 we will start this example what we were about to do yesterday, please take this example let us see so that you know some of those rules what we have learnt probably slightly more clearer now consider the aqueous reaction A plus B going to R and S this is the desired one we have d C R by d T you write there on the opposite straight to this equal to 1 that is K value C A to the power of 1.5 C B to the power of 0.3 d C S by d T equal to again so both are in units units of the rate are given as moles later minute, okay rate units good this is the problem then please write below for 90 percent conversion of A that is X A equal to 0.9 X A equal to 0.9 find C R in product in M F R and P F R so I mean I can also ask 5 P 5 P is once you get C R C R divided by C A not will give you of course that yield 1 and C A not minus C A F will give you yield 2, okay good then please write below equal volumetric flow rates of A and B are fed to the reactor and each stream has a concentration of 20 moles per liter of reactant, right two streams are coming with 2020 moles per liter they join and then enter the reactor so what will be the actual concentration that is entering 10 mole 10 mole that is why be careful about that that is simple mistake you do that in the exam and you think that you have done correctly and if marks are not given you think that a teacher is not giving marks these are the very simple things which you may not even know that you know you have to take those two streams together when two streams are meeting then average will be because here same concentration if it is not same concentration then accordingly you have to calculate, okay one is let us say one third and another one is two third like that then the concentrations again differ so I am just warning you these are the simple things where you may forget you know in the examination and you will not forget in the examination if you do all the assignments because that is the experience you are doing that so you will come across already one situation so that is the reason, okay so that is the one and okay I will write here CA0 actual CA0 that is entering equal to CB0 equal to 10 moles per liter, good okay the definition of instantaneous yield sometimes you can also write like this so that means CR by CA, okay so then I can write also this one we have this equation already DCA not S, okay DCA and this also can be written because I know these two, okay so actually A is now going to R and S together so these two rates will be added, okay anyway I think I will also write that DCR this is equal to DCR plus DCS so that you know you will not get so then this is equal to so now I have to substitute this and then cancel out you tell me how much this will be take DCR and add these two again take those two and then cancel out whatever possible cancellation select CA by CA plus CB to the power of 1.5, yeah so now let us take PFR, PFR what is the definition to find out CR integral CRF equal to integral pi into DCA, see this one DCR I am writing DCR by DT then the other one is this one DCR by DT plus DCS by so then substitute DCR by DT here, okay and also these two added then you cancel out whatever is possible because 0.5, 0.5 will get cancelled there 0.3 and 0.3 will get cancelled here that is why you get 1.5 like that, okay yeah good so now this we have to integrate between CA0 and okay so this is CAF, right so that means here I have minus CA0 CAF then phi value is this this is CA DCA by CA plus CB to the power of 1.5, DCA is integral and how do I convert CB into A, because I have to write CB in terms of CA right, CA is equal to CB, see it is 1 is to 1 and CB equal to CA now you substitute CB equal to CA and then tell me, yeah initial concentrations are same so everywhere CA equal to CB so then you can still further cancel out that so you will have only DCA by okay let me also write because otherwise many people are still sleeping I think today CA equal to CB everywhere CRF equal to CA0 CAF DCA by 1 plus CA to the power of 0.5 now this is what you have to integrate, please integrate and tell me you do not get liable, Calc that is why 2.85 so when you use Calc I will look for exact value okay exact value is 2.86, okay good, CA you are telling a CA, yeah but that solution I do not have but 2.8, 2.86 or 2.5, okay I think you please try 2.01, 2.86, 2.86 moles per liter what is that no problem I think 86, good I think the simplest one now you can try MFR you do not have to integrate I think you know wherever there is integration or differentiation you are not comfortable, yeah for MFR so phi also equal to phi M total you know capital phi M what is the value 1 by 1 plus CA to the power of 0.5 how much is this CA equal to how much 1 by 1 90 percent conversion so that is why 1 so what is the value 0.5 that is phi but what is CRF yeah so that is 0.5 into 9 4.5 moles per liter, good you can also draw this graphically and also try to find out right because I have an equation for phi this is the equation right so actually after substituting CA equal to CB everywhere then this will be only 1 by 1 by 1 plus CA to the power of 0 that you plot graphically phi equal to 1 by 1 plus this is versus CA how do I get this increasing or decreasing or what very