$[$Mathematical Model: Phenomena Law$]$

The following $2$ reactions are taking place in reactor $1$ with cross$-$section area $A_1,[m^2]$ and reactor $2$ with cross$-$section area $A_2,[m^2],$ respectively. The reactant A with concentration $C_A,[\frac{\text{m}\text{o}\text{l}}{m^3}]$ is reacted with reactant $B$ with concentration $C_B,[\frac{\text{m}\text{o}\text{l}}{m^3}]$ to produce $C$ and $D$ with concentration $C_C,[\frac{\text{m}\text{o}\text{l}}{m^3}]$ and $C_D,[\frac{\text{m}\text{o}\text{l}}{m^3}],$ respectively.

$A+B{r}_{A}C+D$

The product of reaction $(1)C$ with concentration $C_C,[\frac{\text{m}\text{o}\text{l}}{m^3}]$ is reacted with reactant $E$ with concentration of $C_E,[\frac{\text{m}\text{o}\text{l}}{m^3}]$

$C+E{r}_{C}F+G$

Both reactions occur at iso$-$thermal condition $\frac{dT}{dt}=0.$

$])$:$\}$

${}_{1in}$

$[darr$

The reactant A and reactant $B$ are pumped into reactor $1$ with volumetric flowrate $F_{1,im}[\frac{m^3}{h}]$ of density ${}_{1,in},[\frac{kg}{m^3}]$ and $F_{2,in},[\frac{m^3}{h}]$ of density ${}_{2,in},[\frac{kg}{m^3}].$ The product of the reaction i

$2$ of $8$

which is output of reactor $1$ is reacted with reactant $E$ with volumetric flowrate $F_{4,in},[\frac{m^3}{h}]$ of density ${}_{4,in},[\frac{kg}{m^3}].$

Assumption

the reaction is homogeneous

there is no change in density

Develop mathematical model or dynamic model of the system above for component balance of $C$ and $E.$