3. (10 points, total) Batch Reactors – First order kinetics A growth experiment

Question

3. (10 points, total) Batch Reactors – First order kinetics A growth experiment of N. oculata was carried out in a 100 L batch photobioreactor to produce a heat-stable enzyme. The doubling time of N. oculata is 4 hours. Assume dry weight of an actively growing cell of N. oculata is 2.8 x 10-12 g. Also assume first-order kinetics. (i) (5 points) Calculate the initial concentration of N. oculata cells (in # of cells/L) if the final dry weight of N. oculata after 48 hours of operation was 1.835 x 10-2 g

(ii) (5 points) A growth experiment of E. coli beginning with a single cell was carried out for 10 hours in a fermentor to produce citric acid. The doubling time of E. coli is 20 min and dry weight of an actively growing cell of E. coli is 3 x 10-13 g. Calculate the dry weight of E. coli biomass after 5 hours from the beginning of the experiment.

Explanation / Answer

Dry weight of single cell is 2.8 x 10-12

So the number of cells = 1.835 x 10-2 / 2.8 x 10-12

                                         = 6.55 x 109 cells

So concentration will be : 6.55 x 106 cells/L

Now we can use the formula: Nt = N0 x 2n

Where n= number of generation which will be = 48/4 = 12

So , N0 = Nt /2n = 2.11 x 103cells/L

ii) Dry weight of single cell is 3 x 10-13

Fermentation was started with single cell.

n= number of generation would be = (5 x 60)/20 = 15

So the number of cells after 5 hours = 1 x 215

                                         = 2.47 x 104 cells

Dry weight after 5 hours can be calculated by: (2.47 x 104) x (3 x 10-13)

                                                         = 7.41 x 10-9 g

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