 module 14 of chemical kinetics and transition state theory. In a series of modules we have now developed the collision theory to calculate rate constants. We have solved several numerical problems we have looked at the derivation very carefully and today is going to be the last module that specifically focuses on collision theory. So what I want to do today is end with an analysis of the assumptions that go into collision theory and essentially this module is one of the most important modules because today is when we will discuss when is collision theory applicable and when is it not. So if some experimentalist come to you and ask you ok I have done a reaction but I want to calculate the rate constant will you apply collision theory to that or not and that is the most important thing to know ok. So we will start and let us go over one by one of all the assumptions that we have made in deriving the rate equation. So the rate equation that we derived is this. So the first big point is that it is valid only for biomolecular reactions A plus B going to some products. Product side might be anything it might be C plus D or it might not be but reactant side it has to be 2 A plus B. A can also be equal to B but it cannot be single molecular or it cannot be termolecular it has to be biomolecular. So that is the whole regime of the model itself. It assumes Newton's laws to be true. We think of these A and B moving classically not only classically we assume essentially there is no potential energy as well these particles we assume as big heart spheres which are colliding with each other ok. So essentially there is no interaction these particles are not charged there is no coulomb force there is no Lennard-Jones force there is no dispersion force there is none of those forces ok. So it is a very simple minded model A and B two spheres they move at a constant speed u until a collision happens that is it. Another very big assumption in this model is what we introduce is a reaction probability at a given speed. So if you remember if you go through your modules carefully we get this exponential term only by including this reaction probability by introducing an appropriate reaction cross section. But in that what we assume fundamentally is that this reaction cross section or the reaction probability depends solely on one number which is the translational energy. That is an assumption and today we will discuss the consequences of this assumption as well. So it does not have any vibrations or rotations by the way why because I have a perfect sphere my molecule does not have a bond to vibrate ok. So collision theory does not look into the structure of your reactants at all. So that is very important that actually transition state theory builds over this missing factor. So that is the really the biggest limitation of collision theory. It does not have the whole idea of chemical bonding in it and well that is a big drawback is not it. Imagine if you go to an organic chemist they really think in this language of electrons moving around putting these arrows of how electrons are moving, how bonds are moving right. None of that is built into this model all of that is completely missing. So we will see in the coming modules how to include that and that correct theory for including or that is essentially transition state theory. So let us start with one question. Consider this reaction of hydrogenation of C2H4 to give C2H6 because I am adding a hydrogen over the double band to give me this molecule. Can you estimate you do not have to calculate ok. So just using your intuition of the assumptions that we have made can you estimate if the rate constant as estimated by collision theory will be much more much less or more or less the same as the experimental answer. So please pause the video take a moment reflect on the question and choose your answer. Hopefully you are back hopefully you will pause the video you thought about it. Let us discuss what one should expect it is a qualitative question your answers might differ from mine. So well here now we have to really think of chemistry I have C2H4 which essentially is this molecule and I have a H2 that is coming and adding here. Now the point is I am first assuming all of these as hard spheres they do not look like spheres ok. Let us assume I can just somehow still model them as a sphere ok I will just not look at them very carefully. But the point is that H2 must come in a very specific direction for a reaction to happen right this essentially H2 has to come in this fashion this bond has to break and these bonds have this bond has to break. Now if H2 approached in this fashion nothing would happen what if H2 approached in this fashion. So these would not be reactive at all this is the reactive one correct. But collision theory considers all of them to be equally reactive collision theory does not understand which direction the collision is happening from all directions are equally good. Therefore collision theory will grossly overestimate the rate of the reaction ok. So the correct answer will be the collision theory answer is much higher than the experimental answer is that what you got ok. So let us look at a few specific examples as one of the problems we had actually looked at the reaction of H2 plus I2 going to 2HI that was actually the problem that was originally studied by Trottes and Lewis in 1918. And it is unfortunate or unfortunate depending on your point of view that for that problem collision theory works beautifully ok it is really a coincidence though we get the observed rate of 3.5 into 10 to the power of 7 litre mole inverse second inverse and collision basic theory essentially gets you the same rate. And actually not only that as a function of temperature as well the rate matches very well for this particular reaction ok. So that is the reason people were very excited about this theory that at least we solved for one problem and that itself by the way is a big achievement at that point it is a first estimate of rate constant from a fundamental perspective where we actually got a number without referring to anything experimental yeah from scratch from ideas of atoms and molecules. But as it turns out there are many other examples where this theory does not work. For most problems you get things like where collision theory grossly overestimates the reaction rate. So this problem that we discussed in the last slide H2 plus C2 H4 here I am giving you the actual numbers the experimental rate is 10 to the power of 6 the collision theory answer is 10 to the power of 11 5 orders of magnitude 1 lakh times more ok. So that is how bad collision theory can be and there are many more examples where collision theory will overestimate. There are also a small fraction of molecules or reactions where collision theory also underestimate. I have given you one example where the collision theory answer is 10 to the power of 11 and the actual answer is 10 to the power of 12. So you have a factor of 5 underestimated