Which one of the following species is stable in aqueous solution?

Options

A. `MnO_(4)^(2-)`
B. `MnO_(4)^(3-)`
C. `Cu^(+)`
D. `Cr^(2+)`

Answer

To determine which species is stable in aqueous solution among the given options, we will analyze the oxidation states and electronic configurations of each species using crystal field theory.

### Step-by-Step Solution:

1. **Identify the Species and Their Oxidation States:**
- The species given are:
- MnO4²⁻
- MnO3
- Cu⁺
- Cr²⁺
- We need to find the oxidation states of the central metal in each species.

2. **Calculate Oxidation States:**
- For MnO4²⁻:
- Let the oxidation state of Mn be \( x \).
- The equation becomes \( x + 4(-2) = -2 \) ⇒ \( x - 8 = -2 \) ⇒ \( x = +6 \).
- For MnO3:
- Let the oxidation state of Mn be \( x \).
- The equation becomes \( x + 3(-2) = -3 \) ⇒ \( x - 6 = -3 \) ⇒ \( x = +3 \).
- For Cu⁺:
- The oxidation state is simply \( +1 \).
- For Cr²⁺:
- The oxidation state is \( +2 \).

3. **Determine Electronic Configurations:**
- For Mn⁶⁺ (MnO4²⁻):
- Atomic number of Mn = 25.
- Electronic configuration: [Ar] 3d⁵ 4s².
- For Mn⁶⁺: loses 6 electrons ⇒ [Ar] 3d¹.
- For Mn³⁺ (MnO3):
- Loses 3 electrons ⇒ [Ar] 3d⁴.
- For Cu⁺:
- Atomic number of Cu = 29.
- Electronic configuration: [Ar] 3d¹⁰ 4s¹.
- For Cu⁺: loses 1 electron ⇒ [Ar] 3d¹⁰.
- For Cr²⁺:
- Atomic number of Cr = 24.
- Electronic configuration: [Ar] 3d⁵ 4s¹.
- For Cr²⁺: loses 2 electrons ⇒ [Ar] 3d⁴.

4. **Analyze Stability Using Crystal Field Theory:**
- Stability in aqueous solution is often related to the filling of d-orbitals.
- For Cu⁺:
- Configuration is 3d¹⁰ (fully filled), which is stable.
- For Mn⁶⁺:
- Configuration is 3d¹ (not stable due to unpaired electron).
- For Mn³⁺:
- Configuration is 3d⁴ (not stable due to unpaired electrons).
- For Cr²⁺:
- Configuration is 3d⁴ (not stable due to unpaired electrons).

5. **Conclusion:**
- The species that is stable in aqueous solution is **Cu⁺** because it has a fully filled d-orbital configuration (3d¹⁰), which provides extra stability.

### Final Answer:
**Cu⁺ is the most stable species in aqueous solution.**