Part A-

The batch growth of a microbe on the substrate glucose is described by the equation below.  

C₆H₁₂O₆ + aO₂ + bNH₃ ----> c(C_5.1H₇N_0.3O_2.1)  + dH₂O + eCO₂

A. Perform atomic balances to find a, b, c, d, and e assuming that 82% (by mass) of the carbon in the substrate is converted to biomass (cells).

Part B-

Problem 1- Media is to be batch sterilized in a 100 liter fermenter before it is used to grow microorganisms.  Using 0.001 as the probability of an unsuccessful sterilization, compute the time required for sterilization at 121°, 125°, 130°C, and 135°C.   Ignore heat up and cool down.  Data are below are for bacillus stearothermophilus spores which is the standard data used in the absence other microbe specific data. (put boxes around your answers)

For Spores present in the media:

Spore concentration:  1 x 10⁶ spores/liter

E = 67.7 kcal/mol

A = 1 x 10^36.2 min-1

Problem 2-  You are trying to make an intelligent choice of which of the 4 pairs of temperatures and sterilization times (from problem 1) to use, one consideration is the effect of the sterilization process on heat labile components in the growth medium such as L-glutamine which can degrade as a function of time and temperature.  The equation for k_d,LG for L-Glutamine is below.  Where E_LG is 10 kcal/mol and A is 1 x 10⁴ min-1.  The equation for the degradation of L-Glutamine is also below.  If your media has a 0.01M concentration of L-Glutamine before sterilization.  Please compute the concentration of L-Glutamine that remains after sterilization for each of the 4 pairs of time and temperature.  Please, then comment on which pair may be the best for this particular sterilization process.

K_d,LG = Ae^-(ELG/RT)

CLG,t = C_LG,0e^-kd,LGt