The acidic strength of the given compounds follows the order
I. `CH_(3)-CH=CH-overset(O)overset(||)C-OH`
II. `CH_(3)-overset(..)underset(..)O-CH=CH-overset(O)overset(||)C-OH`
III. `CH_(3)-CH_(2)-overset(O)overset(||)C-OH`

Options

A. `IIgtIIIgtI`
B. `IIIgtIgtII`
C. `IIgtIgtIII`
D. `IgtIIgtIII`

Answer

To determine the acidic strength of the given compounds, we need to analyze the stability of their conjugate bases. The more stable the conjugate base, the stronger the acid. Let's break down the compounds and analyze them step by step.

### Step 1: Identify the Compounds
The compounds given are:
1. I: `CH₃-CH=CH-C(=O)OH`
2. II: `CH₃-O-CH=CH-C(=O)OH`
3. III: `CH₃-CH₂-C(=O)OH`

### Step 2: Draw the Conjugate Bases
The conjugate base of a carboxylic acid is formed by deprotonating the hydroxyl group (-OH). Let's draw the conjugate bases for each compound:

1. **Conjugate Base of I**: `CH₃-CH=CH-C(=O)O⁻`
2. **Conjugate Base of II**: `CH₃-O-CH=CH-C(=O)O⁻`
3. **Conjugate Base of III**: `CH₃-CH₂-C(=O)O⁻`

### Step 3: Analyze Resonance Stability
Next, we need to analyze the resonance stability of each conjugate base:

1. **Conjugate Base I**:
- The conjugate base has a double bond adjacent to the carboxylate group. This allows for some resonance, but the presence of the double bond can lead to cross resonance, which can destabilize the anion.

2. **Conjugate Base II**:
- This conjugate base has both a double bond and an ether-like oxygen. The lone pair on the oxygen can participate in resonance, leading to extensive cross resonance. This further destabilizes the conjugate base.

3. **Conjugate Base III**:
- The conjugate base here has no adjacent double bonds or lone pairs that can participate in resonance. Thus, it has the highest stability among the three.

### Step 4: Determine the Order of Acidity
Based on the stability of the conjugate bases:
- **III** is the most stable (least cross resonance), hence the strongest acid.
- **I** is next, as it has some resonance but is less stable than III.
- **II** is the least stable due to extensive cross resonance.

### Conclusion
The order of acidic strength of the compounds is:
**III > I > II**

Thus, the correct order of acidity is:
**III > I > II**