 Welcome, this is advanced reaction engineering course. Now, in this course we cover a lot of ground general applications of chemical reaction engineering to our requirements in chemical process industry and as well as in daily life and so on. So, what I would like to do in this session is just to give you an overall perspective of what I want to do in this lecture series of may be 30, 40 hours. So, let me just run through one by one just give you a feel for what is contained in each of these modules. So, let me get a beginning. So, we have begin with an introduction I mean the object here is to try and bring to your attention what we will do in this course of course and then what is the methodology that we will follow and you know how we plan to address various issues and how we will explain the principles through various examples and so on. So, the methodology we will try to adopt here is one of problem solving. So, that we learn how to derive the equations that describe a certain process and or certain idealization that we will look at and also show how it applies to different situations. So, that is the way we will go around in this course and if you I am sure all of you are familiar but see we will look at what I see as design equations for ideal reactors. Now, I mean in the sense that you know we have reaction equipment and that reaction equipment in which certain reaction takes place let us say A goes to B or A goes to B plus C whatever. So, what we need to know is you know how this particular material that is entering reaction vessel how would undergo reaction to what extent it will undergo reaction what are the parameters that will determine the extent to which the reaction would occur. And most importantly what is the size of the equipment that is required for a certain extent of reaction of course as our interest and in some cases you know we are not looking at simply continuous operation we are looking at batch operations in which case or interest is to find out what is the time that is required for a given extent of reaction and so on. And there are situations in which we are neither doing continuous nor doing batch we are doing something like semi continuous semi batch operations in which case you know our interest is to really understand how the process can be written down in terms of mathematics. So, that we can tell what might happen to the process and how we can intervene in a way. So, that the process can be made to move in the direction of our interest. So, the design equations for ideal reactors is essentially a way of trying to idealize what might be happening and so that our equations are able to approximate what might happen in real life. Just as an example I mean more of it you will see when you actually look at these just to put it in the perspective. Let us say you have an equipment like this and in which you know this reaction is occurring a flow is coming in and flow is going out. So, this is got a certain volume b reaction a goes to b or let us say a or a plus b going to c plus t. Now, you will recognize that a b c d you know a can be a gas and b can be a liquid you know it can be it can be same phases may be the same phases may be different products may have some of it may be a gas some of it. Now, the various kinds of situations that are likely. So, for each of these situations you know our equations must be able to appropriately take into account. So, we will look at simple situations as we go along we will modify and then take into account you know more variation that might occur in real life. So, the design equations if you are looking at design equations the object of design equation is to put down in simple terms how inputs and outputs or inputs initial and final can be related in terms of parameters that you and I understand recognize and so on. In the chemical engineering literature chemical process industry frequently we see what we call as tubular reactors. Now, tubular reactors are essentially pipes of various sizes and typically they contain a catalyst which is coming in and going out tubular reactors are common in the industry because they are easy to build. And then you know the flow fields can be easily understood can be measured place lot of techniques have been award over number of years to understand the fluid mechanics. And therefore, it is it is a common device which is employed in the industry. So, often we talk about plug flow in our tubular reactor design equations by plug flow I mean in the sense the reason why we sort of idealize situations like this is that they are easier to treat. And therefore, we are able to get equation that is able to quickly idealize what might might be otherwise difficult to understand and predict. So, we have a first principle understanding of what might happen by plug flow what is meant is that if you have a fluid element here it sort of gets in it sort of moves through the equipment it moves through the equipment and emerges. And there is another fluid element which comes and moves through the equipment and emerges. On other words what we are saying that if we recognize or idealize a flow through an equipment as plug flow it only means that these fluid elements pass without recognizing the existence of other fluid elements. Therefore, the time of residence of these fluid elements can be very precisely calculated and therefore, we are able to tell how long they have spent in the equipment. And therefore, we can tell what is the extent to which the reaction may have take place based on the numbers that we have in our hand. So, plug flow is an idealized version of the reaction equipment that you will see in the process industry often called as tubular reactors. So, we will set up equations as we go along to describe what is called as plug flow reactors. Little earlier we said we talked about stirred vessels these are