Question

2. Consider our chemical reaction system By solving the system Sk = w, where S is the stoichiometric matrix and w = [-3,- k = [ki,k2,k31 k4] of reaction rates that give w as the vector of net changes 2,-2,41, find all vectors 3. Find the null space N (S) of the stoichiometric matrix of Problem 2. Con- vince yourself that for any two solutions ki, k2 that you found in Problem 2 the difference k k2 is in N(S)

Answer 1

(2)

A+2B------->2C

A+2C------->2D

A+B------>D

B+D------->2C

So stoichiometric matrix

S =

- 1. - 2. 2. 0.  
- 1. 0. - 2. 2.  
- 1. - 1. 0. 1.  
0. - 1. 2. - 1

So

sk=w

-k1-2k2+2k3=-3

-k1-2k3+2k4=-2

-k1-k2+k4=-2

-k2+2k3-k4=4

So solving this equations:

k1=1

k2=2

k3=0

k4=0