When `KMnO_(4)` acts as an oxidising agnet and ultimetely from `MnO_(4)^(2-), MnO_(2), Mn_(2)O_(3)`, and `Mn^(2+)`, then the number of electrons transferred in each case, respectively, are

Options

A. `4,3,1,5`
B. `1,5,3,7`
C. `1,3,4,5`
D. `3,5,7,1`

Explanation

To determine the number of electrons transferred when KMnO4 acts as an oxidizing agent and ultimately forms MnO4^2-, MnO2, Mn2O3, and Mn^2+, we need to analyze the changes in the oxidation state of manganese (Mn) in each compound.

### Step-by-Step Solution:

1. **Identify the oxidation state of Mn in KMnO4:**
- In KMnO4, the oxidation state of Mn is +7.

2. **Identify the oxidation state of Mn in MnO4^2-:**
- In MnO4^2-, the oxidation state of Mn is +6.

3. **Calculate the change in oxidation state from KMnO4 to MnO4^2-:**
- Change = +7 (in KMnO4) - +6 (in MnO4^2-) = 1 electron transferred.

4. **Identify the oxidation state of Mn in MnO2:**
- In MnO2, the oxidation state of Mn is +4.

5. **Calculate the change in oxidation state from KMnO4 to MnO2:**
- Change = +7 (in KMnO4) - +4 (in MnO2) = 3 electrons transferred.

6. **Identify the oxidation state of Mn in Mn2O3:**
- In Mn2O3, the oxidation state of Mn is +3.

7. **Calculate the change in oxidation state from KMnO4 to Mn2O3:**
- Change = +7 (in KMnO4) - +3 (in Mn2O3) = 4 electrons transferred.

8. **Identify the oxidation state of Mn in Mn^2+:**
- In Mn^2+, the oxidation state of Mn is +2.

9. **Calculate the change in oxidation state from KMnO4 to Mn^2+:**
- Change = +7 (in KMnO4) - +2 (in Mn^2+) = 5 electrons transferred.

### Summary of Electrons Transferred:
- From KMnO4 to MnO4^2-: 1 electron
- From KMnO4 to MnO2: 3 electrons
- From KMnO4 to Mn2O3: 4 electrons
- From KMnO4 to Mn^2+: 5 electrons

Thus, the number of electrons transferred in each case, respectively, are: **1, 3, 4, 5**.