# Where do the rate laws for the Chlorine Dioxide-Iodine-Malonic Acid reaction come from?

After reading a section on this particular oscillatory reaction, something started bugging me about it.

However, let me lay out the basis of my question. From what I've researched, Lengyel and Epstein proposed a model that captures the overall behavior of the system. There are a few different versions of the model in regard to the dimensions, but this seems to be the most popular:

$\ce{MA+I_2 \rightarrow IMA + I^- + H^+;\hspace{1mm} \frac{d[I_2]}{dt} = -\frac{k_{1a}[MA][I_2]}{k_{1b}+[I_2]}}$

$\ce{ClO_2 + I^2 \rightarrow ClO_2^+ + \frac{1}{2}I_2; \hspace{1mm}\frac{d[CLO_2]}{dt} = -k_2[CLO_2][I^-]}$

$\ce{ClO_2^- + 4I^- + 4H^+ \rightarrow Cl^- + 2I_2 + 2H_2O}$

$\ce{\frac{d[CLO_2^-]}{dt} = -k_{3a}[ClO_2^-][I^-][H^+]-k_{3b}[CLO_2^-][I_2]\frac{[I^-]}{u+[I^-]^2}}$

Personally, I am much more familiar with the mathematics than the chemistry. First, are these rate laws empirical or were they derived from physical laws? Pardon me if this is a naive question, but I am not as familiar with chemistry than the other hard sciences. In basic cases, rate laws are a straight multiplication of the concentrations of the present species. However, that neglects situations involving, for example, autocatalycity. My suspicion is that it is a mixture of processes that I'm not familiar with and simple observation.

Obviously, these reactions don't violate the laws of thermodynamics. My assumption is that the overall free energy of the system continues to decline - meaning that the system eventually reaches equilibrium. Unfortunately, I've been at a loss to find good sources on oscillatory chemical reactions.

• From what I know the rate law of a reaction can only be determined experimentally. I'm not sure if there are any exceptions. – kaliaden Apr 10 '13 at 8:25
• @kaliaden You raise a good point. Rate laws can only be determined experimentally. What I should have said is that the general framework of rate laws may be determined before experiments. For instance, A+B->C (assuming an elementary step) rate law has the general form of r=k[A]^a[B]^b. "k" can only be determined by experiment - thus forming the full rate law. That said, my question is really if a general framework was developed empirically, or there is a an principle forming a basis for the development of the rate laws in my post. – Mlagma Apr 11 '13 at 5:47
• I do not understand what Your question is. Do You know it Yourself? – Georg Apr 16 '13 at 11:27
• @Georg "First, are these rate laws empirical or were they derived from physical laws?" And second: how is the reaction described thermodynamically? (the last paragraph). – Mlagma Apr 17 '13 at 7:40