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Serratia marcescens bacteria are used for the production of threonine. The maximum specific oxygen uptake rate of S. marcescens in batch culture is 4 mmol O2 g-1 h-1. It is planned to operate the fermenter to achieve a maximum cell density of 50 g l-1. At the fermentation temperature and pressure, the solubility of oxygen in the culture liquid is 8 × 10^-3 kg m^-3. The concentration of oxygen in the culture liquid is 0.5 × 10^-3 kg m^-3. At a particular stirrer speed, kLa is 0.17 s^-1.

Required:
Under these conditions, will the rate of cell metabolism be limited by mass transfer?

Respuesta :

Answer:

The rate of cell metabolism is limited by mass transfer since the value of maximum cell concentration obtained (38 g/l) is lower than 50 g l-1, the value planed.

Explanation:

                                                     Data

kLa = 0.17/s

Solubility of oxygen =  8 × 10^-3 kg / m^3

The maximum specific oxygen uptake rate = 4 mmol O2 / g h.

Concentration of oxygen =  0.5 × 10^-3 kg/ m^3

**The maximum cell density = 50 g/l

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The calculated maximum cell concentration:

xmax=  kLa · CAL*/ qo

CAL* is the solubility of oxygen in the broth and qo is the specific oxygen uptake rate

Replacing the data given

xmax= ( 0.17/s ) ·   (8 × 10^-3 kg / m^3)  /  4 mmol O2 / g h

4 mmol O2 / g h  to kg O2/ g s

[tex]4 \frac{mmol}{gh} \frac{1 gmol}{1000mmol}\frac{1h}{3600s}\frac{32 g}{gmol} \frac{1Kg}{1000g}[/tex]

= 3.56 x 10^-3 kg O2/ g s

So then,

xmax= ( 0.17/s ) ·   (8 × 10^-3 kg / m^3)  / 3.56 x 10^-3 o kg O2/ g s

xmax= 3. 8 x 10^4 g/ m^3   = 38 g/l

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