all stirred vessels. Now, stirred vessels cells can be batch equipment or can be a continuous equipment. Now, batch equipment means that you know there is a flow inside, but there is no flow out in the sense it is batch. There is no flow in. So, you start with a certain amount of fluid here and you process the fluid for a certain length of time and we set up equations that would describe what might be going on inside the equipment. On other words there is no inflow, there is no outflow. Therefore, whatever happens in the reaction is like it is sort of it is accounted for by the process or the reaction kinetics that is responsible for that reaction to take place. So, batch you will find batch equipments are generally quite common in small scale industry. If you go to paint industry, if you go to pharmaceutical industry or oil industry various kinds of industries whereas, you want to process them in small scale because the scale of operations are such that the demand is such that it only is amenable to small scales of operation or in places like pharmaceutical industry where purities and then quality etcetera are so stringent that you must be able to keep track of in which batch it was produced. So, that in case you want to recall the product at a later stage it might be possible to actually inform the dealers to recall the product in case it is found to be unsatisfactory for whatever reasons. So, pharmaceutical industry batch process are quite common. Now, it is a batch equipment is essentially a vessel which is got you know there is provision for inlet outlet, there is provision for entering inside and cleaning and so on. So, it is quite common of various sizes may be 10, 20, 5 to 10 kilo liters is typically the sizes you will see in the industry. There is something called CSTR which is quite common in chemical engineering literature which is called continuous third tank reactor which is it is an equipment like this where there is continuous input and there is a continuous output these valves are these are the valves. So, these are open so that there is continuous flow and continuous output. On other words what you are seeing here is that chemical reaction takes place as the flow comes in and goes out and since many of these reactions could be quite you know exothermic. There are coils which might be which might be carrying a cooling or heating fluid. So, as to ensure that the reaction conditions are able to be achieved because of this heating or cooling medium. So, the continuous third tank reactor is one very common device that you might see in laboratories in the universities and research labs and in the industry where the scales of operations are relatively larger not very large relatively larger. Now, continuous third tank reactors in the process industry the most common we might see in places for example, you will find that in polymer industry where you have to deal with very viscous situations you will find that third tank provides you a good amount of mixing and so on. So, that the heat transfer can be satisfactory. So, you will find continuous reaction equipment in polymer industry. There are several other situations where continuous reaction equipments are quite common because of the fact that it permits you to continuously input and output at the same time ensure that the temperatures and process conditions are kept uniform. So, CSTR and batch are the restored equipment that you will see in the process industry and the tubular reactors or plug flow devices that we call is quite common in the very large scale petroleum in other industries. So, for both these situations there are design equations which we call as ideal reactors. So, what is meant by ideal reactors by ideal we mean that the conditions in different parts the equipment in terms of temperature pressure concentrations are uniform. In other words the fluid as soon as it enters it is able to get itself mixed thoroughly. So, that the conditions inside the equipment is same as conditions that is leaving the equipment that is what is called as a continuous stirred tank reactor very popular in chemical engineering literature. So, when we when we said design equations for ideal reactors we will be looking at these two situations and set up equations that will describe how reactions take place in these two how reactions can be understood as they take place in these two kinds of equipments. Now, we find in our in our experience in process industry that a reaction does not go to completion for whatever reasons let us just give an example let us say you have a reaction equipment feed is coming in feed is going out. Now, we find that this is the reactor. So, this is what is called as the plug flow plug flow recycle reactor. Now, when would you engage a process of this nature we would engage process of this nature when we find that the products that come out of this reaction requires to be recycled. There would be situations that you will learn as you go along situations in which the products have to be recycled. They have to be recycled because you find that the products are able to facilitate the rate at which the reaction occurs this could be one reason or the products contain lot of energy like heat for example, it is a very high temperature. So, you have to make use of that energy for your process that could be another example. So, there could be several situations of course, another example could be that you know the reaction has not gone to completion therefore, you want to put a separator somewhere here and then separate the products and then recycle the unreacted products. So, there are various situations that you will encounter where recycle is required. Now, when recycle is required we need to set up our design equations which will take into account the effect of recycle the effect of the recycle on the size of the equipment