Correct order of oxidising strength is :-

Options

A. `MnO_(4)^(-)gt VO_(2)^(+)gt Cr_(2)O_(7)^(2^(-))`
B. `Cr_(2)O_(7)^(2-)gtMnO_(4)gtVO_(2)^(+)`
C. `Cr_(2)O_(7)^(2-)gtVO_(2)^(+)gtMnO_(4)^(-)`
D. `MnO_(4)^(-)gtCr_(2)O_(7)^(2-)gtVO_(2)^(+)`

Answer

To determine the correct order of oxidizing strength among the ions \( \text{MnO}_4^- \), \( \text{VO}_2^+ \), and \( \text{Cr}_2\text{O}_7^{2-} \), we will follow these steps:

### Step 1: Identify the Central Atoms and Their Oxidation States
We will calculate the oxidation state of the central atom for each ion.

1. **For \( \text{MnO}_4^- \)**:
- Let the oxidation state of Mn be \( x \).
- The equation will be:
\[ x + 4(-2) = -1 \]
- Simplifying gives:
\[ x - 8 = -1 \implies x = +7 \]

2. **For \( \text{VO}_2^+ \)**:
- Let the oxidation state of V be \( x \).
- The equation will be:
\[ x + 2(-2) = +1 \]
- Simplifying gives:
\[ x - 4 = +1 \implies x = +5 \]

3. **For \( \text{Cr}_2\text{O}_7^{2-} \)**:
- Let the oxidation state of Cr be \( x \).
- The equation will be:
\[ 2x + 7(-2) = -2 \]
- Simplifying gives:
\[ 2x - 14 = -2 \implies 2x = +12 \implies x = +6 \]

### Step 2: Compare the Oxidation States
Now we have the oxidation states:
- \( \text{Mn}^{+7} \) from \( \text{MnO}_4^- \)
- \( \text{V}^{+5} \) from \( \text{VO}_2^+ \)
- \( \text{Cr}^{+6} \) from \( \text{Cr}_2\text{O}_7^{2-} \)

### Step 3: Determine the Oxidizing Strength
The oxidizing strength is generally higher for species with higher oxidation states. Therefore, we can rank the oxidizing strength based on the oxidation states:
- \( \text{MnO}_4^- \) (Mn at +7) has the highest oxidizing strength.
- \( \text{Cr}_2\text{O}_7^{2-} \) (Cr at +6) has a lower oxidizing strength than \( \text{MnO}_4^- \).
- \( \text{VO}_2^+ \) (V at +5) has the lowest oxidizing strength.

### Conclusion
Thus, the correct order of oxidizing strength is:
\[ \text{MnO}_4^- > \text{Cr}_2\text{O}_7^{2-} > \text{VO}_2^+ \]

### Final Answer
The correct option is \( \text{MnO}_4^- > \text{Cr}_2\text{O}_7^{2-} > \text{VO}_2^+ \).

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