Fluid cracking crackers $($FCC$).$ FCC reactors are among the largest pro$-$

cessing units used in the petroleum industry. Figure P$1\mathrm{.}3$ shows an example

of such units. A typical unit is $4-10m$ ID and $10-20$ m high and contains

about $50$ tons of $=800k\frac{g}{m^3}$ porous catalyst. It is fed about $38000$ barrels

of crude oil per day day at a density $\{$:$$~$=900\frac{kg}{m^3}),$ and it cracks

these long chain hydrocarbons into shorter molecules.

To get an idea of the rate of reaction in these giant units, let us simplify

and suppose that the feed consists of just $C_{20}$ hydrocarbon, or

If $60\%$ of the vaporized feed is cracked in the unit, what is the rate of

reaction, expressed as $-r^{\text{'}}($mols reacted$/$kg cat $\{$:$-s)$ and as $r^m($mols reacted$/$

$m^3$ cat $s)?$