Q$3$

$[35$ Marks$]$

The exothermic irreversible reaction in liquid phase

$AB+C$

will be carried out in a jacketed reactor $($CSTR$).$ Water at ambient temperature $(20C)$ and very high flow rates can be circulated in the jacket to cool the reactor. Heat transfer studies have shown that under these circumstances the heat that can be removed by the jacket is given by:

heat removed $=3\mathrm{.}15(T-20)\frac{J}{s}$

where $T$ is the temperature of operation of the reactor in $C.$

The feed is pure A$,$ concentration $0\mathrm{.}025mo\frac{l}{L},$ at ambient temperature $(20C),$ with a flow rate of $0\mathrm{.}025mo\frac{l}{s}.$

The reaction rate is approximately $1^{st}$ order, with an activation energy of $51k\frac{J}{m}ol$ and the rate constant is equal to $0\mathrm{.}0037s^{-1}$ at $175C.$

a$)$ Determine the heat of reaction at any generic temperature of operation $T.$

$[10$ marks$]$

b$)$ Write the energy balance to the reactor in steady state.

$[10$ marks$]$

c$)$ Determine the temperature of operation that would give a conversion of $A$ of $90\%.$ Comment the result obtained.

$[10$ marks$]$

d$)$ Using now the mass balance, what volume would the vessel need to have for the reactor to be operating with these conditions? Comment the result obtained.

$[5$ marks$]$

Data:

Enthalpies of formation at $25C$:$A=-37k\frac{J}{m}ol$;$B=-65k\frac{J}{m}ol$;$C=10k\frac{J}{m}ol$ Average specific heats: $A=1\mathrm{.}70\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$;$B=2\mathrm{.}37\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$;$C=4\mathrm{.}10\frac{J}{\text{m}\text{o}\text{l}\text{.}K}R=8\mathrm{.}314\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$