Talk:Arrhenius equation

message: Any fundamental reaction, which is any reaction where one or more reactants combine and turn into one or more products with no intermediate steps, will follow this equation.  This is because the Arrhenius equation is identical to a Boltzmann distribution, which is derived from statistical mechanics.  So the Arrhenius equation is not just a handy mathematical approximation.  Physics dictates this must be true.
:Is this really true?  Doesn't the Boltzmann distribution just apply to gases? Olin
:: The Maxwell-Boltzmann distribution of molecular velocities is not restricted to gases - it applies to nearly all liquids (except at very low temperature) and, to a limited extent, even to solids. It is a rigorous result of classical statistical mechanics and, as such, applies whenever classical mechanics is valid. Nevertheless, you are right to be suspicious about the preceding poster's highly exaggerated claims about the Arrhenius equation. The Arrhenius equation is by no means "identical to a Boltzmann distribution". In order to get from the Boltzmann distribution to a formula for a chemical reaction rate, one must introduce a number of additional assumptions. These assumptions are reasonably well satified for a great many chemical reactions, so the Arrhenius equation is very useful. But it is nevertheless an approximation.--Rparson 02:30, 30 January 2006 (UTC)
thread_title: Query2

message: Really, there should be a different article for the Eyring equation than the Arrhenius equation, as they are derived from different theories.
See Eyring equation V8rik 19:33, 20 January 2006 (UTC)
replies: text: The Arrhenius equation is not really "derived" at all - as far as I know there is no microscopic model that leads exactly to the Arrhenius equation. It's a quasi-empirical result. I think it is reasonable to keep some discussion of how microscopic models such as "collision theory" and transition state theory lead to Arrhenius-like expressions, but perhaps the present discussion is too long.   What we really need is a much better, much more thorough article on transition state theory. --Rparson 02:30, 30 January 2006 (UTC)
thread_title:  Eyring equation 

message: How is the Arrhenius equation linked to what is called Kramers or Kramers-Bell theory for a two-state system (e.g. protein folding/unfolding). The equations look pretty much the same.  —Preceding unsigned comment added by 128.214.3.229 (talk) 15:15, 2 October 2007 (UTC)
thread_title: Query3

message: In all articles related to the arrhenius equation it is stated that the exponential factor stems from the Maxwell-Boltzmann distribution.
Can anyone show how this is actually derived?  —Preceding unsigned comment added by 84.191.237.160 (talk) 18:52, 16 December 2007 (UTC)
thread_title:  how to get the exponential factor 

message: The tendency of chemical reaction rates to double with each 10 deg C increase in temperature is a fairly important characteristic of the natural world.  It informs much of what we understand about pedogenesis, chemical weathering,  and biogeochemical cycles.  This article has been the only place in Wikipedia that frames this important concept in a way that is so easily and immediately recognizable, and I urge the watchers of this article to retain this popular treatment. I have restored and referenced a single sentence to this effect. I support expanding it. --Paleorthid (talk) 00:30, 8 August 2008 (UTC)
thread_title: Doubling with 10 deg C increase

message: Really? God EmperorTalk 20:05, 12 June 2011 (UTC)
thread_title:  "Fudge factor" 

message: The article has a quote "it is not feasible to establish ... whether the predicted ... dependence ... is observed experimentally".  I don't have access to the original source, but it appears to be so out of context as to be meaningless.  The precision with which rates of different reactions can be measured, varies by many orders of magnitudes.  What sort of system was the original talking about?  — Preceding unsigned comment added by 131.203.251.94 (talk) 19:26, 14 October 2013 (UTC)
thread_title:  Context for quote re experiment & pre-exponential? 

message: I am new to this page and to Wikipedia editing in general. Perhaps someone has already touched on this point somewhat in earlier discussion. If so, I apologize. 
I attempted to work out the Arrhenius equation given in this article from the viewpoint of statistical mechanics and the canonical partition function. First, view each interaction (reacting or non-reacting) as individual subsystems of the system of all the collisions that occur in a given time interval, assumes to obey the assumptions of the canonical ensemble. Thus, finding the partition function of a system undergoing a reaction is simply the partition function of each pair, multiplied together (assuming no reactions occur with more than 2 reactants). The partition function
:  Z = \sum_{s} \mathrm{e}^{- \beta E_s}
and its associated ensemble yields the probability of a certain collision resulting in a reaction
: P_s = \frac{1}{Z} \mathrm{e}^{- \beta E_r},  where  E_r  is the energy state of the products.
Now, in order to be completely general, we cannot pretend to know what the partition function is, as every interaction can have multiple ways for the reactants to interact, leading to multiple energies to sum over, with perhaps degenerate states. However, if we assume that the temperature remains approximately constant (and that the energies of the reaction and their corresponding degenerates do not depend on the extent of the reaction), we can say that  \frac{1}{Z}  is approximately constant. Thus, when we multiply  P  by the number of collisions per second, we have
:  A\frac{1}{Z} \mathrm{e}^{- \beta E_s}, 
which is the average number of reacting collisions per second. However, this would yield
:k = A \frac{1}{Z} e^{-E_a/(k_B T)}= Ce^{-E_a/(k_B T)} as the Arrhenius equation. This of course would not affect measurements, but it would affect how we interpret the prefactor. Instead of interpreting  A  as the total number of collisions per second, it would be interpreted as the number of collisions per second divided by the partition function of the reaction in question.
Essentially, my argument is that the probability of a collision resulting in a reaction needs to be normalized before it can be interpreted as a probability. 
Physicsman19 (talk) 14:16, 17 July 2014 (UTC)
replies: text: This is not a simple question as I'm sure you realize. For one thing, in chemical kinetics the partition function is part of the transition state theory, whereas the number of collisions is part of the collision theory. So you seem to be mixing two separate theories of the rate constant, each of which has its own article. This leads me to believe that your argument is what Wikipedia calls original research (see WP:OR), that is working things out your own way rather than using reliable sources such as textbooks or review articles. I would suggest you try to find one or more sources which address your points, and then try to summarize their arguments in the appropriate article. This article is really for the empirical Arrhenius law, so a better place would be either Transition state theory or Collision theory. Dirac66 (talk) 19:24, 17 July 2014 (UTC)
thread_title:  Prefactor