 Welcome to the lecture 4 and today we will continue our discussion on how to determine the corrosion rate of a metal. So, to say what are the governing equations that can be used to compute the corrosion rate. Before we proceed on this a brief recapitulation of what we discussed in the previous class will be in order and towards the you know the end of the class we saw that how to predict if a metal will undergo corrosion in a given environment that we saw that right. And we also saw that if the metal is under equilibrium it is not going to corrode it will corrode only when it is deviating from the equilibrium condition. Suppose I immerse let us say iron in hydrochloric acid you know what are the reactions right. The corrosion will occur by the oxidation of iron into a ferrous chloride and the H plus ions in the solution will get reduced to hydrogen gas evolution. These two equations you know one is an oxidation other is a reduction process. So, before we looking at the the governing equation for the oxidation of the iron and the oxidation of a iron or similar metals and the reduction of the reducing species like H flyers or metal ions anything can happen we were trying to discuss what an electrochemical equilibrium is. If you recollect we we said that if I am going to construct an electrochemical equilibrium let us say if I am going to dip zinc zinc in zinc ions. We said that there is going to be an equilibrium between the zinc ions in the solution and the metal that is immersed in the solution right. So, you define this equilibrium as zinc 2 plus plus 2 electrons gives you zinc here. You define this equilibrium by one parameter all of you know what are the parameters which is E. E depends on what? E depends upon the activity of zinc ions in the solution. You can determine using Reynolds equation. What is more happening here? What is happening here is constantly zinc ions or getting formed in the solution by oxidation that these zinc ions will again go back and get deposited on to the metal surface. And we saw this is under equilibrium condition for simplicity we consider that the zinc ions are in the standard state right. Then what happens to E? E equals to E naught right and this is going to be equal to minus 0.763 volts in the standard state you know this. Now, we also said that the rate of zinc going as zinc 2 plus plus 2 electron is is equal to zinc 2 plus plus 2 electron to zinc right which I would say ok. This is the rate of this reaction this is the oxidation and this is going to be the reduction reaction. So, we say that rate of oxidation is equal to rate of reduction right and you can convert this into current right. How do you convert into current? Any of you can recollect r equals to i upon n f and right. Since the rate of forward equal to the rate of backward or whatever and this current is termed as termed as exchange current density. We saw this in the previous class. What are the unit of current density? Amperes per unit area right ok. So, that you know that. Let me go further into this ok. Let me represent this graphically right. I am going to make little more simpler. I am please look at I am plotting current density versus the potentials. It is relatively positive this is relatively negative here. Why? This equilibrium it has got two characters. One is a potential defined, second I define by the current density am I right. Now, for a standard state the potential is minus 0.76. So, this probably let us say it is coming somewhere here it is minus 0.763 volt right this axis now right. It also has a current density am I right or not. So, forward reaction and backward reaction they go equally. So, can I represent in the diagram? So, I represent in the diagram somewhere here. What is this current called? This current density is equal to I naught current density between z 2 plus and that here. Is correct or not? I am going to now disturb this equilibrium. I disturb this equilibrium now. Let us look at the equilibrium again. What is the potential of this? The potential of this measured is equal to 0.763 volt with respect to standard hydrogen electrode. Now, what I am going to do? I am writing this equilibrium here again z 10 2 plus plus 2 electron gives you z 10 is equal to minus 0.763 volt. I am going to take the case 1. I am going to make this potential here minus 0.863 volt. I am going to make this potential minus 0.863 volt. How do I make it? I to make it I need one more electrode here and I need DC sold right. I just make like that. Now, what will happen? This is now made negative by using another electrode. If you make it negative what will happen? The electrons will start flowing towards this. Will the electrons flowing through this? So, make a negative electrons flow through this yes. You can change the potential. But the equilibrium will remain the same that will be a new equilibrium potential right. Assume that the concentration of the electrolyte zinc ion from 1 molar it has become that is a 10 power minus 2 molar right. You calculate the potential. What is the potential called? Still it is called equilibrium potential right. Is it correct or not? And you use the Nernst equation ok. So, even there the metal is in equilibrium with zinc ion, but at a different potential isn't it? Rate of