 Today, we will continue our discussion on electrochemical kinetics. Yesterday we looked at two concepts ok. What are the concepts? One concept was on the exchange current density right. This talks about the equilibrium condition at which the rate of the forward reaction equal to rate of the backward reaction and the potential exhibited by the electrochemical system we define as the equilibrium potentials ok. At this case you have a potential called as the equilibrium potentials. Now, we look at the deviation from the equilibrium. Say any any equilibria that you can take, you can take as let us say the oxidant combines with electrons and giving rise to R. So, in equilibrium here they establish an equilibrium potential, they establish next in condensity. When you apply a voltage a potential on the surface what happens either there is an oxidation or there is going to be a reduction. They said by what? Whether you will undergo oxidation or reduction depend on what? What is that parameter called? That is called as over voltage and we defined what the over voltage means is equal to R is equal to E applied minus E equilibrium condition. And when eta is is going to be equal to negative you get a cathodic reaction and eta is going to be positive then you get an anodic reaction. This reaction rates are given by what law? What is the law called? The reaction rates or the current that relates the over voltage is going to be what equation? The Tafel equation right. The Tafel talks about ok equation which relates eta is equal to plus R minus beta log I upon I naught. You saw that right. So, this is a general equation for anodic and cathodic one and eta would would change whether there is a cathodic reaction or anodic reaction. And what is happening here? What is happening here? What is happening? The electrons are getting transferred to the oxidized species and gets reduced or R gets oxidized to an oxidized species it releases electrons right. So, it is called as this voltage is called as charge transfer voltage. You saw that in the last class ok. So, it is essentially where does the charge get in transferred? The charge is getting transferred at the interface. It is this interface ok you have an oxidant and reductant or under equilibrium conditions right. So, they are at this place the charge is getting transferred ok either ok is this oxidized species ok. And you have electrons here or the oxidized species will come over here and accept the electrons and give rise to reducing species. And the kinetics of that is given by the Tafel kinetics. We also saw one more that the electrochemical reaction if it has to occur at the interface ok if it has to occur at the interface the species let us say a positive species it has to get transported to the interface and accept the electrons. And this is what you have you call this as what it is called as mass transport. So, it has to be transported from the bulk to the interface. It has to go from the bulk to the interface. So, that is a step right. We discussed this in the last class ok. What is the governing equation for that? If it is total diffusion it is not convection what is the equation? It is the fixed law we we discussed that j is equal to minus d d c upon d x we saw this d equal to diffusive d r diffusion coefficient. And the change in concentration over a distance d x ok that is what we saw in the last class. Now, let us define this more in details right. If I have an electrode to start with the electrolyte we saw the electrolytes let us say this is the distance right this is the distance right. Now, at this stage it is under equilibrium condition the oxide species reduce species whatever that you talk about they are under equilibrium condition they are under equilibrium condition. The composition of these species let us take let us take only the oxide species here let us take only the species oxide species. The concentration of the oxide species at the bulk here at the interface will be same right. When there is no reaction taking place the concentration of the species at the bulk under the surface this is the surface C s ok species right. Now, at time t equal to 0 what happens now? The concentration of the oxide species at the surface is equal to the concentration of the oxide species at the bulk understood now. Now, what is happening now? As the reaction suppose I apply a voltage suppose I apply a over voltage here ok apply negative voltage. Suppose, eta is made as negative what happens now? What will happen? See that oxide species will get reduced and form this reaction occurs. So, what will happen to concentration of the species that interface? What will happen to that? Decreases right. So, it decreases the concentration of the oxide species at the interface decreases with respect to time ok. So, if I plot again distance versus now I am plotting now the concentration concentration as I plot it now at time t equal to 0 the concentration right. Now, as the reaction proceeds what happens? The concentration would would drop and then it might drop further and it could reach a steady state am I right. At some time it reaches steady state and there is going to the diffusion between this point and this is what? And this is called as delta or called as diffusion length is it not? The diffusion is