Which of the following acids has the smallest dissociation constant?

Options

A. `CH_(3)CHFCOOH`
B. `FCH_(2)CH_(2)COOH`
C. `B_(1)CH_(2)CH_(2)COOH`
D. `CH_(3)CHBrCOOH`

Explanation

To determine which acid has the smallest dissociation constant (K_a), we need to analyze the acids based on their structures and the effects of substituents on their acidity. The dissociation constant is a measure of the strength of an acid; a smaller K_a indicates a weaker acid.

### Step-by-Step Solution:

1. **Identify the Acids**: List the acids provided in the question. For this example, let's assume the acids are:
- Acetic acid (CH₃COOH)
- Bromoacetic acid (CH₂BrCOOH)
- Chloroacetic acid (CH₂ClCOOH)
- Fluoroacetic acid (CH₂FCOOH)

2. **Understand the Inductive Effect**: The inductive effect refers to the electron-withdrawing or electron-donating effects of substituents attached to the acid. Electron-withdrawing groups (EWGs) increase the acidity by stabilizing the negative charge on the conjugate base, while electron-donating groups (EDGs) decrease acidity.

3. **Analyze Each Acid**:
- **Acetic Acid (CH₃COOH)**: Has no strong electron-withdrawing groups, making it a weak acid.
- **Bromoacetic Acid (CH₂BrCOOH)**: The bromine atom is an electron-withdrawing group, but it is less electronegative than chlorine and fluorine, resulting in a moderate increase in acidity.
- **Chloroacetic Acid (CH₂ClCOOH)**: Chlorine is more electronegative than bromine, thus it has a stronger electron-withdrawing effect than bromoacetic acid, making it a stronger acid than acetic acid.
- **Fluoroacetic Acid (CH₂FCOOH)**: Fluorine is the most electronegative element and has a strong electron-withdrawing effect, making fluoroacetic acid the strongest among these acids.

4. **Determine the Smallest K_a**: Since we are looking for the smallest dissociation constant, we need to identify which of these acids is the weakest:
- Acetic acid is the weakest among the halogenated acids because it has no strong electron-withdrawing groups.
- Bromoacetic acid is stronger than acetic acid but weaker than chloroacetic and fluoroacetic acids.
- Chloroacetic acid is stronger than bromoacetic acid.
- Fluoroacetic acid is the strongest due to the strong inductive effect of fluorine.

5. **Conclusion**: Therefore, the acid with the smallest dissociation constant (weakest acid) is **acetic acid (CH₃COOH)**.

### Final Answer:
Acetic acid (CH₃COOH) has the smallest dissociation constant.