$2.$ An aqueous glucose stream is to be catalytically hydrogenated to sorbitol in a slurry tank reactor. Feeds to the reactor are an aqueous glucose stream with a concentration of $2\mathrm{.}6$kg$$mol $/$ m$^3$ at a flow rate of $10^-3$m$^3/$ s and a $120$ percent of stoichiometric hydrogen gas stream. The reactor is to be operated isothermally at $423$K$,$ where the reaction is observed to follow the kinetics shown here:

$-$r$\_$glucose $=$k c$\_$hydrogea $^0\mathrm{.}6$ c$\_$glucose k$\_423$K$=3\mathrm{.}76\backslash$times $10^-4($kg$$mol $/$ m$^3)^-0\mathrm{.}6$s$^-1$

The reaction is conducted at $10,000$ kPa, the solubility of hydrogen may be assumed to be $5$kg$$mol $/$ m$^3$ at this pressure. The actual kinetics of the reaction require adjustment to account for catalyst masstransfer effects. Neglecting these effects, calculate the conversion for a $2-$m$^3$CSTR$.$