For the following first order gas$-$solid surface reaction, Shrinking Core model is applicable.

$A(g)+bB(S)C$

I. If the rate is known to be ash layer diffusion controlled, calculate the solid holdup that will

be needed for a conversion of $80\%.$ The initial flow rate of $B$ is given as $50k\frac{g}{m}in$ and

the time required for complete conversion is $90$ minutes. The solid particles can be

assumed to be in PF $($Plug flow$)$ with spherical shape having the same size and the gas

can be considered to have uniform composition.

II$.$ What will be the residence time of the solids if the rate is reaction rate controlled $($instead

of ash layer diffusion$)$ with the particle distribution as shown in table below to achieve the

same $80\%$ conversion. The time required for complete conversion for size $R$ is $90$

minutes.