The elementary gas$-$phase reaction A $+$ B $->$ C $+$ D takes place isothermally in a PBR$.$

The reactor has a cross$-$sectional area of $8$ x $10-3$ m$2$ and comprises catalyst particles

with a diameter of $1$ mm$.\backslash$beta o for this reactor is estimated to be $0\mathrm{.}01$ atm$/$m$.$ The inlet

stream to the reactor comprises a stoichiometric mixture of A and B at a total molar

flow rate of $10$ mol$/$min$,$ a temperature of $590$ K and a pressure of $20$ atm. Under these

conditions, the flow can be assumed to be turbulent. The reactor gives a conversion

of $12\%$ when it is loaded with $100$ kg of catalyst. We will cover these concepts in

greater detail in our module on mass transfer. However, for the time being, you are

told that conversion can be modulated by changing the diameter of the catalyst

particles. Plot conversion as a function of catalyst size and comment on this

relationship.