Assignment 2 Solutions

Assignment 2 Solutions - AMATH/BIOL 382 Problem Set 2...

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Unformatted text preview: AMATH/BIOL 382 Problem Set 2 Solutions 1. a) The full reaction mechanism is described by ds ( t ) dt =- k 1 s ( t ) e ( t ) + k- 1 c ( t ) de ( t ) dt =- k 1 s ( t ) e ( t ) + ( k- 1 + k 2 ) c ( t )- k- 2 e ( t ) p ( t ) dc ( t ) dt = k 1 s ( t ) e ( t )- ( k- 1 + k 2 ) c ( t ) + k- 2 e ( t ) p ( t ) dp ( t ) dt = k 2 c ( t )- k- 2 e ( t ) p ( t ) . Making use of the conservation e ( t ) = e- c ( t ) we can reduce the system description to ds ( t ) dt =- k 1 s ( t )( e- c ( t )) + k- 1 c ( t ) dc ( t ) dt = k 1 s ( t )( e- c ( t ))- ( k- 1 + k 2 ) c ( t ) + k- 2 ( e- c ( t )) p ( t ) dp ( t ) dt = k 2 c ( t )- k- 2 ( e- c ( t )) p ( t ) . b) If we apply the quasi-steady state assumption to the complex c , we set 0 = k 1 s ( t )( e- c ( t ))- ( k- 1 + k 2 ) c ( t ) + k- 2 ( e- c ( t )) p ( t ) , which gives k 1 s ( t ) + ( k- 1 + k 2 ) + k- 2 p ( t ) c ( t ) = k 1 s ( t ) e + k- 2 e p ( t ) . That is, suppressing the time dependence c = k 1 se + k- 2 e p k 1 s + k- 1 + k 2 + k- 2 p . c) Then, the overall reaction rate is given by V = dp dt = k 2 c- k- 2 ( e- c ) p 1 = k 2 k 1 se + k- 2 e p k 1 s + k- 1 + k 2 + k- 2 p- k- 2 e p- k- 2 p k 1 se + k- 2 e p k 1 s + k- 1 + k...
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This note was uploaded on 04/11/2010 for the course CHEM 1101 taught by Professor Leroy during the Spring '10 term at University of Toronto.

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Assignment 2 Solutions - AMATH/BIOL 382 Problem Set 2...

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