Q.65 A bacterium produces acetic acid from ethanol as per the following reaction
2CH3CH2OH + 2O2 → 2CH3COOH + 2H2O
The thermodynamic maximum yield of acetic acid from ethanol in g g−1
(rounded off to two decimal places) is _________.
Thermodynamic Maximum Yield of Acetic Acid from Ethanol
Acetic acid bacteria convert ethanol to acetic acid via oxidation, with the thermodynamic maximum yield calculated stoichiometrically. For the reaction 2CH3CH2OH + 2O2 → 2CH3COOH + 2H2O, the yield is 1.30 g acetic acid per g ethanol.
✅ Correct Answer
The thermodynamic maximum yield is 1.30 g/g (rounded to two decimal places).
🔬 Reaction Stoichiometry
The given reaction shows complete oxidation of ethanol to acetic acid by acetic acid bacteria (e.g., Acetobacter species):
2CH3CH2OH + 2O2 → 2CH3COOH + 2H2O
This is the theoretical maximum, as “thermodynamic maximum yield” refers to stoichiometric conversion without losses, equivalent to theoretical yield in bioprocess engineering.
📊 Step-by-Step Calculation
The yield represents grams of acetic acid produced per gram of ethanol consumed under ideal stoichiometric conditions, ignoring cell growth or side reactions.
- Molar mass of ethanol (CH3CH2OH, C2H5OH): 2(12) + 6(1) + 16 = 46 g/mol
- Molar mass of acetic acid (CH3COOH): 2(12) + 4(1) + 2(16) = 60 g/mol
- From the balanced equation, 2 moles ethanol produce 2 moles acetic acid, so 1:1 molar ratio
- Mass ratio: 2×60 / 2×46 = 60/46 = 1.3043 g/g
- Rounded: 1.30 g/g
⚠️ Common Mistakes Explained
No explicit options exist, but typical errors in such numericals include:
- Wrong molar masses: Using 44 for ethanol (confusing with CO2) gives ~1.36 (incorrect)
- Ignoring balanced coefficients: Treating as 1:1 without multiplying by 2 yields same ratio but risks unbalancing
- Observed vs. theoretical: Real yields (e.g., 0.75 g/g from 10 g/L ethanol to 7.5 g/L acetic acid) are lower due to biomass formation
- Degree of reduction confusion: For carbon yields or YX/S, adjust for electrons, but here it’s direct mass yield on product
🏭 Bioprocess Context
In vinegar production, Acetobacter aceti achieves near-theoretical yields under aerobic conditions, but actual processes yield 90-95% due to maintenance energy and byproducts. The value 1.30 confirms ideal mass balance for exam purposes.
