Question

For which of the following the \( E^\ominus (M^{3+}/M^{2+}) \) is negative?

• A. Mn
• B. Co
• C. Fe
• D. Cr

Answer 1

The Correct Option is D

The standard electrode potential \( E^\ominus (M^{3+}/M^{2+}) \) being negative means that the \( M^{2+} \) ion is more stable and resistant to oxidation to \( M^{3+} \), or conversely, \( M^{3+} \) is a strong oxidizing agent and readily reduces to \( M^{2+} \).
We need to look at the electronic configurations and stability.
- Mn: Mn\(^{2+}\): [Ar] \(3d^5\) (half-filled d-orbitals, very stable) Mn\(^{3+}\): [Ar] \(3d^4\) The process Mn\(^{2+}\) \( \rightarrow \) Mn\(^{3+}\) + e\(^-\) involves removing an electron from a stable half-filled configuration.
This is difficult.
So Mn\(^{3+}\) is a strong oxidizing agent and readily accepts an electron to become Mn\(^{2+}\).
Thus, \( E^\ominus (\text{Mn}^{3+}/\text{Mn}^{2+}) \) is positive (actually +1.
57 V).
- Co: Co\(^{2+}\): [Ar] \(3d^7\) Co\(^{3+}\): [Ar] \(3d^6\) Co\(^{3+}\) is a strong oxidizing agent, especially in aqueous solution where it can be stabilized by complexation.
\( E^\ominus (\text{Co}^{3+}/\text{Co}^{2+}) \) is positive (actually +1.
97 V).
- Fe: Fe\(^{2+}\): [Ar] \(3d^6\) Fe\(^{3+}\): [Ar] \(3d^5\) (half-filled d-orbitals, stable) The process Fe\(^{2+}\) \( \rightarrow \) Fe\(^{3+}\) + e\(^-\) leads to a more stable \(3d^5\) configuration.
So Fe\(^{2+}\) can be oxidized to Fe\(^{3+}\).
\( E^\ominus (\text{Fe}^{3+}/\text{Fe}^{2+}) \) is positive (+0.
77 V).
This means Fe\(^{3+}\) is a moderate oxidizing agent.
- Cr: Cr\(^{2+}\): [Ar] \(3d^4\) Cr\(^{3+}\): [Ar] \(3d^3\) (half-filled t\(_{2g}\) orbitals in an octahedral complex, relatively stable).
Cr\(^{2+}\) is a strong reducing agent because it readily oxidizes to Cr\(^{3+}\).
This means the reverse process, Cr\(^{3+}\) + e\(^-\) \( \rightarrow \) Cr\(^{2+}\), is less favored.
Therefore, \( E^\ominus (\text{Cr}^{3+}/\text{Cr}^{2+}) \) is negative.
The actual value is \( E^\ominus (\text{Cr}^{3+}/\text{Cr}^{2+}) = -0.
41 \) V.
So, \( E^\ominus (M^{3+}/M^{2+}) \) is negative for Cr.
This matches option (4).