P$11-9{?}_A$ The reaction

$A+BC+D$

is carried out adiabatically in a series of staged packed$-$bed reactors with interstage cooling $($see Figure $11-5).$ The lowest temperature to which the reactant stream may be cooled is $27C.$ The feed is equal molar in A and B$,$ and the catalyst weight in each reactor is sufficient to achieve $99\mathrm{.}9\%$ of the equilibrium conversion. The feed enters at $27C$ and the reaction is carried out adiabatically. If four reactors and three coolers are available, what conversion may be achieved?

Additional information:

$H_{Rx}=-30,000ca\frac{l}{m}$olA,$C_{P_A}=C_{P_B}=C_{P_C}=C_{P_D}=25ca\frac{l}{g}$mol$*K$

$K_e(50C)=500,000,F_{A0}=10$mol$\frac{A}{m}in$

First prepare a plot of equilibrium conversion as a function of temperature. $($Partial ans.: $T=360K,($:$x_e=0\mathrm{.}984$;$T=520(K),x_e=0\mathrm{.}09$;$T=540(K),x_e=0\mathrm{.}057$