$1.$ The A$->$B$+$C exothermic reaction is carried out in a moving bed reactor.

k$=0\mathrm{.}33$exp$($E$/$R$(1/450-1/$T$))$ and E$/$R$=3777$ K$.$ Heat is removed with water in the heat exchanger. A and inert enter the reactor at an equimolar speed of $40$ atm and $20$ dm$3/$s$.$ Both the catalyst and the feed enter $450$ K$,$ and the heat transfer coefficient between the catalyst and the gas is infinite. The heat capacity of the solid catalyst is $100$ J$/$kg$.$kat.K$.$ Catalyst degradation is first order according to activity.

a$)$ The refrigerant fluid in the heat exchanger moves in parallel flow at a speed of $10$ kg$/$s and is fed at $50$ oC$.$ What is the catalyst loading rate $($kg$/$s$)$ that will give the highest conversion? What is the transformation at this speed?

b$)$ The refrigerant in the heat exchanger moves in parallel flow at a speed of $10$ kg$/$s and is fed at $50$ oC$.$ What is the catalyst loading rate $($kg$/$s$)$ that will give the highest conversion? What is the transformation at this speed?

kd$=0\mathrm{.}01(700$ K$(1/450-1/$T$))$s$-1.$ Determine the amount of catalyst to be used in the bed in kg$.$

CpA$=40$ J$/$mol$.$ K$,$ CpB$=25$ J$/$mol$.$ K$,$ CpC$=15$ j$/$mol$.$K $$H$($T$)=-80$ kj$/$mol A