Which of the following acid has the lowest value of acid dissociation constant :

Options

A. `CH_(3)CHFCOOH`
B. `FCH_(2)CH_(2)COOH`
C. `BrCH_(2)CH_(2)COOH`
D. `CH_(3)CHBrCOOH`

Answer

To determine which of the given acids has the lowest value of the acid dissociation constant (Ka), we need to analyze the structure of each acid and the effects of substituents on their acidity.

### Step-by-Step Solution:

1. **Identify the Acids**:
The options provided are:
- Option 1: CH3CHFCOOH (2-fluoropropanoic acid)
- Option 2: FCH2CH2COOH (3-fluoropropanoic acid)
- Option 3: BrCH2CH2COOH (3-bromopropanoic acid)
- Option 4: CH3CHBrCOOH (2-bromopropanoic acid)

2. **Understand Acid Strength**:
The strength of an acid is determined by its ability to donate a proton (H+). The stronger the acid, the higher the value of its acid dissociation constant (Ka). Conversely, weaker acids have lower Ka values.

3. **Inductive Effect of Halogens**:
Halogens are electronegative and exert a -I (inductive) effect, which stabilizes the negative charge on the conjugate base formed after deprotonation. The closer the halogen is to the carboxylic acid group (COOH), the stronger the -I effect, and thus the greater the acidity.

4. **Analyze Each Option**:
- **Option 1 (CH3CHFCOOH)**: Fluorine is on the second carbon, close to the COOH group. This provides a strong -I effect.
- **Option 2 (FCH2CH2COOH)**: Fluorine is on the third carbon, further from the COOH group, resulting in a weaker -I effect compared to Option 1.
- **Option 3 (BrCH2CH2COOH)**: Bromine is also on the third carbon, and while it has a -I effect, it is weaker than fluorine's effect.
- **Option 4 (CH3CHBrCOOH)**: Bromine is on the second carbon, providing a stronger -I effect than in Option 3 but weaker than fluorine's effect in Option 1.

5. **Rank the Acids by Acidity**:
Based on the proximity of the halogen to the carboxylic acid group and the strength of the -I effect:
- Option 1 (CH3CHFCOOH) > Option 4 (CH3CHBrCOOH) > Option 2 (FCH2CH2COOH) > Option 3 (BrCH2CH2COOH)

6. **Conclusion**:
Since Option 3 (BrCH2CH2COOH) has the weakest -I effect due to bromine being the furthest from the COOH group, it will be the weakest acid among the options provided. Therefore, it has the lowest value of the acid dissociation constant (Ka).

### Final Answer:
**Option 3: BrCH2CH2COOH has the lowest value of the acid dissociation constant.**