forward reaction equal rate of backward reaction. The exchange condensate may not be the same isn't it? The rate of reaction depends upon the activity of the species. So, the exchange condensate may not be the same, but even at lower concentration when you change the potential right. In fact, you do not change the potential. The potential automatically get adjusted that is a new equilibrium potential. I put other way around for simplicity. I take a beaker, I take zinc ions of 1 molar concentration, I put zinc there, I measure the potential using a standard hydrogen electrode is minus 0.63 volt. I pour some water into that ok. So, what will happen now? The concentration of zinc ions will decrease. It will establish a new potential. Zinc ions still will have an equilibrium with the zinc metal. The new potential is different. You can calculate using the Nernst equation. That is not a deviation from equilibrium. It is a new equilibrium not same equilibrium. Am I right or not? This is it is different ok, but it is also an equilibrium potential. So, standard that is why I said what is the difference between a equilibrium potential and a standard potential? Standard potential is a special case of equilibrium potential in standard state. It is not different at all. We are in equilibrium condition. That is why I always say that when you are predicting corrosion you please do a simple calculation of equilibrium potential using Nernst equation. Please do not go into short catch right. Then use that to determine whether corrosion occurs or not. Otherwise you jump in conclusion that minus 0.6 it has become minus 0.7. So, metal is going to corrode. This is not going to corrode at all ok. That is saying you should understand. Equilibrium potential is independent of the concentration of ions independent of even the activity of metal metal on the metal. Because the pure metal we consider the activity of zinc is or metal is unity ok. So, I think it is a good point that you rise that you should understand that. So, let us put the comeback to this. I apply a potential here minus what happens? Now what will happen now? Please look at this reaction. If you do this what will happen? Zinc 2 plus plus 2 electron this becomes faster. And what will happen to this? Zinc going as zinc 2 plus plus 2 electron becomes slower. Agreed? Agreed or not agreed? Let us look at this one right. Let us look at this equation right. If I provide more electrons what will happen to this reaction? The forward reaction will be increasing. The backward reaction will be simple you know some normal chemistry concepts nothing is different right. So, by doing this that means, now the net current is going to flow am I right or not? So, if I am going to have an ammeter here, if I am going to have an ammeter here I can measure the current when the current is going to flow. On this surface earlier rate of oxidation equal to at a reduction here rate of reduction is more. So, there is going to be net flow of electron in this direction like this it goes like that only. So, the ammeter will start showing some values. So, there is going to be net current in. Do you agree or not? No, I think some of you have a problem ok. So, the current is going to increase. So, I am going to move from that to this. So, this value the current is now is increasing now. Agreed? Now I am going to make it even more negative what will happen? I make it let us say minus 0.963 what will happen? The forward reaction will be faster the reverse reaction becomes slower. So, the current will start increasing like that agreed. So, you find that we are going to follow like this. It is a good question I come to the later actually ok. It is a good very important question is a straight line is a slope is fixed variations right. It is a straight line or not? Of course, I put a log scale here I come back to that answer it is a good answer I mean it is a good question right. So, you will also ask a question why not the slope is like this ok. They are right I am going to answer all this because it is a mathematical equation we are going to derive from this ok. So, it happens like that. Now, on the other hand I am going to now apply now I am going to apply now what I am going to do? Now, second I am going to apply let us say minus 0.663 volt please see here I am applying minus 0.63 volt I am not applying plus 0.63 ok. Now, what will happen now? Now, this reaction will start moving faster this becomes so, that means, now I am going to get current given by this by increased voltage further, further you follow or not. Please do not worry right now why I am writing like that, but at least conceptually you agree that when I move the potential relatively positive, annular reaction occurs, relatively negative cathode reaction occurs that is what I want. Do not worry about this slope and all these things all I want to say that ok that ok that how things will be changing. Now, I am going to write this here as zinc going as zinc 2 plus plus 2 electrons represent this and this is what is zinc 2 plus plus 2 electron gives as zinc here. Conceptually understand right, I have some value of potential I move relatively positive that means, I am going to remove electrons from the matrix at this right, is not it? When I am going to