Calculate CFSE of light pink compound formed, when `KMnO_(4)` is reduced by acidified `H_(2)S`.

Answer

To calculate the Crystal Field Stabilization Energy (CFSE) of the light pink compound formed when KMnO4 is reduced by acidified H2S, we will follow these steps:

### Step 1: Identify the reaction and the product
When KMnO4 is reduced by acidified H2S, the reaction produces manganese(II) sulfate (MnSO4), which contains the Mn²⁺ ion. The balanced chemical equation for the reaction is:
\[ 2 \text{KMnO}_4 + 5 \text{H}_2\text{S} + 3 \text{H}_2\text{SO}_4 \rightarrow 5 \text{S} + \text{K}_2\text{SO}_4 + 2 \text{MnSO}_4 + 8 \text{H}_2\text{O} \]

### Step 2: Determine the oxidation state and electron configuration of Mn²⁺
In MnSO4, manganese is in the +2 oxidation state. The electron configuration of manganese (Mn) is:
\[ \text{Mn: [Ar] 4s}^2 \text{3d}^5 \]
For Mn²⁺, we remove two electrons from the outermost shell:
\[ \text{Mn}^{2+}: \text{[Ar] 3d}^5 \]

### Step 3: Determine the geometry of the complex
Assuming that Mn²⁺ forms an octahedral complex in solution, the d-orbitals split into two sets: t2g and eg. In an octahedral field, the energy levels are arranged as follows:
- t2g (lower energy level)
- eg (higher energy level)

### Step 4: Distribute the electrons in the d-orbitals
For Mn²⁺ with a d5 configuration, and assuming it is a high-spin complex, the electrons will fill the orbitals as follows:
- t2g: 3 electrons
- eg: 2 electrons

### Step 5: Calculate the CFSE
The CFSE is calculated using the formula:
\[ \text{CFSE} = (n_{t2g} \times -0.4 \Delta_0) + (n_{eg} \times +0.6 \Delta_0) \]
Where:
- \( n_{t2g} \) = number of electrons in t2g orbitals
- \( n_{eg} \) = number of electrons in eg orbitals

For Mn²⁺:
- \( n_{t2g} = 3 \)
- \( n_{eg} = 2 \)

Substituting the values:
\[ \text{CFSE} = (3 \times -0.4 \Delta_0) + (2 \times +0.6 \Delta_0) \]
\[ \text{CFSE} = -1.2 \Delta_0 + 1.2 \Delta_0 \]
\[ \text{CFSE} = 0 \]

### Final Answer
The CFSE value for the Mn²⁺ ion in the light pink compound (MnSO4) is:
\[ \text{CFSE} = 0 \]

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