well not as bad as this one where you had a 1 lakh factor if the factor is 5 only but 5 is still somewhat large we want better we want to improve. So today we will also discuss why can collision theory underestimate as well. So again just to reemphasize collision theory misses vibrational and rotational entropy. This we will be discussing more detail in transition state theory. It has misses completely the idea of reaction. It has no sense of direction of bonds how the electrons are distributed that for a reaction to happen the two reactants must come together in a specific form that is completely missing here. There are no steric effects here that your molecule of interest might be hindered by this let us say some big organic group. Ideas that are so common in organic chemistry completely missing here. So these are big problems and they all also misses all kind of interactions. Imagine if your reactants had a charge even if it is dipole moment well you know that these dipole moments will attract each other right and because of that the idea of constant speed is a bad one they will be accelerating or de-accelerating right in that or none of that is built into our model. So it is a very simple minded model from which you can get a first estimate think of it that way. So let us just discuss a bit more one important point that we raised is that the reaction cross section that we had introduced earlier is a factor of only translational energy okay that is incorrect experimentally speaking. You have many more factors on which this reaction cross section can depend on. So one simple example can give you is this reaction of k plus hf going to h plus kf. Now this is one example where you can see the difference in different kinds of energy. So if I put the initially a little bit more energy into vibration of hf okay so hf is a bond it has it is vibrating and initially let us say I put in little bit laser or otherwise some more energy into this hf. The reaction will proceed 1000 times faster compared to if I had put this energy in translational energy. So the reaction cross section is not just a function of total energy it depends very selectively on how this energy is partitioned okay. So energy can come in different forms and these different forms affect the reaction differently. So again this is a bit failure of collision theory. The next thing I want to just point out once more just to re-emphasize this because it is such an important point. There is no notion of molecular shapes or bonds in collision theory. So just let us look at one of the simple examples that we study as an SN2 reaction. For example you can cook up your own reaction. So just I am bad at organic chemistry please pardon me for my bad drawing skills here. So this reaction essentially happens as Br minus attacks the carbon opposite to chlorine and this chlorine dissociates for this to give you essentially this gets inverted like this. Now if you think about this let us say reaction actually you can think of spherical shape as a good approximation to be honest. Br minus is an atom atoms are thought of as spheres and even this molecule CH3Cl well you have a central carbon surrounded by these atoms and I can perhaps think of this as a sphere not a bad model. But what is a bad model is assuming all directions to be same. Br minus has to come from a very very specific direction. If Br minus let us say Km in this fashion orientation really matters here you will not get any reaction. So Br minus must come opposite to chlorine that is the idea of an SN2 reaction none of that is present in a collision theory. So one way people try to improve upon this is by introducing what is called steric factor. So this is an ad hoc factor we just say that our collision rate look like this this is what we derived. But to get it right you must multiply it by this P. So P is a number that you can calculate experimentally but P is usually not dependent on temperature. So that is the advantage of using this. So at one temperature perhaps you calculate this P as the measured rate versus the collision theory rate and find the ratio and then you can use the same P for different temperatures. So that is one way of correcting it. But it is not very satisfactory because it is ad hoc it is not from an atomistic perspective which has been our aim. Let us finally discuss this example it is a very interesting case of a K plus Br2 going to K Br plus Br. In this case it is the opposite collision theory underestimates the correct reaction rate. What happens here is something very interesting and cool and I just wanted to highlight that I have K and I have Br2. This reaction is happens under what is called the Harpoon mechanism. What happens actually is that when this K and Br2 comes somewhat close to each other and electron actually jumps from K to Br. So this goes to K plus plus Br2 minus and this eventually reacts to give K Br plus Br. So what is the big deal? The point is the radii at which electron transfers is much larger than the radii of K plus Br2. So if you remember your sigma was pi rA plus rB square. So this distance D but electron jump happens. D at which electron jump happens is much larger than D and once the electron jump happens these become charged and they get accelerated to each other very fast. So the reaction will happen very fast. So in effect the sigma effective is actually closer to D electron jump square. The D at which the electron is jumping which is in much greater than sigma of just this pi of rA plus rB square. So that is the reason that the collision theory which is approximating this as a rate is lesser than the actual rate. As an assignment problem you will see how to estimate this using a very ad hoc calculation. So that I will leave to an assignment in a how to calculate this D electron jump approximately. But in general it is hard to calculate these numbers for this one it works out very well. So with this we end our chapter on collision theory. From next time on we will start building towards transition state theory. For collision theory there are a few things you should keep in mind in terms of when is it valid and when is it not valid. What we have approximated in collision theory is that these are perfectly hard favors moving at constant speed. There is no potential in between these molecules. There is no sense of bonding in between these molecules. So it is a crude approximation. But nonetheless it is a first theory that gives a rate constant from an atomistic picture. Not only that I have been decimating collision theory a lot today. So let me advocate for it a little bit as well. It is nonetheless a good qualitative picture to keep in mind. You can think of these atoms coming together somehow and reacting. The details have been wrong a little bit. But it is still presenting a good way to start thinking about reactions. Okay. So next time let us try to build on transition state theory to get rid of the problems that collision theory faces. Thank you very much.