The given molecules in order of the increasing surface tension at a given temperature are to be ranked. Concept introduction: The molecules on the surface and bulk experience different intermolecular forces. The molecule in bulk is surrounded by the molecules from all sides. Therefore the net force on the molecules is zero. On the other hand, molecules on the surface have molecules only below them so the net attractive force experienced by them is in downward direction. Due to the net attractive forces, the surface molecules will try to move into the bulk and surface area decreases. Surface tension is the energy that is needed to raise the surface area by a given amount. The unit of surface tension is J/m 2 . Surface tension is directly related to the intermolecular forces and therefore increases with increase in the intermolecular forces.

Question

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

Answer 1

Question

Chapter 12, Problem 12.63P

Interpretation Introduction

Interpretation:

The given molecules in order of the increasing surface tension at a given temperature are to be ranked.

Concept introduction:

The molecules on the surface and bulk experience different intermolecular forces. The molecule in bulk is surrounded by the molecules from all sides. Therefore the net force on the molecules is zero. On the other hand, molecules on the surface have molecules only below them so the net attractive force experienced by them is in downward direction.

Due to the net attractive forces, the surface molecules will try to move into the bulk and surface area decreases.

Surface tension is the energy that is needed to raise the surface area by a given amount. The unit of surface tension is J/m2. Surface tension is directly related to the intermolecular forces and therefore increases with increase in the intermolecular forces.

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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

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