only between these two beyond this point the concentration is equal. So, nothing happens and as you move from here there is a concentration gradient. This is your concentration of the oxidant at the bulk and what is this? And this is the concentration of the oxidants at the surface. So, what do you write the equation ok? Equation J becomes minus D concentration upon delta am I right and concentration of oxidants at the bulk minus concentration of oxidants at the surface or I think I just write here J is equal to minus D C of the oxidants at the bulk minus C of the oxidants at the surface by delta yeah ok. Now, this you are right ok I can change this into this point you are right. Earlier I just made that as equilibrium now reaction is now turning into this. If I keep increasing the over voltage here assume that I increase the over voltage what is going to happen? This reaction rate is faster is it not? Now, what will happen to the concentration here? What will happen to concentration of the surface? Reduces. Reduces right and and at one point for a given over voltage C S oxidants tends to become 0. Can you say that? Yeah. Now, J what happens? Then J becomes the J max. You cannot go beyond that can you go beyond this? Why? Now, the J is equal to what is equal to minus D C bulk upon that is your J max cannot go beyond this ok. Let us extend this argument. Now, J max I rewrite again here minus D C oxidant the bulk by delta. So, you know the relationship between I and J right what is the relationship between that? So, this can be equal to I Y N F is equal to minus D C sin upon I now I called as I L here I L here equal to minus D C oxidant by delta N the I L is called as limiting current density. So, what does really mean here? What does really mean? You cannot have a current exceeding the I L whatever be the watt voltage I can keep increasing the voltage as you wish will the current increase beyond that? It would not increase at all. So, it would not go beyond that values and that limits current the system can take beyond which it cannot really do that. So, if I if if ok if the system is system is totally diffusion controlled controlled then you can draw a plot you have and this current density is called as I L. So, can you now look at the equation given above here and tell me what limits the I L a diffusion length then. Excuse me. Where does temperature coming here? Yeah. So, it is influenced by the D value. The D will change if the temperature is changing ok. So, that means, that is taken care of in the D value. So, if D can change the limiting current density can change. What more? Yeah. Link earlier you told right above concentration. So, the concentration of species decide this one. Why I am interested in this? I will before I go I will just try to clarify why we should be worried about. Let us take the case of iron in water containing oxygen there. Now, this is the what is the reaction here? So, you can balance this equation later ok. You can balance this equation and see what it can happen right. So, balance this equation in terms of oxygen there you know see for example. So, you get this reaction right. Now, the corrosion rate of this will depend upon what? Depend upon how much the oxygen go and accept the electrons. Iron is ready to corrode, but what is not possible? The oxygen is not available to take the electrons by the process. Now, in this case the corrosion rate of this depends on what depends upon the diffusivity of oxygen, the bulk concentration of oxygen in the water. So, it is not just only iron that is corroding which is responsible the species which are in the solution is also responsible. Now, I give another example. Suppose I use here let us say another species a zinc suppose. Suppose I have zinc and allow it to corrode in water assume that in both the cases the concentration of of oxygen is same, diffusivity of oxygen is same, the number of electrons are same. So, what will happen to corrosion rate of zinc? If you compare the corrosion rate of zinc and iron what do you think? Can you extrapolate? See zinc if you look at the EMF series what is the equilibrium what is the standard potential of iron? E naught is equal to minus 0.44 volt. What about this minus 0.763 volt. Now, which one you suppose corrode more? Zinc is suppose corrode more. Now, look at the equation now which will corrode more? If oxygen is limiting the diffusion of corrosion. So, what will happen to the corrosion of iron and zinc? Will it be different? I want answer from you the same right. So, even though the thermodynamic tendency for corrosion of zinc and iron are different. The zinc is suppose corrode faster compared to iron. In this case both might corrode at the same rate might corrode at the same rate because it is controlled by the diffusion of oxygen in the system. So, that is why you are concerned with this actually no idea is it not? So, zinc only corrodes and give acid to electrons iron also corrodes and gives to electron, but these two electrons have to be accepted right by what? By oxygen there, but oxygen is not willing to accept because it is not available on the the surface. So, irrespective of the ability of the metal to give electrons the rate is now controlled. Now, it is controlled what is called? It is called diffusion controlled