Arrange in decreasing `pK_(a)`
`(a) F - CH_(2) CH_(2) COOH `
(b)`Cl - underset(Cl)underset(|) (CH) - CH_(2) - COOH `
`(c) F - CH_(2) - COOH`
(d)` Br - CH_(2) - CH_(2) - COOH`
Correct answer is

Options

A. `b gt d gt a gt c`
B. `a gt c gt d gt b`
C. `d gt a gt b gt c`
D. `d gt b gt a gt c`

Answer

To arrange the given compounds in decreasing pKa values, we need to analyze their acidic strengths based on the substituents attached to the carboxylic acid group (-COOH). The presence of electronegative atoms (like F, Cl, and Br) can stabilize the conjugate base formed after deprotonation, thus increasing the acidity of the compound.

### Step-by-Step Solution:

1. **Identify the Compounds**:
- (a) F-CH₂CH₂COOH
- (b) Cl-CH(Cl)-CH₂COOH
- (c) F-CH₂COOH
- (d) Br-CH₂CH₂COOH

2. **Determine the Effect of Substituents**:
- **Fluorine (F)** is highly electronegative and will stabilize the conjugate base effectively.
- **Chlorine (Cl)** is also electronegative but less so than fluorine.
- **Bromine (Br)** is the least electronegative among the three.

3. **Analyze Each Compound**:
- **Compound (c) F-CH₂COOH**: The fluorine is directly attached to the carbon adjacent to the carboxylic acid. This will greatly stabilize the conjugate base, making this compound the most acidic.
- **Compound (b) Cl-CH(Cl)-CH₂COOH**: The presence of two chlorine atoms increases acidity due to their electronegativity, but the effect is less than that of fluorine.
- **Compound (a) F-CH₂CH₂COOH**: The fluorine is further away from the carboxylic acid compared to compound (c), making it less effective in stabilizing the conjugate base than in (c).
- **Compound (d) Br-CH₂CH₂COOH**: The bromine is the least electronegative and will stabilize the conjugate base the least, making this compound the least acidic.

4. **Rank the Acidity**:
- Based on the analysis, the order of acidity (from strongest to weakest) is:
- (c) F-CH₂COOH > (b) Cl-CH(Cl)-CH₂COOH > (a) F-CH₂CH₂COOH > (d) Br-CH₂CH₂COOH

5. **Convert to pKa Order**:
- Since pKa is inversely related to acidity, we can now arrange them in decreasing pKa values:
- pKa order: (d) > (a) > (b) > (c)

### Final Order of pKa:
- **Decreasing pKa**: (d) Br-CH₂CH₂COOH > (a) F-CH₂CH₂COOH > (b) Cl-CH(Cl)-CH₂COOH > (c) F-CH₂COOH