Standard Electrode Potentials & Chemical Reactivity

Standard Electrode Potentials of the 3d Metals

The standard electrode potential $E^\circ(\text{M}^{2+}/\text{M})$ tells us how readily a metal is oxidised to its $+2$ ion in water. Across the 3d series these values are mostly negative (the metals tend to be oxidised) but show irregularities rather than a smooth trend.

$E^\circ(\text{M}^{2+}/\text{M})$ depends on three energy terms: the enthalpy of atomisation, the ionisation enthalpy (to form M$^{2+}$), and the hydration enthalpy of M$^{2+}$. The balance of these explains the bumps.

The copper anomaly: $E^\circ(\text{Cu}^{2+}/\text{Cu}) = +0.34$ V is positive — unique in the series. This means copper is not oxidised by H$^+$ (it does not dissolve in dilute non-oxidising acids to give H$_2$). The reason: copper's high enthalpy of atomisation and high ionisation enthalpies are not balanced by its hydration enthalpy.

The Mn and Zn Bumps; M3+/M2+ Trends

Two more anomalies in $E^\circ(\text{M}^{2+}/\text{M})$:

• Manganese has an unexpectedly low (more negative) value — because forming Mn$^{2+}$ ($3d^5$, stable half-filled) from the metal is favourable.
• Zinc also has a low value — linked to the stability of the filled $3d^{10}$ in Zn$^{2+}$.

The $E^\circ(\text{M}^{3+}/\text{M}^{2+})$ values tell us how easily the $+2$ ion is oxidised to $+3$:

• Sc has no stable $+2$, so this couple starts the series.
• $E^\circ(\text{Mn}^{3+}/\text{Mn}^{2+})$ is highly positive — Mn$^{2+}$ ($d^5$) strongly resists oxidation to Mn$^{3+}$, confirming Mn$^{2+}$'s stability.
• $E^\circ(\text{Fe}^{3+}/\text{Fe}^{2+})$ is small and positive — Fe$^{2+}$ is fairly easily oxidised to the stable Fe$^{3+}$ ($d^5$).

[JEE Tip] When asked to explain an $E^\circ$ anomaly, cite the stability of $d^5$ or $d^{10}$ configurations and the balance of atomisation, ionisation and hydration enthalpies.

Stability of Higher Oxidation States and Reactivity

The stability of higher oxidation states is greatest with the most electronegative ligands:

• The highest states (e.g. $+7$ for Mn, $+6$ for Cr) appear in fluorides and oxides.
• The $+7$ state of Mn is not found in simple halides other than indirectly; fluorine best stabilises high states.
• Lower halides (iodides) tend to stabilise lower oxidation states (iodide is a reducing ligand, so e.g. Cu$^{2+}$ + I$^-$ does not give CuI$_2$ but Cu$_2$I$_2$ + I$_2$).

General chemical reactivity:

• Most 3d metals (except Cu) have negative $E^\circ(\text{M}^{2+}/\text{M})$, so they liberate H$_2$ from dilute acids.
• They are fairly electropositive and reactive, though a protective oxide layer can passivate some (e.g. Cr, Ti).

Key Point: Two ideas explain almost every redox/stability question in this chapter: (1) the special stability of half-filled ($d^5$) and filled ($d^{10}$) subshells, and (2) the role of small electronegative ligands (O, F) in stabilising high oxidation states.

Solved Examples

Example 1: The copper anomaly

The $E^\circ(\text{Cu}^{2+}/\text{Cu})$ is +0.34 V (positive). What does this imply?

Solution: A positive value means copper is not oxidised by H$^+$ — it does not liberate H$_2$ from dilute HCl or H$_2$SO$_4$. Copper's high atomisation and ionisation enthalpies are not offset by its hydration enthalpy, making the oxidation unfavourable.

Example 2: Why Mn2+/Mn is low

Why is $E^\circ(\text{Mn}^{2+}/\text{Mn})$ more negative than expected?

Solution: Forming Mn$^{2+}$ gives the stable half-filled $3d^5$ configuration, which is energetically favourable — making manganese easier to oxidise to $+2$ and giving a more negative electrode potential.

Example 3: High E(Mn3+/Mn2+)

Why is $E^\circ(\text{Mn}^{3+}/\text{Mn}^{2+})$ strongly positive?

Solution: Mn$^{2+}$ ($d^5$, stable half-filled) strongly resists oxidation to Mn$^{3+}$ ($d^4$). A large positive $E^\circ$ for the M$^{3+}$/M$^{2+}$ couple means Mn$^{3+}$ is a strong oxidising agent and Mn$^{2+}$ is very stable.

Example 4: Fe3+/Fe2+ couple

What does the small positive $E^\circ(\text{Fe}^{3+}/\text{Fe}^{2+})$ tell us?

Solution: Fe$^{2+}$ ($d^6$) is fairly easily oxidised to Fe$^{3+}$ ($d^5$, stable half-filled). The small positive value indicates Fe$^{3+}$ is only a mild oxidising agent and Fe$^{2+}$ is moderately stable.

Example 5: Metals liberating hydrogen

Which 3d metals can liberate H$_2$ from dilute acids, and which cannot?

Solution: Metals with negative $E^\circ(\text{M}^{2+}/\text{M})$ (most of the series — Sc to Ni, plus Zn) liberate H$_2$ from dilute acids. Copper cannot because its $E^\circ$ is positive (+0.34 V).

Example 6: Stabilising the highest state

In which compounds does manganese show its $+7$ state?

Solution: In oxoanions and oxides with electronegative oxygen, such as $\text{MnO}_4^-$ (permanganate) and $\text{Mn}_2\text{O}_7$. Oxygen (small, highly electronegative) stabilises the high $+7$ state.

Example 7: Why CuI2 does not exist

Why does copper(II) not form a stable iodide, CuI$_2$?

Solution: Iodide is a reducing ligand. Cu$^{2+}$ oxidises I$^-$: $2\text{Cu}^{2+} + 4\text{I}^- \rightarrow \text{Cu}_2\text{I}_2 + \text{I}_2$. So copper(II) iodide is unstable and decomposes to copper(I) iodide and iodine.

Example 8: Passivation

Why does chromium resist corrosion despite a fairly negative electrode potential?

Solution: Chromium forms a thin, adherent oxide layer on its surface that passivates it, preventing further reaction. This is why chromium is used for protective plating.

Example 9: Which is a better oxidising agent

Using configurations, decide which is the stronger oxidising agent: Mn$^{3+}$ or Fe$^{3+}$.

Solution: Mn$^{3+}$ is the stronger oxidising agent. It is reduced to the very stable half-filled Mn$^{2+}$ ($d^5$). Fe$^{3+}$ is already the stable $d^5$, so it has little tendency to be reduced further — making it a weaker oxidising agent.

Example 10: Reactivity vs hydrogen

A metal has $E^\circ(\text{M}^{2+}/\text{M}) = -0.44$ V. Will it displace hydrogen from dilute acid?

Solution: Yes. A negative $E^\circ$ means the metal is oxidised more readily than H$_2$, so it displaces H$_2$ from dilute acid (this is iron).