Week 5.1 - Compact Notation Derivation for a simple Mechanism

Reaction rate is the speed at which a chemical reaction takes place and the reactants are converted to products.

These reaction rates can be modelled as an ordinary differential equation ODE for the concentration of species. The rate of product formation is the rate of depletion of reactant species. To solve these ODE functions various numerical techniques are applied.

So we use some compact notation scheme to derive the rate of a simple reaction mechanism

The reaction mechanism model is given below:

`CO+O2⟺CO2+O`

`O+H2O⟺OH+OH`

`CO+OH⟺CO2+H`

`H+O2⟺OH+O`

j = no of reacting species [CO O2 CO2 O OH H2O H]

the rate of reacting species are given as :

`d[CO]/dt=-Kf1[CO][O2]+Kr1[CO2][O]-Kf3[CO][OH]+Kr3[CO2][H]`

`d[O2]/dt=-Kf1[CO][O2]+Kr1[CO2][O]-Kf4[H][O2]+Kr4[O][0H]`

`d[CO2]/dt=Kf1[CO][O2]-Kr1[CO2][O]+Kf3[CO][OH]-Kr3[CO2][H]`

`d[O]/dt=Kf1[CO][O2]-Kr1[CO2][O]-Kf2[O][H2O]+Kr2[OH]^2+Kf4[H][O2]-Kr4[OH][O]`

`d[OH]/dt=Kf2[H2O][O]-Kr2[OH]^2-Kf3[CO][OH]+Kr3[CO2][H]+Kf4[H][O2]-Kr4[OH][O]`

`d[H2O]/dt=-Kf2[O][H2O]+Kr2[OH]^2`

`d[H]/dt=Kf3[CO][OH]-Kr3[CO2][H]-Kf4[H][O2]+Kr4[OH][O]`

The heat flow rate

`q1=Kf1[CO][O2]-Kr1[CO2][O]`

`q2=Kf2[O][H2O]-Kr2[OH]^2`

`q3=Kf3[CO][OH]-Kr3[CO2][H]`

`q4=Kf4[H][O2]-Kr4[OH][O]`

The production rate of the system:

`w1=-q1-q3`

`w2=-q1-q4`

`w3=q1+q3`

`w4=q1-q2+q4`

`w5=2q2-q3+q4`

`w6=-q2`

`w7=q3-q4`

The production rate is equal to the rate of reacting species: