4. Stoichiometric model. (3 pts)
E. coli cells (CH$_{1.8}$O$_{0.45}$N$_{0.15}$) are cultured under chemostat condition without the supply of air.
(a) The culture volume is V = 1 L. A feed containing 16 g/L glucose and 1 g/L NH$_3$ is fed at a rate of
v = 0.1 L/h.
(b) In the effluent, following compounds are detected, 1 g/L glucose, 2.46 g/L biomass, 4.2 g/L lactic
acid, 3.91 g/L ethanol, and NH$_3$.
(c) The offgas (effluent gas) sensor detects CO$_2$ formation at 0.005 L/min.
(1) Calculate the specific growth rate of the cells.
(2) Calculate the volumetric consumption rate of glucose ($q_{glu}$) and the volumetric production rate
of biomass ($q_x$), lactic acid ($q_{lac}$), ethanol ($q_{eth}$), and CO$_2$ ($q_{co2}$) in unit of mole/L/h. (You can
use ideal gas equation for CO$_2$ calculation. P = 1 bar, T = 300 K)
(3) The balance of carbon atoms in the process (often called carbon balance) can be used to
examine the consistency of the experimental data. Please write the carbon balance equation
using the volumetric rates in (2), determine whether the data is consistent.
