3.2.5 (Chemical kinetics) Consider the chemical reaction system A+X 2X X +B-C. This is a generalization of Exercise 2.3.2; the new feature is that X is used up in the production of C. a) Assuming that both A and B are kept at constant concentrations a and b, show that the law of mass action leads to an equation of the form i q,x-c,x, where x is the concentration of X, and c1 and c2 are constants to be determined. b) Show that x* = 0 is stable when k2b > kja, and explain why this makes sense chemically.

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3.2.5 (Chemical kinetics) Consider the chemical reaction system
A+X 2X
X +B-C.
This is a generalization of Exercise 2.3.2; the new feature is that X is used up in the production of C.
a) Assuming that both A and B are kept at constant concentrations a and b, show that the law of mass
action leads to an equation of the form i = c,x-c,x, where x is the concentration of X, and c1 and c2 are
constants to be determined.
b) Show that x* = 0 is stable when k2b > k1a, and explain why this makes sense chemically.
Transcribed Image Text:3.2.5 (Chemical kinetics) Consider the chemical reaction system A+X 2X X +B-C. This is a generalization of Exercise 2.3.2; the new feature is that X is used up in the production of C. a) Assuming that both A and B are kept at constant concentrations a and b, show that the law of mass action leads to an equation of the form i = c,x-c,x, where x is the concentration of X, and c1 and c2 are constants to be determined. b) Show that x* = 0 is stable when k2b > k1a, and explain why this makes sense chemically.
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