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GATE 2021 BT – Question 65

Fundamentals of Biological Engineering · Bioreaction Engineering: Kinetics of cell growth, substrate utilization and product formation, structured and unstructured models · 2 marks · Numerical answer

For $2CH_3CH_2OH+2O_2\to2CH_3COOH+2H_2O$, the thermodynamic maximum acetic-acid yield from ethanol (two decimal places g/g) is _______.

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Correct answer: 1.29 to 1.31

Explanation

**Reaction:** $2\,CH_3CH_2OH+2\,O_2\to2\,CH_3COOH+2\,H_2O$.

**Step 1: mole ratio.** 2 mol of ethanol give 2 mol of acetic acid, so the conversion is 1 mol to 1 mol.

**Step 2: molar masses.**
- Ethanol, $C_2H_6O$: $2(12)+6(1)+16=46$ g/mol.
- Acetic acid, $C_2H_4O_2$: $2(12)+4(1)+2(16)=60$ g/mol.

**Step 3: theoretical maximum mass yield.**
$$Y=\frac{60}{46}=1.304\approx\mathbf{1.30\ g/g}.$$