$[$OL $5\mathrm{.}25]$ The aqueous decomposition of A was studied in an experimental CSTR$.$ The table below shows the steady state measurements.

$\backslash$table$[[c_A(mo\frac{l}{L}),$Space time $($s$)],[$In feed,In exit stream$],[2\mathrm{.}00,0\mathrm{.}65,300],[2\mathrm{.}00,0\mathrm{.}92,240],[2\mathrm{.}00,1\mathrm{.}00,250],[1\mathrm{.}00,0\mathrm{.}56,110],[1\mathrm{.}00,0\mathrm{.}37,360],[0\mathrm{.}48,0\mathrm{.}42,24],[0\mathrm{.}48,0\mathrm{.}28,200],[0\mathrm{.}48,0\mathrm{.}20,560]]$

Determine the space time of a PFR for $75\%$ conversion of A with a feed of $c_{A0}=0\mathrm{.}8mo\frac{l}{L}.$

Hint: $1)$ Rate law is a function of $T$ and $c_A,$ but not of the type of reactor $=>$ Can use CSTR data to find rate law, then use PFR design equation and the identified rate law to find $t.$

you are suggested to use differential analyses to find rate law;

a reaction may not follow the same order in the entire concentration range $($recall enzyme kinetics where substrate has $1^{st}$ order at low concentration and $0^{th}$ order at high concentration$)$;

Ans: $300s$ or $290s($depending on the method used$)$