make it minus 0.63 what does it mean? I mean the electrons are going to leave out of the system right, because it is moving out system that means, there is going to be oxidation. When I make it relatively negative the electrons will move in there is going to be reduction process. So, depending upon that the things are start moving up and down like this. Please understand this is if you understand this you understood corrosion full you will have no problems in anywhere in understanding the electro chemical corrosion process at all. This is basic thing please see here why I am saying it is important. I have started with the potential of minus 0.763 I moved to a value which is let us say let us say I have moved to a value I give some value let us say minus 0.560 ok. I moved to a value here let us say minus 0.9638 I am just giving some arbitrary value do not worry about it ok. At 0.63 I am sorry 0.763 no oxidation no reduction because same I move up this oxidation please look at the sign here. The sign is negative here the sign is negative here I can have a sign negative and I can still have oxidation you can still have reduction. So, you do not have to change the sign in order to call it an oxidation reaction reduction reaction otherwise the old convention European convention used to say e is negative its reduction e is positive oxidation incorrect. I can have ok a negative things here and still I can have oxidation I can have a negative over here and still I can have reduction. If I put a equilibrium potential there is no oxidation no reduction takes place. So, it is positive negative has no meaning at all in this case. To illustrate further if I take copper suppose I take copper what will be the value here what will be the value here for a copper plus 0.337. 337 right if I move out move sorry if you move up it is positive slightly moved down it is still positive I can have oxidation and I can have reduction. This is a important thing do not get carried away with the sign and tell there is oxidation there is reduction process no that is totally incorrect to attribute the sign for oxidation and reduction process. e is independent of convention it is value that you determine from the from the equation that you get from here and please notice we said last time it is measurable just not only calculable I can measure it. Only thing is I had to measure with respect to a another reference electrode that is all ok. You understood this actually any of you have any questions here please yeah. Whole changing current does equilibrium stabilize again? No that we call steady state. What is the difference between a steady state and the equilibrium? Steady state means there will be a drift slowly and then it becomes constant. So, when you when you change the potential I understand the reaction rate will not jump immediately it will take some time but at some time it is just a value a steady state value. Yeah when you say equilibrium no oxidation no reduction steady state no it can be oxidation some reduction but does not change with respect to time steady state means it is not changing with respect to time. So, do not confuse between equilibrium state and the steady state they are totally different at all ok they are not the same. Let us continue this this is a important one you should continue will we continue this spending some time on this ok. Now, come back to this this discussion now. What happen if we consider tangent or unsteady state? See I will tell you right now we do not bother because now we are trying to tan walk run then we going to take up walk ok. People do calculate transients when you do research for examples these transients have meaning at all actually ok that probably we have time we talk about it. Transients do have meaning they are used in understanding the electrochemical interface but right now we are not going to talk about transients. We are talking about steady state because that is only a state where I can define very well right you cannot define about it right. Otherwise transients have a meaning you do it electrochemical, ember, spetoscopy all this we do that where the transients are being used ok. Right now we will not talk about that particular one. Let us let us talk about the difference between chemical reaction and electrochemical reaction. What are the difference between these two? Metallurgy should tell chemistry I should tell everybody should tell everybody right ok. Let me give a lead rate of chemical reaction ok. What are the factors that affect the rate of the chemical reaction concentration temperature pressure ok. Pressurize I can talk about temperature pressure order of reaction. So, the rate of the chemical reaction is a function of what function of concentration temperature pressure rate equation right is what happens right the rate equation is what you get to use this right. Let us look at rate of electrochemical reaction. What is this function of what can somebody guess now we are reasonably now we have seen depends on what. So, it depends upon the concentration, temperature, pressure and what and I can alter the rate of reaction by altering the potential. So, when you are talking about reaction kinetics rate of corrosion for example, we talk about what is the concentration of