 Yeah. Yeah. Okay. So next we'll see a thermodynamics of reduction process. Okay. Overall, what are the processes we have? How do we, you know, what are the processes involved in the reduction that we discussed? So next we are going to see thermodynamics involved in the reduction processes. So heading you write down thermodynamics of dynamics of reduction process. It is only we have Ellingham diagram. Ellingham diagram will discuss what it is, but you need to just understand like two, three information that we can extract from Ellingham diagram. Okay. It is basically the plot of or the graph of right on the heading Ellingham diagram. It is basically the graph or plot of delta G naught, delta G naught and temperature graph of delta G naught and temperature delta G naught versus temperature. And in this what happens, the reaction we are considering is the formation of oxide, formation of oxide of various elements. And these diagrams, these diagrams can be used to predict, can be used to predict the feasibility of the feasibility of the thermal reduction of an ore, the thermal reaction right down, thermal reaction of an ore. Like if you have any reaction, suppose M solid we have, it combines with oxygen, basically it is a formation of oxide. So we can also do this for halides and sulphides, Ellingham diagram we can draw. In the slavers and mostly that they ask is for oxides. So we are discussing oxides only. M plus O2 gives a MxO to, I'll write down here, 2x this side. So you see here what happens. This oxygen is a gas. It is converting into solid. So since we have the reaction of the graph of delta G naught and temperature, correct. So could you tell me in this reaction, what could be the change in entropy, delta S naught greater than 0, less than 0 or 0? Less than 0. So delta S since gas will have more entropy than solid, gas is converting into solid. So we say that delta S entropy change is negative, which means if delta S is less than 0, which means delta G naught becomes less negative. Yes or no? Because delta G naught is equals to delta H naught minus T delta S naught. So delta G naught becomes less negative here. So it increases with temperature, correct. This means as temperature increases, as temperature increases, delta G naught increases. That's the one first thing that we have. So we need to understand the relation of delta G naught and temperature only. So do we have anything about entropy then? Enthalpy whatever it is, see. Enthalpy whatever it is, delta G naught delta H naught minus T delta S naught, right. So if this is negative, so overall delta G will increase only. Enthalpy change is there, but that is not a major effect here. This becomes positive, delta G is increasing. Next one more line you add over here, next line. The free energy change that occurs when one gram molecule of a common reactant the free energy change that occurs when one gram molecule of a common reactant which is oxygen here because we are talking about oxides, correct. So common reactant in bracket right on oxygen, the free energy change that occurred when one gram molecule of a common reactant oxygen is plotted against, wait a second, one gram molecule oxygen is plotted graphically against temperature, then this graph is known as Ellingham diagram, correct. So delta G naught for one gram of substance plotted against temperature. So the graph is called Ellingham diagram, okay. We can do this for halides as well as sulphides, okay. But there we have the reaction of sulphur and halogens here, but in the syllabus we have for oxides only, correct. We have also seen delta G naught increases and increases in temperature, that's one thing. Now if you look at the graph, I'll show you the Ellingham diagram here. Yes, I have. So this is the Ellingham diagram we have, you see. It is given in NCRT also, you can open up and see. It's fine visible, all of you? Yes, sir. So this is the graph we have. You see it is zero degree Celsius and then delta G naught is increasing, negative, the value is increasing, correct. Here temperature is increasing. You see for all the reactions MgO, Mg plus O2 we have positive slope and then there's a sharp change in the slope. We have this also slope increases, slope increases, slope increases. For this carbon the slope is decreasing, okay. So mostly for all the reaction you see, the slope increase, we have positive slope, right. With the graph going up with increase in temperature, delta G naught value is increasing and at some point we have a sharp change in the slope here. This is what the observation we have, right. So when you calculate delta G for all these reactions at different different temperature, this is the plot we get. So but why does it increase sharply for some, not at all increase and decrease also for some? Yes, yes, one second. We'll discuss. Sure, sir. Write down the, this you don't have to draw. If you want you can roughly you can just draw, okay, but it is given in the, roughly you just draw because when you refer your notes it should be there, okay. So roughly you draw for a few reactions, like carbon reaction you must draw, okay. Magnesium you must draw, okay. We have somewhere HG also, HG, carbon, magnesium you must draw, CO2 also you draw, correct. Done. Let me know