Stoichiometry, yield and extent of reaction We have fermenter where the followin

Question

Stoichiometry, yield and extent of reaction

We have fermenter where the following biological reaction is taking place:

For a particular bacterial strain, the molecular formula was determined to beC4.4H7.3O1.2N0.86. These bacterial cells are grown under aerobic conditions with hexadecane (C16H34) as substrate.

Assume that 60% of the hexadecane is used for producing cells (also called biomass) and the remaining 40% of the hexadecane is used for other cell functions. You have been put in charge of a small batch fermenter for growing the bacteria and aim to produce 10 kg of cells for inoculation of a pilot-scale reactor.

a) Assuming this 60% conversion, what is the yield of cells from hexadecane in kg/kg?

b) What minimum amount of hexadecane substrate (in kg) must be contained in your culture medium? Remember that only 60% of the hexadecane is converted to cells.

c) What must be the minimum concentration of hexadecane (in kg/m3 ) in the medium if the fermenter working volume is 4.3 cubic meters? Remember that only 60% of the hexadecane is converted to cells.

PLEASE HELP! I think the last person who tried to help got there numbers all messed up. It is a 60% yield

Explanation / Answer

a) As per stoichiometry of equation

1 mole of hexadecane will give 1.65 moles of bacterial cell with mol formula C4.4H7.3O1.2N0.86

60% conversion means that from 1 mole we will obtain only 60 X 1.65 / 100 moles = 0.972 moles

Molecular weight of hexadecane = 226 g / mole

mol wt of bacterial cell = 12X4.1 + 7.3 + 16 X 1.2 + 14 X 0.86 = 52.8 + 7.3 + 19.2 + 12.04 = 91.34 g / mole

226 grams should give 1.65 X 91.34 grams of cell = 150.71

so 1Kg should give = 150.71 / 226 Kg = 0.667 Kg

But the yield is 60% so

It will give 60 X 0.667 / 100 Kg = 0.4002 Kg

so yield is = 0.4 Kg / Kg of hexadecan

b) To obtain 0.4 Kg of cell we need = 1Kg of hexadecane

So for 10Kg we will need = 1 X 10 / 0.4 Kg of hexadecane = 25 Kg of hexadecane

c) The volume is 4.3 m^3

And amount of hexadecane require = 25Kg

so 25Kg in 4.3 m^3

So in 1m^3 = 5.81 Kg

So concentration is 5.81 Kg / m^3

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