reaction the diffusion controlled corrosion process. So, that is why we are interested in understanding these kinetics ok understood? Not understood. Let me just go to the next question. Just go to next question now. The next question is there is a steel pipeline steel pipeline that is what it is through which the water is moving. The same water is there in a tank this is steel again where will the corrosion rate be more yeah. Pipe flowing. Why? Velocity increases. So, when velocity increases what happens? Delta decreases. Delta decreases right, the delta decreases. When the delta decreases the surface concentration increases. So, you can use the equation now you can say that I L is equal to minus D the oxidant the bulk upon D delta of course, you have N cap ok. This oxidant you can replace anything you can also put reductant also I mean this is ok I mean anything that you want you can write it ok. So, when you increase the velocity when the velocity is increased what will happen to I L you get this. So, it is I L 0 I L 1 it is I L 2. So, the rate of corrosion of this is going to be more. An example also there is a ship in the sea it is at the harbor the ship is sailing will the ship hull undergo same corrosion rate or different corrosion rate yeah. The water answer different where the corrosion rate will be more? Yes. Is sailing will be more because the sea the corrosion rate is dictated by reduction of oxygen in water. In another case I take a tank I have water this is now fully aerated fully aerated now right it is water. So, what will happen to corrosion rate of the steel tank here compared to the previous ones yeah it will increase the corrosion rate increases. So, in the case you know you see lot of pipelines carrying several products maybe crude oil or a refinery products, but as some water it has an oxygen there the corrosion rate will change the velocity has an effect. The velocity has velocity has another effect we see later ok. Right now the role of velocity seen here is in terms of mass transport not more than that ok. So, that is why this particular equation becomes very important. Now, let us take the case slightly different case where the reaction partly diffusion control you can say it is a mixed control. If I draw a diagram an advanced diagram you have equilibrium potentials this is what this is activation control and this is diffusion control and between these two mixed control. Let us take the case of diffusion control eta diffusion is given as 2.303 by nf logarithm of 1 minus i upon il. So, we can derive this equation and we do not have time to do this ok. You can start from the fixed law and and derive this conveniently. And for the mixed control eta total this is is equal to eta charge transfer plus eta diffusion ok. So, for a cathodic reaction for a cathodic reaction eta total is equal to what minus beta log i upon i naught plus 2.303 by nf logarithm of 1 minus i upon. So, this equation describes completely this curve ok is this decide by this particular equation. What about the anodic reaction? Will there be diffusion control? Do you think so? What do you think? I want a firm answer. It would not be why? Yeah for the corrosion process you have infinite amount of iron present on the surface. No matter what amount of reducing species travel they travel from the bulk to this. When they travel the metal is there on the surface it can give you infinite amount of electrons. So, it is not generally a diffusion control process. There is no transport involved there. There is also one case where there is called passivity. We will talk about over there we talk about somewhat similar to diffusion control. Otherwise anodic reaction is generally not considered as diffusion control. We talk about corrosion not in all I do not talk about all electrochemical reactions no. I think that is not correct to say that any electrochemical reaction anodic reaction will not be diffusion controlled. No it is not correct. We are talking about in relation to the corrosion process because the metal that is supposed to get oxidized the concentration of the surface is quite quite large you have infinite atoms you have actually ok. So, this now we come to the end of the discussion on the electrochemistry of what we know need to know about electrochemistry we are now come to almost we have completed. I do not say we have gone much deeper, but what is required we have seen. So, if you summarize what we have seen we have seen was giving a criteria for corrosion using electrochemical potential we started before electrochemical potential equilibrium potential is one criteria. Second we talked about the reaction kinetics in terms of what in terms of the Tafel relationship where when the reaction occurs the charge is transferred across the metal solution interface and we also saw that if there is a migration of the species from the bulk to the interface for corrosion what kind of governing equations are available that also you have seen. So, from electrochemistry point of view whatever you have seen so far are adequate enough to understand the corrosion process. We have not of course, answered how do I calculate corrosion rate that you have not done it. We have only seen the governing equations how do I compute corrosion rates without doing