once you're done. Sir, the carbon one is a straight line, horizontal line. Yes, sir. Yes, okay. We have two reactions here. One is it is forming carbon dioxide and other one is forming monoxide. Done. Finish. Okay. So I think you're done. Yeah. Okay. Now you see we will discuss why this sharp change we have over here. Sharp change we observe whenever there is a phase change, okay. Like you see at this temperature why we have this sharp change over here because at around 630 Kelvin this mercury boils, okay. So HG boils at this temperature, HG boils at this temperature. That's why we have a sharp change in this. So wherever we have the sharp change it represents the phase change of the reaction. Magnesium also at certain temperature, which is this here, at this temperature magnesium also boils. Okay. Because continuously we are increasing temperature. So we must have the boiling point of metal, correct. So it will boil at this temperature. So whenever we have the sharp change it represents a phase change of the reaction, correct. Understood this point. Yes, sir. Sharp change is this. Second point you write down which is more important. Metal switch lie above in the allingum diagram. Metal switch lie above in the allingum diagram. Get reduced by, okay, properly write down this, okay. Metal switch lie above in the allingum diagram. Get reduced by the metal, which is below. Get reduced which is below. What do you mean by this particular line? So what I said, metal switch lie above, get reduced with the metal which is below. So magnesium can reduce aluminium, okay. Magnesium can reduce aluminium till the temperature is around 1623 Kelvin, okay, 1623 Kelvin, roughly. Because at this temperature now, beyond this temperature you see the magnesium line is up and aluminium is below this, correct. So reduction of aluminium is done by magnesium when the temperature is below 1623 Kelvin. This is the another information we have. If you talk about this one, silicon and magnesium. So it is possible till 1966 Kelvin, till this point. Till this temperature, magnesium can reduce silicon but beyond this temperature it is opposite. This is the property, like you know, the features of allingum diagram. Whatever graph is there up, like all metals which are placed or the graph which is there below one particular metal. So the upper wall we have the metal, the graph which is above, that metal will get reduced by the metal which is present below in the graph, right. So temperature based reaction it is, right. It's not like it is universe always it happens. It will be there for a certain temperature and then it may get changed. That is the second point over here. Third feature in this write down that we easily see that gives free energy change increases with increase in temperature, increases with increase in temperature. Fourth point, the sharp change, the sharp change in the slope or turn you can also write down the sharp turn in the graph but the sharp change in the slope represents the change in state. The sharp change in slope represents the change in state when the metal melts or vaporizes, melts or vaporizes. Another very important point, you see this line you consider corresponding to delta G is equals to zero, this line, right. You see below this line for all the reaction delta G is what, less than zero, correct. And when delta G is less than zero, it is spontaneous and the oxides are quite stable. Can we say that? Obviously we have certain temperature for all the reaction. You see this graph is also going at some temperature it will cross the line, right. This graph is also going like this at some temperature it will cross the line. So when delta G is less than zero till that temperature, the oxide of a certain metal is said to be stable. But when the delta G becomes positive at any temperature, then the oxide is not a stable and it can easily decompose into its metal. Are you getting it? Right. So this point first you write down below delta G is equals to zero line, below this line where delta G is equals to zero, below this line delta G is equals to zero. The oxides are stable and when delta G becomes positive and when delta G becomes positive, the oxides become unstable and dissociates into metal, dissociates into its metal. Now the last property here why this carbon will have two types of graph, right. We have graph here for carbon. One is we have minimal change or there is no change in delta G when it forms CO2 and then we have this negative slope. The graph goes down like this when it forms carbon monoxide that is CO. So write down to this. Write down the carbon with oxygen. I'll write down next slide. Carbon with oxygen shows two types of reaction. One is when C plus O2 gives CO2, suppose this is a reaction one and the another one C plus half O2 gives CO the reaction two. Correct. Okay. Now if you look at this reaction, we have a carbon solid O2 gas CO2 gas. Okay. Gas, it is CO is also gas, it is solid. So see in the first reaction what happens, right. In first reaction, in first reaction, the volume of CO2 obtained, the volume of CO2 obtained is same as the volume of O2 used in the reaction, volume of O2 used in the reaction. Correct. So you see one mole of this gets consumed and one mole of CO2 forms. So if