Q$2.$ An isothermal gas$-$solid reaction follows the shrinking core model:

$2A(s)+3B(g)2C(s)+D(g)$

Solid particles of A with a radius of $6mm$ attain full conversion in $4$ minutes when reacted in a

rotary kiln at $750C$ with pure $B$ gas at $1\mathrm{.}5$ bar pressure. Solid A has a density of $5\mathrm{.}5\frac{g}{c}m3$ and

a molecular weight of $115\frac{g}{m}ol.$ The external mass transfer and product layer diffusion control

the overall rate.

a$)$ The effective diffusivity in the product layer is $D_e=3\mathrm{.}5c\frac{m^2}{s}.$ Determine the external

mass transfer coefficient.

b$)$ Under the same conditions as part a$),$ what would be the time required to achieve the

same conversion if the solid particle diameter was halved?

c$)$ Under the same conditions as part a$),$ what would be the conversion if the residence time

in the kiln was reduced to $3$ minutes? This requires numerical solving. Please attach your

spreadsheet$/$code that is sued to do this solving. This needs to be presented clearly with

suitable annotation and units.