In a batch reactor, there is no flow into or out of the reactor, and thus those terms

drop out. The accumulation term can be written as $\frac{dCx}{dt},$ while the

generation$/$consumption term comes from the rate law for the reaction $($rx$,$ wh

is the chemical species. For this series reaction, the rate laws are as follows:

$r_a=-k_1**Ca$

$r_b=k_1**Ca-k_2**Cb$

$r_c=k_2**Cb$

Plugging in the rate law for A into Eqn. $2$ written for $Ca,$ gives

$-k_1*Ca=r_a=\frac{\text{d}\text{C}\text{a}}{dt}$

Plugging in the other rate laws will give the other material balances, resulting in a

system of three ordinary differential equations $($ODEs$).$ P$3$ would like you to use an

ODE solver to calculate the concentrations of A$,$ B$,$ and C as a function of time in the

reactor for $T=200C.$ At reactor startup, the concentration of $A$ in the reactor is $1$

$mo\frac{l}{L},$ and no $B$ or $C$ is present.

P$3$ has requested a plot of concentration vs$.$ time that looks professional, with

legend, title, axis titles, and data for all three species plotted over an appropriate

length of time $($i$.$e$.$ Make sure the concentrations are fully developed, but not sitting

constant for $75\%$ of the plot$).$ Finally, determine the maximum concentration of B over

the course of the reaction at this temperature $($Hint: numpy.max$($array$\_$name$).).$ For

extra credit, determine the time at which this maximum cb occurs and the ratio of

undesired by$-$product to desired product $(C\frac{c}{C}b)$ that coincides with the maximum $Cb.$

Now that you have solved the system of ODEs for $T=200C,P3$ would like you to

consider $T=160,180,$ and $220C.$ Compare the maximum ratio of $C\frac{b}{C}$ c at these

consider $T=160,mb,$

It is perfectly acceptable to do this by changing the temperature and running the

same program three more times. However, for extra credit, loop through the

temperature values $($using and array and a "for loop"$)$ or use the input function $($from

our first weeks$)$ to request the temperature from the command line.$)$

All the material needed to solve these engineering problems was covered in lecture

and the homework. I promise it will go better if you rely on the class material instead

of "googling" how to do these steps. Remember to submit your final project as a

memo to P$3$ with: $1)$ appropriate background, $2)$ a description of the approaches

used for solving the problems, $3)$ results reported clearty, both values $($with error$)$

and graphs, $4)$ a conclusion and recommendation, and $5)$ Include your codes as an

appendix. I highly recommend you write separate codes for tasks $1$ and $2.$