The following are the data from a new liquid phase chemical reaction products$)$ slated for process development.

$\backslash$table$[[c_A(mo\frac{l}{L}),0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}8,1\mathrm{.}2,2],[-r_A(mol{L}^{-1}{s}^{-1}),0\mathrm{.}018,0\mathrm{.}033,0\mathrm{.}055,0\mathrm{.}082,0\mathrm{.}094,0\mathrm{.}100]]$

$($a$)$ How to obtain these data from batch reactor, CSTR and PFR$,$ respectively?

$($b$)$ Use differential analyses $($direct analysis$)$ to identify whether the reaction kinetics follows a simple power law.

$($c$)$ It is suspected that the following rate law may be applicable to the reaction in question:

$R=\frac{k_1{c}_A}{(1+k_2{c}_A{)}^2}$

Suggest a graphical method which can extract the parameters $k_1$ and $k_2.$

Hint: for b$)$ you may guess reaction rate follows power law; for c$)$ rearrange the equation so one would be able to make a liner plot based on experimental data.

Ans: $($c$)k_1=0\mathrm{.}2s^{-1},k_2=0\mathrm{.}5mo{l}^{-1}L$