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20. The Brusselator. This hypothetical system was first proposed by a group work- ing in Brussels [see Prigogine and Lefever (1968)] in connection with spatially nonuniform chemical patterns. Because certain steps involve trimolecular reac tions, it is not a model of any real chemical system but rather a prototype that has been studied extensively. The reaction steps are A-X. B+X-Y+D. 2X+ Y-3X, X-E. 305 It is assumed that concentrations of A, B, D, and E are kept artificially con stant so that only X and Y vary with time. (a) Show that if all rate constants are chosen appropriately, the equations de scribing a Brusselator are: dt A-(B+ 1)x + x²y, dy =Bx-x²y. di

20. The Brusselator. This hypothetical system was first proposed by a group work- ing in Brussels [see Prigogine and Lefever (1968)] in connection with spatially nonuniform chemical patterns. Because certain steps involve trimolecular reac tions, it is not a model of any real chemical system but rather a prototype that has been studied extensively. The reaction steps are A-X. B+X-Y+D. 2X+ Y-3X, X-E. 305 It is assumed that concentrations of A, B, D, and E are kept artificially con stant so that only X and Y vary with time. (a) Show that if all rate constants are chosen appropriately, the equations de scribing a Brusselator are: dt A-(B+ 1)x + x²y, dy =Bx-x²y. di

Chemistry: The Molecular Science
Chemistry: The Molecular Science
5th Edition
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:John W. Moore, Conrad L. Stanitski
Chapter12: Chemical Equilibrium
Section: Chapter Questions
Problem 102QRT
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20. The Brusselator. This hypothetical system was first proposed by a group work- ing in Brussels [see Prigogine and Lefever (1968)] in connection with spatially nonuniform chemical patterns. Because certain steps involve trimolecular reac tions, it is not a model of any real chemical system but rather a prototype that has been studied extensively. The reaction steps are A-X. B+X-Y+D. 2X+ Y-3X, X-E. 305 It is assumed that concentrations of A, B, D, and E are kept artificially con stant so that only X and Y vary with time. (a) Show that if all rate constants are chosen appropriately, the equations de scribing a Brusselator are: dt A-(B+ 1)x + x²y, dy =Bx-x²y. di
Transcribed Image Text:20. The Brusselator. This hypothetical system was first proposed by a group work- ing in Brussels [see Prigogine and Lefever (1968)] in connection with spatially nonuniform chemical patterns. Because certain steps involve trimolecular reac tions, it is not a model of any real chemical system but rather a prototype that has been studied extensively. The reaction steps are A-X. B+X-Y+D. 2X+ Y-3X, X-E. 305 It is assumed that concentrations of A, B, D, and E are kept artificially con stant so that only X and Y vary with time. (a) Show that if all rate constants are chosen appropriately, the equations de scribing a Brusselator are: dt A-(B+ 1)x + x²y, dy =Bx-x²y. di
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