GATE 2026 BT – Question 34
Given below is the Gibbs free energy change ($\Delta G$) in kilo Joules per electron equivalent (kJ e-eq$^{-1}$) at pH 7.0, of organic and inorganic half reactions.
Acetate synthesis: $\frac{1}{8}CO_2 + \frac{1}{8}HCO_3^- + H^+ + e^- \rightarrow \frac{1}{8}CH_3COO^- + \frac{3}{8}H_2O$, $\Delta G = 27.4$ kJ e-eq$^{-1}$
Reduction reaction: $\frac{1}{4}O_2 + H^+ + e^- \rightarrow \frac{1}{2}H_2O$, $\Delta G = -78.72$ kJ e-eq$^{-1}$
The free energy change of acetate oxidation to $CO_2$, $H_2O$ and $HCO_3^-$ is _______ kJ e-eq$^{-1}$. (rounded off to two decimal places)
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Correct answer: -106.65 to -105.59
Explanation
The overall reaction is the reduction of oxygen (the acceptor) coupled to the oxidation of acetate (the donor), and $\Delta G = \Delta G_{acceptor} - \Delta G_{donor}$, where the donor value is that of the half reaction as a reduction. So $\Delta G = -78.72 - 27.4 = -106.12$ kJ e-eq$^{-1}$.