`MnO_(4)^(-)` is good oxidising agent in different medium changing to - `rarr MnO_(4)^(2-)`
`rarr MnO_(4)^(2-)`
`rarr MnO_(2)`
`rarr Mn_(2)O_(3)`
Changes in oxidation number respectively are -

Options

A. 1,3,4,5
B. 5,4,3,2
C. 5,1,3,4
D. 2,6,4,3

Answer

To determine the changes in oxidation number for the given transformations of the permanganate ion (MnO₄⁻), we will analyze each species step by step.

### Step 1: Determine the oxidation number of Mn in MnO₄⁻
The oxidation state of manganese (Mn) in MnO₄⁻ can be calculated using the formula:

\[ \text{Oxidation state of Mn} + 4 \times (\text{Oxidation state of O}) = \text{Charge} \]

Given that the oxidation state of oxygen (O) is -2, we have:

\[ x + 4(-2) = -1 \]

Solving for x:

\[ x - 8 = -1 \implies x = +7 \]

So, the oxidation number of Mn in MnO₄⁻ is +7.

### Step 2: Determine the oxidation number of Mn in Mn²⁺
For Mn²⁺, the oxidation state is simply +2.

### Step 3: Determine the oxidation number of Mn in MnO₄²⁻
For MnO₄²⁻, we set up the equation similarly:

\[ x + 4(-2) = -2 \]

Solving for x:

\[ x - 8 = -2 \implies x = +6 \]

So, the oxidation number of Mn in MnO₄²⁻ is +6.

### Step 4: Determine the oxidation number of Mn in MnO₂
For MnO₂, we have:

\[ x + 2(-2) = 0 \]

Solving for x:

\[ x - 4 = 0 \implies x = +4 \]

So, the oxidation number of Mn in MnO₂ is +4.

### Step 5: Determine the oxidation number of Mn in Mn₂O₃
For Mn₂O₃, we can find the oxidation state of Mn as follows:

\[ 2x + 3(-2) = 0 \]

Solving for x:

\[ 2x - 6 = 0 \implies 2x = 6 \implies x = +3 \]

So, the oxidation number of Mn in Mn₂O₃ is +3.

### Summary of Changes in Oxidation Numbers
1. From MnO₄⁻ (+7) to Mn²⁺ (+2): Change = 7 - 2 = 5
2. From MnO₄⁻ (+7) to MnO₄²⁻ (+6): Change = 7 - 6 = 1
3. From MnO₄⁻ (+7) to MnO₂ (+4): Change = 7 - 4 = 3
4. From MnO₄⁻ (+7) to Mn₂O₃ (+3): Change = 7 - 3 = 4

### Final Changes in Oxidation Numbers
- MnO₄⁻ to Mn²⁺: 5
- MnO₄⁻ to MnO₄²⁻: 1
- MnO₄⁻ to MnO₂: 3
- MnO₄⁻ to Mn₂O₃: 4

### Conclusion
The changes in oxidation numbers are 5, 1, 3, and 4 respectively.

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