number 1. Effect of recycle on the extent of reaction the various issues that we must consider when we prepare a recycle. It can be steady state it can be unsteady state because you know you might be encountering situations in which you also want to understand how long it takes for a certain process to reach steady state or you are interested in the unsteady state part of the process because you are starting of the process and you want to know how long it is taken to reach steady state. The various issues that might come up in a process that we would like to understand and then set up our mathematics. So, that we can actually tell how long it will be before the steady state is achieved. So, we need situations like this in process industry. So, we will set up equations that takes into account the effects of recycle. So, that we can set up our equations appropriately. I mean said this we want to look at plug flow recycle reactors. So, illustrations illustrative examples. Now, what we will when I say plug flow illustrative examples what I like to bring to attention to in such lectures is that we I mean what are the physical situations where you might want to do a recycle and how would that recycle benefit you in a process. Let us take an example say for example, a going to b let us say as an example where the reaction the reaction is auto catalytic is auto catalytic. What is meant by auto catalytic auto catalytic we mean that the reaction rate at which this reaction occurs is dependent on a it is also dependent on b. Now, when a reaction is auto catalytic which means that the rate at which the reaction moves really depends upon how much of product has been put into the system. So, clearly speaking unless you put product appropriately the reaction does not move. Now, if you look at the recycle recycle this recycle device provides a way by which you can put products back into the feed. So, auto catalytic reaction is a good example where recycle becomes very very important for the process to move forward. So, auto catalytic reactions require recycle and very clearly it do there might be an optimum recycle at which you must operate and. So, on which is important from the point of your process optimization all those features will have to be appropriately taken into account into a design equations plus it has to be appropriately explained it has to be appropriately explained when we look at illustrative examples. Now, I mean if you look at real life for example, what are the real life situations where we have to deal with auto catalytic reaction the finest example you will think of are biological reactions. Say for example, you have let us say you have you have a reaction I am just giving a small example you have C 6 H 12 O 6 this is glucose it is reacting with some cells let us say saccharomyces saccharomyces this is a fungi is a fungi which feeds on glucose under certain conditions of P H and temperature and oxygen tension and so on gives you alcohol it gives you alcohol and carbon dioxide. Now, you can see here is 3 C 2 H 5 O H and C O 2 you can balance this how many carbon is there you can balance is anyways not so critical right now. So, you have glucose giving you alcohol and water alcohol and carbon dioxide. Now, this particular reactions you will find that if unless you put in saccharomyces and get the appropriate conditions you will not be able to produce alcohol. So, what is being said is that. So, the presence of saccharomyces makes this reaction happen in that process more cells are formed. So, in principle in principle this cells can be harvested and then put back into the process that is one way or alternatively alternatively you find that as more and more cells are formed it is able to catalyze the reaction in the forward direction. So, autocatalyze is a good example in which you will find that the addition of the product which cells are a product to enhances the rate of forward reaction. Just look at some more examples of recycle reactors. Now, there is another situation that you would have seen in real life and some of you may have seen is if you go to a waste treatment plant. See if you I mean all over the world you will find that we produce a lot of let us say sewage which comes out of human settlements there could be a waste coming from dairy sensing which contains lot of waste material. So, typically what is done is that these materials is taken into a basin in which you put in oxygen you put in oxygen by aeration and then presence in the presence of oxygen and the sewage which contains organics like carbohydrates and things like that. The cells which is present in that environment grows and as a result you will find that the waste material gets consumed and then the water that comes out is relatively clean or this is called as waste treatment this is called waste treatment. Now, you will find that that sewage let us say sewage contains carbohydrate. So, you are putting oxygen. So, this gets oxidized. So, it becomes carbon dioxide and water and the cells that are present in the water produce more cells. So, this is another example this is another example where the the the whole reaction goes forward only if there are cells and the cells produce more cells and the effect of the cells is to further enhance the reaction. On other words this is another very good example of auto catalytic reactions. Now, whether you use devices we can use various types of devices we can use devices which is called stirred tanks which is called these are all stirred tanks. We can use stirred tanks as devices for doing this process or you can do recycle devices like what I have said. In both cases the principles are that the product which is cell enhances the rate at which the reaction occurs this is what we are trying to say. So, plug flow recycle devices or recycles in general are very common in process industry