components that free energy G is listed okay from there calculate delta G I think that is very good once more I can repeat because some of you still would have not got that idea right calculate delta G that is equal to minus RT ln K but you have to assume it T for particular T what is K right so depending on that K value you can say that whether it is reversible irreversible all kinds of things you can interpret from that okay good so that is the one so the next one is we have to we are now trying to discuss about the graphical design of non isothermal reactors the graphical design that means from we are not going to get exactly the quantitative numbers like okay volume of this is 10 meter cube but the procedure for you know the graphical analysis that is what what we are going to discuss now provided the time is infinite any reacting system provided the time is infinite can I do that please repeat again what is that time coming here say a time in infinity like reaction will eventually come here because if I know the K value is very very large then it is irreversible okay if the K is may be that is all what you can get from that time will not come here okay what is equilibrium is it reaction equilibrium or you are talking about something else reaction equilibrium you do not have to talk about for irreversible reaction also can I write for irreversible reaction what do you want to write tell me what is that you want to write like model of the what model what kinetic model you are telling for example I have a batch reactor first order reaction and I know the equation what is the equation for design because I have written the my model equations and then got okay for plug flow K tau equal to yeah K tau equal to let me write that K tau P equal to minus ln 1 minus X A so which one you are talking here because this equation I am I got only by writing the model equation that means what is entering what is leaving and all that but this is for isothermal system what you are writing you cannot make equilibrium assertion for the reactor I am considering the reaction is like very fast and irreversible still I can work for equilibrium what is the use because still you can write the because X A anyway for irreversible you can get 90% conversion 99% conversion right but when you have reversible reaction that will limit it will tell you fellow you cannot go to 99% you can only go to 60% at that temperature so it is always associated with the temperature so that is why in Gibbs free energy you will get temperature versus conversion graph also you can plot that is what is the meaning of this in fact when I when I am operating exothermic reaction at very low temperatures this is the conversion I can get equilibrium conversion but the descent rate is of operating at very low conversion here the rate of reaction itself will be very very low X A you can get that much but the rate is very very low this is thermodynamic information okay so equilibrium conversion almost one means I can also get actual conversion almost one but how much time I have to wait because there it is not equilibrium coming it is only the rate of reaction coming when the temperature is very very very low then the rate of reaction is not very fast right so that is why my reaction will be very very big because I have to provide that much residence time for the reaction to take place okay so I think that question of writing a model for equilibrium model for irreversible reaction it will not come into picture at all as far as I know it won't come into picture what is exactly your I mean that able to not able to understand because something must be worrying you something must be bothering you so what is that point okay okay so you see I think maybe some of you also may have the same doubts there what we do here is that if I know from Gibbs free energy I will find out capital K value that will decide whether I have irreversible or reversible right irreversible I can go to any conversion but only thing is depending on the temperature and you know what conversion that means volume of the reactor may be more sometimes I told you know sometimes from 0.9 to 0.95 the volume may be triple or may be 4 times from 0.95 to 0.96 97 98 the volume will be tremendously increasing so academics will tell you fellow don't go beyond this otherwise all money will go only for constructing the reactor so then I think it is a problem don't go like that again academic analysis that is one thing but that is irreversible the moment I have reversible reaction now I know at what temperature I am going to conduct that we should know at what temperature we are going to conduct the reaction now let us say 150 degrees I am going to conduct the reaction that will automatically fix my equilibrium conversion if 150 is somewhere here that is what is the equilibrium conversion for irreversible sorry for reversible exothermic reaction beyond that no one can do that is why I feel many times you know thermodynamics is God because that tells you you cannot go beyond this that is what God also tells you you won't directly tell you but through others some other systems he will tell okay that I think only you can get maximum this degree beyond that you cannot get whatever you try you cannot get that degree I tell you okay if your life is written only like okay M Tech is the maximum degree you may join PhD something will happen you have to leave and then go back that is the God's law that is all that is the point beyond that you cannot cross exactly thermodynamics also will tell you XAE here only 60 percent you can never cross that but sometimes we cheat we have what is called process intensification if it is reversible reaction then what we do is we will take out the product so that only always it is forward reaction so forward reaction alone means very good I mean I can increase the conversions so that cheating also is there we also cheat sometimes no so you may not get degree