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The universal gas constant R has indeed the same units as the Boltzmann's constant (normally also written as "k", not to confuse with the "k" in Arrhenius equation!).
Let me explain:
[R] = E K-1 mol-1
[k] = E K-1
and the potential confusion comes from the facty that a mol is indeed dimensionless (it is as if you say "a dozen", though a "mol" is much bigger (Avogadro's number)). So, RT has also dimensions of energy, and E/RT is indeed dimensionless as expected. jbc
I have a request - I know (or believe I know :) that there are reactions that don't follow the Arrhenius equation. Could someone knowledgeable update the page with the categories of reactions that don't obey the equation? I understand that the equation won't be accurate when, for example, the output energy of the equation drives other reactions that consume the reactants for the reaction you're interested in. I'm wondering if there are other examples.
--Could you give a more specific example of your output energy driving other reactions example?
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.
The problem is when a reaction we're looking at is not fundamental. Then there are actually a bunch of sub-reactions going on. There might be steps that are not reactions at all - for example, if it's a catalytic reaction, some chemical needs to stick to a solid surface before it reacts. Adsorption (the chemical sticking of a molecule to a solid) goes *down* with temperature. The rate constant of the fundamental reaction steps increase with temperature, but at different, er, rates. There could also be reverse reactions, and if they increase with temperature, the overall rate for a reaction (forward minus backward) will go down.
The rate for a complicated reaction will (hopefully) consist of an algebraic expression of the reactants and the rate constants for many of the fundamental reactions that comprise the overall reaction. Each one of these fundamental rate constants will follow an Arrhenius law, but the overall reaction cannot follow an Arrhenius model because there is more than one rate constant. ---Alchemy3083 26 April 2005
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)
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)
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)
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)
Really? God Emperor Talk 20:05, 12 June 2011 (UTC)
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)
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
and its associated ensemble yields the probability of a certain collision resulting in a reaction
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 is approximately constant. Thus, when we multiply by the number of collisions per second, we have
which is the average number of reacting collisions per second. However, this would yield
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)physicsman19 7/17/2014
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
![]() | This article is substantially duplicated by a piece in an external publication. Please do not flag this article as a copyright violation of the following source:
|
The universal gas constant R has indeed the same units as the Boltzmann's constant (normally also written as "k", not to confuse with the "k" in Arrhenius equation!).
Let me explain:
[R] = E K-1 mol-1
[k] = E K-1
and the potential confusion comes from the facty that a mol is indeed dimensionless (it is as if you say "a dozen", though a "mol" is much bigger (Avogadro's number)). So, RT has also dimensions of energy, and E/RT is indeed dimensionless as expected. jbc
I have a request - I know (or believe I know :) that there are reactions that don't follow the Arrhenius equation. Could someone knowledgeable update the page with the categories of reactions that don't obey the equation? I understand that the equation won't be accurate when, for example, the output energy of the equation drives other reactions that consume the reactants for the reaction you're interested in. I'm wondering if there are other examples.
--Could you give a more specific example of your output energy driving other reactions example?
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.
The problem is when a reaction we're looking at is not fundamental. Then there are actually a bunch of sub-reactions going on. There might be steps that are not reactions at all - for example, if it's a catalytic reaction, some chemical needs to stick to a solid surface before it reacts. Adsorption (the chemical sticking of a molecule to a solid) goes *down* with temperature. The rate constant of the fundamental reaction steps increase with temperature, but at different, er, rates. There could also be reverse reactions, and if they increase with temperature, the overall rate for a reaction (forward minus backward) will go down.
The rate for a complicated reaction will (hopefully) consist of an algebraic expression of the reactants and the rate constants for many of the fundamental reactions that comprise the overall reaction. Each one of these fundamental rate constants will follow an Arrhenius law, but the overall reaction cannot follow an Arrhenius model because there is more than one rate constant. ---Alchemy3083 26 April 2005
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)
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)
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)
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)
Really? God Emperor Talk 20:05, 12 June 2011 (UTC)
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)
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
and its associated ensemble yields the probability of a certain collision resulting in a reaction
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 is approximately constant. Thus, when we multiply by the number of collisions per second, we have
which is the average number of reacting collisions per second. However, this would yield
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)physicsman19 7/17/2014