Q$2$ Porous spherical catalyst pellets of $4mm$ in diameter were filled in a packed

bed to carry out a $2^{nd}$ order isothermal gas$-$solid catalytic reaction $2AB.$ The bulk density

of the pellets $({}_{\text{c}\text{a}\text{t}1})$ was $5000$kgca$\frac{t}{m^3}$cat. The packed bed can be treated as a plug flow

reactor $($PFR$).$ When the gas feed rate $(\{$:$V^{\text{'}})$ of $2m^3$ gas $\frac{?}{s}$ and a bulk concentration of $)$

of $0\mathrm{.}8$kmo$\frac{l}{m^3}$ gas were employed, the observed rate $(-r_A{)}_{\text{o}\text{b}\text{s}1}$ was found to be $95$

$).$ Under such a gas flow rate, external mass transfer limitation may be

neglected. Kinetic evidence suggested that the rate constant $(k_{\text{c}\text{a}\text{t}1})$ was $425($unit$).$

a$)$ Derive the unit of $k_{\text{c}\text{a}\text{t}1}$ above for the $2^{nd}$ order isothermal gas$-$solid catalytic reaction

Salculate the weight of catalyst required to produce $90\%$ conversion of A$.$

A new bed of $2mm$ diameter catalyst pellets of the same original material was then tested.

The bulk density $({}_{\text{c}\text{a}\text{t}2})$ was $5200$kgca$\frac{t}{m^3}$ cat and kinetic estimation indicated that the rate

constant $(k_{\text{c}\text{a}\text{t}2})$ was $90\%$ of $k_{\text{c}\text{a}\text{t}1}$ of the old bed.

b$)$ Determine the weight of catalyst in the new bed under the same conditions

Comment on the differences