as chemists and chemical engineers, we often deal with rate constants.
Chemists often deal with a close system, but chemical engineers often deal with open system. The rate equation for both cases are: rate = k[A]n (considering a single=step reaction).
I am not sure if the rate constants for both open and close system should be the same, because there is mass exchange in an open system.
Arrhenius equation gives the rate constant as k = Ae-E/RT, where A is a function of the probability that the colliding reactant molecules possess sufficient kinetic energy and colliding at the required orientation.
I don't think A would be the same in an open system versus the close system, because there is prevailing direction of mass transfer in an open system (especially in the case of chemical reactors, where forced convection is dominant). There is no prevailing direction of mass transfer in a close system.
Well, the question is that nature is multihierarchical and and each level of molecular description you need different variables. Imagine that you needs variables n = (n1, n2) for description of state of your system. If variable n1 is related to processes with a characteristic time T1 and n2 with processes with T2, you can ignore one of those variables when one of the characteristic times is much more grater than the other. This is called contraction of the description.
Example, you have three processes in your chemical reactor: mixing, external flows, and the single chemical reaction for A <--> B. In principle you would need the vectorial variable n = (a1, a2, a3,..., b1, b2, b3,...) where each a (or b) measures the number of moles (or concentration) of chemical A (or B) in each point of your reactor. Call tR, tM and tF the characteristic times of reaction, mixing and flows respectively. There is several posibilities. Take the next example.
Imagine that flows of A and B are "fast" and mixing is "perfect" (that is, tR >> tM, tF), then one can mathematically
prove that all variables 'collapse' except two and your description collapse to n = (a, b) = (a1, b1) = (a2, b2) = (a3, b3) = ... for any
time of the order of tR.
This can be mathematically and rigorously proven but intuitivally understood. If mixing is perfect, this means that any inhomogeneity into the reactor is diluted in a tM time and therefore to greater times you can substitute the local concentration (e.g. a3) by a single concentration (for instance a) valid for the overall reactor.
In fact, we usually exploit time scales in our laboratories. For instance, when you work in the picosecond scale, electrons are in different configurations and you may use them. In a femtosecond scale, however, electron motion can already be ignored and you can work with stationary electronic wavefunctions (because nuclear motion is more slow that electronic one). Still motion of nucleus is perceptible in that scale and there is not molecules in the usual chemical sense just atomic-molecular systems.
Below the femtosecond, nuclear motion can be ignored and you can asume that different molecular configurations are equilibrated and, therefore, you work with chemical species; such as benzene. In fact, benzene is a collective denomination for different molecular species all formed by 6C and 6H. In nanoseconds, benzene can suffer chemical reactions but in a cosmological temporal scale, for instance, almost all reactions "happen" and one would even ignore the composition. In fact, in cosmological studies it is really unnecesary talk of chemical composition and just we talk of mass of the universe. That is description is again contracted.
Take your chemical example of rate constant as k = Ae-E/RT
This is already asuming a slow time scale. So slow, that system has thermalized and you can define a local equilibrium temperature T. If external flows are fast, there is no time for thermalization inside the reactor and there is not T! Then one may use the concept of nonequilibrium temperature, usually denoted by theta.
Do Theta = T + F(flow), where F is some known function of flows. For times >> characteristic time of flows F--> 0 and, therefore, Theta --> T. In the more general case, you may use Theta.
Imagine that F is a small correction to T then you can use the serie
(1/Theta) = (1/T)(1 - ...) =(1/T) + X.
Perhaps you would write some like
k = Ae-XE/R
with A' not equal to A.
This topic is extensive and i cannot deal here in detail. Note that not only one needs modification of usual kinetics knowledge of textbooks (usually focused to chemicals in homogeneous bulk). Other macroscopic disciplines as usual hidrodynamics are not valid in presence of rapid flows in open OR closed systems.
A book i read in the topic of rapid processes some time ago ishttp://www.amazon.com/gp/product/0387983732/002-6900299-7958415?v=glance&n=283155
The book is devoted to rational extended thermodynamics. There is other approaches like Extended irreversible thermodynamics. I do not like none of those and prefer use own methods (i have not still published anything in this point but i will do when i have got time). For example, i do not agree with definition of nonequilibrium heat defined in above monograph.
The book have a chapter in reactive mixture that could be of interest for you but i do not remember now much about it. I think that they finalized the chapter saying "this is a very difficult topic and we have done no significant advance" or similar.
If you are interested, the next wednesday i will go to library and will revise the chapter for you. But please say me tomorrow via posting or personal message.