species or the temperatures or the pressure you are going to add one more dimension what is that potential is going to be there. And potential and current are interrelated we have seen in the previous in the previous thing right I will I show you here please the potential and current are interrelated. I have not completed the story here, but I just wanted to tell you that rate of reaction depends upon potential and current are interrelated to each other ok. You talked about what happened to the change of concentration that will change. So, that is the difference between a chemical reaction and electrochemical reaction. Let us look at other things what difference between these two we have. Suppose I have hydrogen and oxygen I put them together do you think water will form very easily? I put take oxygen I put some combination of it will be explosion, but otherwise you just take hydrogen and oxygen put in a cylinder. The free energy change is negative that is why we have water right otherwise water will not be will not be there. So, the free energy change for hydrogen combining with water I am sorry hydrogen combining with oxygen given as to water is negative right, but put oxygen hydrogen together and it does not form water easily. People can ask questions differently. You heard the concept called activation energy right there is activation energy barrier unless you cross activation energy barrier you cannot. So, how do you cross the activation energy barrier in chemical reaction to raise the temperature? So, temperature is the catalyst kind of thing right or we add a catalyst and do that. So, in the case of in the case of chemical reaction ok we use temperature as a factor to control in electrochemical reaction we use potential to work on the barrier corrosion does not occur just like that. You apply more potential then only corrosion occurs otherwise the free energy change is negative only it does not happen. So, we need to understand what is an equivalent of of activation energy barrier in electrochemical reaction ok. So, I am going to now talk about what they are ok. So, let us go into that concept of what it is. Now, we all know this is I I call it as a how do you use the term G? E is a potential right I use the term G maybe you know in the distance A turning into B there is a barrier for that and B coming to A you have bigger barrier for that. So, this is all you guys know about it right. In electrochemical reaction also there is a barrier ok. What is happening in electrochemical reaction? There is a zinc here goes in the solution as zinc 2 plus ions it cannot simply come out it is a lattice it has to break the bond right. So, there is a barrier of activation from this to come over here it is not exactly correct ok. So, there is a barrier it has to overcome unless you have this barrier to overcome the lattice zinc will not come to solution ok. And for that to overcome we use what is called as the potentials. I come back to this concept here ok. Let us see what it is E versus log I this is true for most of the electrochemical reaction B to H plus H zinc zinc plus copper 2 plus copper whatever and this is your oxidation and this is then and what is this? This is your I naught what is this? This is your am I right. Now, please notice give let us say let us say the reaction is let us say the reaction I give in here I just change the reaction here what is you can use any reaction you want right I use this if this is the equilibrium. What is the reaction here can tell me yeah quick what reaction for this is the equilibrium that I am representing what is the reaction here hydrogen evolution reaction I wanted to speak what is this one? This is hydrogen oxidation reaction. Now, if I have to increase the rate of reaction suppose you know rate of you know suppose I want to increase rate of reaction to this I need to move the potential to this point to this point am I right I have to move this potential here. So, what is the equilibrium state? I call it is a 00 you want it ok if the standard state you call it 00. Now, please look at I moved from this one to this one in order that the reaction takes place of my own rate I wanted you want to increase it I move further I move further and you further I want oxidize it I move up move up move up ok. Please look at as I move down down like that what happens the reaction becomes either oxidation or become reduction and the electrode is now set as the electrode is polarized. What is polarization? Yeah net now earlier it was just it is not any character at all it is simply both are forward same now it is polarized if I what means if I move down it becomes a cathode so move up it becomes a anode so it is now polarized. So, that means the electrode is now polarized ok. So, and this is called as polarization a deviation from the equilibrium condition is called as polarization that is polarization means that means, you want to say the concept polarization means deviation from the equilibrium is called as polarization anybody has a problem ok. Let me move further into this diagram the concept now let move further into this. Let us draw this diagram fresh again ok. I move to this value and this is called as eta ok ok. So, eta eta is a wall potential right is a term is called a wall potential