Non-viable yeast cells are immobilised in alginate beads. The beads are stirred in glucose medium under anaerobic conditions. The effective diffusivity of glucose in the beads depends on cell density according to the relationship: ( mathcal{D}_{Ac} ) = 6.33-7.17yC

• A. nwhere ( mathcal{D}_{Ac} ) is effective diffusivity 10¹⁰ m² s^-1 and y_C is the weight fraction of yeast in the gel. Rate of glucose uptake can be assumed to be zero order; the rate constant at a yeast density in alginate of 15 wt% is 0.5 g l^-1 min^-1. For maximum reaction rate, the concentration of glucose inside the particles should remain above zero. Estimate the value of k₀, Converting k₀ to units of kg, m and s?
• B. 8.33 x 10^-3 kg m^-3 s^-1
• C. 6.33 x 10^-3 kg m^-3 s^-1
• D. 4.33 x 10^-3 kg m^-3 s^-1
• E. 2.33 x 10^-3 kg m^-3 s^-1