$($a$)$ We have $500$ same CSTRs in series, the reaction is $1^{st}$ order liquid phase reaction. The volume for each reaction is $1m^3,$ with volumetric flow rate $5\frac{m^3}{s},$ if we know the initial concentration of limiting reactant is $1$mol$\frac{e}{L},$ please calculate the reaction rate at $4^{th}$ reactor. $(10$ points$)$

$($b$)$

$=\frac{R{T}_0}{(MW)A_C{}_C{g}_C{P}_0^2{D}_P{}^3}G[\frac{\text{o}\text{b}\text{r}\text{a}\text{c}\text{e}(150(1-){)}^{\text{T}\text{e}\text{r}\text{m}1}}{D_P}+$obrace$(1\mathrm{.}75G{)}^{\text{T}\text{e}\text{r}\text{m}2}]$

The pressure drop parameter is shown above, how will you pick up the particle size $($Dp$)?$ Please justify your answer. $(10$ points$)$