 to the course on chemical kinetics and transition state theory. This course ah essentially will be ah focusing on how to think of kinetics and estimating rate constants. So, ah in terms of course outcomes we have two important outcomes. In this course we will be looking at two specific theories. The first one is the collision theory and the second one is the transition state theory. Both these theories calculate rate constants of reactions. So, this course will cover ah how to calculate these rate constants under these two theories. So, the ah first point is knowing the derivation, knowing the conceptual framework under which these theories operate, ah knowing when they are applicable and when they are not applicable, ah and the second course outcome is actually applying these two theories and calculating rate constants out. So, essentially at the end of this half semester course if a new reaction that you have not seen before is given to you, you should be in a position to make educated guesses on how to go about calculating the rate constant. That is the main objective that is where ah you will be after doing this course. So, ah there are a few prerequisites that are ah you can cover rather quickly. Most of it assumes 12th class knowledge. ah The course assumes a very minimal amount of mathematics. ah So, you have to know basic algebra, variables, how to add variables, equations, inequalities like the most trivial of those things, nothing fancy there. ah You have to know basic operators like exponentials or logarithms or sine cosine things like that. Exponentials come very very frequently in rate theories. Minimal amount of calculus, if I give you a simple function to differentiate, if I give you e to the power of k x to differentiate, you should be able to differentiate that. And the same holds true for x integration, most trivial of integrations, integrating x into dx, integrating e to the power of x into dx. Ah complex integrations for example, integrating a Gaussian function e to the power of minus x square which is hard. Those things we will always provide that you do not have to know for this course. ah Simple ideas like chain rule. So, if you I ask you to differentiate x into e to the power of x, how do I do that? So, those basic things you should know for this course. Very fundamentals of thermodynamics, the second law and the first law of thermodynamics as applicable to chemistry, ah idea of Gibbs free energy, ah idea of equilibrium constant and the relation of equilibrium constant with Gibbs free energy. So, there are enough ah resources out there where you can access these. Here I am referring to one NPTEL module which you can look at which is sufficient, ah module 5 of chapter 21 of this course. So, one chapter is enough. And finally, we will also assume a little bit of basics of kinetics. At class 12th knowledge effectively, ah what is first order kinetics? What is a rate law itself? Those kind of thing. What is order of reaction? Ok elementary steps and mechanism. ah Again I have provided a couple of resources. You can actually look at the NCIT book of class 12th. ah One chapter of it is enough the chapter 4 of part 1 of class 12th. I have also provided you in NPTEL module. ah These two chapters suffice in understanding it. ah So, ah to give you a clear cut outline, we will start with a revision of the prerequisites particularly of chemical kinetics. We will start by defining rate formally, ah we will work out how to write rate equations and all. ah After that we will move on to understanding how to calculate rate constant, particularly we will start with Vanthos and Arrhenieses analysis. These are the two people who really started the field of chemical kinetics. It is late 1800s. Beautiful work and back then only they had written very fundamental equations on how rate constant changes with temperature. So, we will look at that analysis as part of this course. ah We will move on to build on ah how do we calculate these rate constants from an atomistic picture then ok. And to understand ah how atoms move the kinetics of atoms, we will need to know a little bit of a phase space. So, we will introduce this explicitly in this course and we will introduce whatever is necessary in calculating rate constants which will be Boltzmann distribution and partition functions. ah Then we will discuss the collision theory ah kinetic theory of collisions ok. So, that is the first theory that was given by Trott and Lewis to calculate rate constant from atomistic picture. And following that we will discuss the transition state theory which is one of the main focuses of this course. ah And this transition state theory was fully developed in 1935 the first equation was given and it is still used as was written in 1935 85 years ago. We still use the equations the same equations it is a very powerful theory ah that is used across fields. So, we will look at this very very carefully in great detail. ah We will end with a little bit of a flavor of molecular dynamics and how this molecular dynamics is used to calculate rate constants. So, the textbooks we will be following we will mostly be following the book by Ledler. This is a very standard textbook very famous textbook ah it is called chemical dynamic chemical kinetics by Ledler. I will be following third edition if you have access to any other edition please do not worry. All editions are more or less the same ah you can freely ah whatever I am teaching will also be present in a different edition. I will also be time and again refer to two other books one is by Steinfeld, Francisco and His Chemical Kinetics and Dynamics another very standard textbook on kinetics. ah But not very often only for a few things and also we will be referring a little bit to Atkins book on the Atkins physical