and we need equations to take care of how to deal with recycles in real life and that is what we will do in these kinds of lectures. Now, we often find if I mean I mean it is not very unusual that in chemical process there are many many reactions that occur there are many many reactions that occur. And we have to deal with what is called as multiple reaction multiple multiple reactions mean what do you mean by multiple reactions. What we want to say here is that suppose let us say I am just as an example I write a plus b going to c plus d this is single reaction. Now, if you want to talk about a multiple reaction I can write the multiple reaction like this a 1 alpha 1 1 a 1 plus alpha 1 2 a 2 up to say alpha 1 n a n. Similarly, alpha p 1 a 1 plus alpha p 2 a 2 up to alpha p n a n equal to 0. What is being said here is that you have written a plus b equal to c plus d as a reaction this can also be written as c plus d minus of a minus of b equal to 0. I mean it is what is being said is that if you have a chemical reaction each can write it as an algebraic equation it is convenient or if you have many many reactions occurring as I have said here alpha 1 1 a 1 to alpha 1 1 a n as this is one reaction there are p such reactions. So, reaction there are p reactions here. Now, the important point when there are large number of reactions are happening. So, we also like to know I mean how to manage how to understand very large number of reactions. Now, therefore, we need a systematic procedure by which we are able to deal with very large number of reactions. So, that we can account for them we can find out what is what is happening in the reactions and so on. So, there is general technique which is used to understand how many reactions are independent you know independence of reactions is an idea which has come in because of the fact that there are many many reactions are happening. Once we recognize what is called the independence of reactions we can also understand that if there are many many reactions how many of them are independent how many of them are dependent and so on. Just illustrate this let me just illustrate this what I am saying say for example, you have a reaction a going to b and the reaction b going to a what is meant by this we are saying that this reaction a to b is and this is actually a reversible reaction. That means reaction go in the forward direction and go in the reverse direction. So, which means when we are conducting a reaction a going to b in principle in principle perhaps both the rate process are occurring both the rate process are occurring what we see is that the reaction seems to go from a to b because one rate process faster than the other. Therefore, the net in the net you see that the reaction is going for in one direction and there are techniques I mean you would have learnt or you will learn as you go along by which you can actually measure the rate process in both directions. There are techniques available and there are methods available you will learn all these as you go along. Therefore, in principle all these are possible to be measured. So, but the fact of interest to us is that if there are there is a going to b and b going to a how many of these reactions are independent is a question that we frequently will ask ourselves. Now, it is common sense by looking at it we can say that you know if you just take one sample of suppose this reaction is occurring in an equipment like this a going to b b going to see if you just take a sample of a and of this of this material and analyze for a. If you analyze for a start in a 0 as the total moles and then we determine what is the moles at any other time. So, once you know this difference once you know this difference you can tell what is the amount of b that has been formed because that is coming from stoichiometry. And other words what we trying to say is that if you know the independence of reactions you can tell what is the composition of the system. So, what is what is generally suggested in multiple or in what is called as reaction networks is that we determine the number of independent reactions we just determine number of independent reactions. Once we know the number of independent reactions we can tell the composition of the system fully because that is what will determine the composition of the system. And as you go along we will use these general methods to deal with multiple reactions and you will find as you go along particularly in biology when huge number of reactions are occurring. You will find extremely useful to deal with use these techniques because it makes a very convenient and there are computational methods available. So, by which we can deal with them very effectively. Now having said this let me sort of draw attention to some very very interesting situations that we might encounter. One situation which we will is multiple reactions in soil environment as you all know that just give a small example just to just put this in the context. Suppose you have a reaction let us say n o 2 minus giving you n h 4 plus. So, n o 2 minus giving you n o 3 minus. So, n o 2 minus reacting with n h 4 plus giving you n o 3 minus. So, this gives you n 2 plus h 2 o 1 2 3. And then you could also have a situation that n h 4 plus which is formed in reaction 1 goes for cell synthesis. How does it happen? This ammonium nitrate is actually incorporated into the cells due to it is reactions that happen in the soil environment. Of course, you could also have a situation that the carbohydrates gets oxidized to give you carbon dioxide and water plus energy. So, the context here is something like this. I mean this in this planet we produce close to about 2 billion tons of grains to feed the population of the world. And all this comes from about 1300 million hectares of cultivated land in different parts of the world. India