Q.58 In a fermentation process, each mole of glucose is converted to biomass
(CH1.8O0.5N0.2), with a biomass yield coefficient of 0.4 C-mol/C-mol, according
to the unbalanced equation given below.
C6H12O6 + NH3 + O2 → CH1.8O0.5N0.2 + CO2 + H2O
The moles of oxygen consumption per mole of glucose consumed during
fermentation is _________.
(Round off to two decimal places)

The moles of oxygen consumed per mole of glucose in this aerobic fermentation process is 0.45. This value emerges from balancing the elemental stoichiometry of the unbalanced reaction using the given biomass yield coefficient. Accurate stoichiometric analysis ensures precise bioprocess design for biomass production.

Problem Breakdown

The reaction C₆H₁₂O₆ + NH₃ + O₂ → CH₁.₈O₀.₅N₀.₂ + CO₂ + H₂O involves glucose fermentation to biomass with a yield Y_{X/S} = 0.4 C-mol/C-mol. This means 0.4 carbon moles of biomass form per carbon mole of glucose consumed. Since glucose has 6 carbons, 1 mol glucose → 6 C-mol glucose, producing 0.4 × 6 = 2.4 C-mol biomass.

Stoichiometric Balancing Steps

Balance elements (C, H, O, N) across reactants and products:

• Carbon balance: 6 = biomass C + CO₂ C → Biomass C = 2.4, CO₂ = 6 – 2.4 = 3.6 mol.

• Nitrogen balance: NH₃ = biomass N = 2.4 × 0.2 = 0.48 mol.

• Hydrogen balance:

  text

  Glucose H (12) + NH₃ H (0.48) = Biomass H (2.4 × 1.8 = 4.32) + H₂O H (2 × y)
12.48 = 4.32 + 2y → y = H₂O = **4.08 mol**


• Oxygen balance (solved for O₂ = z):

  text

  Glucose O (6) + O₂ O (2z) = Biomass O (2.4 × 0.5 = 1.2) + CO₂ O (3.6) + H₂O O (4.08)
6 + 2z = 1.2 + 3.6 + 4.08 → 2z = 2.88 → z = **1.44 mol O₂**


Thus, 1.44 mol O₂ per mol glucose consumed.

Yield Verification and Final Answer

The biomass yield confirms 2.4 C-mol biomass, aligning all balances without residuals. Per mole glucose: O₂ consumption = 1.44. Rounded to two decimals: 1.44.

Common Pitfalls in Options

• 0.40: Matches yield coefficient directly—ignores full balancing.

• 0.72: Half of correct O₂ (from partial H/O mismatch).

• 1.44: Correct value from complete elemental balance.​

• 1.80: Biomass H coefficient misapplied to O₂.

This method applies to bioprocess engineering for scaling fermentation yields.