good may decrease something like this maybe I do not know because CA initially very large right CA initially very large 10 for example CA equal to 10 then as you are moving this side this is decreasing by increasing yeah anyway I am just giving explanation because you are moving in this direction right okay so then you know that you have CA not equal to 10 here right and this is 9 CA equal to 9 very good yeah CA equal to 1 so then what is happening which reactor will give you the best yield M F R M F R M F R M F R M F R M F R M F R yeah it is not minimization we have to maximize the area because we are talking about CRF right so far M F R all this M F R and this one only for P F R yeah okay so actually that is also will be very easy if you are able to plot but that means you know you must be artistic in drawing the graphs and all that I just want to again point out I do not know you would have just simply solved the problem you would have got 2 point 86 and also 4 point 5 you could have closed your mind but beyond that you have to think in this case why are you getting in a mixed flow reactor more conversion than plug flow yield which order you are talking which is more overall ratio for CS is less compared to CR that is less CS is less order see what is our rule what is our rule in terms of concentration when and you want to keep when the order of desired reaction is more order of desired reaction okay but here it is more or less it is less because it is 2 point 8 and this is overall overall if you take this is 1 point 8 this is 2 point 3 that is the reason that is the reason that small difference okay you know that is what you know when you are solving after solving after getting the value we would also think a little bit know why I am getting this yeah you tell me know very good so in this case what happened yeah it is less than the undesired reaction rate so I mean reaction order so that is the reason why you get here in MFR more value than PFR excellent very good so now on your own there are many problems in Levenspiel various nice beautiful problems you have to solve solve solve I can give anything in that also as next week what is that you are thinking take the overall no but what is the use because both the a and b both are participating in the reaction this here by DCS yeah but that is you know you are talking now not need you are talking about selectivity we are talking about with respect directly we are trying to get this one desired product itself okay so he is now trying to write the other one selectivity but even then you should get the same argument you cannot get different argument for that not here again you should write DCR by DCS okay yeah DCR by DCS is not yield for us it is not yield but selectivity okay yeah so now what is the argument if DCR by DCS is and you should keep that value low or high as a as possible yeah yeah a is as a as possible b is as low as possible then you have side streams or you have another alternative mixture flow reactors with side streams okay so that is one I think you know here you will have many many alternatives I think this many people will not touch this multiple reactions but there are many many things here particularly when you go to that find a reaction and also then be reaction you will have lot of conflicts okay but still our basic rules are same when they decide rate is more okay for particular desired product then you have to maintain concentration as a as possible or undesired product if you want to keep as low as possible if that rate is low the direction will take place at all as low as low as also means there should be a balance 0 you put as a reaction should happen okay yeah but you know you have only distribute that the concentration such that you know you have low whatever is required either low a is low or b is low depending on the situation lower than c a yeah so this is very nice now we have not talked anything about volume of the reactor till now right we are only talking about crf but none of you asked how do you calculate tau or I also did not tell I have been mentioning this all the time now I would like to get what is the value for the volume numerical value for this kind of multiple reactions how do you do that like same I have yeah I think I am just only restressing the same thing but let me take parallel reactions we are talking about only parallel reactions all the time of a scheme a going to r and a going to s okay so here I have k1 k2 as usual epsilon equal to 0 right how do you get an equation for plug flow from this yeah rate may be simply this is yeah dcr by dt equal to k1 ca dcs by dt equal to k2 ca and minus r a equal to k1 plus k2 ca okay good now for pfr how do I get an equation in terms of volume either tau or v by fn r same means what you tell me what is the equation I am asking final pfr equation v by fn r a equal to ca and now tell me the equation ca and now integrate and tell me v by fn r equal to minus sir v by fn r equal to minus ln 1 minus xa 1 minus xa upon k1 plus k2 ca what is now I have written here dx a by minus r a I have written this one in terms of ca you convert that in terms of xa then only you have to integrate otherwise write the equation in terms of ca and then again integrate