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    Hello everyone, let’s start lecture 4.And the topic it is continuation of what we have been discussing for the last 3 lectures.So, it is activation polarization and concentration polarization and now wewill try to get into mixed potential theory we have already talked little bit at the endof lecture 3 mixed potential theory. So, we saw we wanted to explain dissolution of zincin acid medium which is HCl at some pH and you could see that the overall reaction wouldbe zinc plus HCl zinc chloride plus H2.So, this is the overall reaction and we are trying to explain zinc dissolution or corrosionin HCl which is pure and deaerated means no dissolve oxygen. Now you could also see thatthe anodic process is and cathodic process is, so this anodic, thisis cathodic. Hence these are electrochemical reactions and we could also see the separatelyif we consider a zinc plate dipped in zinc containing solution we will have a situationlike this situation will get.This is ia, this is ic and in this way neeta a and this direction neeta c and this pointcorresponds to i zero of zinc or I can just go down little bit which is i zero zinc onzinc surface and this corresponds to E equilibrium or E zinc plus plus zinc. Now this value woulddepend on what is the concentration of zinc ion in that electrolyte. Similarly, for thisreaction we can also have similar type of polarization where this is log i and if Isee the 2 segments.This segment corresponds to ia which corresponds to this reaction which is nothing but H minuse equal to H plus and this part is nothing but H2. So, this is anodic process, this iscathodic process because both these processes I can have anodic as well as cathodic. So,I can here also I will have E equilibrium and now here E equilibrium which is nothingbut E H plus H2 E zero H plus H2 this is we are considering reduction potential plus RT2F because here we are considering 2 electrons, this is 2 electrons.So, now ln activity of H plus because there are 2 H plus ion and partial pressure of hydrogensorry this there should be nothing like this. And if I take 25 degree Celsius temperature1 atmosphere pressure, so then this value is zero and this becomes 59 by 2 into 2 logH plus. Because if it is 1 atmosphere, this is one atmosphere then this becomes minus0.059 log of H plus and it can be written as pH. Since we know pH equal to minus logof H plus ion concentration.So, now these value will be decided by the pH of that HCl medium. So this is equilibriumvalue and this point is nothing but i zero of hydrogen on zinc surface. Because thisparticular electrode will be constituted like this you have HCl medium and you have a zincplate. So, this is zinc now you have hydrogen gas which is flowing in and this is at 1 atmospherepressure this is HCl. So, and we are maintaining H plus ion concentration if it is 1 then thepH will be zero.And that time E zero would be E equilibrium would be E zero H2 which is nothing but zero.But if this H plus ion concentration has got some other value other than 1 then it canhave equilibrium potential value related to this equation which is E 2H plus H2. Fine.And since it is happening on the zinc surface we are taking a zinc electrode, so then thathydrogen evolution exchange current density we have to write in the with respect electrodethat is what this subscript we are taking zinc in the bracket it form zinc.Now these 2 situation can have if we have a separate process like zinc dipped in zinccontaining solution and if I consider a hydrogen electrode like this.But once we combine them. Okay. So once we have a situation like in an HCl solution witha pH let’s say 1 there if I put zinc pure zinc then we will have this reaction this2 reaction will start happening. Depending on the concentration of zinc in the when thedouble layer forms on the zinc surface that means on the zinc surface we will have a doublelayer which is here it will have zinc ion and this is zinc.So, we will have a double layer and that double layer formation we will have IHP, OHP andthen it can also have E equilibrium which is nothing but E zinc plus plus zinc dependingon the concentration of zinc plus plus ion in the vicinity of that zinc plate. Similarly,the hydrogen will start bubbling on this particular surface it will also form double layer andthen that will also decide it’s equilibrium potential depending on the pH value.See if we combine in a plot these 2 plots we are now combining assuming that the zincion concentration we are taking whatever zinc ion concentration will experience here. So,that time here we will have E zinc plus plus zinc and here we will have E hydrogen H2.These 2 levels will have. Since we already know that E zero zinc plus plus zinc equalto minus 0.76 around 761 volt or I can write volt and E zero H plus H2 equal to zero volt.So, that means in the potential access with reference to the hydrogen standard hydrogenelectrode this SHE is nothing but standard electrode SHE. Fine. So, with reference tothat these value will be on top of this value, if we consider in the standard state of that2 partial or the half cell but since it is not a standard condition we have some pH 1.So, in this case the potential will not be same as this or potential would be minus 0.059PH is nothing but 0.059 volt.And in this case we are not maintaining zinc ion concentration to be 1 rather it is muchlower than that. So, these potential value will further go down in this case, so E equilibriumwhich is nothing but E zinc plus plus zinc would be less than E zero zinc plus plus zinc.Because zinc ion concentration in the actual system is lower than the unit activity orunit concentration. Now that case of course that level would be like this but of coursehere the value would be decided by what is the concentration that zinc metal is facingin front of it.Now it will have its own polarization individually we will have polarization like this, thisvalue is i zero zinc on zinc surface and similarly I can havei zero hydrogen on zinc surface. So, this line is nothing but 2H plus plus 2 equal toH2, this line is 2H minus 2e equal to 2H plus, this is zinc minus 2e equal to zinc plus plus,this is zinc plus plus plus 2e equals to zinc. So, this is corresponding to ic of zinc correspondenceto ia of zinc, this is corresponding to ic of hydrogen, this is corresponding to ia ofhydrogen, fine.So, these are the current densities we could see, now whenever we have a system, 2 systemworking in tandem particular system like this we have to make use of mixed potential theory.We have already explained mixed potential theory at the end of third lecture sayingthat there could be number of cathodic and anodic reactions and at the same time thesystem will try to find the mixed potential where the net current density correspondingto cathodic current.And the net current density corresponding to anodic current