Electrode Potential Anomalies ($$E^\circ_{M^{2+}/M}$$ and $$E^\circ_{M^{3+}/M^{2+}}$$)

Trend / Formula (Redox Potential Trends):

$$E^\circ(\text{M}^{2+}/\text{M}) \text{ Trend Across } 3d \text{ Series: Irregularly becomes less negative towards Copper}$$

$$E^\circ(\text{Cu}^{2+}/\text{Cu}) = +0.34 \text{ V} \quad (\text{Only positive } E^\circ \text{ in } 3d \text{ series})$$

$$E^\circ(\text{M}^{3+}/\text{M}^{2+}) \text{ Key Values: } \begin{cases} E^\circ(\text{Mn}^{3+}/\text{Mn}^{2+}) = +1.57 \text{ V} & (\text{Strongly Oxidizing due to stable } d^5 \, \text{Mn}^{2+}) \\ E^\circ(\text{Cr}^{3+}/\text{Cr}^{2+}) = -0.41 \text{ V} & (\text{Strongly Reducing due to stable } t_{2g}^3 \, \text{Cr}^{3+}) \\ E^\circ(\text{Fe}^{3+}/\text{Fe}^{2+}) = +0.77 \text{ V} & (\text{Moderate redox couple}) \end{cases}$$

Concept: Standard electrode potentials ($$E^\circ$$) depend on the sum of three thermodynamic factors: Enthalpy of Atomization ($$\Delta_a H^\circ$$), Ionization Enthalpy ($$\Delta_i H^\circ$$), and Hydration Enthalpy ($$\Delta_{\text{hyd}} H^\circ$$). For Copper, high sublimation and ionization energies are not compensated by its hydration enthalpy, making $$E^\circ(\text{Cu}^{2+}/\text{Cu})$$ positive. $$\text{Mn}^{3+}$$ is a powerful oxidizing agent because reducing to $$\text{Mn}^{2+}$$ yields a stable half-filled $$d^5$$ shell.

Notation:

• $$E^\circ$$ = Standard reduction potential (in Volts)
• $$\Delta_{\text{hyd}} H^\circ$$ = Enthalpy of hydration