$(30$ marks$)$ A researcher conducted several experiments to measure reaction rates from a variety of

spherical catalyst pellets. The following data were obtained from the experiments, where the bulk

concentration of the pure reactant, $c_{AG},$ is $0\mathrm{.}25mo\frac{l}{L}.$

a$)$ Stating and justifying all assumptions, for the $1mm$ and $10mm$ catalyst fractions, determine

the effectiveness factor $(),$ the shape$-$independent Thiele Modulus $(\text{'}),$ and the observable

modulus $().$

b$)$ Determine the intrinsic reaction rate constant, in $s^{-1},$ and effective diffusivity, in $m\frac{m^2}{s}.$

c$)$ Predict the observed reaction rate for a $15mm$ diameter pellet.