 So, welcome back. In the last class, we were looking at acid and base catalysis. So, we had already classified acids as specific and general acids. And we had looked at specific acid catalysis in the earlier lecture, where specific acid catalysis involves proton transfer before the rate determining step. In the last lecture, we had focused mainly on general acid catalysis. So, in general acid catalysis, you have proton transfer in the rate determining step. So, as with the specific acid catalysis, here also we had looked at the rate loss and here what we had seen is that the rate depends on concentration of HA. So, if you plot k observed versus concentration of HA, you would see a steady increase. General trends are seen for general base catalysis as well. The other thing is if you look at dependence with pH, what you would see is that it would remain constant for a while and then you would observe a dip in the log k value and that dip would be seen at the point corresponding to pKa of the acid which is HA. So, what happens is when you cross the pKa of the acid, you would have more dissociation of the acid and hence a smaller concentration of HA. So, then we had also looked at examples of acetone and acetal hydrolysis. In acetone, we had looked at both specific as well as general catalysis. In acetal, we had only looked at specific acid catalysis and I had asked you to work out the general acid catalysis. So, let us see if you were able to work it out. So, hydrolysis of acetal to hemiacetal, how will you represent it when you are trying to represent it for general acid catalysis? So, let us see if you got this correctly. So, when you think of general acid catalysis, what you would have is you would have, so this is your acetal, correct? So, now you would have this coming in. Now, as you know, RO- will not be as great a leaving group. So, what you would do is you would have this being protonated at the same time. So, what you would get would be and this would be the slow step and of course, once you have this intermediate, you can then think of water adding in to give you and of course, further proton transfer will give you your product. Now, in which situation do you think you would observe general acid catalysis, right? So, if you want to think of a specific substrate, so earlier we had looked at the previous class, a substrate which underwent specific acid catalysis, the Hammett plot for that was also obtained which supported that. So, now which kind of substrate do you think will prefer to undergo general acid catalysis? Logically, it would be a substrate which would have a good OR leaving group and that is what is actually observed. So, this particular acetal here, when you think of its hydrolysis, so if you have para-nitrofinoxide as the leaving group, so it is assisted by this acid. So, now what you will get would be this intermediate. So, what is observed is for this particular acetal, it prefers to undergo the hydrolysis by a general acid catalysis mechanism. So, what you see is looking at the substrate, you can logically deduce whether it would undergo specific or general acid catalysis and of course, experimentally it is easy to determine if you look at how the rate constants vary with pH. Now, there are several reactions where you actually have concerted or sequential general acid general base catalysis, especially in biology. So, you have multiple species working together, one is a general acid, one is a general base and you have both of these actually working together to give you an intermediate which then gives you the product. So, if you were to write the rate law for this, what would it be? The rate law would be, so this would be equal to concentration of R, concentration of HA and concentration of B. So, here what you would see is you would actually see a dependence on both HA as well as HP, sorry B. So, you would see a dependence on both HA and B here alright. So, this is commonly seen in biology. So, now if you have a situation like this, I will go back for a second to the previous slide. So, you have a dependence on HA as well as B. So, here if you were to plot log of K observed versus pH, what do you think the plot will look like? Alright. So, we have already seen in the previous two classes what the plot will look like in the case of a general acid and a general base right. In the previous class actually we looked at what the plot will look like for a general acid and a general base. So, now what you need to do is you need to figure out when you have both of these together, what will the kinetic plot look like? Obviously, it will look like a mix of the two. So, I want you to press the pause button and try to work out what this plot will look like. So, let us see if you have this correctly. So, what you would see is it would be a bell shaped plot. So, what you get actually is a hybrid of both the plots. So, for a general acid, what did the plot look like when you are plotting it and you can remember what it looked like for a general base as well. So, in the general acid what you had is the plot look like this and a general base you had the plot look like this. So, here what you see is at low pH what would happen is because you have a lower concentration of B right. So, as you increase the pH, so you have more of BH plus. So, as you increase the pH you will increase the concentration of B till you reach the state where you have maximum amount of rate. So, you will have maximum rate when you have both good concentration of B as well as HA. Now, what will happen is as you again go on increasing the pH, HA will now dissociate to H plus and A minus. So, now what you would see is again you would have the rate drop off. So, here you will have a high concentration of B but the concentration of HA will decrease. So, this is what the kinetic plot will look like. So, now we will go to what is called as the Bronsted catalysis law. So, now we will go to what is called as the Bronsted catalysis law alright. So, when you have the general acid base catalysis you have the acid or base react in the rate determining step correct. We have done that since the last class. So, there is no doubt there. So, the rate of the reaction K depends on concentration of HA and B depending on which reaction you are looking at, general acid or general base. Now, should there be a dependence on the structure alright. So, do