experiments that was our original question I think we moved towards that particular one in the subsequent lecture ok. Now, the question is can we compute corrosion rates of a metal what is the question and that is answered by the concept called mixed potential theory. To understand the mixed potential theory let us take a corrosion reaction I involve some metal M I am going to expose it to an acid what does acid consist of H plus and it leads to what is called as M N plus plus N by 2 hydrogen right. Can I say this? So, you have a corrosion process wherein the metal is getting oxidized to M N plus the hydrogen ions are getting reduced to hydrogen gas or molecules. Why I called mixed potentials? Because of the fact you start with 2 equilibria here M you have H plus plus electron gives you hydrogen. The two different equilibria that we have and this has one equilibrium potential I term it as M N plus M I write like this is subscript of that and for this E is equal to what is you have H plus plus hydrogen. Please look at there are two independent equilibria are there on the metal surface. Why they are independent? Because it also has its own exchange current density I naught of M N plus M you also have I naught of H plus H on M. Please look at it is on M particular metal actually you know this on this metal is happening. So, this is all we know about it. Now, what is happening? For a moment you think that there is one equilibria here N plus and M this is another equilibria here H and this one taking place. At two different sites you have two independent equilibria taking place and this has one potential and one exchange current density this is got one potential and one exchange current density am I right? Correct or not? So, they are two independent equilibria existing on the surface. So, what happens? Assume that this potential is assume that this potential is let us say minus 0.56 volt for some reason you assume that. Assume that it is 0 0, metal is a conductor right. Will this potential here and here remain the same? Will the potential remain same? They are shorted right. So, what will happen is because they are shorted the potential will start dropping towards this and this will start moving towards this and you will achieve a potential somewhere in between that is called as the mixed potentials. So, the mixed potential lies in the electro chemistry and people have been talking about mixed potentials even around about 1900, but it was the Wagner and Trott I think somewhere 1938 I think I am not mistaken ok. The year they formalized a mixed potential theory ok and it is also called as Wagner Trott mixed potential theory. How do you solve this problem? You have one potential which is different, another potential is different you have different exchange condensities when you when metal is conducting you are not going to retain all of them intact. Each equilibria will get disturbed by other the other equilibria right. So, what is the basis? The basis to look forward is the following. The mixed potential theory will say that any electrochemical reaction can be partial reactions to be split to two or more partial reactions first one. The second there is no net accumulation of charges these are the the criteria of the mixed potential theory. Let us try to illustrate this. Corrosion of the metal right again you say this M sulfuric acid gives you M sulfate is hydrogen is a corrosion reaction all right. I can split it into two partial reactions can I? Isn't it? What are the two reactions? M going as M plus plus two electrons and H plus converting into hydrogen they are two partial reactions. I can make one more if you want how I can make it one more? For example, assume that the sulfuric acid is exposed to air what happens in that case you are going to have one more cathodic reaction going to be there. So, I can have at least two because there has to be one oxidation one reduction it can be more. But what is important? The important is this there is no net accumulation of charges it is only states the law of conservation of charges ok. The two the point two is what? Point two is point two is law of conservation of am I right? What does it mean? What is the meaning of this? You extend this in corrosion or any endochemical process always always rate of oxidation is equal to rate of reduction this is a very important thing. The second point is very very important point. What happens if one is more? Assume that I am immersing iron in the solution right this is iron piece I am immersing iron in the solution and assume that iron corrodes at a higher rate corrodes like that. So, what will happen? It it corrodes at a higher rate than the reduction process. So, what will happen to the surface? Yeah what will happen? Can be precise what will happen? Be precise exact What what charge? Positive charge or native charge? Yeah you say that no. So, it it will have more electrons on the surface. Then subsequent iron cannot leave it will come back to the surface. If you say other way around the rate of reduction is is faster than the rate of oxidation the surface will be more positive then the reducing species cannot work together. So, the rate of oxidation is equal to rate of reduction that is the key in all your kinetic calculations ok. Now, use this now let us