Compact Notation Derivation for a simple Mechanism

1.CO + O2 -> CO2 + O

2.O + H2o -> OH + OH

3.CO + OH -> CO2 + H

4.H + O2 -> OH + O

i `rarr` reaction number

`K_i =` reaction rate of the `i^(th)`reaction

j Species

1 `O_2`

2 CO

3 O

4 `H_2O`

5 OH

6 H

7 `CO_2`

`v_{ij}`= `[(-1,-1,1,0,0,0,1),(0,0,-1,-1,2,0,0),(0,-1,0,0,-1,1,1),(-1,0,1,0,1,-1,0)]`

`q_1 = k_1[CO][O_2]`

`q_2 = k_2[O][H_2O]`

`q_3 = k_3[CO][OH]`

`q_4 = k_4[H][O_2]`

`w_j = sum_(i=1)^4 v_(ij)^\' xx q_i`

`[(w_1),(w_2),(w_3),(w_4),(w_5),(w_6),(w_7)] = [(-1,0,0,-1),(-1,0,-1,0),(1,-1,0,1),(0,-1,0,0),(0,2,-1,1),(0,0,1,-1),(1,0,1,0)]xx[(q_1),(q_2),(q_3),(q_4)]`

where the column vector w is the reaction rate ode of the species