these 2 will be similar.So, we will find E mix where I will have summation of ic equal to summation of ia and of courseI am taking mod. Since we have considered ic to be the negative current it is the directionnot the value magnitude wise it is height is having a finite magnitude but the directionis opposite to the current ia and remember this ia is nothing but the current in theouter circuit and the ic is the current corresponding to electron flow.Now let us just analyze this for example if we have a cell like this, this is let us saycopper sulphate solution this is zinc sulphate solution. And let us say concentration ofcopper ion is equal to 1 and here zinc ion concentration equal to1 and then if we haveas copper rod and if we have zinc rod in those solution. If we allow them to stabilize wewill develop some potential here, we will develop some potential here.Now if we connect with salt bridge this is saltbridge and now if we connect them with conductor we will see if we put an ammeter here willsee that the current is flowing this way. This is the system current and the electronflows this way, so now the electron flow corresponds to ic and the current flow corresponds toia. So, now we could see that the current in the external circuit or the conductor itflows from positive terminal to the negative terminal.And in the solution it is basically from negative to positive terminal but the system currentis opposite to the electron flow and the electron flow direction nothing but the ic that isthe concept. Now we have to find out here we could see that there are 2 reactions 1cathodic and 1 anodic now it has to reach a situation a potential which will be betweenthese 2 potential and at that potential we could see that the net current density forthe cathodic process.And the net current density for the anodic process will be similar and I could see thatsituation is arriving when they are approaching and intersecting at this point. And here Icould see that these ic, ic hydrogen equal to ia zinc and this potential correspondsto E mix and that is the whole concept of mixed potential theory. Fine. So, this isthe potential the system will achieve. Now coming to some salient features in this diagram.So, this is of course log i scale because these 2 plots are done on thus basis of logi. So, this is also log i, log i cell this is potential axis, now if we consider thispoint, this point and this point, 3 points they are having some unique features. If Iconsider let us say I am giving some name let us say S, T, U. now if I go to if I talkabout S and U there the potential which is nothing but the non-corroding systemor non-corroding situation.And I achieve i zero in case of S it is nothing but hydrogen on zincsurface and in case of U it is i zero zinc on zinc surface this is U. And interestinglyat this 2 points I could achieve steady state and forward and backward reactions are equallythe rate of forward and backward reaction at this 2 points are same. And in this caseis basically this 2 reactions and in this case this 2 reaction they are happening atthe similar rate.Now coming back to this point this is an interesting point, this point you see that the ic andia both are same. Here also you see ic and ia are same here also ic and ia are same thispoint these 2 values are same here also these 2 values are same at this point. But theyare corresponding to the same species zinc, zinc plus plus and here it is H plus H2. Nowbut in this case though it is ia equal to ic but they are of different species. In 1case it is zinc and here it is hydrogen.So, though here you somebody can say that these are 2 rates are similar because i isnothing but the rate of the process that means rate of the cathodic reaction is similar tothe rate of anodic process. Here also the rate of cathodic reaction and rate of anodicreaction both are same but in this case there are different species then that means we cannotsay that this point is an equilibrium position.But we can say that the rate at which zinc dissolution is taking place is steady, thatmeans it is happening at the same potential all throughout of course it is a open systemthat means hydrogen is continuously going out and that is what the reaction is continuouslytaking place at that particular rate. So, this condition it is though we can say thatthe rate is fixed but it is not equilibrium but here the rate is fixed but it is equilibrium.Now coming to further just to add it to this particular thing, so here I can say this isnothing but i corr of zinc. Why? This is ia, is nothing but the dissolution of zinc inthe form of zinc ion, so that is what it becomes the corrosion current density of zinc in HClof pH 1. So, this is the connection between activation polarization and mixed potentialtheory because both the cases we are actually expressing all the lines this line, this line,this line all 4 lines we are expressing with a general expression beta log of i plus someconstant C.So, this is nothing but tafel equation and the tafel equation is valid in the case ofactivation polarization. Fine. So, this is the connection between activation polarizationand mixed potential theory for a simple system. Now there will be one more important aspectof polarization which is called concentration polarization. Fine.So, let us look into this part, now when we consider activation polarization. We haveconsidered this is IHP, OHP. We have considered atomic jump from one into another this isM n plus M and if ia is more than that. So, this will be the distribution of energy freeenergies, so this becomes my over voltage and if it is A, B, C so AB by AC equal toalpha which is symmetry factor. So, that means this particular case and in this case ia greaterthan ic for the dotted case.And this is the corresponding situation for i zero equal to ic equal to ia. Now in thiscase if I look at it is basically the thermal activator jump process and it happens at asmaller current density level. And the basic assumption is when these happens the concentrationat this particular end does not change. So, if the concentration here is C zero in thebeginning, so the C zero concentration remains there, okay, with the polarization.But if we go to higher and higher current density that means if we switch to higherand higher level of polarization then I would have a different situation. Okay. So, noweven if it is for ia and ic for if I do it for ic greater than ia, so that case the plotwill be like this. Fine. This is the green colour for situation ic greater than ia, okay.So, if we go to a higher polarization, so that is over voltage becomes very high thoughsituations C zero at OHP will change.And that lead to another kind of polarization we call it concentration polarization. Fine.So, let us stop here we will continue our discussion on concentration polarization andit is relation it is interaction with the mixed potential theory. Thank you.