Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

2.2 Kinetics of irreversible first-order reactions 18
I
Conclusion:
Thehalflifetimeforafirst-order reactions is independent of the initial concentration!
I Experimental determination of k:
(1) Plot of ln [A] vs. gives a straight line with slope = − (see Fig. 2.5):
ln ([A] [A] 0
)=− (2.45)
Advantage: We do not need to know the absolute concentration of [A].
(2) Numerical fit of to the exponential decay curve using the Marquardt-Levenberg
non-linear least-squares fitting algorithm (Fig. 2.6; see Appendix B for details).
This method is useful in particular for analyzing experimental decay curves with
a constant background term. Again, we do not need to know the absolute concentration
of [A].
Advantages: Can be applied in presence of a constant background signal (noise,
weak DC signal). Can also be applied for analyzing data from pump-probe experiments,
when the duration of the pump is not short to the decay (deconvolution).
I Figure 2.6: Exponential decay curve of a particular vibration-rotation state of
the CH 3 O radical resulting from its unimolecular dissociation reaction according to
CH 3 O → H+H 2 CO (Dertinger 1995). The small box is the output box from a fit
using the software package ORIGIN.