you look at delta S change in entropy here, it is minimal like almost zero. Correct. Because we have two different gas, we can also delta S is equals to zero but the change is not that great. Okay. Hence what happens, change in delta S is minimum over here. That's why the Gibbs free energy change delta G0 is also minimal. That's why if you go back and see the graph we have here, in the graph, you see the change in delta G is minimal for CO2. You see it is almost a straight line or slightly decreases almost minimal. Yes. So this is for the explanation for the first, you know, a reaction of CO2. Correct. Now what happens in CO when CO forms? You see you can easily understand the number of moles in this reaction, we have this reaction. So half moles of O2 consumes one mole of CO forms. Correct. Or the ratio is like one is to two, one mole of O2, two moles of CO, 10 moles of O2, 20 moles of CO. So one is to two ratio we have. Correct. It means for this reaction what we can say delta S is positive. Right. Delta S is positive. That's why everything is reversed over here. Right. So when delta S positive, delta G becomes more negative as T increases. I don't hear. Delta G becomes, becomes more negative as T increases. And that's why the graph goes like this. Okay. Like this, the obtuse angle slope we have. Correct. One more thing I would, I would like to add here. Okay. So we have T. Here what happens? At this point, we have the two reaction, right? CO and CO2 reaction is this. So this temperature is around, you know, 630 Kelvin is this. So slightly above this, around 700 up to 710 Kelvin. Right. 700, around 700 Kelvin, the reaction gives CO2. We have this reaction because the line is below. Right. So around 700 Kelvin below that, below less than, I'll add on here. If the temperature is less than 700 Kelvin, approximately 10, 15 degree maybe, maybe there, right. Like increase or decrease, 710, 700, no, 15 maybe there. But if temperature is less than 700 Kelvin roughly, correct, then the reaction of carbon and oxygen gives CO2. If the temperature is more than this, then it will give carbon monoxide. That is the information we can extract from Ellingham diagram. The point simple here is what? That it gives the feasibility of the oxide forms of various elements, metals, okay, at different, different temperature. Okay. The sharp change represents the change in phase. That's what we have discussed. The metal which is above in this, you know, diagram will get replaced by the metals which is present below. All these things are temperature dependent process. Okay. Like you see below this temperature, magnesium can reduce aluminium, but above this temperature, aluminium will reduce magnesium. Okay. So the three, four points I have given you, mostly they ask questions on them only theoretical questions. You just need to understand these two, three points. If you keep these two, three points in mind, you can answer all the questions based on Ellingham diagram. Okay. Done. Sir, what is the change of state represent for the carbon monoxide one? Where? Sir, in the, I can't see your question. No, yes, sir, that one. This one, right? So phase change will occur over here. So before that carbon monoxide would be liquid. Yes. And then it converts into gas. So, but isn't it cautious at true temperature itself? Oh, we say that, see, when we write down the reaction of CO plus O2 give CO2, we always write, it's a gaseous form. We don't talk about temperature over here. But actual understanding is this, like based on temperature, because we have some gas, no. So if you have higher temperature, correct. Then the current interaction will be less. Correct. Interaction is less than liquefaction is difficult. Right. So it is possible that we'll have some liquid form because you see temperature is extremely low. You see. Oh, no, not this side. The reaction is possible here. You are increasing the temperature. Correct. So it is possible that at some point it may get spoiled. But usually when we say C plus O2 gives you CO2 gas, we don't talk about reaction temperature over there, no. So the state of the compound or molecule that you are getting, it may depend upon temperature, because we know interaction of molecules, you know, whether it intermolecular force lies in the range of gaseous state, then it will be a gas solid state, then it will be a solid. Correct. So actual understanding will have this over here. So you can say at less temperature, maybe CO2 will be in the liquid form. We have one more thing here that at some times, you know, this will get boils at some temperature metal, you know, melts also. Right. The temperature is below. We are talking about higher temperature over here. So all these represents the phase change. Usually why we are confused over here that whenever we write down the reaction of carbon and oxygen, we don't talk about temperature. We'll say we'll get a gas over here. But yes, temperature is a condition that we need to think of. Okay. Correct. Yes. Yeah. If you want to understand this reaction, you can, why the slope is this, phase change the logic. Correct. If you look at the delta S for this, for this reaction I'm talking about delta S is what? Less than zero, greater than zero. This is gas. Correct. This