In a batch reactor of $18$ L volume an isothermal irreversible reaction takes place R $->$P$,$ in liquid phase. The kinetic constant is expressed as k $=4\mathrm{.}48$x $10$to$6$ exp$(-7000/$T$),$ in s$-1,$ where T is the process temperature expressed in Kelvin.

a$)$ Calculate the time required to reach a conversion of $80\%$ at $40$C if $[$R$]$o $=3$ mol$/$L$.$

b$)$ Indicate the daily molar production of P under the conditions in section $($a $),$ knowing that the load, unload and conditioning time is $22$ minutes $($assume $24$ working h$/$day$).$

c$)$ If the conversion desired is $95\%,$ without changing the operating conditions in section $($a$),$ calculate the time necessary to achieve it$.$

d$)$ What should be the temperature of the process for a conversion rate of $95\%$ without changing the time of the reaction determined in $($a$)?$

Solution:

a$)$ t $=0\mathrm{.}509$ h

b$)$ Daily production of P $=1166\mathrm{.}4$ moles P$/$day

c$)$ t $=0\mathrm{.}948$ h; daily production $=936$ mol P$/$day

d$)$ T $=48\mathrm{.}9$C