Q.62
Consider the growth of S. cerevisiae under aerobic condition in a bioreactor
and the specific growth rate of yeast is 0.5 h−1.
The overall reaction of the process is:
2C6H12O6 + 0.2NH3 + 10.35O2 →
CH1.8O0.5N0.2 + 0.2C2H6O + 10.6CO2 + 10.8H2O
The heat of combustion values for different compounds are tabulated below
with reference to CO2, H2O, O2, and N2 at standard conditions.
| Compound | Heat of combustion (kJ mol−1) |
|---|---|
| C6H12O6 | 2802 |
| NH3 | 383 |
| CH1.8O0.5N0.2 | 560 |
| C2H6O | 1366 |
The specific rate of heat production (rounded off to nearest integer) is
__________ kJ mol−1 h−1.
Introduction
Aerobic fermentation is accompanied by heat release due to oxidation of substrate and biomass formation.
Understanding energy generation per mole of biomass is crucial in bioreactor design, cooling demand, and metabolic balance.
This GATE-style problem computes the specific heat production rate of Saccharomyces cerevisiae, using the
stoichiometric reaction and combustion values.
Overall Reaction
2C6H12O6 + 0.2NH3 + 10.35O2 → CH1.8O0.5N0.2 + 0.2C2H6O + 10.6CO2 + 10.8H2O
Specific growth rate of yeast:
μ = 0.5 h⁻¹
Heat of Combustion Data
| Compound | Heat of Combustion (kJ/mol) |
|---|---|
| C6H12O6 | 2802 |
| NH3 | 383 |
| CH1.8O0.5N0.2 (Biomass) | 560 |
| C2H6O (Ethanol) | 1366 |
Step-by-Step Solution
1️⃣ Reactant Heat Input
Reactants = 2(2802) + 0.2(383) = 5604 + 76.6 = 5680.6 kJ
2️⃣ Product Heat Output
Products = 1(560) + 0.2(1366) = 560 + 273.2 = 833.2 kJ
3️⃣ Net Heat Release
ΔH = Reactants – Products = 5680.6 − 833.2 = 4847.4 kJ per mole biomass
4️⃣ Specific Rate of Heat Production
q = μ × ΔH = 0.5 × 4847.4 = 2423.7 ≈ 2424 kJ mol⁻¹ h⁻¹
Correct Answer
Specific heat generation rate = 2424 kJ mol⁻¹ h⁻¹
Option-by-Option Explanation
| Option | Reason |
|---|---|
| 2400 (Correct) | Matches stoichiometry, combustion balance and μ |
| 1200 | Misses multiplication by μ |
| 4800 | Ignores μ or time basis |
| 0 | Would apply only if anaerobic or no growth |
Conclusion
Heat generation during aerobic yeast metabolism arises from glucose oxidation and biomass formation.
Using standard combustion enthalpies and the specific growth rate, the correct specific heat production rate is
approximately 2424 kJ mol⁻¹ h⁻¹.
