Species Lifetimes and Timescales

The simplest way to decompose the timescales of a chemical system is according to individual species. The half-life ry2 of a species is the time during which the concentration of a species would be halved, estimated by assuming that the investigated species is not produced, and all rate coefficients and other concentrations remain at their initial value. More specifically, only those species concentrations have to remain constant, which influence the consumption rate of the investigated species. It is clear from this definition that cases where the concentration of the species is really halved during the half-Ufe may be exceptional ones. 

Such exceptional cases usually form the examples given in textbooks. For example, when the only reaction of species A is its first-order decay A- B with rate coefficient k, and at initial time t = 0, its concentration is ao, the change of its concentration over time is given by 

The linearised form of this expression can be obtained by taking the natural logarithm of both sides  

After time ti/2, the concentration of A will be half (ao/2) of the initial value. 

This means that in a first-order decay, the half-life is independent of the initial concentration. 

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