[Excoriate]

Hi,

I do not claim to be much of a chemist but instead I have an MSc. in Computational Biology. The question I have is whether there is a deeper basis physical basis for reaction rate equations perhaps justified in terms of some sort of (classical/quantum) mechanical laws. I guess I am basically curious about how much we know about bond formation be it ionic or covalent in nature.

Thanks in advance.

[renge ishyo]

Yes, there is a deeper mathematical basis for the theory of reaction rates in chemical reactions. In fact, Chemical Kinetics is an entire discipline in and of itself, and a very challenging one I might add.

The main line to start with are the Arrhenius equations. You can at least see what they are from the wiki:

http://en.wikipedia.org/wiki/Arrhenius_equation

A deeper understanding of these equations can be had when you see them derived from statistical mechanics. Statistical mechanics is a very hard subject to study; its accomplishment is that it provides for a molecular description of thermodynamic and kinetic systems and equations. The phenomenon of reaction rates cannot be understood from the behavior of a single molecule as it is more a phenomenon related to statistics and populations of molecules with different bond characteristics (hence, why the reaction rate depends on the concentration of species and not the individual nature of species).

[Excoriate]

Thanks for the reply. I guess I will try to find a good textbook on chemical kinetics and do some reading. My understanding is that there is still somewhat of a gap between mechanics (classical/quantum) and statistical mechanics and arriving at the probabilitistic/statistical nature of statistical mechanics from these principles. I have some physics books I intend to work through to get a better handle on these things. Have the actual mechanisms which are described on a macroscopic level in terms of reaction equations been studied?

[renge ishyo]

The gap between the two disciplines has more to do with the fact that statistical mechanics deals with the behavior of a large number of atoms or molecules whereas quantum mechanics is best applied applied to individual atoms or molecules studied in isolation. The gap is that their focus is different, but the two studies do complement each other very well. For example, kinetic and thermodynamic data can tell you how fast a particular reaction got to equilibrium (suggests how reactive the species involved are) and thermodynamics can tell you which of the species is more stable (tells you something about the relative bond strengths). Then quantum mechanics can then step in to analyze the structure of the molecule involved in more detail to try and rationalize why the equilibrium under a given set of conditions favors one molecule over and over. Each study focuses on a different aspect of the overall description of a chemical reaction. I wish there was a shortcut to all of this, but I have been studying it for quite some time and I haven't found one yet 

[Excoriate]

I guess the problem that some people are trying to tackle is the relationship between mechanics and the probabilistic Boltzmann type approaches. I still dont really understand the area of ergodic theory or related notions but it seems like quite an interesting area and probably quite difficult.

Basically you are saying for even simple reactions there have been no collision type studies where the mechanism of what happens when molecules react (even simple ones) has been explored?

[renge ishyo]

Basically you are saying for even simple reactions there have been no collision type studies where the mechanism of what happens when molecules react (even simple ones) has been explored?

No no, that is not what I am saying. What I am saying is that the mechanistic approach is very much distinct from the thermodynamic and kinetic studies even if you are describing the same reaction with each approach. The mechanism is basically a rationalization of the thermodynamic and kinetic data which is typically obtained empirically. From the mechanisms that have been worked out to successfully explain certain reactions, general principles about reactant/product structures can eventually be obtained. These can then be used to predict what might happen in novel circumstances even before the kinetic and thermodynamic data are collected. So the overall way in which these disciplines interact isn't linear in the end. What I am saying is that the different disciplines are *artificially* subdivided and focus on different things. The kinds of questions you ask when gathering and interpreting kinetic and thermodynamic data are different than the kinds of questions you ask when trying to rationalize the result by focusing on one chemical structure at a time.

[Yggdrasil]

This is not my area of expertise, but here is my insight:

Kinetics is a very complicated field of study drawing on multiple different branches of chemistry and physics.  Often it can require significant amounts of quantum mechanics to calculate potential energy surfaces for the reaction and significant amounts of statistical mechanics to figure out how particles behave on that potential energy surface.  As in all models, assumptions must be made to solve these problems and obtain workable models at the end.

Thus, the particular kinetic model that you use to describe a reaction depends a lot on the particular reaction and which assumptions you can apply to the system.  Are the reactants strongly interacting with the environment (e.g. dissolved in a liquid) or are interactions with the environment weak (e.g. in the gas phase)?  Do the reactants behave quantum mechanically to an appreciable extent (e.g. in proton/electron transfer) or can they be treated classically?  Are the energetic barriers large in comparison to the thermal energy or small?  Depending on the answers to these questions and other similar questions, you may choose a different model/theory to describe your system.  For example, transition state theory (Eyring theory) works well for gas phase, classically behaving particles with high activation energies compared to thermal energy, but fails if these criteria are violated.  For example, in cases where quantum mechanical behavior becomes important, something like Marcus theory may be more applicable.

Accordingly, when these models are tested in experiment, the results vary depending on the system.  Collision theory (which calculates the Arrehnius prefactor from the rate of collisions between molecule in an ideal gas) works fairly well for the reactions of atoms in the gas phase but fails spectacularly for molecules reacting in gas phase because molecules must collide in a particular orientation to react and the model does not take this into account.

[Excoriate]

Thanks. Are there good places where I could find the details of some of these approaches in textbooks? I am particularly interested in seeing this from a physics point of view. The few books on chemical kinetics I did find seemed to in general elide the ordinary differential equation mathematics for reaction rates and didn't really go into the specifics of when collisions occur which orientations would lead to reactions and the quantum physics involved. Seems to be a fascinating subject :-).

[renge ishyo]

If you are looking for a general introduction to this area of study the first place you should start is a good P.Chem textbook (such as Ira Levine's which I highly recommend). P.Chem as an academic subject in fact is split up into three areas of study: thermodynamics, kinetics, and quantum theory. So if you are looking to develop skill in this area it is right up your alley. As far as details about collisions and structures those are very situation specific, and you will find them a lot in actual published research papers down the road. I can't think of a good introductory book that intentionally mixes kinetics with structural studies at the moment (as Yggdrasil mentioned, the problem is that to study kinetics at that level of detail you have to bring together so many things). Sometimes they do take the time to mix the two disciplines together in a textbook if a molecule is really special. I have seen it done for instance with ATP where the energy yielding reaction is rationalized based on entropic and electric effects.

Hoped this helped.

[Excoriate]

Thanks that was very helpful. Do you happen to remember the name of this ATP textbook?

[renge ishyo]

The ATP treatment is more or less covered in many Biochem textbooks due to its importance in Biological systems. I remember reading about it as an undergraduate in both Raymond Chang's Physical Chemistry for the Chemical and Biological sciences, and in Lehninger's Principles of Biochemistry and probably a few others that I am forgetting as well. Of course, these descriptions are in short blurbs due to the broad nature of textbooks, and you can easily just read them in a few moments by looking at these books in a library. You'd get much more satisfying descriptions if you farm through some current research papers concerning kinetic mechanisms of reaction in p.chem journals. Either way I wish you well in your studies!

[Excoriate]

Thanks :-). I am not studying at the moment just looking for some sort of direction if I pursue more school or perhaps I just want to develop a deeper understanding of my field .