The first order, gas$-$phase catalytic reaction

A $->$ B

with reaction rate constant, $1$

$=0\mathrm{.}017106$

cm$/$s $,$ catalyst surface area, $=150$ m$2$

g

$,$ and catalyst

density, $=3\mathrm{.}95$ g$/$cm$3$

$)$ takes place in a spherical catalyst pellet of radius, $=2\mathrm{.}5$ cm$.$ The effective

diffusivity of A in the pellet is$,=0\mathrm{.}015$ cm$2/$s$.$ The reactant $$ is carried in a stream at a bulk

concentration, $,=104$mol$/$cm$3$

$.$ The concentration of $$ at the surface of the pellet is$,$

$,=3105$ mol$/$cm$3$

$.$

a$)$ Determine the value of the external mass transfer coefficient.

$[5]$

b$)$ Calculate the conversion achieved in a packed bed reactor, where the catalyst pellets operate

with the same internal and external resistances as above. Assume the reactor operates as a

pseudo$-$homogeneous PFR with a space time of $30$ s$,$ an inlet reactant concentration,

$,0=104$ mol$/$cm$3$

$,$ bed void fraction $=0\mathrm{.}4$ and negligible pressure drop.