chemistry very popular book and once more please do not worry about edition any other edition will do the job the chapter number changes not the content. ah Anytime by default we will be following Ledler anytime I am following any other resource I will always mention. So, today we will just cover very preliminaries we will define what is rate ah and before defining rate we will also cover ah how all this history of kinetics came about on whose shoulders we are standing on ah. So, you can actually look at a very very good reviews on this point on the history of chemical kinetics in these two papers very very readable papers one by Ledler whose book we are following and by another giant called the Pollock ok. So, these references are extra ah more interested students can go to this for extra knowledge. So, let us just look at a little bit of the history ok. So, the history is more than 100 years old we cannot cover every single point, but the salient points the biggest of the biggest giants in the field whose contributions are immense. So, the first two names are really Vanthoff and Arrhenius. Vanthoff essentially in 1884 did a very thorough analysis of how rate constants changes with temperature and he actually wrote what is called Arrhenius equation today in 1884 paper. So, that Arrhenius equation was written by Vanthoff interestingly 1889 Arrhenius wrote a seminal paper one and a half page paper that we I will show you in the second module powerful paper and that paper is the first paper that postulated the idea of a transition state pure hypothesis pure speculation but very powerful speculation and he gives reasons for it in a very beautiful fashion. So, that is the reason that Arrhenius equation is called Arrhenius equation because of that paper of 1889 of the idea of an activated complex ok. So, these people really started the field they said I want to I have done a reaction, but I am not happy enough with that I want to know more. So, how do I calculate this rate constants? 1918 saw the first paper on calculating these rate constants from an atomistic perspective actually getting a number out then by Trott and Lewis it is called kinetic theory of collisions that we are going to cover in some detail in this course. 1920s saw lot of discussion on some of the simplest reaction which is unimolecular ok. Bimolecular is somewhat more complex you have bonds making and forming so they said ok let us try simple we are beginning. So, a lot of focus was spent on unimolecular reactions which turned very insightful. So, that developed our intuition of chemical kinetics a lot. 1931 and 32 and 35 saw some very important works. 1931 the idea of doing dynamics occurred by Eyring and Poliani. Building on that idea in 1932 Wigner gave a theory which is the precursor to TST and in 35 two different papers one by Eyring and the second by Evans and Poliani came they both came simultaneously and so the credit is given to all three of them and that paper is the revolutionary paper that changed everything this year 1935 that laid the foundation of transition state theory. This we are going to cover in great detail in this course and the equations written in this paper are still used as there not only that almost all developments beyond 1935 take this work as the base and develop upon it make the equations better. But this is still the intuition that is still used today in even development of chemical kinetics ok. So, that is why I put this one in bold ok. 1940 saw beautiful work by Cramer on thinking of including solvent effects in transition state theory. I am moving a little bit fast now lot of work is done. 1952 Marcus did another beautiful work he essentially solved the unimolecular decay the people the work that was done in 1920s Marcus entered said I can now solve it completely and what he did is to use transition state theory that is the reason in 1920s they were not able to solve it because transition state theory did not existed back then. After that Marcus also solved another problem which is that of electron transfer how so a bond is not breaking and forming only an electron is transferring from one side to another. So, Marcus got a noble price for that in 1960s Keck has a very nice work on quantifying transition state. So, remember almost 100 years later I mean 80 years roughly in 1889 Arrhenius had postulated the existence of a transition state in 1960 basically Keck said I can mathematically tell you exactly what it is I can write a mathematical description of transition state. So, a lot of development ideas of introducing quantum mechanical effects in transition state theory were introduced in 70s and 80s and it is still happening till today. And essentially since then we have been developing over transition state theory introducing if it we cannot do full quantum mechanics can we do semi quantum mechanics or semi classical mechanics how do we apply it to a variety of problems I want to understand protein folding I want to understand kinetics of enzymes of catalysis of photosynthesis of energy transfer and the list can go on it is a very active field you can open any modern journal that was published let us say this year in physical chemistry and you will find a few papers at least in every public in any every journal every week that will be on this topic. So, what I will be covering today you can find in the chapter 1 of Laidler or you can also read the class 12 book of NCRT on top of that I have also given you an online resource from chem library test ok. So, let us start informally so that everybody is on the same page and we have the same notation. The first thing we will define is what is called stoichiometry to give you one example let me write a chemical reaction 2 H 2 plus O 2 makes 2 H 2 what I mean by this reaction I mean 2 