The oxoanion which contains all equivalent `M-O` bond is:
(I)`CrO_(4)^(2-)` (II)`MnO_(4)^(-)` (III)`Cr_(2)O_(7)^(2-)`

Options

A. III only
B. I, II, III
C. I, II
D. I only

Answer

To determine which oxoanion contains all equivalent M-O bonds, we will analyze each of the given options: \( \text{CrO}_4^{2-} \) (chromate), \( \text{MnO}_4^{-} \) (permanganate), and \( \text{Cr}_2\text{O}_7^{2-} \) (dichromate).

### Step 1: Analyze \( \text{CrO}_4^{2-} \) (Chromate Ion)
- The chromate ion has the formula \( \text{CrO}_4^{2-} \).
- In its structure, chromium is bonded to four oxygen atoms.
- The bonding involves resonance, where the double bonds can shift among the oxygen atoms.
- As a result, all \( \text{Cr-O} \) bonds are equivalent due to resonance, and they exhibit partial double bond character.

### Step 2: Analyze \( \text{MnO}_4^{-} \) (Permanganate Ion)
- The permanganate ion has the formula \( \text{MnO}_4^{-} \).
- Similar to chromate, manganese is bonded to four oxygen atoms.
- The structure also allows for resonance, where the double bonds can shift among the oxygen atoms.
- Therefore, all \( \text{Mn-O} \) bonds are equivalent due to resonance, exhibiting partial double bond character.

### Step 3: Analyze \( \text{Cr}_2\text{O}_7^{2-} \) (Dichromate Ion)
- The dichromate ion has the formula \( \text{Cr}_2\text{O}_7^{2-} \).
- In this ion, there are two chromium atoms bonded to seven oxygen atoms.
- The structure includes both double bonds and single bonds. Specifically, three of the bonds are equivalent (double bonds), while the remaining bond is a single bond.
- The bond lengths differ: the double bonds are shorter (approximately 163 pm) compared to the single bond (approximately 179 pm), indicating that not all \( \text{Cr-O} \) bonds are equivalent.

### Conclusion
- From the analysis, \( \text{CrO}_4^{2-} \) and \( \text{MnO}_4^{-} \) have all equivalent \( \text{M-O} \) bonds due to resonance.
- \( \text{Cr}_2\text{O}_7^{2-} \) does not have all equivalent bonds because of the presence of both double and single bonds.

Thus, the correct answer is that the oxoanions which contain all equivalent \( \text{M-O} \) bonds are \( \text{CrO}_4^{2-} \) and \( \text{MnO}_4^{-} \).

### Final Answer
The oxoanion which contains all equivalent \( \text{M-O} \) bonds is: (I) \( \text{CrO}_4^{2-} \) and (II) \( \text{MnO}_4^{-} \).