whatever so if I write also the same thing in terms of e4 minus k1 plus k2 tau because it is constant density system we can write happily okay so that is the equation where you can calculate either volume or this one and we can also do the same thing in terms of cr in terms of r also this one I have not done till now I think I have to do at least once always we have been writing in terms of only reactants okay let us write this in terms of products where this is again plug flow reactor where we have the same reaction we are talking even this even this equation you got only by material balance right you take a volume and then what is entering what is leaving what is reaction under steady state conditions all that so we will write here f r entering we are writing now for product one of the products right f r because yes this is the same reaction let me also have here a going to r s only so this is f r d f r so tell me what is entering what is leaving f r is entering f r plus d f r is leaving f r plus d f r is leaving plus what is reaction term minus r into v yeah it is not plus here because we are now writing for product yeah so minus r r into d v this is d so f r f r we will get they get cancelled so d f r equal to d v r r into d v yeah so now this also I can convert in terms of our usual expression because f r yeah f r also can be written as v into c r you know volumetric flow rate and concentration correct no yeah so now differentiate these d f r equal to we are applying this one for constant density system that is why v is constant throughout okay otherwise that also becomes d v c r into d v plus v into d c r okay but that is not I mean that is slightly more complicated so this is what we are taking now I have to substitute this here for d f r so v d c r equal to r r d v so I will write here d v by v equal to d c r by r r so when we integrate this this will be v by v which is nothing but tau this is integral 0 to c r d c r by r r so that is why I just wanted to this one do once because every time you know you see even the limits also without doing yourself you are telling c r not to c that depends on what equation you are now talking about okay yeah or this also can be written as this equation before differentiating this will be d tau okay d v by volumetric flow rate is equal to d tau okay right then I have this side d c r by r r d c r by d c r by r r so otherwise I write this one as that is also another expression which can be written this is another format which is definitely useful this is another format which is I do not know whether you have seen that use now okay that use I will tell you immediately though that you can do it you can do that what is the use now d c r by d tau equal to r r what is r r no in terms of equation what is r r k 1 c k 1 c right so okay this is equal to d c r by d tau equal to yeah I said k 1 c a and you have an equation for k 1 c a c a here already right you have this one so now you can also get c r in terms of tau correct no so this equation c a by c a not equal to this so now d c r by d tau equal to k 1 for c a I am substituting yeah for c a I am substituting c a not into e power minus k 1 plus k 2 tau this is integrable correct no because here I have tau this side also I have tau so now you find out c r integrable so that you will get as k 1 plus k 1 plus k 2 k 1 k 1 plus k 2 yeah this is 1 minus e power minus k 1 plus k 2 into tau able to see or shall I write somewhere shall I write here yeah I think I will write that final one here c r equal to k 1 k 1 plus k 2 1 minus there also I have misread it here also I have write c a not you see this is beautiful I think I do not know may be you are worried about I am making it more and more mathematical you have to worry about sometime in c r you also have to worry definitely but you know what we can do is from phi you can calculate c r correct no yield you substitute there and calculate tau for a new reactor this is much beautiful no right I think it is not given in 11 sphere I have taken this in some other book right r e has given I think he has not given yeah so this part has not been given so that is why this is another way of looking into so we are also able to write in terms of product where that may be that is slightly complicated than simple c a to calculate volumes but normally what our idea is from the graph or from analytical expression you calculate c r f right now you have to find out what is the volume for that c r f for that yield so then go to this equation like this for every reaction you have to we have taken simple reaction the other one will be same procedure but only complicated mathematics that is all so then you will have tau and because c r you know already k 1 k 2 you know you should know definitely kinetics then you can calculate what is tau so that is the volume of the reactor those things definitely that means k 1 k 2 values you need right that is why which one is easier that is you are writing in terms of a but you know there you are now based on you are calculating based on conversion of a here you are calculating based on yield of r okay I mean both should give the same values tau should be same whether I use this equation which equation this equation or that equation