is also gas. So three moles converts into two. Delta S is decreasing. No. Yes. Property is decreasing. So with increasing temperature, then property will also, the delta G will also, it means normal relation we have, like we had for the gases. Delta G increases. At this point, we'll have a phase change and then a sharp change. Correct. Okay. So we had done all these things. Now we need to see some extraction of some metals. Okay. We have a, I'll show you the flow sheet. Okay. How to go through the process of extraction of like copper and extraction of silver. Obviously we have zinc and other metals also. So all we are not going to do because not that important. Since we have discussed the you know, the basic process, what all the steps we have in extraction of metals, we have seen concentration of different methods into that. Calcination we have seen, roasting we have seen, we have seen the reduction method. So all those methods only we are going to use for any metals. But yes, there may be few changes, few changes, few process will be different here and there, but more or less, we'll have the same thing that we need to do. Okay. That we had discussed already. Few examples we'll discuss, flow sheets we'll discuss for the metals. So first one is extraction of copper right down. Heading right down, extraction of copper. So what you need to memorize here, first of all, that what ore we use for the extraction of any metal. Okay. Since we are discussing copper, so copper calia we use what we use copper pyrite ore. We have many minerals, but the mineral that we use for extraction is the ore and that is copper pyrite. Flow sheet is what? The flow sheet you see. You also copy this down like this only because if you go to write down the theory for each step, it will take a lot of time and not that required. Okay. I suppose if you do for other metals also on your own, write down in this manner only flow sheets. So that once you go through, you will understand it properly and revision will be easier in that way. So we take this ore that is copper pyrite. Okay. Copper pyrite, C-U-F-E-S-2. And what we did? We did the grinding. Okay. Crushing also we call it as. Terms may be different. In English word, you can understand. Grinding, crushing. So crushing and sieved. Sieved, you understand, no? Filtering, right? Like what are the larger impurities we have that you can easily remove? So hand picking is one of the way. Another one is sieving. We can filter it, right? Sieves we can use for that purpose. That's the next one. Crush, small size, sieved. Whatever impurities we can remove, we'll do that. And then we'll move on next. That is the concentration of ore. So here, again you see what we need to do. Concentration of ore, which we also called as dressing. Dressing of ore. Dressing of ore. What method we use? This is important for you to memorize. The method we use is froth flotation process. Now, since we have discussed this in detail, so I'm not going to discuss this again over here. That is why I've discussed in general. What is froth flotation process? That is what we are going to use over here based on obviously the property of metal and impurities. So here we are using froth flotation. Okay. So in froth flotation, you see we add pine oil, right? Why we add pine oil? Why we add pine oil? To generate froth. Yes. So to increase the froth, like to generate large amount of froth you require, right? And one more thing we add into this. That is potassium or sodium zenthate. Correct. So the froth flotation process just go through once. You'll get it. What all things we have over here. So in short, I'll just write down here, not in detail. So we have powdered ore. Correct. See a little bit of understanding you must have, like the way we have discussed the general, you know, process. But eventually you have to mug this up. There's no other way. Right. So powdered ore, H2O, we add pine oil, pine oil to generate a froth and air also will pass through it. It converts into the sulfite ore in the froth, in the, you know, froth, sulfite ore in the froth. Okay. We add pine oil, potassium zenthate, sodium zenthate we can add and we agitate it, mix it properly. The impurities settle down. So in short, step-wise, I'll write down here. So we add pine oil, detail we have discussed. We also add potassium zenthate or sodium zenthate zenthate and the mixture will agitate, right? Or we agitate, you can say, or we can, you know, rotate the what we have there paddle, right? In which there is a blade so that we can mix the entire mixture properly. So we'll agitate it, right? When you agitate it, whatever impurities we have, not all obviously, whatever impurities can settle down, the impurities will settle down and then we can filter out the froth from the top, which contains the mineral, okay, the ore that you have. Correct? Copy this down. Can we, can we move now? Can we go to the next slide? Done all of you? Yeah. So next step is what? After this, we have roasting. We know roasting will done how? In presence of air or in absence of air? In presence of air. So next step is roasting. So roasting what we do into this one, the concentrated ore are strongly heated in presence of air. So what happens in this process? You see, all these, you