In which of the following the carbon-oxygen bonds are of equal lengths?

Options

A. `CH_(3)COO^(-)`
B. `CH_(3)COOH`
C. `CH_(3)COOC_(2)H_(5)`
D. All of these

Answer

To determine which of the given compounds has carbon-oxygen bonds of equal lengths, we need to analyze the resonance structures of each compound. Here’s a step-by-step solution:

### Step 1: Analyze the first compound (A) CH3COO⁻
- The structure of CH3COO⁻ can be represented as:
```
O
||
CH3-C
\
O⁻
```
- This compound exhibits resonance. The resonance structures can be drawn as follows:
1. CH3-C(=O)O⁻
2. CH3-C(O)O⁻ (where the double bond shifts to the other oxygen)

- In both resonance forms, the carbon-oxygen bonds have partial double bond character due to resonance. Therefore, both C-O bonds are of equal length.

### Step 2: Analyze the second compound (B) CH3C(=O)OH
- The structure of CH3C(=O)OH is:
```
O
||
CH3-C
\
OH
```
- The resonance structures for this compound would be:
1. CH3-C(=O)OH
2. CH3-C(OH)⁺ (where the double bond character shifts to the hydroxyl oxygen)

- Here, the C=O bond and the C-OH bond do not have equal bond character, as one is a double bond and the other is a single bond. Therefore, the bond lengths are not equal.

### Step 3: Analyze the third compound (C) CH3C(=O)OC2H5
- The structure of CH3C(=O)OC2H5 is:
```
O
||
CH3-C
\
O-C2H5
```
- The resonance structures for this compound would be:
1. CH3-C(=O)OC2H5
2. CH3-C(O⁻)C2H5⁺ (where the double bond character shifts to the ether oxygen)

- Similar to compound B, the C=O bond and the C-O bond do not have equal bond character, leading to different bond lengths.

### Step 4: Analyze the fourth compound (D)
- Since we already established that A is the only compound with equal bond lengths, we can conclude that D is incorrect without needing to analyze it further.

### Conclusion
The only compound where the carbon-oxygen bonds are of equal lengths is:
- **Answer: A (CH3COO⁻)**