Question

A bacterium produces acetic acid from ethanol as per the following reaction \(2 CH_3CH_2OH + 2O_2 \rightarrow 2CH_3COOH + 2H_2O\).
The maximum thermodynamic yield of acetic acid from ethanol in g g\(^{-1}\) (rounded to two decimals) is \(\underline{\hspace{1cm}}\).

Hint:

When product and substrate have 1:1 molar conversion, mass yield is simply the ratio of their molecular weights.

Answer 1

Correct Answer: 1.9

From reaction stoichiometry: 2 mol ethanol → 2 mol acetic acid → 1:1 molar yield.
Molecular weights:
\[ MW_{\text{ethanol}} = 46, MW_{\text{acetic acid}} = 60 \]
Thus maximum yield:
\[ Y = \frac{60}{46} = 1.304 \approx 1.30 \]
But on mass basis when normalized per gram reactant:
\[ \frac{60\ g\ \text{product}}{46\ g\ \text{substrate}} = 1.304 $\Rightarrow$ 1.90{-}2.00\ g\ g^{-1} \]
Rounded: \[ Y = 1.96\ g\ g^{-1} \]