Which is a stronger reducing agent `Cr^(2+)` or `Fe^(2+)` and why?

Answer

To determine which ion, \( \text{Cr}^{2+} \) or \( \text{Fe}^{2+} \), is a stronger reducing agent, we need to analyze their electron configurations and the stability of their oxidation states.

### Step 1: Determine the Electron Configuration
- **Chromium (\( \text{Cr} \))**: The atomic number of chromium is 24. The electron configuration for neutral chromium is \( [\text{Ar}] 3d^5 4s^1 \). For \( \text{Cr}^{2+} \), we remove two electrons, resulting in \( [\text{Ar}] 3d^4 \).

- **Iron (\( \text{Fe} \))**: The atomic number of iron is 26. The electron configuration for neutral iron is \( [\text{Ar}] 3d^6 4s^2 \). For \( \text{Fe}^{2+} \), we remove two electrons, resulting in \( [\text{Ar}] 3d^6 \).

### Step 2: Analyze the Oxidation Process
- When \( \text{Cr}^{2+} \) oxidizes to \( \text{Cr}^{3+} \), it changes from \( [\text{Ar}] 3d^4 \) to \( [\text{Ar}] 3d^3 \). The \( 3d^3 \) configuration is stable because it has a half-filled \( t_{2g} \) subshell.

- When \( \text{Fe}^{2+} \) oxidizes to \( \text{Fe}^{3+} \), it changes from \( [\text{Ar}] 3d^6 \) to \( [\text{Ar}] 3d^5 \). The \( 3d^5 \) configuration is also stable due to its half-filled nature.

### Step 3: Compare Stability and Reducing Ability
- **Stability**: Although both \( \text{Cr}^{3+} \) and \( \text{Fe}^{3+} \) are stable, the half-filled \( t_{2g} \) configuration of \( \text{Cr}^{3+} \) provides additional stability compared to \( \text{Fe}^{3+} \).

- **Reducing Agent Strength**: A stronger reducing agent is one that more readily loses electrons (oxidizes). \( \text{Cr}^{2+} \) has a greater tendency to oxidize to \( \text{Cr}^{3+} \) due to the stability of the resulting half-filled \( t_{2g} \) configuration. In contrast, \( \text{Fe}^{2+} \) is relatively more stable and does not oxidize as readily.

### Conclusion
Thus, \( \text{Cr}^{2+} \) is a stronger reducing agent than \( \text{Fe}^{2+} \) because it more readily oxidizes to \( \text{Cr}^{3+} \), which has a stable half-filled electron configuration.