Tuesday, May 8, 2012

Oscillating Chemical Reactions


Some chemical reactions proceed from reactant (Species A) to product (species B) in a steadfast manner, viz.,
                                                                                    A → B
That is, as reactant A is consumed, B is produced.  In general, however, most reactions proceed through a series of steps which lead to the observed products.  These reaction steps are referred to as the mechanism of the reaction.  For example, the Lotka-Volterra reaction converts species A to species B  by means of the following mechanistic steps:

(1)        A + X → 2X
(2)        X + Y → 2Y
(3)        Y → B

If you add all these equations together (you should treat the arrows in chemical reactions as equals [=] signs) you see that the X's and Y's all cancel out and the overall reaction is just
A → B.  This mechanism predicts that the intermediate species X (blue) and Y (amber) will oscillate in concentration as depicted in the accompanying graph.  The x-axis in the plot is time and the y axis is the concentrations of species X and Y.

This type of reaction is called an oscillating reaction, an example of which is the Briggs-Rauscher Reaction shown in a YouTube video posted by kviht:


If you're still awake after that soothing video you may have noticed that the blue species and the amber species alternately dominated in concentration.  You may also have noticed that I labeled the two species as Rabbits (blue) and Foxes (amber) in the above plot.  This is because Alfred Lotka, who proposed the above reaction mechanism as a theoretical chemical exercise in 1920, realized a few years later that this mechanism would also describe the population dynamics of a closed predator-prey animal system.  Vito Volterra independently came to the same conclusion at about the same time.  Thus, in the mechanism above, species A becomes rabbit food (grass, clover, whatever) present in great abundance, species X corresponds to the rabbits who reproduce after eating A, Y denotes the foxes who reproduce after eating rabbits, and B stands for foxes that have passed on by natural causes.  As the population of foxes increases it becomes a bad day for bunnies and the rabbit population plunges.  When the greedy foxes deplete the rabbit population, the foxes fade away.  Not so many foxes allows the rabbit population to recover, then spike, and so on.

 So, the next time you're walking through the woods and you spot a sly fox slinking about, warn him about Lotka-Volterra and the dangers of rabbit over-indulgence.