Sweetzyme Q is a commercial preparation of glucose isomerase immobilized in a porous

spherical particle $($Novo Industries, Denmark$).$ Plotted below are initial rates of xylose

isomerization catalyzed by Sweetzyme Q $($in units of $$mols xylose isomerized$/$mg

particle$$min$).$ The external concentration of xylose is $1\mathrm{.}5$ M the density of the catalyst is

$1\mathrm{.}4$ g$/$cm$3$

$,$ and the measured KM is $0\mathrm{.}209$M$.$ Assume that the maximum activity plotted in

the figure would not increase if the particle diameter were further reduced. $($ref$.$ Blanch

and Clark, Biochemical Engineering, p$\mathrm{.}155).$

i$)$ Estimate the effective diffusivity of xylose in the Sweetzyme Q catalyst. Use

definition of Actual Modulus.

ii$)$ What is the largest potential source of error in the calculation in part i$.$

iii$)$ Using the effective diffusivity calculated in part i$.,$ for a particle diameter of $620$

$$m$,$ estimate the internal effectiveness factor.