Deriving the reaction rate ODEs of a simple reaction mechanism

Compact Notation Derivation

The below are the reactions that are taken to derive notation

Reaction Mechanism

Let us assaign numbering with a variable index j to the especies so that it would be helpfull in deriving the equations

j	Species
1	CO2
2	O2
3	CO2
4	O
5	H2O
6	OH
7	H

And numbering reaction with an variable index i

Stoichiometric Matric reactants and Products

Here we change reaction to stoichiometric matrices individually for reactants and products where superscript of V with a single quote is reactants matrix and double quote is product matric

Vji is the stoichiometric difference of reactants and products

Reaction rate

Net Reaction rates for 4 reactions where X is the concentration of species per unit volume, Kfi is rate of forward reaction of i the reaction and Kri is rate of reverse reaction of i the reaction

Production Rate

In production rate we ar summing up the prodycts of stoichiometric matrix and net reaction rate

production rate for different species from 1 to 7

The below are the reaction rate ODEs of a above given reaction mechanism

Ordinary Differencial Coupled equations