included and the cultivated land in India is something like out of total land area of about 180 or 200 million hectares is the total crop area in this country. So, in the sense that if you want to understand what is happening in soil environment, we can understand this by looking at these 5 reactions. Now, we can do experiments to find out what happens to n o 2 minus n o 3 minus n h 4 plus and then carbohydrate can be measured appropriately. On other words, we can do a small experiment to find out how these nutrients n o 2 minus n o 3 minus n h 4 plus and then carbohydrate is actually channeled into various pathways through simple experiments. Now, you notice here this is what this if I call this is reaction 1, then call this is reaction 2, call this is reaction 3, call this is reaction 4, call this is reaction 5. Essentially what we are trying to say here is that here are just 5 reactions. And these 5 reactions are able to tell us how you are producing various cells, it can be food crops are in around the world. So, through some simple experiments, I mean in the kind of power that these experiments have on is enormous as you can see, you can do these experiments and find out how the nitrogen that we add that we add to soil and how they are related to production of food crops and how the carbohydrate that might be present in the soil environment is used for the production of food crops. You see these kinds of inter linkages we can understand by doing some simple experiments in multiple reactions using a soil environment in a laboratory, it do not have to go into the field. And you will find that you are able to get results which are able to explain what happens in different parts of the world. Giving you a feel for how fairly simple experiments done in a laboratory, which does not cost you a lot. It give you an insight into very very complex happenings in agriculture, plantations, plantation crops in the world and so on. So, that is the power of trying to understand multiple reactions in soil of which we will look at some examples to illustrate how we can get insights into fairly complicated situations using fairly simple techniques. Next we will try to look at is what we call as catalyst deactivation. Now, the context to looking at catalyst deactivation is that if you look at our process industry or process industry many of them require catalyst for the reactions to take place. I mean we know of ammonia synthesis of which Haber won a Nobel Prize in 1915 for the development and for the discovery of the synthesis catalyst of course, lot of improvements have come since then. And there are in fact catalyst is the center of many many important processes which make life so easy for us today compared to what it was may be 100 years ago. So, but catalyst undergo deactivation fundamentals of deactivation is a chemistry that we must know so that we can prevent it we can improve upon it and so on. But from the point of view of chemical engineers who run processes what is important is that we would like to know what is the kinetics of catalyst deactivation at what rate they can deactivate. So, that we have some way for understanding how long our catalyst will last in the process environment so that we can replace them alternatively we can regenerate them appropriately. So, the whole process of catalyst deactivation requires you to find out methods by which we can understand the kinetics of deactivation kinetics. So, we must know the kinetics of deactivation I mean for which we must do measurements and even if you do measurements you see what is important is that we must know how to use those measurements to derive and to get the kinetic information of our interest. So, what is important in catalyst deactivation is to be able to develop our mathematics to represent what is going on in the process so that we can get the information of our interest. So, in these lectures and catalyst deactivation what we will try to emphasize and give you methods is to how do we conduct our experiments. So, that we can get data in a form that we can use to extract the deactivation kinetics from our experiments. So, this is what is the content of the catalyst deactivation that we will do in these lectures. Now, if you know if I say that catalyst deactivation kinetics is given by an equation of this form equation of this form some function of concentrations and so on. So, our important thing is to recognize that what is the value of m what is this function which is depends which determines the deactivation kinetics. So, that when we write the rate at which the catalyst deactivates by this we are able to convert this and appropriately integrate this into our design in the reactor design. So, that we are able to understand how this process under catalyst deactivation will run. So, that we can appropriately tune the process to take care of this deactivation and ensure that we produce product products at the rate at which we design we have design that plan for. So, the object of this particular this set of lectures is to determine this function. So, that we are able to go forward and use this information for our design operation and control of processes involving catalysts. Now, this is the related issue which we must bear in mind. So, what I call here as a process evaluation process evaluation under catalyst deactivation. Now, what we would try to learn here is that say let us for example, let us say let us say we have a we have a reactor and then let us say it goes through a separator products come out and then the unreacted goes back and this is the most common that we will see in the process industry is a reactor there is a separator. Now, if I call this as f a 0 if I call this as f a go let us say a goes to be as an example. Now, what we will see in a process is that as this catalyst there is a catalyst here catalyst here catalyst