Please give me a polymath or mathlab code if it is necessary

The pyrolysis of acetone in the gas phase to form cetane and methane is one of the key

steps in the industrial synthesis of acetic anhydride:

$CH3$COCH$3-CH2CO+CH4$

$A-B+C$

The reaction is first order with respect to acetone and will take place in a non$-$isothermal

PFR with no pressure drop. The reactor must be designed to process $38\mathrm{.}26mo\frac{l}{s}$ of

acetone. Acetone enters the reactor pure at a pressure of $1\mathrm{.}6$atm and $1035K.$ For adiabatic

operation, plot the conversion vs volume and temperature vs volume profiles from $0$ to $0\mathrm{.}3$

conversion $(5$ extra points$)$ and answer the following:

a$)$ Calculate the temperature in $K$ of the reactor so that a $30\%$ conversion is achieved.

b$)$ What will be the volume in liters to achieve the same conversion.

Additional data:

$F_{A0}=38\mathrm{.}26\frac{\text{m}\text{o}\text{l}}{s}$

$H_{273K}=80000\frac{J}{\text{m}\text{o}\text{l}}$

$C{p}_A=160\frac{J}{\text{m}\text{o}\text{l}\text{K}}$

$C{p}_B=85\frac{J}{\text{m}\text{o}\text{l}\text{K}}$

$C{p}_C=72\frac{J}{\text{m}\text{o}\text{l}\text{K}}$

$lnk=34\mathrm{.}34-\frac{34222}{T}$

Has to be one of these:

a$)876K,$ b$)15770$ litros

a$)976K,$ b$)20770$ litros

a$)676K,$ b$)13770$ litros

a$)376K,$ b$)20770$ litros