try to understand the corrosion of metals. Let us continue with this example of let us say some metal metal M in an acid how do I start with? I start with identifying the equilibrium ok. What will be the equilibrium here? M is in equilibrium with M N plus 1 equilibrium. What is the second equilibrium? Second is H plus is in equilibrium with the H. Then what do I identify here? I identify here the equilibrium potential for that E and identify I naught for the for for the for the M plus I am going to divide this here ok and I am going to identify E for this I naught for that. Then I identify beta A beta C identify beta A beta C. I suppose these are known to you already right how how we later. So, I have I can look at the tuple here I can look at the tuple here I will identify both of them. Now, I am going to represent this into current versus log plot ok. Now, let us identify just first take this one ok. Let us take this case I have identified assume that is in the standard state let us take in the standard state now. So, E equal to E naught suppose you take this. So, I have somewhere 0 0 this I can identify what I naught I identify something somewhere here. This is in equilibrium for this and I can also draw a tuple lines you can draw. So, H giving as H plus is to electrons electrons here like this and hydrogen is accepting electrons and giving rise to hydrogen gas. I can do similar thing for the metal right. Here I identify this is the potential and this is a naught. Now, can you understand this these lines now? Let us take the case of hydrogen ok. When I apply a a potential above the equilibrium potential you are going to get an oxidation reaction. The current follows the potential in this manner it has got its own tuple slope. On the other hand I reduce it the H plus ions get reduced and form forms hydrogen gas. The same is true for metals right. If I apply a relatively please look at a relatively positive potential it moves up. When I say relative positive potential this is positive for this, but this potential is is negative for this please you should not get confused right. And I apply a relatively a negative potential starts moving down that is what will happen ok. You have a a metal here equilibrium assume that a hydrogen equilibrium here what will happen now? As the potential starts you know drifting what will happen now? This potential starts moving towards this this starts moving towards this and the rate of the reaction is given by these these these kinetics. But only one point in the whole diagram which satisfies the mixed potential theory tell me what is that point? Intersection. Yeah. Intersection. Intersection what intersection this intersection? No. This no if this intersection satisfies the point right. So, that is the place it satisfies and so, you have this we call them as Icar called as Icar nowhere else it will satisfy the mixed potential theory. When I say nowhere else I am talking about nowhere else of the corroding metal we are not talking about you know otherwise even this is also in equilibrium condition equilibrium condition ok. Now, look at this now the potential lies somewhere between this point and this point in this point and this point lies here. Dictated by what? Dictated by by the table of slope of this the X-ray in current density the equilibrium potentials. Similarly, the the table of slope of this line beta c and and you have beta a. Please understand beta c of the cathodic reaction and beta a of the anodic reactions are important beta a of the other equilibria and beta c of other equilibria are not important. These are no consequence there are no consequence only these two are important. So, when you solving the problem you must know which one to use. Now, you guys are all good in mathematics is it possible to compute without doing experiment this value? Is it possible to compute I car is it possible to compute E car given this given these values can you ok at least graphically you can do right. If you can do graphically then you can do mathematically all you need to know is a two simultaneous equation to solve two variables. How many variables are here? E car and I car there are only two variables. So, I need two simultaneous equations and to solve the two variables it is a simple mathematics it is nothing more nothing less ok, but what is required is understand the concept here ok. If you do not understand the concept you look at only as mathematics as you will have problems either ok. So, look at what it really means is. So, beta a of corroding metal beta c of the cathodic reaction we are important for the tapered slopes point of view the equilibrium potentials both cases are very relevant and also the x-ray incandescent cities are also very relevant for that. Now, if you know this then it becomes easier for you to compute the corrosion rate of metals here anybody has any question let us try to sort that out ok because you are going to now make it more and more complex ok. Is it clear to you people? Anybody who has any difficulty here? Looking at this we talked about the the driving force for corrosion the tendency for corrosion rate we said earlier it depends upon E cell right E cell equal equals to E cathode minus E anode. So, if you consider the metal which is more having a more negative