An isothermal gas$-$phase decomposition reaction is given by Eq$.1$:

$ABC$

The reaction is set at $300F$ and $10$atm. The reaction takes place in a $2-m$ plug flow reactor

$($PFR$)$ that initially has A and B at $5$ and $2$kmo$\frac{l}{m^3},$ respectively.

g$)$ A Levenspiel plot vs $\{$:$x)$ is a plot used in chemical reaction engineering to determine

the required volume of a chemical reactor, given the experimental data on the chemical

reaction taking place in it$.$ Based on Table $2,$ use any appropriate integration method to

determine the most accurate volume of the PFR needed to achieve the conversion of $0\mathrm{.}8.$

The entering molar flow rate of $B(F_{B0})$ at $0\mathrm{.}867mo\frac{l}{s}.$ The volume of PFR can be

calculated using Equation $2$:

$V_{PFR}={\displaystyle \underset{0}{\overset{x}{}}}\frac{F_{B0}}{-r_B}dx$

Table $2$: Reaction rate as a function of conversion

h$)$ The same reaction is performed in an isothermal batch mode reactor. Since the process is

in the gas phase, it is a must to monitor the pressure profile during the reaction. The design

equation is explained in Equation $3$:

$\frac{dP}{dt}=k^{\text{'}}(3P_0-P{)}^{}$

Using Euler's and Runge$-$Kutta Fourth Order methods, plot the pressure$-$time data in the

range of $0-20$min on the same graph paper. Set the step size to $5$min. Before the reaction

begins, the pressure inside the reactor is $7\mathrm{.}5mmHg.$ Based on previous experiments, the

reaction kinetics parameter $k^{\text{'}}$ is $0\mathrm{.}08mi{n}^{-1}$ and the $$ value is $1.$