which deactivates this is deactivates. So, what you would expect as this deactivates the amount of product that you will produce here will keep on decreasing and clearly which means the amount of product that formed here is decreasing and therefore, what you are going to get here is also will decrease. Now, this separator has been designed to process a certain amount of the product. Now, as this keeps decreasing you will find that this material this separator is not working to your design. So, it is suboptimal and therefore, your process is not satisfactory. Now, clearly when you design this reaction equipment we have to anticipate what is the deactivation we have to anticipate we have to anticipate the effects of this deactivation a is the activity and appropriately design your process which means you would have which means that if you are rate at which component a that is formed let us say this is some this is the activity which is changing some other function c. So, this effect this effect you should account for in the design. So, that with time with time as this catalyst activity keeps on decreasing there might be must be a process tuning that you will do or process adjustments that you will do which will ensure that the catalyst even though if it deactivates the product that comes out here does not change with time. So, that in other words there are strategies by which we can run processes despite the fact that there is deactivation and it is these strategies that we will learn in these lectures. And we will illustrate these through examples where you can actually I mean use these principles to understand how we can run these processes. We pointed out that commercial processes like deactivating catalyst we need to continuously adjust the process conditions. So, that the quantity of material that is produced here per unit time etcetera is in variant with time. So, that we are able to produce these products. So, essentially these are all time dependent kind of operations. So, time dependent time dependent operations we just now pointed out that catalyst deactivation is an example of time dependent operation. And we also said that there are strategies by which we can manage the time dependent operations by appropriate adjustment of the process conditions. So, that the output does not see a time dependence you see these are the kinds. Now, there is another set of situations in real life where actually there is time dependence. That means we accept the fact that there is time dependence. And we want to be able to understand those time dependence mathematically. So, that we can set up our equations we have all the numbers in front of us. Therefore, you know how the time dependence actually happens how we take that into account in our. So, time dependent operations are one you have a batch process a batch process. What is a batch process you have a reaction happening here. And then you have put in at 0 time at time t equal to 0 you have started with some C A naught and C B naught and so on. And your product A plus B goes to C plus D. Therefore, this tells you how long you must run this process. So, that you can get your products. So, that is one in fairly elementary example of time dependent operation. There is a more involved time dependent operation is that you have let us say a reactor which is producing a product. Now, this particular reactor we have to there is a start up the start up of this. So, start up what is meant by start up you have a reaction you have a reactor which you want starting now. And you want to know how long it takes to reach steady state and so on. Therefore, this during the start up up to reaching steady state there is some time gap involved. What is the time line and how do we understand that time line and how do we ensure that during the process of starting up to the point it reaches steady state everything is very safe nothing goes out of control. So, start up of a plant start up of a reactor is an issue which is time dependent. So, the effects of time must be appropriately accounted in appropriately incorporated in the mathematics. So, that we know how the evolution of the composition of the system is dependent on system parameters etcetera. So, time dependence start up is a very good example of time dependent operations. And for that matter all start ups you know it is not just chemical reactor alone you will find that any start up that you have to deal with you will have to deal with time dependence. And therefore, your mathematics should take into account all the concerns that will that will that will determine the time dependence of your process. Let us let us just take an example to illustrate what I am saying. So, what happens suppose you have a CSTR see you have a reaction taking place a reaction is taking place. Now, I mean this is an example it does not mean that it happens in daily life or in industry, but it is something that helps us to understand how mathematics in help us to get a feel for what happens. And mathematics in help us to tell how we can prevent many of the difficulties we might typically face if you do not formulate your problem in mathematical terms. For example, this is an instance of a stirred tank it is called CSTR. Now, we start the CSTR with an initial condition C a i this is the initial condition C a i equal to some value I will call this C a i equal to some value C a naught. Now, you will realize by formulating the mathematics that if you choose the C a i appropriately carefully then the start up the start up time. What is meant by start up time the time that is required for the process to reach steady state start up time is the time that is required time required to reach steady state reach steady state. Now, if this time required to reach steady state is very large you see then clearly you see you are not the process is not doing