equilibrium potential you expect what happens? Can you visualize this? I am I am I am dropping a metal in acid and another metal the difference between these two are one has got relatively lower equilibrium potential when I say lower it means I mean use sign also right more negative one is relatively positive which one do you expect to corrode more in sulfuric acid relative more negative right, but it is not necessarily ok. Why? Look at this diagram the diagram will tell you why it is not necessary at all right. Of course, that is important why what are the factors involved here? The exchange condensity for example, if some metal has got very low exchange condensity some has got high exchange condensity the corrosion rate will change. Can it? Can you not? And a different tuffle slope can also change the corrosion rate. So, that is the reason why the metals behave differently. I am not going to give an answer here you can if you want you can refer the the Fontana book is given there. I just want to give two examples of iron in sulfuric acid the zinc in sulfuric acid. So, you would expect zinc to corrode more and iron to corrode less, but it is not going to happen you will find zinc will corrode less the iron will corrode more. The reason being what? The reason being is the exchange condensity of H plus H on zinc and the exchange condensity of H plus H on iron. You you guys have this handout with you you guys have the handout you know you see the table there has in the table. So, if you look at this table you will see that the exchange condensity for hydrogen equilibria of various metals are vastly different. For example, if you look at aluminum the exchange condensity is what is 10 power minus 10 amperes per centimeter square. You would take platinum what is the value yeah 10 power minus 3 platinum has minus 3 amperes centimeter square ok. So, you look at this you will see that the the the exchange condensity vastly varies between metal to metal you know nickel is minus 6 10 power minus 6 amperes centimeter square and that of iron is 10 power minus 6 what is not given here is zinc. Zinc is is is about you can assume that zinc is equal to 10 power minus 9 amperes per centimeter square this is 10 power minus 6 ampere per centimeter square ok. If you have this and and so you would expect that zinc will corrode less as compared to iron. So, this calculation that you can do that is not so difficult if you you know and that is what the truth is ok. The iron will corrode less and zinc will corrode I am sorry iron will corrode more and zinc will corrode less. This has an indirect relevance to metal finishing. How many of you know of electro galvanizing? You know what is galvanizing? You apply a zinc coating on steel you can do hard dip galvanizing you take it and in a molten zinc and dip it. Electro galvanizing you make the steel and make it as a cathode you have a zinc bath zinc solution maybe zinc chloride zinc sulfate whatever you apply a cathodic current zinc will deposit. It is very easy to deposit zinc, but not easy to deposit iron because on iron you will have more hydrogen evolving and zinc the amount of hydrogen evolution is going to be very less. So, it is very easy to have electro galvanizing of zinc, but it is not easy to deposit iron in the electrolytic baths. So, technologically it is important and this concept is useful to say that you can deposit zinc and unfortunately you cannot deposit iron even though it is more noble as compared to zinc actually ok. So, this is something that you should you should understand and we can stop our discussion today here and we will take it more complex things in the in the in the next class ok. And any any questions people have? Why does X n's current density vary with different metal with different environment? Yeah, you are perfect all right you know X n's current density very much depends upon the solution I told you other day because it is the thing that happens with the interface. Now, there are so many factors are affected by this. For example, I take platinum, I take nickel, I take say iron, I immerse in same sulfuric acid let us say. Why would each of them have different X n current density? So, this is a very interesting question I I think you guys are not asked at all. The X n current density is what is the ability of the metal to give electron and and take back the electron am I right? That depends upon the work function. Some metal can give electrons much easier, some of them cannot give electrons much easier. So, it is mostly it depends upon the work function and that is the reason why some metals have high X n current density some of them do not. That is the reason why people use platinum as a catalyst right it is much easier for the platinum platinum brodeum all these are catalyst they can exchange this much easier actually ok. Because there is not part of a corrosion though, but that is the reason why the X n current density vastly differs between these metals. But they have implications from the corrosion point of view and we will see this when you talk about galvanic corrosion how with X n current density affect the galvanic corrosion of metals you know differently ok. So, that I think we will see later any other question ok. So, then I think we will end the lecture today.