A sample of the catalyst supplied to a petroleum refinery catalytic reforming unit has the following size distributions,

$\backslash$table$[[\backslash$table$[[$Catalyst$],[$stample$],[$diameter$],[($hm$)]],25,50,75,100,125,150],[\backslash$table$[[$Cumulative$],[$weight $\%],[$undersize$]],0,16\mathrm{.}7,41\mathrm{.}7,75,91\mathrm{.}7,100]]$

An operator to the reformer requires the catalyst to be of specific and precleterminor $($i$)$ surface area $($ii$)$ number of particles per unit mass of the sample.

$($a$)($i$)$ State wether or not the sample above meets the specifications of surface area $\frac{?}{gm}$ we $14\mathrm{.}667{10}^{4}m\frac{m^2}{g}m$ and the number of particles per unit mass of $8\mathrm{.}61{10}^5$ particles $\frac{?}{gm}.($ii$($ Determine the mean surface diameter Ds of the supplied sample. $($Deasity of catalyst $=7500k\frac{g}{m^3},$ sphericity $=0\mathrm{.}57,$ volume shape factor of the catalyst, $=2).$ In all cases, $K=5,g=9\mathrm{.}81\frac{n}{s^2},1$ Poise $=0\mathrm{.}1N\frac{s}{m^2},1ft=0\mathrm{.}3048m$