and what is this one which is called as E applied and what is this potential called it is E equilibrium potentials ok. So, eta is equal to E applied minus E equilibrium please remember this equation if you or confuse this equation you will have a problem ok. Let me see here now for a anodic reaction when anodic what will be eta will be positive or negative positive right great cathodic because this is the cathodic side this is your anodic this is the cathodic. Now you will ask question you have been asking question before what is this? This is a slope I call them as beta a is a slope I call them as beta c. So, beta c is a cathodic slope, but I am going to use cathodic please use the term daffyl slope a equal to anodic. If you use I use the t h capital here the name of the person right he you found this relationship in the year 1905 you got this relationship actually we did an experiment ok. We did an experiment we got this similar trend we measured the slope that time we called a slope to recognize this contribution we call that we call that slope as the daffyl slopes. So, the daffyl slope now defines the rate at which the reaction occurs am I right or not ok the slope is equally important right. Now you can now use this we have also derived equation eta anodic equals to plus beta a log of the mouth I upon I naught beta cathodic minus beta c log I upon I naught c you guys are all now good in mathematics right you should be able to see how this can be derived. It is a simple linear equation right nothing more right because you know this is your I naught right the daffyl slope you know that right. Now this is the the difference that you have here. So, you define this with eta. So, I at any given eta I at any given eta can be given by I naught if I know the daffyl slope this these are called as daffyl equations because see here beta is what beta is a negative slope right that is why they put here ok slope is negative. So, you have minus beta and log now what is beta can I take it out what is beta beta is equal to 2.303 hot T by alpha what is alpha coefficient also called as symmetry generally normally alpha is equal to 0.5 I will spend a minute on this ok. Just take this not a good diagram ok, but I just made it ok. This energy right versus the reaction coordinate right it is called reaction coordinator distance reaction co-ordinate. This is let us say this is let us say zinc 2 zinc here ok zinc zinc I say zinc 2 plus please look at this one. If the guy has to move from zinc has to move from here to this see I am describing this I am describing this like this right what is this 2 plus this guy goes back and forth like that right zinc has to move from here to this is much easier it is because the slope is less, but for zinc 2 plus to come up here it is going to be more difficult that means, what is here alpha is given as this is let us say this is y. Now, alpha alpha for what alpha for zinc to go as zinc 2 plus given as dx divided by x plus y for zinc to gamma what happens? For zinc to come out this is similarly let us say some other alpha for zinc 2 plus moved towards zinc it is going to be 1 it is going to be y upon and you guys would have seen it before ok. That means, this is much easier now alpha is alpha is smaller here right alpha is smaller this is going to be here. So, r I would say this is equal to 1 minus alpha can I say this? If this is alpha this is equal to 1 minus alpha you can able to get this alpha plus 1 minus alpha is equal to 1 ok it is going to be there this is you guys should have studied in many chemical equations and all actually. So, alpha and is what this really means please notice please notice very clearly here ok ok. If alpha is going to be small beta is yeah if alpha is going to be small it is going to be it is larger here ok. So, it relate this to much more easier in this case actually ok. Can I move or you have any questions in this case ok? Is beta a characteristics property? It is ok. Let us look at what is alpha? Alpha depends upon the hill that moves here beta is equal to 2.303 RT by alpha n F. What is n? The number of electrons involved 2, 3 whatever F is a Faraday is a temperature or is a gas constant. So, beta is a characteristic property. And what is that? Yeah i not of the characteristic property right because the guy going to move right alpha means the guy goes you know left and right right. So, i not is characteristic of a given system ok it is very important. In fact, you will see later i not is going to decide what is the rate of corrosion more or less if i not is small corrosion rate is small if i not is more corrosion rate is going to be more we will see later ok. Right now I want you to get a clarity in terms of the electrochemical equations that is dictating the kinetics of that actually ok. That is that is what you should be knowing ok. So, this is so far we we understood ok excuse me the equations. Now, can somebody somebody you know able to tell what are we have discussed so far you know what is what is what is the what you understood actually what are you understood in the discussion we had so far. See in order that in electrochemical reaction to occur either oxidation or reduction there has to be in over voltage over potentials you have to deviate from the