know, impurities we have, it gets oxidized and removed, SO2 removes, okay. Some impurities are like arsenic present, okay. This also combines with oxygen, forms oxide to AS2O3. It is the volatile oxide. It also will escape, okay. Antimony we have SB plus, we have 302. This also forms 2 SB2O3. All these are volatile oxides, right? So all these escapes into the atmosphere. So we'll choose the process, the steps, the process based on the impurities present so that we can have the maximum advantage of the given process, okay. Since all these are forming volatile oxides can escape into the atmosphere, we'll use this roasting, correct. So copper pyrite that you have, the reaction would be here Cu Fe S2, Cu Fe S2 reacts with oxygen because we are adding oxygen in this reaction, converts into sulphide first. So Cu2S Fe S plus O2 and then further it converts into the oxides. Cu2O, this converts into FeO. Overall, in roasting step, we'll get the oxide of copper here, right? Then the entire mixture here will send this into the blast furnace. Blast furnace is again the machine, the device we use for the process of smelting, okay. Removal of impurities again. So we'll send this into blast furnace. This we haven't done, okay, because it is not required. Like the process is smelting only, but we used to have it in a machine called blast furnace, okay. The device in that device is blast furnace. So we send this into blast furnace for smelting. Smelting in blast furnace, in presence of air. So what happens here? Ion sulphide, you see, FeS plus Cu2O converts into FeO, Cu2S, this is one reaction which happens there. Further, this FeS in presence of oxygen, the reaction is taking place. So it converts into oxide again and SO2 and then this oxide FeO with SiO2, it converts into FeSiO3. What is this SiO2, could you tell me? This is the slag we have. Remember flux, acidic flux? Yes, flux plus impurity, it becomes slag, correct. So first all the impurities will convert into oxide. That oxide combines with acidic flux and it forms slags and then it comes out. So yeah, right, right ranker, correct. So in this process smelting, what happens? We add the roasted ore that we get in this step, okay. The roasting is done, so ore that we get, we call it as roasted ore. So in this roasted ore we mix with, we'll add Coke and silica. Coke or silica you can add, you'll have this reaction, correct. Now, after this we have bessemerization. Bessemerization is nothing but the removal of impurities again, whatever the iron sulphide is left, we need to remove that further. So we'll do bessemerization. For bessemerization also we add silica. Okay, I'll write down next, first you copy this down. The last, second last step is bessemerization. Bessemerization is done in bessemer converter, again the name of the device machine, right, bessemer converter. What we'll do into this? We'll add silica. We'll add silica, okay. So the reaction is FES, whatever iron sulphide is left in the previous step. This get oxidized and convert into oxides, sulphur dioxide forms, then this FEO reacts with SiO2 that we are adding here, converts into FESIO3 which is again a slag will remove it and the copper sulphide that you have, Cu2S, this combines with O2, converts into Cu2O and SO2. Okay, now this you see it goes under auto reduction next. What was auto reduction? This Cu2S sulphide and Cu2O copper. This reacts and it converts into Cu and sulphur dioxide signals, correct? So like this the copper that we get is 98% pure, right? We call it as blister copper, blister copper. Further if you want we can do electro refining also in the next step, electro refining also we can do here, auto reduction also we can do, electro refining also we can do here. So tell me one thing in electro refining because sometimes they ask you what should be the anode here in electro refining? Anode is pure or impure metal? Thin or thick? Anode is thick one. Anode is the thick one and cathode is pure thin. It is impure thick slab, copper slab, right Cu slab. Cathode is pure thin slab, right? It is pure thin Cu electrode. What should be the electrolyte? Electrolyte must contains which ion? Cu2 plus ion that is the only condition. So we can take CuSO4 plus H2SO4 electrolyte, right down there CuSO4 and H2SO4 electrolyte we can do. So this is the extraction of copper we have. So like this for other metals also you can do the same thing you need to understand that what is actually happening. Almost we have done the entire process how to do the extraction of any metal. One more we will discuss extraction of silver. Others you know zinc, ion, for sure you must go through once through NCRT or whatever book you have, correct? So extraction of silver next you write down. This is the smaller one we can finish it in five minutes and we don't have time also after that. So we'll do this. Next write down extraction of copper. 