$(25$ marks$)$ Kinetics experiments were performed to evaluate the performance of a spherical catalyst for NOx control. The reaction may be written as A $$ products, and can be considered second order with respect to A$.$ During the experiments with $5mm$ and $10mm$ diameter catalyst particles, pure reactant was fed to the test reactor at $200$kPa and $600K.$ The reactor was configured to ensure isothermal, isobaric operation. The diffusivity through the porous catalyst was evaluated in a separate set of experiments conducted under similar conditions. These experiments established that $k_A=0\mathrm{.}050m^{3}mo{l}^{-1}mi{n}^{-1},$ and $D_e=0\mathrm{.}025c\frac{m^2}{m}in.$

a$.$ Assuming no external gradients, what would be the observed reaction rate in each size of catalyst particle? State any other assumptions.

b$.$ If you reduced the particle size to $1\mathrm{.}0mm,$ would operation be in the kinetics limited regime? Explain$/$justify your answer.

c$.$ If there is an external concentration gradient, the overall effectiveness factor would need to be calculated. Given an external mass transfer coefficient $k_{Ag},$ develop a set of equations to calculate the overall effectiveness factor for this catalyst $($do not solve$)$

Answers:

$($a$)5mm$:$=0\mathrm{.}91$;$(-r_A{)}_{\text{o}\text{b}\text{s}}=63mol{m}^{-3}mi{n}^{-1}$;$10mm$:phi$=1\mathrm{.}82$;$(-r_A{)}_{\text{o}\text{b}\text{s}}=42mol{m}^{-3}mi{n}^{-1}$