you think there would be a dependence of the K value on the structure. So, say if you have a stronger acid or a stronger base do you think that would have an impact on the K value. So, remember when you talk about acid base and acid strength it is a thermodynamic property right. You are talking about the pKa. But when you look at the reaction kinetics we are talking about the kinetics or the rate at which you are protonating or adding OH-. So, that is the difference between these two. So, the question to use do you think that the kinetics of the reaction will depend on strength of the acid or base. And the answer is yes it will. And this dependence is given by what is called as the Bronsted catalysis law. So, in the Bronsted catalysis law log of K is given by is equal to minus alpha pKa plus C. C is just a constant to show you the intercept of the graph that you get if you plot log K versus pKa. Alpha is a sensitivity factor. So, just like the name suggests alpha will tell you how sensitive your reaction is to the acid strength or in other words pKa. Similarly for a general base log of K is given by beta pKa plus C and both alpha and beta are called as sensitivity constants. So, I want you to closely look at these equations. Now if you notice there is a negative sign in the case of general acid catalysis. Whereas there is no negative sign for general base catalysis. So, why is that do you think again look closely at the expression you can press the pause button and look closely at the equation to figure out why there is a negative sign that is put. So, if you are not able to figure out I will give you a hint as the pKa of the acid increases again as the pKa of the acid increases would you expect the rate to increase or decrease. So, pKa increases means less acidity. So, with the less acidity will the K value increase or decrease it will obviously decrease right you are looking at acid catalysis. If the acid strength is decreasing how will catalysis increase. So, essentially because of this inverse relationship a negative sign is put when you look at alpha. But that is not the case for beta because here you are looking at pKa of the conjugate acid alright. So, you need not put this negative sign here. So, now let us try to understand this more closely. So, does this remind you of any equation that you had seen earlier where you are correlating the rate to some sort of a dissociation constant. Think little more it is similar to the Hammett equation correct. So, in the Hammett equation what you had is you were looking at a reaction and correlating that with the dissociation of benzoic acid. So, this here was your substituent constant for your Hammett equation. But here what you have is the pKa instead and what is pKa how do you define the pKa? The pKa tells you what is the tendency of the acid to give proton to water correct. So, when you think of acid dissociation constants you are thinking of HA plus water giving A minus plus H3O plus. So, when you talk about pKa you are talking about the ability of the acid to give proton to water right. So, this is similar to sigma in your Hammett plot alpha is similar to rho. So, what it tells you is that for any particular acid you are looking at a particular reaction now for that particular reaction what is the tendency of the acid to protonate that substrate. So, you are comparing that tendency to protonate with its tendency to protonate water alright. So, this is analogous to a Hammett plot. So, you have log K is equal to minus alpha pKa where this alpha which is the sensitivity coefficient tells you how sensitive the reaction is to this protonation alright. So, now you can even compare two acids using this relationship. As you know you can correlate the K value with the delta G right. So, you can so this is similar to a linear free energy relationship. So, I am going to write it directly in the form of the K value, but to compare two acids say you are comparing an acid Ka with any other acid Kx alright. So, you are trying to compare how good these two acids would be for a given reaction. So, you can give that by log of Ka minus log of Kx will be equal to alpha times log of capital Ka minus log of capital Kx alright. Where both of these are the dissociation constants. You can also look at it in terms of a ratio if you so wish alright. And again if you were to write it in terms of free energy it would be. So, when you talk of small K we are talking about the delta G for the transition state based on the Eyring equation. So, you have again this would correspond to the acid free energy for the dissociation of the acid in water. So, now we have found out another free energy relationship which compares the acidity of two general acids alright. And this coefficient that you have alpha tells you how sensitive a particular reaction is to protonation or deprotonation alright. Maybe if we look at some more examples this will make a little more sense to you. So, what is the significance of alpha and beta? I am just focusing on alpha here the same you can think of when you think of beta. So, shown is on your screen the equation for general acid catalysis. Now sensitivity constants as I told you indicate the extent of protonation in the transition state of the rate determining step. So, I had not explicitly told this to you earlier. But if you have extensive protonation in the transition state that would indicate that the acid strength actually has an effect on the reaction rate. So, more protonation in transition state implies the acid has a greater effect. Typically values lie of alpha between 0 and 1. So, we are talking about values of alpha. Now why is that? What would a value of 1 indicate? A value of 1 in this equation indicates that you have a linear correlation between the rate constant and the pKa of the acid. So, what does that tell you? The kinetics depends directly on the acid dissociation strength. So, which indicates that you essentially have complete protonation in the transition state. So, this is the best possible scenario for you to see an effect right on the reaction rate to have a correlation with pKa. So, that effect would be most when you have complete protonation in the transition state. So, if that is the case that means you will have a direct correlation of small k and big k. So, that is why the maximum possible value would be 1. What will a value of 0 indicate? 