moles of H 2 reacts with 1 mole of O 2 produce 2 moles of general let me write a reaction that will look like a a plus b b make it somewhat more general. So, the big letters in this course will refer to atoms or molecules and the small letters in this course will be numbers typically stoichiometry. So, I have this stoichiometry let us try to quantify what this means. So, let us just consider one thing let us say time t equal to 0 have moles NA naught, NB naught, NC naught and ND naught in general. So, these are the number of moles corresponding to A B C D at some initial time t. I measure the moles at some later time t and I get NA, NB, NC and ND. Can you tell me a relation between these NA and NA naught and NB and NB naught with the stoichiometry A and B's can you write an equation. So, what I want you to do is to pause the video think about this how do you calculate how do you construct a relation take your time solve this problem and then we will solve it together. So, please pause the video and solve this on your own hopefully you have equation with you you have solved the problem if not if you have not been able to solve no worries we will solve it together now. So, the first thing to note is how much moles changed. So, the delta N is NA minus NA naught equal to delta NA well I can write the same thing for others I wrote an M I will erase the M and convert it back to NB naught NB and so on and so forth. Now, we will do our analysis first what does this stoichiometry mean what do we understand from this if A moles of A consumed B moles of B are consumed that is the meaning of this reaction here by definition this is always true there is absolutely no exception this is the definition. So, I want to find out how many moles of B will be consumed if delta NA moles of A are consumed. So, we do it in a simple fashion if 1 mole of A is consumed then B over A it is all linear moles of B are consumed simple if delta NA mole of A is consumed then delta NA into B over A moles of B are, but delta NB is the actual moles of B that have been consumed from this. So, delta NB must equal delta NA into B over A. So, I simplify this as delta NA over A equals delta NB over B and as a convention we use a negative sign for consumption that is the convention. So, I will this equation is true. So, this equation is also true I can put a negative sign that is my choosing. So, for consumption I choose a negative sign and for production I will choose a positive sign. So, you can work the same thing out for C and D as well and by convention then what we write is delta NA over A equal to minus delta NB over B this is equal to delta NC over C equal to delta NB over B. So, I am not working of C and D part explicitly, but you can easily work it out following the same logic. So, we define this quantity as the extent of the reaction and this equality this is a definition, but the equality here will always hold if this reaction is true there is no exception to it this is by definition this is by mathematics. So, if this is true the whole thing we do not want to write again and again when we call it the extent of the reaction and the idea is if delta NA equal to 0 then the extent is 0 that means nothing has happened you are at T equal to 0 and if delta NA is 1 if delta NA is A then eta is 1. So, eta equal to 1 implies A moles of A are consumed B moles of B are consumed C moles of C are produced. So, it is an easy way to think about it. So, we quantify it in this number a dimensionless number ok. So, we have defined this extent of reaction how do we define rate of reaction. So, the rate is defined to be by definition 1 over volume. So, I use 3 equal to signs 3 these 3 arrow these 3 lines to define that is a definition that change of extent of reaction per unit volume that is defined to be the rate of the reaction ok. Some of you might be curious why we divide by volume little bit of extra information it is just so that rate becomes an intensive variable we do not want it to depend on the overall volume ok nonetheless. Let us just put it in this equation here let us substitute it. So, I will substitute it for A. So, rate is equal to 1 over volume d over dt of minus delta NA over A ok. So, I have used this here. So, I will take A outside and what is the definition of delta NA it is NA minus NA naught. So, this is equal to 1 over AV minus dNA over dt plus dNA naught over dt what you notice that this is 0 because NA naught is not a function of time it is simply the number of moles at initial time ok. So, that was just a number the actual change is NA. So, this is 0. So, at the end I get 1 over volume into 1 over A minus dNA by dt. So, this rate that I have got 1 over volume into A minus sign dNA over dt if volume is constant there is a big if and in chemistry we often deal with such reactions in solutions. So, when you mix two reagents typically the volume is not changing by a lot, but nonetheless if volume is constant I can write this as dNA over volume over dt and so, this becomes equal to minus 1 over A d concentration of A over dt where concentration is defined to be NA over volume ok. So, this formula of rate holds true only for constant volumes in this course at least we are going to stick to this definition we are going to assume volume is constant. So, in summary today we have looked at a brief history of chemical kinetics and we have looked at the very fundamental definition of rate as 1 over volume into d extent of reaction over dt and at constant volume we have proven that the rate of the reaction is given by this equation. We have explicitly showed it for one term rate equal to minus dNA over dt, but it is also easy to show it for these three other terms. In the next module we will look into what is rate constant and elementary reactions. Thank you very much.