I am just trying to tell you there is another way of doing okay and also we have not written till now an equation in terms of the products so that is why I think at least once or twice if I write this kind of new methodologies then you will also be aware that yes this is also possible yeah so this is over now I think this is nice you can also calculate from this c s and all that I think from material balance you know c s equal to c a naught minus c r minus c a okay that material balance I think all of you will be knowing that okay so now this is only for plug flow reactor what we have written now let us write for mixed flow reactor same parallel reactions mixed flow reactor we have to write equations in terms of products also we have to write in terms of reactants reactants already you know that means reactant entering reactant leaving reactant reacting okay yeah so the other one is product entering product leaving and rate of product forming okay good so this is MFR now parallel reactions same reactions continued I will write that same reactions continued so what we do here is because like exercise if you do this I think then you will remember here I have volumetric flow rate volumetric flow rate this is total volume here I may have c a naught c r naught equal to zero usually c s naught also zero so this side I have c a c r c s I can also write if I want you know in terms of f a naught all these f a's f a f r f s okay good for parallel reactions how do you write the material balance parallel reactions again to make you remember this is k 1 k 2 r and s okay usually that is a desired product does not matter right so now m b for a steady state always you know we are not talking about in unsteady state okay what is entering for a we will ask one by one Kalpana what is entering here in terms of a v into c n r what are the chair what are the units of this v into c n r most one excellent good so next area what is leaving a leaving from the reactor okay good then what is reacting we will tell Kalpana and what is minus area here for this reaction minus area equal to k 1 k 2 c a right okay similarly r r is k 1 c a r s is k 2 c a right so this is one equation then for r we will tell for r I think this side what is entering 0 why 0 v into c a naught c r naught which is 0 okay that is leaving v c r and plus reacting r r into v that is the equation and for s same how can I write same I said okay so this is again 0 c s naught v c s plus r s into v oh oh yeah very good very good minus very nice good good so these are the equations and then of course you can write tau in terms of either this or this or this any equation you can use okay I think I will at least try here for this 1 2 3 okay from 1 we can write c a by c a naught equal to 1 by 1 plus this is 4 okay for c r c r by c a naught we can write we can get that from those equations k 1 tau by okay what should be for c s yeah so these are the equations phi m you can tell me c a by c a naught that is phi m 1 1 yield 1 that is c a by c r by c a naught c r by c a naught where is that okay then tell me 2 this one 2 is what I am asking is c r by c a naught minus c a or c a f okay if I take final you are right k 1 by k 1 plus k t okay can you also try puja for phi p plug flow I have this equation for c r by c a naught right anyway I think we will record what puja told this is also k 1 something wrong or what what is this I think p f r and is there something wrong because everyone is getting same it must be right same thing why what is the problem I think why you should not get for plug flow and mixture flow same thing wrong so why I think not logical no because I think in plug flow the contacting is different and mixture flow contacting is different that is right again the basic thing what we have learnt is when desired product or undesired you know product that reactions are having the same order concentration does not have any so that means whether mixture flow reactor or plug flow reactor concentration does not have any effect okay so that is the one okay Rahul you would have told something why funda which I have not understood but I think okay but you know that is the one concentrations are the concentration they do not have an effect because orders are same okay so under these conditions you have to only try if you want to have difference what do you try now increase not different you cannot have difference yeah temperature you have to increase so that you can get more and more because concentration is not a parameter for you you cannot play with concentration either high or low so that is why temperature is another one but now temperature is again depending on activation energy more or less you have to choose desired reaction has got more activation energy or undesired product that reaction has more activation energy so depending on those values again you either you have to increase or decrease the temperature Abdul what do you do if I have desired rate has more activation energy otherwise undesired product high temperature sorry high energy then you have to have low temperature then only you will get comparatively better products better lean or desired okay good very nice good so I think this we will close now I think we will stop and then