In a stirred reactor component $\text{'}1\text{'}$ is completely converted to product $\text{'}2\text{'}.$ The reaction is

exothermal. The feed contains component $\text{'}1\text{'}$ and an inert solvent $\text{'}3\text{'}.$ The solvent partly boils

off to cool the reactor. The solvent vapour passes through a compressor, is condensed at a

higher pressure and then returned to the reactor.

The enthalpies of formation of the two reacting components and the molar heat capacities are:

$H_{f,1}^{\text{r}\text{e}\text{f}}=-120kJmo{l}^{-1},T_{\text{r}\text{e}\text{f}}=298K$

$C{p}_1^L=60Jmo{l}^{-1}{K}^{-1}$

$H_{f,2}^{\text{r}\text{e}\text{f}}=-150kJmo{l}^{-1}$

$C{p}_2^L=70Jmo{l}^{-1}{K}^{-1}$

The feed $($with solvent$)$ has a temperature of $20C.$ The reactant and the product are not

volatile. The reactor is cooled by evaporation of the solvent $\text{'}3\text{'}$ at point $\text{'}\text{'}.$ This is sucked

through a compressor and is condensed in a heat exchanger before being returned to the

reactor at $\text{'}\text{'}$ at a the same temperature as the reactor of $50C.$ The boiling point, enthalpy of

vaporisation and liquid and gas molar heat capacities of the pure solvent are:

$T_b=(70+273)K,H_3^{\text{v}\text{a}\text{p}}=30kJmo{l}^{-1}$

$C{p}_3^L=50Jmo{l}^{-1}{K}^{-1},C{p}_3^G=30Jmo{l}^{-1}{K}^{-1}$

The vapour pressure of the pure solvent is given by:

$P^{\text{v}\text{a}\text{p}}=({10}^5(Pa))exp[-\frac{H^{\text{v}\text{a}\text{p}}}{R}(\frac{1}{T}-\frac{1}{T_b})]$

The solvent forms an ideal solution with the reactant and product.

$($a$)$ Set up the energy balance of the reactor and calculate the molar flow rate of solvent

vapour at $\text{'}\text{'}.[27\mathrm{.}8$ mol$/$s$]$

$($b$)$ What is the mole fraction of solvent in the feed? $[0\mathrm{.}5]$ And the pressure at point $\text{'}\text{'}?$

$2\mathrm{.}607{10}^4(Pa)$

$($c$)$ The condenser operates with an internal temperature of $50C.$ If vapour and liquid are in

equilibrium there, what is the pressure in the condenser? $5\mathrm{.}213{10}^4(Pa)$

$($d$)$ Calculate the power required by the compressor, taking it to be isentropic$.[57\mathrm{.}2$ kW$]$

$($Additional: the cooling duty of the condenser $Q=878kW($this was not asked for$))$