The irreversible liquid$-$phase reaction: $AB+C,$ was carried out in a batch reactor at $50C.$ The following data were collected during the course of the reaction and processed for the differential method

$\backslash$table$[[t(min),10,20,30,40,50,60],[C_A(mo\frac{l}{d}{m}^3),2\mathrm{.}45,1\mathrm{.}74,1\mathrm{.}23,0\mathrm{.}88,0\mathrm{.}62,0\mathrm{.}44],[d\frac{C_A}{d}t,-0\mathrm{.}081,-0\mathrm{.}061,-0\mathrm{.}043,-0\mathrm{.}0395,-0\mathrm{.}022,-0\mathrm{.}014]]$

$($a$)(35$ pts$)$ Use the attached graph and the provided data to plot a straight line to determine the values and units of $($reaction order$)$ and $k($reaction rate constant$)$ for the given reaction.

$($b$)(25$ pts$)$ The same reaction is to be carried out in a CSTR at $50C.$ What is the design equation in terms of $F_A($mole flow rate$)$ or $C_A?$ Use it to determine the space time $$ needed to achieve $90\%$ conversion of $A.$