To produce B according to the chemical reaction $AB$ we have the following CSTR reactor

$($Continuous Stirred Tank Reactor$),$ shown in Figure $1,$ whose feed flow is $q=15\frac{L}{m}in$

considering a tank volume of $V=100L.$

Through the dynamic model of the reaction kinetics given by:

$r_1=k_0{e}^{-\frac{Ea}{RT}}{C}_A$

Where $k_0=0\mathrm{.}6mi{n}^{-1},Ea=0\mathrm{.}1\frac{J}{m}ol,R=8\mathrm{.}31\frac{J}{\text{m}\text{o}\text{l}\text{K}}$ and $T=323K.$ We wish to

study the behavior of the concentration of reactant $C_A$ and of product $C_B$ inside the reactor. $($Supose a concentration for CA and CB$)$

For this analysis, you have been asked as a Process Engineer to determine the following

points:

List $3$ important assumptions that must be considered in the material and$/$or energy

balance in the above process to model the $AB$ reaction kinetics described above

as a first$-$order differential equation.

Determine the first$-$order differential equation that models the behavior of chemical

kinetics inside the tank for the consumption of reagent $A.$

Determine the first$-$order differential equation that models the behavior of chemical

kinetics inside the tank for the production of compound $B.$

For both differential equations, express the dynamic model as a Transfer Function

and justify whether the consumption model of A and the production model of $B$ are

stable $($argue your answer with the Argand Diagram$).$

For both models, calculate the time constant $$ and the profit of the process $K.$

Determine the units and explain which is faster, the consumption of $A$ or the

production of B $($justify your answer$).$

How long does it take for the chemical reaction to stabilize?

What is the concentration $C_A$ What remains in the reactor upon reaching the steady

state in the kinetic model, if an input feed $($step type$)$ of this substance of $C_{A_{in}}=20$

$mo\frac{l}{L}$ is considered?

Determine the $C_B(t)$ equation obtained by the inverse Laplace transform of the model

that represents the concentration of compound B inside the CSTR reactor.

Graphically shows the dynamic behavior of the concentration of $B$ over time. What is

the maximum concentration of $B$ that was obtained in the reactor in this experiment?