equilibrium potentials and that is also called as a polarization. If we increase the over voltage if we increase the eta what will happen to rate of reaction will automatically increase. If you look at the tabular equation there ok if you visualize more i is going to be more beta is less i is going to be less. So, higher the eta higher is the polarization the higher is going to be the rate of reaction taking place. So, this is the most important aspect of the the electrochemical reaction electrochemical kinetics ok and you have any questions so far we can we can clarify this and then move further no questions. When concentration is changed then equilibrium potential also changes. So, does i naught changes with changing concentration of ion corresponding to new equilibrium potential? You need to have yeah you need to have these values either you should theoretically calculate or you should experimentally measure the i naught values they are required very much the same that equilibrium potential change with change in concentration the i naught also will change. Because let us look at this now see the chemical reaction the electrochemical reaction there are lot of commonalities that you have. Suppose go back to this suppose if this are going back and forth right how do you determine the rate of this reaction r equal to k into concentration it is a first order reaction all right. If r is changing I mean it has to change if the k is changing and c is changing if r is changing then i is going to change. So, the exchange condensate will change automatically, but only thing it will happen is the exchange condensate for a forward reaction is equal to backward reaction that is not going to change. The difference between i and i naught is i naught there is no net oxidation reduction, but when it is i it is either oxidation or reduction process yeah i naught will change if you change the concentration of if you change even temperatures things will change ok. So, but all it means it is an equilibrium and no oxidation no reduction takes place ok. So, I am not going to details actually some of you are more interested please go through the book Bacchris and Reddy modern electrochemistry all these are given in details, but since it is not electrochemistry course I am not talking. So, I am discussing electrochemistry to the extent that you can understand corrosion better that is no way a comprehensive treatment of electrochemistry ok it is not at all ok. But those who are interested please read that book or you can read the book Buckanan right that is also a good book I referred in the in the beginning of my my first class and I said what are the books I am referring you can refer that book as well. But Bacchris and Reddy I would call it it is like a Bible or Giza whatever we can call it ok the ultimate in terms of in my view in understanding clarifying your concepts or you can also read by Baud Baud is another you know big guy in the field of electrochemistry ok. Now, so let us now look at these things and now what I am going to look at here is now what ok. So, what you should know? You should know one the equilibrium potential calculations you should know what is over voltage you should know that is E voltage. Now, you should know how eta is related to we have not done much so far we are just only you know made only three concepts clear to us actually how fully they are clear. Actually there is one more if you are really more keen I will write the equation here and those of you you want to understand better. A better equation to represent this electrochemical kinetics is I is equal to I naught exponential 1 minus alpha eta n F r t minus exponential minus beta sorry minus minus alpha eta n F i. What is this? Please look at I what is I here I is the net current density ok and this corresponds to I anodic current it corresponds to I cathodic. That means, I is given as I anodic always minus I cathodic. These are the equations we have and this is called as Butcher-Walmer equation and I am not going to discuss this in details, but those of you who are interested can read the book and understand it or if time permits we will discuss this during the somewhere in the middle of the course we will discuss this ok. Let me just before I proceed let me just clarify this. So, you should be in a position to calculate the current density right. Can you can you solve the numericals if I give some values based on the Caplet equations would you be able to do that ok. So, you will have some numericals to to understand these concepts ok and probably by the coming week we will give you these numericals actually. Let us go to the electrochemical reaction more in details. Let me take this steel say in sea water steel in sea water. What is the corrosion? Now, you will have iron going as Fe 2 plus now we also have oxygen water is it clear is it is it right. You guys are aware of this equation that is right pictorially here the sea water it has some oxygen there dissolved oxygen somewhere all the places iron corrodes the electrons are liberated here. What is the cathodic reaction? This is the cathodic reaction this is cathodic anodic reaction. The anodic reaction occurred the cathodic reaction to occur the oxygen has to migrate from here to this place right