To determine the stability of the +2 oxidation state for the transition elements chromium (Cr), manganese (Mn), iron (Fe), and cobalt (Co), we will analyze their electronic configurations and reduction potentials.
### Step-by-Step Solution:
1. **Identify the Electronic Configurations**:
- For each element in the +2 oxidation state, we need to write down their electronic configurations.
- **Chromium (Cr)**: Atomic number = 24
- Ground state: \[ \text{[Ar]} \, 3d^5 \, 4s^1 \]
- In +2 state: \[ \text{[Ar]} \, 3d^4 \]
- **Manganese (Mn)**: Atomic number = 25
- Ground state: \[ \text{[Ar]} \, 3d^5 \, 4s^2 \]
- In +2 state: \[ \text{[Ar]} \, 3d^5 \]
- **Iron (Fe)**: Atomic number = 26
- Ground state: \[ \text{[Ar]} \, 3d^6 \, 4s^2 \]
- In +2 state: \[ \text{[Ar]} \, 3d^6 \]
- **Cobalt (Co)**: Atomic number = 27
- Ground state: \[ \text{[Ar]} \, 3d^7 \, 4s^2 \]
- In +2 state: \[ \text{[Ar]} \, 3d^7 \]
2. **Analyze Stability Based on Electronic Configurations**:
- The stability of the +2 oxidation state can be influenced by the electronic configuration. Half-filled and fully filled d-orbitals provide extra stability.
- Manganese with a half-filled \(3d^5\) configuration is particularly stable.
- Chromium in the +2 state has \(3d^4\), which is less stable compared to Mn.
- Iron has \(3d^6\) and cobalt has \(3d^7\).
3. **Consider Reduction Potentials**:
- The stability of the +2 oxidation state can also be assessed using the standard reduction potential (E°) values:
- Cr²⁺ + 2e⁻ → Cr: E° = -0.90 V
- Mn²⁺ + 2e⁻ → Mn: E° = -1.18 V
- Fe²⁺ + 2e⁻ → Fe: E° = -0.44 V
- Co²⁺ + 2e⁻ → Co: E° = -0.28 V
- A more negative E° value indicates a stronger reducing agent and thus less stability in the +2 state.
4. **Determine the Order of Stability**:
- From the E° values, we can conclude:
- Mn²⁺ has the highest stability due to its half-filled d-orbital.
- Fe²⁺ is more stable than Cr²⁺ because it has a less negative E° value.
- Cr²⁺ is less stable than Fe²⁺ due to its strong reducing nature.
- Co²⁺ is the least stable among these due to the least negative E° value.
- Therefore, the order of stability of the +2 oxidation state is:
\[ \text{Mn} > \text{Fe} > \text{Cr} > \text{Co} \]
### Final Answer:
The stability of the +2 oxidation state for the elements Cr, Mn, Fe, and Co is in the order:
\[ \text{Mn} > \text{Fe} > \text{Cr} > \text{Co} \]
