Question $3.(30$ pts$)$ The following gas phase reversible reaction

A$+$Bc

is taking place in a CSTR with a mounted heat exchanger. The heat exchanger has an overall

heat transfer coefficient of $0\mathrm{.}01k\frac{W}{m^2}.K,$ the heat transfer area of $2m^2$ and the cooling medium

temperature is $290K.$ The equimolar feed of A and $B$ at $0\mathrm{.}58$MPa and $350K$ is sent to the

reactor for which the molar feed rate of $A$ is $1200$mole$\frac{s}{m}in.$ The rate constant of the reaction

is $5\mathrm{.}83{10}^{-4}d\frac{m^3}{m}ol.s$ at $273K$ and the activation energy of the reaction is $70k\frac{J}{m}$ole. The

enthalpy of formation values of A$,$ B and C at $298K$ are $-40000,-30000$ and $-45000\frac{J}{m}$ole,

respectively. The heat capacities of A$,$ B and C at $298K$ are $0\mathrm{.}025,0\mathrm{.}015$ and $0\mathrm{.}02k\frac{J}{m}$ole.$K,$

respectively. The equilibrium constant for the reaction at $298K$ is $25000.$ Determine the

conversion of A which can be achieved in a $1500d{m}^3$ reactor.