Modeling Higher Order Reactions

GoldSim was designed to simulate first-order decay reactions.  Note, however, that by defining the decay rate as a function of concentration(s), higher order reactions can also be represented.

For example, suppose you wanted to simulate the following reaction within GoldSim:

     A ⇒ B

in which the reaction was second order:

     d[A]/ dt = -k [A]2                          

where [A] is the mole concentration of A in the Cell of interest and k is the second order rate constant, with units of [(mole/m3)-1 yr-1].  First, of course, you would specify that B was a daughter of A.  How then, would you represent the second order reaction rate?

In this case, we could rewrite the rate law as:

     d[A]/dt = -{k cA / MWA} [A] = -k' [A]

where cA is the mass concentration, and MWA is the molecular weight.  k' then represents a “pseudo first-order” rate constant.   Specifying the "pseudo first-order" decay rate for A as the function “(k) (MWA)/AA” has the effect of simulating the second-order rate law.

Note that defining the decay rate as a function of the concentration creates a recursive model (since the dissolved concentration is a function of the decay rate, and the decay rate is a function of the dissolved concentration).  Hence, when you do this, you must utilize a previous value element.   

   Note: In order to model reactants, you must have the RT Module.  If you are using the CT Module, you can model decay, but cannot model any reactants.

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