Consider the gas$-$phase reactions:

$A2B,H_{R1}=-10,000ca\frac{l}{m}$olA

$A+2BC,H_{R2}=+5000ca\frac{l}{m}$olA

which take place in an adiabatic $200L$ PFR$.$ Pure A is fed to the reactor at $323K$ with a

molar flow rate of $100mo\frac{l}{m}in$ and a concentration of $0\mathrm{.}5mo\frac{l}{L}.$

a$)$ At what volume in the reactor is the temperature a maximum?

b$)$ At what volume is the concentration of B a maximum?

Additional information:

$C_{PA}=50ca\frac{l}{m}ol-K,$

$C_{PB}=25ca\frac{l}{m}ol-K,$

$C_{PC}=100ca\frac{l}{m}ol-K,$

$,$

$r_1=k_1{C}_A^2,k_1=2\mathrm{.}77\frac{L}{m}ol-$min $at323K,E_1=5\mathrm{.}0$kca$\frac{l}{m}ol$

$r_2=k_2{C}_A{C}_B^2,k_2=0\mathrm{.}0199\frac{L^2}{m}o{l}^2-$min $at323K,E_2=25$kca$\frac{l}{m}ol$