The gas phase reaction $($A$->$ B$+$C$)$ must be carried out in a fixed$-$bed tubular reactor using a solid catalyst in a spherical shape of $0\mathrm{.}4$ cm in diameter. The reactor must operate isothermally at $573$ K and an inlet pressure of $1$ atm. The reaction is first order and the reactor is fed with pure A at a molar flow of FA$0-1$ g$-$mol$/$s$.$ The internal diameter of the reactor must be $2\mathrm{.}54$ cm$.$

It is known: $-$The reaction on the surface of the catalyst is of the type rA$=$kCA.; $-$The particle density gp$=2$ g$/$cm$3$; $-$The porosity of the bed gl$=0\mathrm{.}40.$

$-$This reaction, when carried out using the catalyst in powder form, obtained a speed of R A$=1\mathrm{.}10^-3$ g$-$mol$/$g$-$cat.s$,$ at a temperature of $573$ K and pure reagent A at a pressure of $1$ atm $.$

$-$Consider that the reactor is being operated under conditions free from resistance to external mass transfer to the particle.

$-$The effective molecular diffusivity in the gas phase $($DAB$)$ to solve this exercise must also be considered constant with the temperature and composition DAB$=2\mathrm{.}0\mathrm{.}10^-4$ cm$2/$s$.$

We ask:

a$)$ Make the differential mass balance, in steady state, for one of the reactants inside an infinite plate of porous catalyst.Dimensionlessize the resulting resolution, so that it applies the Thiele differential modulus.

b$)$ Perform the steady$-$state differential mass balance for one of the reactants within an infinite porous occurrence plate. Dimensionlessize the resulting resolution, so that it applies the Thiele differential modulus.

Calcule: $1)$ O valor do modulo de Thiele; $2)$O valor do fator de efetividade; $3)$ O comprimento do reator para se obter a convers$$o na sa$$da do reator XA$=0,8.$