or not. Similarly, the iron has to migrate from here outside has to migrate from here you cannot just accumulate it there. So, what are the reaction here? What are the process involved here? The process involved here are at the interface there is charge transfer. What does it charge transfer? Iron becomes Fe 2 plus strips the two electrons out the oxygen moves here and change the electrons it becomes ways minus. So, charge transfer occurs at the interface, but for that to occur you have to have the migration of this. So, to put it simply some pieces ok maybe it is a a negative a negative charge or a positive charge to move here what happens then what happens here? Charge transfer and this charge transfer you have seen the relationship now what is the relationship here? It is the capital relationship what you have seen before is a charge transfer is a relationship and what is this? This is your diffusion control. So, the over voltage we talked about so far it is eta a and eta c they are all called as charge transfer over voltage they are called as charge transfer over voltage ok. They are called as charge transfer over voltage or over potential what are we going to call it? That is the potential required for metal to get oxidized or reduced what happens? Now, we have one more thing so, we need to know how these are happening at all. If you do this then you have a complete understanding of electrochemical corrosion process right. You already seen how the relation between the potential and current exists at the interface. Now, we also know that if the ions have to take charge they have to move from the bulk the interface. So, we need to know the governing equation for that. So, what is the governing equation for that? Ok. So, that you can completely define any electrochemical corrosion reaction understood ok. So, we are going to look at this now and see how we can understand that yeah. What about the cemented present in the steel? Oh ok I am well it is a good question ok. Right now we are not talking in terms of microscopic processes on the surface we are looking at a macroscopic. I gave steel as an example here. So, that you get an idea about how the steel corrode in the sea water ok. You can take an iron you want ok. You can take nickel you want actually ok. The idea of giving here is that the oxen you know I gave oxen here. I did not put sulphuric acid. I have given you a problem I think I have not given it. I think T s have not given the A to H to be ok. So, the difference between an acid the sea water containing or exposed to air is that the solubility of oxen here is what is about 6 ppm to 7 ppm maybe 8 ppm something like that. So, they are not going to be easily available on the surface. They have to migrate from here. The corrosion now depends upon what? Depends on not this. It depends upon how quickly the oxygen molecule migrate to the interface. If they do not migrate then the reaction will not occur. These equations have no use. So, I am talking in reference to why you should care this one. Please look at this. This is in series. Please look at this in series right. This move like this. If this is faster and this is slower the rate determining reaction is going to be this. Right. If this is the slowest the fastest this is not going to control this is going to control. I mean I do not know I am jumping at all ok. This should be easier for you. This is a series process right. If assume that transport is much slower I apply more over voltage right. I apply more over voltage. Just go to this just go to this reaction ok. I apply more over voltage the current is increasing right increasing. But, current will increase only when if the species are available for reaction. If they are not available what happens? You only increase the voltage nothing happens right. So, this current will increase only when your species to accept the electron or release electron if they are not there. So, that means, you have a transport process and then it is getting accepted here right. So, it is a coupled reaction. The transport is an integral part of electrochemical process for any chemical process is also you know there is a transport happening at all. So, I did not use sulfuric acid because sulfuric acid the concentration of H plus ions are a huge H plus move very fast you never have diffusion control process. But, oxygen is less soluble and so, in this case the transport becomes very important. We will see this later when you talk about corrosion of steel in sea water how important these equations are. These equations are very important when you talk about corrosion of steel in sea water corrosion of stainless steel in sea water they are very important. Why? Because that is governed by this transfer process that is why we are now trying to understand the equation governing the transport of ions in the solution at all ok. Am I making this point clear to you ok. So, we look at this now transport there are two laws governing a transport what are the laws? I am talking diffusion. What are the governing laws of diffusion? Fick's law you cannot forget that there are the great guys. So, there are Fick's law the one is called Fick's first law second is the Fick's second law. What is the difference between a first law and second