For $M^{2+}/M$ and $M^{3+}/M^{2+}$ systems the $E^\circ$ values for some metals are as follows:

| System | $E^\circ$ | System | $E^\circ$ |
|---|---|---|---|
| $Cr^{2+}/Cr$ | $-0.9$ V | $Cr^{3+}/Cr^{2+}$ | $-0.4$ V |
| $Mn^{2+}/Mn$ | $-1.2$ V | $Mn^{3+}/Mn^{2+}$ | $+1.5$ V |
| $

Question

For $M^{2+}/M$ and $M^{3+}/M^{2+}$ systems the $E^\circ$ values for some metals are as follows:

| System | $E^\circ$ | System | $E^\circ$ |
|---|---|---|---|
| $Cr^{2+}/Cr$ | $-0.9$ V | $Cr^{3+}/Cr^{2+}$ | $-0.4$ V |
| $Mn^{2+}/Mn$ | $-1.2$ V | $Mn^{3+}/Mn^{2+}$ | $+1.5$ V |
| $Fe^{2+}/Fe$ | $-0.4$ V | $Fe^{3+}/Fe^{2+}$ | $+0.8$ V |

Use this data to comment upon:
(i) the stability of $Fe^{3+}$ in acid solution as compared to that of $Cr^{3+}$ or $Mn^{3+}$ and
(ii) the ease with which iron can be oxidised as compared to a similar process for either chromium or manganese metal.

Accepted Answer

> [!TLDR]
> The key idea is to use the standard electrode potentials to compare the tendency of $M^{3+}$ to get reduced (stability in acid) and the ease of oxidation of $M$ to $M^{2+}$. For (i), $Fe^{3+}$ is more stable than $Mn^{3+}$ but less stable than $Cr^{3+}$ in acid. For (ii), iron is harder to oxidise than chromium but easier than manganese.

## Understanding the Concept: What the Potentials Tell Us

The two sets of potentials given — $E^\circ$ for $M^{2+}/M$ and $E^\circ$ for $M^{3+}/M^{2+}$ — are like two different thermometers for the same metal. The first tells us how easily the metal loses electrons to become $M^{2+}$ (oxidation of the metal). The second tells us how easily $M^{2+}$ loses another electron to become $M^{3+}$ (oxidation of the +2 ion), or equivalently, how stable the $M^{3+}$ ion is against being reduced back to $M^{2+}$.

A more positive $E^\circ$ for $M^{3+}/M^{2+}$ means the half-reaction $M^{3+} + e^- \rightarrow M^{2+}$ is more spontaneous — so $M^{3+}$ is a stronger oxidising agent and is *less stable* in solution (it wants to grab an electron and become $M^{2+}$). Conversely, a more negative $E^\circ$ for $M^{3+}/M^{2+}$ means $M^{3+}$ is harder to reduce, hence *more stable*.

For the metal itself, a more negative $E^\circ$ for $M^{2+}/M$ means the oxidation $M \rightarrow M^{2+} + 2e^-$ is more spontaneous (since the reverse reduction is less favourable). So the metal is *easier to oxidise*.

Let's apply this logic step by step.

---

### (i) Stability of $Fe^{3+}$ in acid solution compared to $Cr^{3+}$ and $Mn^{3+}$

**1. Compare the $M^{3+}/M^{2+}$ potentials.**  
The relevant values are:
- $Cr^{3+}/Cr^{2+}$: $E^\circ = -0.4$ V
- $Fe^{3+}/Fe^{2+}$: $E^\circ = +0.8$ V
- $Mn^{3+}/Mn^{2+}$: $E^\circ = +1.5$ V

**2. Interpret the sign and magnitude.**  
A more positive $E^\circ$ means the reduction $M^{3+} + e^- \rightarrow M^{2+}$ is more favourable. So $Mn^{3+}$ (with $+1.5$ V) is the strongest oxidising agent among the three — i

System	Meaning	More positive $E^\circ$ →
$M^{2+}/M$	Tendency of $M^{2+}$ to get reduced to $M$	$M^{2+}$ is easier to reduce (less stable as ion)
$M^{3+}/M^{2+}$	Tendency of $M^{3+}$ to get reduced to $M^{2+}$	$M^{3+}$ is easier to reduce (less stable as $M^{3+}$ )

System	$E^\circ$	System	$E^\circ$
$Cr^{2+}/Cr$	$-0.9$ V	$Cr^{3+}/Cr^{2+}$	$-0.4$ V
$Mn^{2+}/Mn$	$-1.2$ V	$Mn^{3+}/Mn^{2+}$	$+1.5$ V
$Fe^{2+}/Fe$	$-0.4$ V	$Fe^{3+}/Fe^{2+}$	$+0.8$ V

Understanding the Concept: What the Potentials Tell Us

(i) Stability of Fe3+Fe^{3+}Fe3+ in acid solution compared to Cr3+Cr^{3+}Cr3+ and Mn3+Mn^{3+}Mn3+

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(i) Stability of $Fe^{3+}$ in acid solution compared to $Cr^{3+}$ and $Mn^{3+}$

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