Calculate the standard gibbs free energy change

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Reference no: EM133743736

Assignment: Microbial growth kinetics

Introduction:

As we learned in the last couple of weeks, reaction kinetics investigates the relationship between reaction rates and the conditions that affect them. In this assignment, we will review and practice

how to determine the rates and rate constants of cell growth, substrate uptake, and product formation,
concepts related to reaction thermodynamics and stoichiometry,
calculation of microbial growth in batch or continuous bioreactors; and

basic biotechnology principles covered in the first week.

Question 1: Escherichia coli is used to produce recombinant porcine growth hormone. The bacteria are grown aerobically in batch culture with glucose as the growth-limiting substrate. Cell concentrations are measured as a function of culture time with the following results. [You can use Excel or Google Sheets to plot graphs or assist in calculation.]

You decided to use the average rate-equal area method to determine growth rates from the cell concentration.
Fill out the table below using the average rate-equal area plot and the calculation results.

Mark the x-axis and y-axis scales in the average rate-equal area plot based on the calculation.

Plot μ as a function of time.

What is the value of μ_max? Please express it as an average value.

Time	Cell Concentration, x	Δx	Δt	Δx/Δt	r_x	μ
(h)	(kg m^-3)	(kg m^-3)	(h^-1)	(kg m^-3h^-1)	(kg m^-3h^-1)	(h^-1)
0	0.2
0.33	0.21
0.5	0.22
0.75	0.32
1	0.47
1.5	1
2	2.1
2.5	4.42
2.8	6.9
3	9.4
3.1	10.9
3.2	11.6
3.5	11.7
3.7	11.6

Question 2: Explain the process of using E. coli to produce recombinant protein, such as porcine growth hormone.

During the fermentation process, bioprocess engineers need to monitor the stability of the plasmid containing the gene encoding porcine growth hormone. Which method do you recommend for determining the concentration of E. coli cells with the plasmid? Why?

The recombinant E. coli cells used in Q1 are cultivated at 30°C. The activation energy for the thermal growth of the bacterium is 31.2 KJ/mol. What is the doubling time of E. coli cells at 37°C?

Question 3: Estimate the theoretical growth and production yield coefficients for ethanol fermentation by Saccharomyces cerevisiae as described by the following overall reaction:

Glucose (C₆H₁₂O₆) → 2 Ethanol (C₂H₅OH) + 2 CO₂

a. Calculate the standard Gibbs free energy change of this reaction.

Table 3.1 Free energies of formation (G_f⁰) for some substances (kJ/mol)
Compound	G_f⁰ (kJ/mol)	Compound	G_f⁰ (kJ/mol)
Butyrate	-352.63	H₂	0
H₂O	-237.17	H⁺	-39.83 at pH7
Glucose	-917.22	acetate	-369.41
O₂	0	CO₂	-394.4
		Ethanol	-181.75

During the ethanol fermentation process, S. cerevisiae produces 2 mol of ATP from 1 mol of glucose. The biomass yield from ATP is 10.5 g (dry weight)/mol ATP. Calculate the theoretical yield of ethanol from cell biomass, and the theoretical yield of biomass from glucose.

For the particular strain of S. cerevisiae used, the maintenance coefficient is 0.20 h-1, and μmax is 0.38 h-1. What is the specific rate of ethanol production by this strain?

Calculate the total productivity of ethanol production in a 50 m3 bioreactor with a biomass concentration of 10g/L.

Question 4:

Pseudomonas methylotrophus is used to produce single-cell protein from methanol in a 1000-m³ pressure-cycle airlift fermenter. The biomass yield from the substrate is 0.41 g g?¹, KS is 0.7 mg l?¹, and the maximum specific growth rate is 0.44 h?¹. The medium contains 4% (w/v) methanol. A substrate conversion of 98% is desirable. The reactor may be operated in either batch or continuous mode. If operated in batch, an inoculum of 0.01% (w/v) is used, and the downtime between batches is 20 h. If continuous operations are used at a steady state, a downtime of 25 days is expected per year. Neglecting maintenance requirements, compare the annual biomass production achieved using batch and continuous reactors.

Question 5: Develop a mind map of the content we learned in Lectures 3-7.

Reference no: EM133743736

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