Question

For the reaction 2Fe$^{3+}$(aq) + 2I$^{-}$(aq) → 2Fe$^{2+}$(aq) + I₂(s) the magnitude of the standard molar free energy change, $\Delta_r G^o_m$ = - _________ kJ (Round off to the Nearest Integer). [Given : $E^o_{Fe^{2+}/Fe(s)}$ = -0.440 V; $E^o_{Fe^{3+}/Fe(s)}$ = -0.036 V $E^o_{I₂/2I^{-}}$ = 0.539 V; F = 96500 C]

Hint:

Always use $\Delta G$ to calculate unknown electrode potentials, as $E^o$ values are not additive.

Answer 1

Correct Answer: -45

Step 1: Find $E^o_{Fe^{3+}/Fe^{2+}}$. $\Delta G^o_{(3 \to 0)} = \Delta G^o_{(3 \to 2)} + \Delta G^o_{(2 \to 0)} \implies -3FE^o_{(3/0)} = -1FE^o_{(3/2)} - 2FE^o_{(2/0)}$. $E^o_{(3/2)} = 3(-0.036) - 2(-0.440) = -0.108 + 0.880 = 0.772$ V.
Step 2: $E^o_{cell} = E^o_{cathode} - E^o_{anode} = 0.772 - 0.539 = 0.233$ V.
Step 3: $\Delta G^o = -nFE^o_{cell} = -2 \times 96500 \times 0.233 \approx -44969$ J $\approx -45$ kJ.