Arrange the following in the decreasing order of oxidation number of Mn :
(i) `KMnO_4` (ii) `MnO_2` (iii) `Mn_2O_3`
(iv) Mn (v) `K_2MnO_4`

Answer

To determine the decreasing order of oxidation numbers of manganese (Mn) in the given compounds, we will calculate the oxidation state of Mn in each compound step by step.

### Step 1: Calculate the oxidation state of Mn in KMnO₄

1. **Identify the oxidation states of other elements:**
- Potassium (K) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation:**
- Let the oxidation state of Mn be \( x \).
- The equation becomes:
\[ +1 + x + 4(-2) = 0 \]
- Simplifying this gives:
\[ +1 + x - 8 = 0 \implies x - 7 = 0 \implies x = +7 \]

### Step 2: Calculate the oxidation state of Mn in MnO₂

1. **Identify the oxidation states of other elements:**
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation:**
- Let the oxidation state of Mn be \( x \).
- The equation becomes:
\[ x + 2(-2) = 0 \]
- Simplifying this gives:
\[ x - 4 = 0 \implies x = +4 \]

### Step 3: Calculate the oxidation state of Mn in Mn₂O₃

1. **Identify the oxidation states of other elements:**
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation:**
- Let the oxidation state of Mn be \( x \).
- The equation becomes:
\[ 2x + 3(-2) = 0 \]
- Simplifying this gives:
\[ 2x - 6 = 0 \implies 2x = 6 \implies x = +3 \]

### Step 4: Calculate the oxidation state of Mn in K₂MnO₄

1. **Identify the oxidation states of other elements:**
- Potassium (K) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation:**
- Let the oxidation state of Mn be \( x \).
- The equation becomes:
\[ 2(+1) + x + 4(-2) = 0 \]
- Simplifying this gives:
\[ 2 + x - 8 = 0 \implies x - 6 = 0 \implies x = +6 \]

### Step 5: Calculate the oxidation state of elemental Mn

1. **Elemental manganese (Mn) has an oxidation state of 0.**

### Summary of Oxidation States

- KMnO₄: +7
- K₂MnO₄: +6
- MnO₂: +4
- Mn₂O₃: +3
- Mn (elemental): 0

### Final Arrangement in Decreasing Order

1. KMnO₄ (+7)
2. K₂MnO₄ (+6)
3. MnO₂ (+4)
4. Mn₂O₃ (+3)
5. Mn (0)

### Conclusion

The decreasing order of oxidation number of Mn in the given compounds is:
1. KMnO₄
2. K₂MnO₄
3. MnO₂
4. Mn₂O₃
5. Mn