For the reversible reaction following the chemical equation ;

$AB$

The rate law given is as follows :

$-r_A=k{C}_A$

a$.$ Combine the rate law and stoichiometry of the reaction to give $-r_A$ as a function of $k,C_{A0}$ and

$x.$

b$.$ Find the CSTR volume that is necessary to achieve $90\%$ of the adiabatic conversion when

inlet temperature is $480K,C_{A0}=10mo\frac{l}{d}{m}^3$ and volumetric flowrate is $5d\frac{m^3}{m}in.$

DATA:

Enthalpy change of reactant $A,H_A(298K)=-45000ca\frac{l}{m}ol$

Enthalpy change of product $B,H_B(298K)=-60000ca\frac{l}{m}ol$

Rate constant, $k=3\mathrm{.}5{10}^{-5}{e}^{(\frac{Ea}{R}(\frac{1}{298}-\frac{1}{T}))}$min$-1$

Activation energy, $Ea=10000ca\frac{l}{m}ol$

$C_{pl}$:$50ca\frac{l}{m}ol.K$

$C_{pA}$:$30ca\frac{l}{m}ol.K$

$C_p$:$30\frac{J}{m}ol.K$

$=1$