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

2.8 References 41
3. Kinetics of complex reaction systems
Real reaction systems are usually much more complicated:
• Net reaction mechanisms may consist of ≈ 100 - 10 000 elementary reactions.
• No analytical solutions for the rate laws.
• In favorable cases, one may be able to use certain approximations to simplify the
reaction systems, like
— apply steady-state approximation where possible,
— take into account reactions in equilibrium,
— take into account microscopic reversibility (detailed balancing).
• For more acurate descriptions, however, one usually needs numerical solutions
for the rate equations. Using modern computers, this is not a problem even for
10 000 reactions, as long as the transport processes are not too complicated
(as, for example, 1D reaction systems such premixed flames or 1D models of atmospheric
chemistry). However, numerical solutions are still extremely challenging
for instationary 3D reaction systems, such as
— 3D models of atmospheric chemistry including daily/annual variations and
couplings to the ocean,
— ignition processes (internal combustion engines).
3.1 Determination of the order of a reaction
Any reaction mechanism which we may postulate has to explain the observed reaction
order. Thus, the determination of the reaction order is a central topic.
We explore some general methods for determining the reaction order by considering an
example:
= − [A] = [A] (3.1)
I First-order and second-order reactions: Test whether plots of ln vs. or 1 vs.
, give the straight lines expected for first-order or second-order reactions, respectively.
I Log-log plot of reaction rate vs. concentration: We see from Eq. 3.1 that a
log-log plot of vs. [A] gives a straight line with slope :
lg ∝ lg [A] (3.2)