$1.-$ Develop an equation to calculate the effectiveness factor from Eq$.1,$

obtained from the mass balance in a spherical particle in a steady state where

an irreversible first$-$order reaction occurs using boundary conditions

specified.

$2$

$2+$

$2$

$=$

$1$

Eq$\mathrm{.}1$

c$.$f$\mathrm{.}1$: $=0$;

$=0$

c$.$f$\mathrm{.}2$: $=$ ;

$($

$)=4$

$2($

$)$

$=$

$2.-$ Perform an analysis of the effect of internal resistances on selectivity and verify

$($mathematically$)$ if the following statements are true:

For the reactions:

$1$

$2$

Where B is the desired product.

a$)$ If they have the same reaction order, the selectivity is not affected.

b$)$ If the second reaction is second order and the other is first order, the selectivity

towards B is improved by the effect of transport resistances.

$3.-$ At $10$ atm and $100$ C$,$ determine the effective diffusivity of hydrogen in a system

hydrogen ethane $($yH$2=0\mathrm{.}5)$ assuming the pore radius is $50.$ The porosity is

$0\mathrm{.}304$ and the tortuosity factor of $4.$ Assume a parallel pore model