For the liquid$-$phase reaction $2A+BC+D,$ the reaction is first$-$order in both A and B $.$ The reaction rate constant $k=0\mathrm{.}0022\frac{m^3}{k}$mol$*min$ at $204C$ with the activation energy $E=10024ca\frac{l}{m}ol.$ The initial entering concentrations of A and B are $8\mathrm{.}6$kmo$\frac{l}{m^3}$ and $4\mathrm{.}8$kmo$\frac{l}{m^3},$ respectively.

$(15$ pts$)$ Please write the expression of the effluent rate of the reactor for species B using $F_{A0}$ and $x.$

$(15$ pts$)$ Please write the reaction rate $-r_A$ solely as a function of cornversion X $.$

$(20$ pts$)$ What the rate constant is when the temperature is $160C?$

$(20$ pts$)$ What is the rate of reaction at $T=160C,$ and $x=0\mathrm{.}9?$

$(20$ pts$)$ What would be the corresponding CSTR volume at $160C$ necessary to achieve $90\%$ conversion for a feed rate of $2d\frac{m^3}{m}in?$