0 indicates that the acid strength has absolutely no effect on the k observed or the small k value. So, essentially what that tells you is that the transition state is probably not yet protonated. So, it is probably a very early transition state and you probably do not see much of an effect on the acid. Sometimes a negative value is seen. So, what a negative value indicates is that increasing the acid strength leads to decrease in catalytic activity. This is usually not very common but we look at an example so that it makes sense because usually if the acid strength increases the understanding is that its ability to protonate any other substrate will also increase proportionally. But a negative value indicates that that is not the case and we look at an example so that it makes more sense to you. A value larger than 1 would indicate what? The value greater than 1 would indicate that the reaction that you are studying is actually more sensitive to protonating ability of the acid as compared to water. And why do you say as compared to water? Because when you talk about pKa you are looking at the ability of the acid to protonate water. So, value greater than 1 indicates that whatever reactant you choose that has that is more sensitive to protonation than even water. So, this is again not very common. So, let us look at again with respect to numbers what these values of alpha and beta mean. So, we will come back to hydrolysis of acetone. So, if you have acetone alright and you are converting it to this diol. So, when you convert it to the diol let us look at 3 different reactions. So, these 3 different reactions is so I have shown you 3 different substrates on your screen. So, what these in each of these case you are talking about hydrolysis of this instead of acetone alright. So, you are measuring K for this particular reaction in the presence of different acids. So, just so that you are not confused I will repeat again. The reaction we are looking at is hydrolysis of a ketone to the diol. So, for each of these ketones or aldehydes. So, you have 2 aldehydes and a ketone here. What is done is say for this aldehyde the first one here the reaction is carried out with different acids alright. To give you a correlation like we saw in the earlier slide and what you get out of that would be the alpha value alright. Similarly, it can be done for formaldehyde and this benzaldehyde derivative. So, the alpha values were determined for each of these and remember to determine alpha value on the left side you have the rate constant on the right side you have the acid dissociation constant. So, what you see is that the alpha values follow this trend of 0.27, 0.24 and 0.46. So, what this tells you is that the extent of protonation is probably not as much in the transition state it is probably partially protonated just like how you would think of. So, you are looking at a situation where you have. So, where you do not have complete protonation in the transition state and if you see the value is lower for formaldehyde and the dichloroacetone derivative as compared to the benzaldehyde derivative. In the benzaldehyde derivative you have a value closer to 0.5 which indicates that you have greater protonation in the transition state which might also be explained by the fact that if you have a greater protonation here this is again in conjugation to the aromatic ring. So, maybe in this case you see a greater extent of protonation as compared to the other two cases. I had told you we look at an example of a negative alpha value. So, shown on your screen are three different acids. So, these are nitroalkanes. So, what you see on your screen is that the two nitro propane is more acidic than nitroethane which is more acidic than nitro methane. So, what I want you to think about is why this order of acidities. So, you can press the pause button and think about it. So, here this is your acid right. So, the conjugate base that it generates is. So, you can write a resonance structure for this which will look like this. So, now what you see is when you think of the pKa you are looking at stability of the conjugate base right. We had looked at this earlier I will put that as Cb. So, what you see is in the case of propane when you have this double bond structure resonance structure which has a significant contribution what you see is that due to hyper conjugation interaction the propane derivative is more stable than the ethane which is more stable than the methyl. So, which is why if you compare the acidities two nitro propane is more acidic than nitroethane which is more acidic than nitro methane. Now, what is seen is that the alpha value for the deprotonation was found to be minus 0.5. So, what does that mean? It means that the kinetics for the deprotonation follows the reverse order of the acidity. So, in other words what it means is that it is leased for the most acidic nitro alkane and why is that? Because in this case what you see is you do not have complete deprotonation. So, when you look at your rate determining step. So, this will be protonating some reactants. So, let us call it Rh plus. So, what happens is probably in the transition state you do not have complete deprotonation. So, it does not have any substantial amount of double bond character like you saw for the conjugate base. So, in this case what you see is it is the inductive effect or the electronic properties that play a larger role. So, what you see is propane which has the two methyl groups is more releasing and it destabilizes the transition state as compared to methyl which has only one releasing group. So, which is why the kinetics of protonation is much faster for nitromethane as compared to two nitro propane. Whereas if you compare the acidity it is just the reverse. So, shown here is an example where you can get a negative value of alpha. But typically as I told you the value is between 0 to 1. So, again coming back towards the end of this class. So, so far we have looked at acid base catalysis. I spent a lot of time on this because that is what you see most often when you think of catalysis and reaction mechanisms. So, over the next 2, 3 classes remaining what we do is we quickly look at the other types of catalysis and towards the end of this week we will wrap up with a summary of whatever we have done so far. So, thank you and see you in the next class.