The liquid phase reaction

$A+2BC+2D$

takes place in an isothermal, constant$-$volume stirred$-$tank reactor $($CSTR$).$ The rate of reaction is expressed by:

$-r_A=k{C}_A{C}_B$

where the reaction rate constant at $25C(298K)$ is $k=0\mathrm{.}025L(mol*min),$ and the activation energy is $5,000J/$mol$.$ The reactor operates isothermally at $65C.$ The feed stream consists of equal concentrations of species A and $B$ at a value of $2$mol$/$L$.$

Remember: $R=8\mathrm{.}3144\frac{J}{\text{m}\text{o}\text{l}\text{.}K},K=C+273$

$($a$)$ Estimate the reaction rate constant at $65C$ by using the Arrhenius Eqn.

$($b$)$ Calculate the residence time in minutes required to obtain $35\%$ conversion of species A under steady$-$state conditions.

$($c$)$ What should be the volume of the reactor in liters $(L)$ if species $C$ is to be produced at a rate of $15$mol$/$min $?$