$2$a$.)$ Assess the importance of Hatta number $(($:$M_{11}\}$ to determine the type, reaction location and a suitable contactor for a fluid$-$fluid reaction. $(5$ marks$)$

b$.)$ A batch of solids of uniform size is treated by gas in a uniform environment. Solid is converted to give a non$-$flaking product according to the shrinking$-$core model. Conversion is $0\mathrm{.}936$ for a reaction time of $1h.$ Conversion is complete in $1\mathrm{.}67h.$ What mechanism is rate controlling if the shape of the particle is spherical?

$(12\mathrm{.}5$ marks$)$

$3$a$.)$ A stream of particles of one size are $80\%$ converted $($shrinking core model$/$ ash diffusion control, uniform gas environment$)$ on passing through a reactor. If the reactor is made twice the original size but with the same gas environment, same feed, and same flow pattern of solids, what would be the conversion of solids if the solids are in plug flow.

$(8\mathrm{.}5$mks$)$