Which of the following acids has the smallest 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 smallest dissociation constant (Ka), we need to analyze the acidic strength of each acid based on the presence and position of substituents (halogens in this case) that can influence the acidity through their electron-withdrawing effects.

### Step-by-Step Solution:

1. **Identify the Acids**: The given acids are:
- Option A: CH3CHFCOOH (Fluoroacetic acid)
- Option B: FCH2CH2COOH (Fluoroacetic acid with fluorine on the first carbon)
- Option C: BrCH2CH2COOH (Bromoacetic acid with bromine on the first carbon)
- Option D: CH3CHBrCOOH (Bromoacetic acid with bromine on the second carbon)

2. **Understand the Dissociation Constant (Ka)**: The dissociation constant (Ka) indicates the strength of an acid. A higher Ka value means a stronger acid, while a lower Ka value indicates a weaker acid.

3. **Consider the Electron-Withdrawing Effects**: Halogens are electronegative and exhibit a -I (inductive) effect, which stabilizes the negative charge on the carboxylate ion (RCOO⁻) formed after deprotonation. The more effective the -I effect, the stronger the acid.

4. **Analyze the Position of Halogens**:
- In **Option A (CH3CHFCOOH)**, the fluorine is on the second carbon, which provides a strong -I effect.
- In **Option B (FCH2CH2COOH)**, the fluorine is on the first carbon, which also provides a strong -I effect, but it is closer to the carboxyl group.
- In **Option C (BrCH2CH2COOH)**, the bromine is on the first carbon, providing a -I effect, but bromine is less electronegative than fluorine.
- In **Option D (CH3CHBrCOOH)**, the bromine is on the second carbon, which is further away from the carboxyl group, resulting in a weaker -I effect compared to the other acids.

5. **Compare the Acids**:
- The acids with fluorine (Options A and B) will have stronger acidity due to the stronger -I effect of fluorine compared to bromine.
- Between Options C and D, since bromine is less electronegative, the -I effect will be weaker, and since in Option D the bromine is further away from the carboxyl group, it will have the least effect on acidity.

6. **Conclusion**: The acid with the smallest dissociation constant (weakest acid) will be the one with the least effective -I effect. Therefore, **Option D (CH3CHBrCOOH)** has the smallest dissociation constant.

### Final Answer:
**Option D: CH3CHBrCOOH (Bromoacetic acid with bromine on the second carbon) has the smallest dissociation constant.**