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.

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 e The doubling time of N. oculata is 4 hours. Assume dry weight of an actively growing cell of N. oculata is 2.8 x 1012 g. Also assume first-order kinetics. (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 1.835x102 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

1.835 * 10^-2 dry weight of N. oculata will contain 1.835 * 10^-2 / 2.8 * 10^-12 = 0.65 * 10^10 cells.

Now, if one doubling takes 4 hours, then in 48 hours, 12 doublings have occurred.

So, number of cells initially = 0.65 * 10^10/ 2^12 = 1.6 * 10^6 cells.

Dry weight of 1.6 * 10^6 cells will be: - 1.6* 10^6 * 2.8 * 10^-12 = 4.4 * 10^-6 gm.

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