Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...
Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ... Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...
3.6 Oscillating reactions* 67 I Figure 3.5: Autocatalysis. • Ascanbeseenfromthesigmoid(-shaped) concentration-time profile of [B] in Fig. 3.5, the rate of increase of [B] increases up to the inflection point ∗ . • This curve is typical for a population increase from a low plateau to a new (higher) plateau after a favorable change of the environment due to, e.g., the availability of more food, a technical revolution, a reduction of mortality by a medical breakthrough, ... Many interesting games which can be played based on these ideas are described in (Eigen 1975). 3.6.2 Chemical oscillations The presence of one or more autocatalytic steps in a reaction mechanism can lead to chemical oscillations. a) The Lotka mechanism The origin of chemical oscillations can be understood by considering the reaction mechanism proposed by Lotka in 1910 (see Lotka 1920): (3.175) A+X 1 → X+X (1) X+Y 2 → Y+Y (2) Y → 3 Z (3)
3.6 Oscillating reactions* 68 • Both reactions (1) and (2) are autocatalytic. • The Lotka mechanism illustrates the principle, but it does not correspond to an existing chemical reaction system. • A real oscillating reaction is the Belousov-Zhabotinsky reaction; this reaction may be described using a more complicated mechanism (see below). In order to model the resulting chemical oscillations, we assume that the reaction takes place in a flow reactor, which is constantly supplied with new A such that the concentration of A stays constant ([A] = [A] 0 ), while the product Z is constantly removed. I Rate equations and steady-state solutions: [X] [Y] =+ 1 [A] 0 [X] − 2 [X] [Y] (3.176) =+ 2 [X] [Y] − 3 [Y] (3.177) Steady-state solutions: [X] [Y] =+ 1 [A] 0 [X] − 2 [X] [Y] = 0 (3.178) =+ 2 [X] [Y] − 3 [Y] = 0 (3.179) Dividing these equations by [X] and [Y], respectively, we find 2 [Y] = 1 [A] 0 (3.180) 2 [X] = 3 (3.181) Since [A] = [A] 0 , the steady state solutions for [X] and [Y] are independent of time! I Displacements from steady-state solutions: What happens if the concentrations are displaced from the steady-state values by small amounts and ? (1) Ansatz: [X] = [X] + (3.182) [Y] = [Y] + (3.183)
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3.6 Oscillating reactions* 67<br />
I<br />
Figure 3.5: Autocatalysis.<br />
• Ascanbeseenfromthesigmoid(-shaped) concentration-time profile of [B] in<br />
Fig. 3.5, the rate of increase of [B] increases up to the inflection point ∗ .<br />
• This curve is typical for a population increase from a low plateau to a new (higher)<br />
plateau after a favorable change of the environment due to, e.g., the availability<br />
of more food, a technical revolution, a reduction of mortality by a medical<br />
breakthrough, ...<br />
Many interesting games which can be played based on these ideas are described in (Eigen<br />
1975).<br />
3.6.2 <strong>Chemical</strong> oscillations<br />
The presence of one or more autocatalytic steps in a reaction mechanism can lead to<br />
chemical oscillations.<br />
a) The Lotka mechanism<br />
The origin of chemical oscillations can be understood by considering the reaction mechanism<br />
proposed by Lotka in 1910 (see Lotka 1920):<br />
(3.175)<br />
A+X 1<br />
→ X+X (1)<br />
X+Y 2<br />
→ Y+Y (2)<br />
Y<br />
<br />
→<br />
3<br />
Z (3)
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