Question 7 of 10: Thermodynamic Feasibility of Nitrobenzene Reduction by Iron(II)

Question 7: Thermodynamic Feasibility of Nitrobenzene Reduction by Iron(II) (15 points)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Reduction half-reaction, nitrobenzene → aniline: $E^0_{\text{NB}} = +0.42\ \text{V}$ ($n=6$ electrons). Reduction half-reaction, $\text{Fe}^{3+} + e^- \rightleftharpoons \text{Fe}^{2+}$: $E^0_{\text{Fe}} = +0.77\ \text{V}$.

Find. Whether Fe(II) can reduce nitrobenzene to aniline under standard conditions — the overall cell potential $E^0_{\text{cell}}$ and Gibbs free-energy change $\Delta G^0$.

Approach. For Fe(II) to act as the reducing agent, it must be oxidized to Fe(III) — the printed Fe³♠/Fe²♠ half-reaction must therefore run in reverse, paired with the nitrobenzene half-reaction running forward (as the reduction/cathode reaction). $E^0_{\text{cell}} = E^0_{\text{cathode}} - E^0_{\text{anode}}$ (both written as reductions), and $\Delta G^0 = -nFE^0_{\text{cell}}$.

1. Overall coupled reaction. Nitrobenzene reduction (cathode, as printed) coupled to Fe(II) oxidation (anode, reverse of the printed Fe³♠/Fe²♠ reduction): $$\text{C}_6\text{H}_5\text{NO}_2 + 6\text{Fe}^{2+} + 6\text{H}^+ \rightarrow \text{C}_6\text{H}_5\text{NH}_2 + 6\text{Fe}^{3+} + 2\text{H}_2\text{O}$$
2. Standard cell potential. $$E^0_{\text{cell}} = E^0_{\text{cathode}} - E^0_{\text{anode}} = E^0_{\text{NB}} - E^0_{\text{Fe}} = 0.42\ \text{V} - 0.77\ \text{V} = \boxed{-0.35\ \text{V}}$$
3. Standard Gibbs free-energy change. With $n=6$ and $F = 96{,}485\ \text{C/mol}$, $$\Delta G^0 = -nFE^0_{\text{cell}} = -(6)(96{,}485\ \text{C/mol})(-0.35\ \text{V}) = \boxed{+202.6\ \text{kJ/mol}}$$

$E^0_{\text{cell}}$ is negative and $\Delta G^0$ is strongly positive, so the reaction as written is not spontaneous under standard conditions — ferrous iron (Fe²⁺) alone cannot reduce nitrobenzene to aniline, because the Fe³⁺/Fe²⁺ couple is a weaker reducing agent (higher, more positive reduction potential, $+0.77\ \text{V}$) than nitrobenzene is an oxidizing agent ($+0.42\ \text{V}$) requires. This result explains why dissolved ferrous iron is not used as a reductant for nitroaromatic contaminants in practice. By contrast, zero-valent iron, Fe(0), has a much more negative $\text{Fe}^{2+}/\text{Fe}^0$ standard potential (about $-0.44\ \text{V}$, literature value), giving $E^0_{\text{cell}} = 0.42 - (-0.44) = +0.86\ \text{V}$ and a strongly negative $\Delta G^0$ — a thermodynamically favourable reaction. This is the actual basis for permeable reactive barriers (PRBs) using granular zero-valent iron to reduce nitroaromatic and chlorinated contaminants in groundwater: it is the metallic Fe(0) surface, not dissolved Fe(II)/Fe(III) chemistry, that supplies the driving force.