law? First law is steady state and second law is a non steady state. So, we are not getting into non steady state is very complex ok. So, they are useful we are going to do research electro chemically you solve that also, but I am not going to use this in the class. So, the so, the diffusion processes starts with the Fick's law you cannot start from that. What is the Fick's law it says? Fick's law says j is equals to minus d dc upon dx. What is j is a it is a flux the reaction rate is given in terms of moles per centimeter square area per second am I right? Reaction rate all of you guys may be knowing. What is d diffusivity? What unit of this linked to square load by time? What is dc concentration difference? dx is what is the between two points right ok between the two points where the diffusion occurs. Let us define the electro chemical system. Now, you have the bulk a concentration ok and what is this concentration here? It is a surface concentration right. This is a bulk concentration surface and assume that the diffusion distance is assume this is your x for example. What do you have here? Now, can you convert flux into current? What is the unit of flux? Moles centimeter per second. How do you convert this? No j is equal to j multiplied by anywhere can you not? Is it right or not? So, what happens? i is equal to minus d dc upon dx difficult equation or easy equation. See if you know the number of moles can you not convert that into see there is a number of moles per centimeter square per second is a rate no it is a rate right it is a rate of reaction. So, you how do you convert that into current? Is the equation correct or incorrect? So, you can somebody point out. Correct. How do you get this? Please look at your notes ok see that is why you see we are now making a slow progress ok and they are not difficult. But if you are not you know following up completely you might find it very difficult to understand what it is it is simply very simple equations only ok. So, it is possible for us to relate the flux to this. So, you we will find out what is called as as the governing equation for what is called as a diffusion process. And how the diffusion is related to the current see what is for example, I take s plus ion I start moving from here to this what does it mean? Is it only mass is moving or something else is moving? Charge moving when charge is moving what does it mean? Current is moving right try to try to understand they are not total molecules right. So, if these ions are moving they carrying the charges and so the current is going to flow accordingly depends upon what direction the ions are moving and which ions are moving positive and negative right. So, the flux is related to current ok. So, far flux was related to what in terms of moles and all this now we are going to relate the flux to current. Why I am interested? Because I need to know what is the diffusion rate of oxygen to find out the corrosion rate otherwise I do not know ok. How do I calculate this? So, I need so I am really worried or I am bothered I would say that I need to know what happens to the corrosion of steel in water having 5 ppm oxygen there or 100 ppm for example, if the diffusion coefficient of species changes what happens? Corrosion rate is going to change. So, what is the basic equation for that? So, these are the basic equations ok. So, when I say I can calculate corrosion rate I can able to calculate corrosion rate by knowing all this they are not difficult I think you guys have done it in earlier subject at all actually ok. So, please brush up your things when you come back and we will see this in the in the next class ok. Please understand we are now slowly complicating the subject. Why? I talked about so far zinc oxidation, zinc reduction by one one Tafel equation you have two Tafel equations right. In the actual corrosion process what is happening? Zinc is getting oxidized, H plus is getting reduced. So, there are going to be four Tafel governing equations am I right or not? So, please understand ok. They are very simple, but there are two equilibria we are talking about in corrosion one is zinc is in equilibrium with zinc ions, H plus is in equilibrium with the H. So, we talk about only one equilibrium of zinc having two Tafel equations. Now, there I am going to talk about four Tafel relationships because one equilibrium for H plus H, other one for zinc and zinc plus. So, solving that equation becomes more difficult unless you understand it ok. Please do understand it ok. Get that things clear to your mind it is not difficult again I repeat, but please look at the equation and then try to understand what these equations are actually ok. So, I mean like solving any mathematical problem, but you should know the physics behind these governing equations at all ok. So, please come prepared for the next class. Next class I can assure you it is going to be more complex more complex and more more complex ok, but they have a very common simpler understanding of the auto chemical concepts that I can say ok. So, that is not difficult ok. So, please come prepared for the next class I will I will really appreciate that. So, we will close today's discussion just introducing the relation between diffusion and the current ok. Thank you.