Why is the $E^\circ$ value for the $Mn^{3+}/Mn^{2+}$ couple much more positive than that for $Cr^{3+}/Cr^{2+}$ or $Fe^{3+}/Fe^{2+}$? Explain.

Question

Accepted Answer

> [!TLDR]  
> The unusually positive $E^\circ$ for $Mn^{3+}/Mn^{2+}$ arises because $Mn^{2+}$ has a half-filled $3d^5$ configuration (extra stability), making its oxidation to $Mn^{3+}$ energetically unfavourable. In contrast, $Cr^{2+}$ and $Fe^{2+}$ gain stability upon oxidation — $Cr^{2+}$ to $Cr^{3+}$ (half-filled $t_{2g}^3$) and $Fe^{2+}$ to $Fe^{3+}$ (half-filled $3d^5$). Hence, $Mn^{3+}$ is a strong oxidising agent, giving a high $E^\circ$ value.

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### The Core Idea: Stability of Oxidation States and Electronic Configuration

The standard electrode potential $E^\circ$ for a redox couple $M^{3+}/M^{2+}$ tells us how easily $M^{2+}$ gets oxidised to $M^{3+}$. A **more positive** $E^\circ$ means the $M^{2+}$ state is **more stable** relative to $M^{3+}$ — it resists oxidation. Conversely, a less positive (or negative) $E^\circ$ means $M^{2+}$ is easily oxidised.

The key lies in the electronic configurations of the ions, specifically the stability associated with half-filled and fully-filled $d$ subshells. In aqueous solution, these are high-spin complexes for first-row transition metals.

Let's examine each case.

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### Step-by-Step Reasoning

**1. The $Mn^{3+}/Mn^{2+}$ couple: The half-filled $d^5$ fortress**

- $Mn^{2+}$ has the electronic configuration $[Ar]\,3d^5$. In an octahedral field (high-spin), this is $t_{2g}^3 e_g^2$ — each of the five $d$ orbitals is singly occupied.
- This is a **half-filled $d$ subshell**, which confers exceptional stability due to:
    - Maximum exchange energy (Hund's rule).
    - Symmetrical distribution of electron density.
- To oxidise $Mn^{2+}$ to $Mn^{3+}$, you must remove an electron from this stable $3d^5$ arrangement. $Mn^{3+}$ has $3d^4$ ($t_{2g}^3 e_g^1$), which is less stable (Jahn-Teller distortion also adds instability).
- Therefore, the oxidation $Mn^{2+} \rightarrow Mn^{3+} + e^-$ is **energetically very difficult**. This means $Mn^{2+}$ strongly resists being oxidised, so the equilibrium $Mn^{3+} + e^- \ri

Ion	Configuration	d-electrons
$\text{Cr}^{3+}$	$[Ar]\,3d^3$	$t_{2g}^3$ (half-filled $t_{2g}$ )
$\text{Cr}^{2+}$	$[Ar]\,3d^4$	$t_{2g}^3 e_g^1$
$\text{Mn}^{3+}$	$[Ar]\,3d^4$	$t_{2g}^3 e_g^1$
$\text{Mn}^{2+}$	$[Ar]\,3d^5$	$t_{2g}^3 e_g^2$ (half-filled d⁵)
$\text{Fe}^{3+}$	$[Ar]\,3d^5$	$t_{2g}^3 e_g^2$ (half-filled d⁵)
$\text{Fe}^{2+}$	$[Ar]\,3d^6$	$t_{2g}^4 e_g^2$

Q.Why is the $E^\circ$ value for the $Mn^{3+}/Mn^{2+}$ couple much more positive than that for $Cr^{3+}/Cr^{2+}$ or $Fe^{3+}/Fe^{2+}$ ? Explain.

Concept understanding — Stability of Oxidation States

Stability of Oxidation States – From Intuition to Precision

The Core Intuition

The Precise Statement

Examples That Make It Concrete

How to Think About It in Exams …

Why this formula?

Stability of Oxidation States: Why It Works

The Core Idea: Energy Minimisation

Key Principle 1: Inert Pair Effect (for p-block elements)

Key Principle 2: Half-Filled / Fully-Filled Subshell Stability

Key Principle 3: Lattice Energy / Hydration Energy Compensation

Key Principle 4: Disproportionation

The Core Idea: Stability of Oxidation States and Electronic Configuration

Step-by-Step Reasoning

Method: Electronic Configuration & Stability Analysis

Step 1: Write the electronic configurations

Step 2: Identify the stability factor

Step 3: Compare with Cr and Fe

Mistake 1: Only Mentioning the Electronic Configuration (Without Linking to Stability)

Mistake 2: Confusing the Direction of the Reaction

Mistake 3: Ignoring the Role of Hydration Enthalpy

Mistake 4: Forgetting the Exact $E^\circ$ Values

Why the medium matters

Step-by-step reasoning

Why Lanthanoids Love +3: Electronic Configuration and Stability

Step-by-Step Reasoning

Why this is a trick question — and how to see through it

Step-by-step reasoning

Why this question tests a core idea

Step-by-step reasoning

Q.Why is the E∘E^\circE∘ value for the Mn3+/Mn2+Mn^{3+}/Mn^{2+}Mn3+/Mn2+ couple much more positive than that for Cr3+/Cr2+Cr^{3+}/Cr^{2+}Cr3+/Cr2+ or Fe3+/Fe2+Fe^{3+}/Fe^{2+}Fe3+/Fe2+? Explain.

The Core Idea: Stability of Oxidation States and Electronic Configuration

Step-by-Step Reasoning

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Q.Why is the $E^\circ$ value for the $Mn^{3+}/Mn^{2+}$ couple much more positive than that for $Cr^{3+}/Cr^{2+}$ or $Fe^{3+}/Fe^{2+}$ ? Explain.

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