Astrain of escherichia coli has been genetically engineered to produce human protein. a batch culture is started by inoculating 12 g of cells into a 100-litre bubble column fermenter containing 10 g 1^- 1 glucose. the culture does not exhibit a lag phase. the maximum specific growth rate of the cells is 0.9 h^-1; the biomass yield from glucose is 0.575 g g^-1
1. estimate the time required to reach stationary phase.
2. what will be the final cell density if the fermentation is stopped after only 70% of the substrate is consumed?

1. 4.32 h

2. 4.12 g/L

Explanation:

1. For a batch culture, the time (tb) can be calculated by:

tb =  ln (X/X0)/μmax

Where X0 is the initial mass concentration of the cells (12 g/100L = 0.12 g/L), X is the mass concentration of the cells at tb, and μmax is the maximum specific growth rate of the cells.

The biomass yield (Y) is:

Y = (X - X0)/ (S0 - S)

Where S is the mass concentration of the substrate at tb and S0 the initial mass concentration of the substrate (glucose in this case).

Reorganizing:

X = Y*(S0 -S) + X0

Let's assume that at the stationary state all substrate was consumed, so S = 0.

tb = ln[(YS0 + X0)/X0)]/μmax

tb = ln[(0.575*10 + 0.12)/0.12]/0.9

tb = 4.32 h

2.  If 70% of the substrate is consumed, S = 10 - 0.7*10 = 3 g/L

tb = ln[(0.575*(10-3) + 0.12)/0.12]/0.9

tb = 3.93 h

The initial concentration is X0 = 0.12 g/L, the X:

tb =  ln (X/X0)/μmax

3.93 = ln(X/0.12)/0.9

ln(X/0.12) = 3.537

X/0.12 =

X/0.12 = 34.36

X = 4.12 g/L

the number of valence electrons for each molecule or ion is shown beneath the structure. remember hydrogen will not have more than two electrons. this hydrogen is part of a covalent bond (sharing two electrons). a double bond here would cause hydrogen to share four electrons with phosphorus.

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.