Kinetic fits to some experimental data sets results in an exponent greater than 2. The equation is question is dC/dt = -kCn, where C is concentration, t is time, k is the rate constant, and n is the exponent on C. The question is, has anyone found it useful to allow n to exceed 2, that is to go to a kinetic order greater than 2nd?
Thanks!
Quick comments first. The exponential kinetics means that n = 1 (the first order with respect to [C]). If n= 2, this reaction is called the second order with respect to [C]. In this case the reaction might be a bimolecular: C + C -> products. For the complex reaction mechanism n could be >2. An example C + C B, B + C -> products
Let me clarify. We are not assuming anything about the mechanism, although it can be presumed to be microbial metabolism, with perhaps hydrolysis active as well. We are looking for the best approximation to a first-order fit, when the decline curve is clearly not first-order. How far from n = 1 is appropriate?
How do you measure [C]? I can have a look on your kinetic curve and make some conclusions, if you send me raw data.
C is usually measured by liquid scintillation counting, as the test compounds are 14-C labelled. If you look at my conference paper "Standard Operating Procedure for Degradation Kinetics in U.S. EPA Office of Pesticide Programs" on my publications page, and look at slide 16, you will see a good example of what I am talking about.
As far as I know and I've seen in different experimental data and papers, mostly those kinetic equation are valid for values of n, when it is mines or equals 2. The most common one is when the n=1, the first order kinetic equation. I have not viewed any other practical process which has a n, more than 2, at least in my field. It's somehow just like normal distribution, which variables in the real life prefer to follow this probability distribution and maybe for kinetic equation most of mechanisms obey for n
I am not familiar with microbiology, but in comparison with heterogeneous catalysis, it seems, that you are measuring a so called "macro"-kinetics, i.e. an average kinetics of many elementary reactions. In this case your variable n is an apparent reaction order and have no physical meaning anymore (it can take any value you want). However since you have 2 variables (n and k) you can fit more or less what you want in your model. n is supposed to represent the dependency of the concentration on your system. If you change your initial concentration (i assume that you work in batch mode) of product C but keep all other experimental conditions identical, the reaction rate k should be the same (or fixed in your fitting) but you may get a better estimation of the variable n. Don't know if it help but hope so.
Would you say that if the pesticide was tested for degradation is several soils (usually it is 4 to 6), and most of them came out as n = 1, that the first-order results should be used for that pesticide in all soils?
William,
as I wrote you the best is to use at least two initial concentrations for one soil type. k and n are characteristic values for each soil, they should not be the same. But you can find correlation between k and n with soil properties.
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