Q$1.$ Consider the following reversible and elementary liquid phase reaction conducted in a

jacketed batch reactor:

$A(l)+B(l)$ harr $C(l)$

The reactor has a solution volume of $20,000L.$ The solution has a density of $900k\frac{g}{m^3}$ and a

heat capacity of $5\frac{J}{g}.C.$ Both A and $B$ have an initial concentration of $8mo\frac{l}{L}$ and the

reactant solution is initially at $30C.$

For the reaction, the following data is available:

$k_f=8{10}^8{e}^{-\frac{8000}{T}}\frac{L}{m}ol*min$

$K_C(25C)=5\frac{L}{m}ol$

${}_{r}H=-80k\frac{J}{m}ol$

a$)$ Derive the two ODEs that can be integrated to determine conversion of A and temperature

versus time. This should account for heat transfer to the jacket.

b$)$ Using the equations from part a$)$ integrate and plot conversion and temperature $($in $C)$

versus time up to $100$ minutes when the reactor is adiabatic $($hint: set the heat transfer

area to $0).$ Put them on a single plot. Usual expectations for clear plots apply. To answer

this question will require numerical integration. Attach your clear and annotated

code$/$spreadsheet you use to do the integration. If is a spreadsheet, only attach the first

page that includes all relevant data and the first several lines of the integration.

c$)$ Consider when the cooling jacket is used with a constant coolant temperature of $30C$ and

an overall heat transfer coefficient of $500\frac{W}{m^2}C.$ What heat transfer area $($in $m^2\frac{+}{-}1$

$m^2)$ is required to ensure the temperature does not exceed $50C?$ If the reactor has a

diameter of $3m,$ does the jacket have enough heat transfer area to provide this cooling?

Use the code from part b$)$ to integrate and plot conversion and temperature versus time

up to $100$ minutes with this heat transfer area and a constant cooling water temperature.

No need to re$-$attach your code$/$spreadsheet$.$ It will be assumed the same

code$/$spreadsheet is used to generate this plot.