Enzyme is immobilised in 8 mm diameter agarose beads at a concentration of 0.018 kg protein m^-3 gel. Ten beads are immersed in a well-mixed solution containing 3.2 ×10^-3 kg m^-3 substrate. The effective diffusivity of substrate in agarose gel is 2.1 × 10^-9 m^2 s^-1. Kinetics of the enzyme can be approximated as first order with specific rate constant 3.11 × 10^5 s^– 1 per kg protein. Mass transfer effects outside the particles are negligible. Estimate the volume per bead.
(a) 2.65×10^-7 m^3
(b) 2.66×10^-7 m^3
(c) 2.67×10^-7 m^3
(d) 2.68×10^-7 m^3
I have been asked this question by my school teacher while I was bunking the class.
The origin of the question is Internal Mass Transfer and Reaction topic in section Heterogenous Reactions of Bioprocess Engineering