General Dynamics of Unimolecular Conversion
For a general unimolecular reaction involving interconversion of different species, whose concentrations at time are denoted by through, an analytic form for the time-evolution of the species can be found. Let the rate constant of conversion from species to species be denoted as, and construct a rate-constant matrix whose entries are the .
Also, let be the vector of concentrations as a function of time.
Let be the vector of ones.
Let be the × identity matrix.
Let be the function that takes a vector and constructs a diagonal matrix whose on-diagonal entries are those of the vector.
Let be the inverse Laplace transform from to .
Then the time-evolved state is given by
- ,
thus providing the relation between the initial conditions of the system and its state at time .
Read more about this topic: Rate Equation
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