Candida $sp.$ strains are known to form self$-$immobilized aggregates having average diameter of $5mm.$ The effective diffusivity of $O_2$ in the aggregates is $1\mathrm{.}75{10}^{-9}{m}^2{s}^{-1}.$ The $O_2$ consumption rate at a bulk $O_2$ concentration of $8{10}^{-3}kg{m}^{-3}$ is $8\mathrm{.}7{10}^{-5}kg{s}^{-1}{m}^{-3}$ of biomass, in a fixed$-$bed reactor. The liquid solid mass tranfer coefficient is $3\mathrm{.}8{10}^{-5}m{s}^{-1}.$

a$.$ Does external mass transfer effect the $O_2$ uptake?

b$.$ What is the external effectiveness factor?

c$.$ When both internal and external mass transfer resistance were elimineted, what reaction rate would be measured?