9th December crash course is starting, right? You know that? Got the info? Yes sir. All of you. Ask me all of you. Prepared for it? You can type also. Yes sir. Yes sir. Yes sir. Yes. So yeah. So it will be mostly a problem solving session. Okay. We'll discuss theory also a bit but you need to come prepare because everything we won't be able to discuss, right? So whatever chapter is there given for a date, you need to come prepare, revise your notes, at least solve 10, 15, 20 problems, at least 20 problems you must solve and then come for the class. Then only it will help. Otherwise it will be like you know wasting of time, right? If you have any doubt since you won't be able to ask yours every small, small doubt. No, we'll have a plan of in the entire 11th and 12th grade, right? So we'll do all the chapters mostly, correct? So whatever chapter it is, come prepare for it. All of you. Okay. Extraction of silver. It is done by Sinite process. This also they have asked many times, okay? It is done by Sinite process, correct? This you must remember Sinite process, the name or we use that is urgent type or the formula of urgent type or is ag2s. So we'll take the urgent type or grinding is done. We'll take the fine, you know, powder of it and then we'll allow this to pass. Allow this to go for the concentration of ore and the concentration or dressing of ore is again done here by froth flotation process. The process we are using is froth flotation. So again, pine oil we add, we add, you know, air. So froth carrying sulphide particles, ag2s will be up and below the impurities will happen, okay? And then we have a step over here. We call it a Sinidation. This step is based on the property of metal impurity. We can have few changes, but more or less it will be same. Okay. It is nothing but we have just a reaction here. We have ag2s, urgent type ore, which we get after the concentration. So it is the concentrated ore is allowed to react with NaCn, sodium Sinide. Okay. So it forms a complex compound of NaAgCn2, agCn2 plus Na2s. Okay. It is the impurity Na2s. So Na2s is further allowed to react with O2 and H2O. 2 Na2sO4 plus NaOH plus sulphur is removed here on this. And then we'll filter it, right? So that is filter it in the next step. We'll filter it. We'll get the filtrate to silver here, NaAgCn2. From this silver will get precipitated with the help of zinc. We'll add zinc over here. So the reaction would be 2 NaAgCn2 plus Zn. It gives Ag forms and we'll get Na2, ZnCn4. We'll get the black precipitate of silver here. Black precipitate of silver, right? Zinc is more electropositive. So it can displace silver here and we'll get silver. One second, sir. What do we do with the black silver? No, this is the, we'll get the black precipitate of silver. Further step is left now. Okay, sir. One second. After this, we add some, you know, alkali solution into it, like KNU3 we can add so that the impurities are oxidized and we'll get silver metal. Oh, okay, sir. Done, sir. Done. Okay. So after this, what is that noise on your side, Venkat? We had some plumbing work. Okay, same here. Oh, okay. For me, it is to every day. Like I have shifted into the new apartment. So it's like every day there is some work here and there. So cut, cut, cut, cut every day. Full wash base and all they're doing stuff. Ag plus KNU3 will have the fusion now. So this black precipitate of it, it converts into silver metal and all the impurities here will get oxidized and it will, it will rise as the scum, which we can filter out. The impurities we can remove like that. Okay. So we'll get Ag metal, silver metal after cooling, after cooling. This is the one we have. And the last step in this is again the same thing, that is electro-refining to get the, you know, more purity of the, of the metal, electro-refining to get the more pure form will do this. Again, anode here, the same logic that we did. It is impure, thick, silver metal. Like this question also they ask, okay, impure, thick, Ag electrode and cathode is the pure one, pure Ag electrode. Electrolyte will choose in which the silver iron is present. Like we have Ag NO3 plus HNO3 solution will have you. And this is the pure silver deposited at cathode. Okay. So this is it. Like iron, at least iron, you must do iron and zinc you can do two more. Okay. We'll have this steps only. If you revise two, three times, you'll be understanding this how to do this. But again, you will forget. Okay. Because the things like this only, this kind of chapters, you should revise before a week of exam, definitely before a week of exam. Like this one we have, we have polymers kind of chapter. Surface chemistry is also of similar category. But a few things we can understand in surface chemistry. Right. This kind of chapters you should revise in the last minute. Okay, guys. So fine. We're done with this chapter. Next class, we will start with surface chemistry. Probably we'll finish it next class. Don't know. We'll see. Otherwise, next next class definitely we'll finish the entire syllabus. Okay. So we have time, 9th of December, we are starting the crash course. So after finishing surface chemistry, we'll probably taking practical organic chemistry we haven't done. No, like those methods, Jildal methods, Dumas methods and all, it was there in 11th grade. We haven't done. So not much important, but yes, we'll finish it off since we have time. So we'll do it also. It is a concept of more concept you need to apply not much. It will take half, like one or two or not more than that. So we'll do that also. Correct. Fine, guys. Thank you. Take care. See you in the next class. Thank you, sir.