Question $2.(50$ pts$)$ The elementary reversible liqurid phase reaction $A+B,C$ is carried out adiabatically in packed bed reactors which are connected in series. These reactors have enough catalyst packing to achieve $99\%$ of the corresponding equilibrium conversion for this reaction. There are interstage coolers between these reactors that cool the reaction medium exiting from each reactor to $350K.$ The molar fractions of A$,B$ and inert solvent in the feed to the first reactor are $0\mathrm{.}25,0\mathrm{.}25$ and $0\mathrm{.}50,$ respectively. The temperature of the feed is $27C$ and the amount of $A$ in the feed is $0\mathrm{.}01$kmol$\frac{e}{m}in.$ The heat capacities of the A$,$ B$,$ C and inert solvent are $20\mathrm{.}92,8\mathrm{.}37,29\mathrm{.}28$ and $6\mathrm{.}28\frac{J}{?}$ mole. $C,$ respectively. The heat of reaction at $273K$ is $-41839\frac{J}{m}$oleA. The following fractional equilibrium conversion vs temperature data is available for this reaction:What should be the number of packed bed reactors in series to achieve overall $0\mathrm{.}55$ fractional conversion of A in this system?