A culture medium containing a vitamin is to be sterilized by the thermal method. The vitamin can be deactivated by heat. The deactivation of this vitamin follows a similar kinetic model as cell death. Assume that the number of initial spore contamination is 105/l in the bioreactor. The values of the pre-Arrhenius constant (a) and E0d for the spores are E0d = 65 kcal/g-mol and α = 1036 min-1. For the inactivation of the vitamin, the values of E0d and a are E0d = 10 kcal/g-mol and α= 104 min-1 The initial concentration of the vitamin is 30 mg/l. Calculate the amount of active vitamin in the sterilized medium for 10 L and 10,000 L fermenters when both are sterilized at 121⁰C. Both processes require in the probability of an unsuccessful fermentation to be 0.001. (Use the sterilization chart and ignore the effects of the heat-up/cool-down periods.)