from IIT Madras you may buy one from many places correct no there are many places who are selling PhD degrees yeah and then you are very happy I got the degree okay even though God said you cannot do it he said only you cannot do it not get it okay okay range of okay for reversible reaction around 1 2 3 you cannot tell even 0.5 okay so that again automatically that K value whatever you get from the reaction itself that depends on the temperature it will be fixed by temperature limit right beyond certain temperature slightly that flexibility is there with you you can conduct the temperature over 50 degrees okay so beyond that or may be 100 degrees depending on each case but we cannot generalize that K must be only this value for a reversible reaction you can never right and the example which I gave earlier asked to you know K equal to XAE by 1 minus XAE if K equal to 1 what is the equilibrium conversion 0.5 that is all you cannot go beyond that so like that okay so but that is also fixed at one temperature right because K changes with some other temperature so that is all that is only you cannot fix exactly what is this value must be like this that depends on the process type of reaction materials of construction many many things will come into picture okay Abhishek not able to get that K will be 10000 that K only I am telling that K is 10000 that you got already K but only thing is that K equal to K1 by K2 this K equal to K1 by K2 so what is the meaning of 10000 the backward reaction is almost 0 that is why we are telling that it is irreversible it is only going for one direction you got already that right the K value are you talking about equilibrium constant or rate constant there is equilibrium constant which is very large value because Gibbs free energy when you calculate and then get very large value that means there is a K value if you have stoichiometry and if you have the components those components have that G values you can calculate and then when you calculate you will get let us say 20000 so your idea is okay my forward reaction is very very large very fast and my backward reaction is very very small so this is theoretically irreversible or reversible reaction but practically it is irreversible you have K value you got K value that means you will have purely irreversible K2 equal to 0 you will get infinity yeah okay that is purely theoretically right so that is why what we are taking there is that the forward reaction is very very large when compared to backward reaction that is why that is why you know there is one statement that all reactions are reversible correct no yeah so then depending on the value of K you decide whether you have yeah and as Abhishek asked we cannot fix what is the value for K capital K right but you can specify temperature automatically capital K is fixed because K1 K2 you can also get in a different way you can actually conduct kinetic expressions get K1 value get K2 value and also you at a given temperature again you can also get K that is to check your thermodynamics as well as kinetics not able to understand okay good yeah so the next one is the graphical design for isothermal reactors what is the graphical design okay I think nano thermal reactors are there graphical design yeah for isothermal you tell me nano thermal is just above yeah so 1 by minus r a verses but what is the problem here or what is the problem that is going to be here now temperature now temperature now you have to draw actually three dimensional okay so again we cheat there instead of drawing three dimensional graph what do you do we fix one parameter and then draw the other two that is all so because I have three here what are the three I have rate temperature okay okay rate r is looking awkward okay rate you know may be awkward x a these are the three so far isothermal it is easy for me because I think this fellow will be sleeping so these two only will be active so we plot so because there are three now you can draw a three dimensional graph three dimensional graphs we cannot understand okay so that is why we better go for two dimensional graph by fixing yeah you see many times we say parameter what is the difference between a parameter and a variable parameter will be constant variable variable that is what the meaning of what is the meaning so so parameter is a constant yeah tell me what is parameter there is one value yeah I think you know variables are shown in the x and y parameters are shown as fixed numbers and then only for that number for that value particular value you see the behavior and then again increase or decrease and then see how the behavior is changing that is only for cheating you know there because we cannot understand that three dimensional graphs that is why what we are doing here now we can also plot here the graphs like okay this is minus r a versus okay minus r a versus temperature I can plot good similarly I can also plot r versus x a and we can also plot x a versus temperature so here r will be parameter and here temperature will be parameter and here x a will be parameter so any one of these things we can choose okay but normally what we choose is yeah in fact if you if you plot minus r a versus temperature general graphs you may have like this like this like this this may be x 1 x a 1 x a 2 x a 3 so in this case r versus yeah r versus x for different temperatures you may get something like this yeah something like this something like this this is t 1 t 2 t 3 just I am showing you know some general graphs or otherwise if I plot x versus t you may get okay like this so this will be minus r a 1 minus r a 2 minus r a 3 these are the three different graphs you get but what you what actual type of graphs you get we can also derive that is what what I am going to do okay good anyway I think tomorrow we will meet and you see actually we have not covered much in non isothermal so that is why this also can be included in the examination