anything useful for you and then whatever you produce is unsatisfactory it has to be recycled anyway. So, it is a cost that you are earnestly incurring. So, if you can keep this time very small it is very advantages and your mathematics will tell you how to do it. So, these are the advantages of being able to formulate your problem mathematically because lot of the answers that you would learn through experimental through trial and error it will come to you without having to go through those trial and error and save time save cost plus huge insight into what is going on in the process. You see that is something that gives you a great confidence of how to deal with otherwise difficult situations. This confidence is what makes it important in running processes designing processes managing crisis managing safety issues and so on. So, this is the important part that we will try to illustrate through an example to say how start up and how the initial state that you can choose. So, that we can keep the start up time as small as possible. Now, what we have tried to do in the in these lectures of 7, 8 lectures is to set up the basic basic foundations of for dealing with chemical reactions and then setting up the equation that are required to explain what is going on. See we have so far talked about situations where the system has been assumed to be at constant temperature. That means you are really not accounted for effects of temperature in the process. Now, I mean I am sure you all recognize this that a chemical reaction typically releases heat or requires heat. So, adding heat or removing heat are two important situations that we all have to account for. So, adding and removing heat is crucial to managing chemical reaction. I am just give a small example. I mean it is not that you know about. Suppose, you are looking at a power plant in which you are burning coal to make steam as an example. I mean coal combustion is a very well studied chemical reaction releases a huge amount of energy which we use to make steam and then the steam is used for turning turbines and making electricity and so on. Now, the important thing is that the rate at which the coal is burning and the rate at which the steam water the going through the tube is able to pick up that heat and then convert it into steam you have to match the two connect. So, the rate of combustion must be equal to the rate of the rate of production of steam. So, that design these are the kinds of design features that we have to look into when we are looking at chemical reactions. So, energy balance. So, what we are saying now is that energy balance energy balance is crucial for reactor design crucial to reactor design which means we must take into account whatever energy is going into the process. So, the energy is coming out of the process and the energy that we are putting into the process might be in the form of internal energy. Well, energy that is coming out of the process might be in the form of sensible heat. So, we have to see how the energy of internal energy or enthalpy as we call say is actually used in the process and therefore, we have to see how heat is generated because of chemical reaction. How heat coming out of the chemical reaction can be appropriately channeled into the process and so on. So, energy balance is crucial to understanding how reactions will take place. So, our reactor design actually requires not just understanding of material balances of which we have talked about so far, but requires an understanding of how material and energy balance are connected are related. So, we have to write the energy balance and see how material balance is energy balance are related and deal with both material and energy balance together in the design of reactors involving heat effects. These are instances where there are huge chemical energy that is released because of reactions or required to conduct the reaction. In both cases we have to transfer heat through an appropriate device in the reaction equipment. So, energy balance is crucial to our process. Now, energy balance can be in stirred vessels. Now, stirred vessels we pointed out we had a stirred vessel like this and we said we have a coil into which putting a cooling or a heating fluid. Now, this coil instead of putting a coil we might put a jacket. Let us see that is also as good as through which you can circulate a fluid and then take out the fluid. So, there could be various ways by which we can put energy in and take energy out and, but important point is that your equation your mathematical description must appropriately account for energy going in. So, that we energy going in in which form it is going in then typically goes in the form of enthalpy energy that comes out may be of the form of sensible heat and so on. So, we have to appropriately take that into account. So, that if there is huge amount of heat release appropriately it can be removed through a devices that we can design and incorporate into the system. So, energy balance stirred vessels energy balance for plug flow vessels. So, let us just appreciate how when there is a stirred vessel the removal of energy is relatively simple. Because of the fact that it is stirred and therefore, heat transfer coefficients are quite satisfactory we are able to remove the heat or add heat more effectively. When it is a plug flow vessel in the sense that we have a vessel like this when the flow inside is a gas or a liquid they have to be removed only through an external heat exchange. And here the situations are far more involved and the designs have to be proper and in more importantly our equations must adequately represent how these exchanges occur and what are the heat transfer coefficients involved and so on which we will take into account when we write our energy balance. We will explain more of the things as we go along. Thank you.