A culture consisting of 100 litres of nutrient medium containing 12 g l-1
of growth limiting
substrate is inoculated with 10g of bacteria in a batch fermenter. The yield of biomass
from substrate is 0.05 g g-1
. The maintenance coefficient is 2.0 g g-1
h
-1
. The specific rate
of product formation due to maintenance is 1.0 h-1
. The maximum specific growth rate of
the organism is 0.3 h
-1
. YPX= 7.7 and product formation is directly linked with metabolism.
a) What is the time required to produce 15 g of biomass? Ans: 3.05 hours
b) Derive the expression for batch time (tb) in terms of substrate concentration and
calculate what percentage of substrate is used up over the time period calculated in (a)
Ans: 33.3 %
c) Derive the expression for batch time (tb) in terms of product concentration and
calculate how many grams of product are formed during the time period calculated in (a)
Ans:  165 g
d) How long will it take for 95% of the substrate to be consumed? Ans: 5.54 hours
e) How long will it take to produce 200 g of product? Ans: 3.45 hours