Q$3$

$[30$ Marks$]$

The following irreversible reaction in liquid phase will take place in a perfectly mixed continuous reactor of $1,000L$ volume:

$A+2BC$

The rate law at the temperature of $80C$ is:

$-r_A=0\mathrm{.}000391C_A{C}_B^{2}mo\frac{l}{}(L.s)$

The activation energy is $125k\frac{J}{m}ol.$ The reactor will be fed with a solution with $2\mathrm{.}17mo\frac{l}{L}$ of $A,5\mathrm{.}0mo\frac{l}{L}$ of $B$ and the remaining to a total molar concentration in the feed of $57mo\frac{l}{L}$ is a solvent $($that doesn't react$),$ pre$-$heated to $50C.$ The reactor is to function at $100C$ with the required flow rate to ensure a conversion of $85\%.$

a$)$ Determine the heat of reaction at $100C$ from the heats of formation and specific heats given below.

$[10$ Marks$]$

b$)$ Write the energy balance to the CSTR

$[5$ marks$]$

c$)$ Determine the amount of cooling or of heating required to keep the reactor at $100C.$

$[15$ Marks$]$

DATA:

Ideal gas constant: $8\mathrm{.}314\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$

The specific heats $($averages$)$ and heats of formation of the various components at $25C,$ are $($note that the enthalpies of formation are in $k\frac{J}{m}ol)$:

$\backslash$table$[[,$A$,$B$,$C$,$solvent$],[C_p(\frac{J}{m}ol.K),1\mathrm{.}07,1\mathrm{.}158,2\mathrm{.}17,3\mathrm{.}8],[h_f(k\frac{J}{m}ol),-5\mathrm{.}17,7\mathrm{.}5,-10\mathrm{.}2,$not relevant$]]$