The conversion of ortho molecular hydrogen to para molecular hydrogen is catalyzed by

NiO catalyst. Consider a supported catalyst of this type with a specific surface area of

$305$ m$2/$g and a void volume of $0\mathrm{.}484$ cm$3/$g$.$ The catalyst is available in spherical pellets

with an apparent particle density of $1\mathrm{.}33$ g$/$cm$3$ and a diameter of $0\mathrm{.}5$ cm$.$ If the ortho$-$

para hydrogen mixture is not too far from equilibrium, an apparent $1$ st order rate constant

is given by the following relation:

rate of approach to equilibrium $=$ kr$($C$-$C eq$.)$

In a system where the hydrogen pressure was $1$ atm and the temperature $77$ K$,$ the

experimentally observed $($apparent$)$ rate constant was $0\mathrm{.}159$ cm$3/($s gcatalyst $).$ Using the

straight cylindrical pore model discussed in class, determine:

a$.$ The mean pore radius

b$.$ The combined diffusivity for hydrogen in the pores of this catalyst

c$.$ effectiveness of catalyst