(i) `F_(3)C-COOH,` (ii) `CH_(3)COOH`, (iii) `C_(6)H_(5)COOH,` (iv) `CH_(3)CH_(2)COOH`
Correct order of `pK_(a)` value is :

Options

A. 1 gt 3 gt 2 gt 4
B. 4 gt 2 gt 3 gt 1
C. 4 gt 3 gt 2 gt 1
D. 1 gt 2 gt 4 gt 3

Answer

To determine the correct order of pKa values for the given carboxylic acids, we need to analyze the stability of their conjugate bases. The acidity of a compound is inversely related to the stability of its conjugate base; the more stable the conjugate base, the stronger the acid, and thus the lower the pKa value.

### Step-by-Step Solution:

1. **Identify the Carboxylic Acids and Their Conjugate Bases:**
- (i) **Trifluoroacetic acid (F₃C-COOH)**: Conjugate base is F₃C-C(=O)O⁻
- (ii) **Acetic acid (CH₃COOH)**: Conjugate base is CH₃C(=O)O⁻
- (iii) **Benzoic acid (C₆H₅COOH)**: Conjugate base is C₆H₅C(=O)O⁻
- (iv) **Propanoic acid (CH₃CH₂COOH)**: Conjugate base is CH₃CH₂C(=O)O⁻

2. **Analyze the Stability of the Conjugate Bases:**
- The stability of the conjugate base is influenced by the substituents attached to the carboxyl group.
- **F₃C-COO⁻**: The trifluoromethyl group (F₃C) is a strong electron-withdrawing group (−I effect), which stabilizes the negative charge on the conjugate base.
- **CH₃COO⁻**: The methyl group (CH₃) is a weak electron-donating group (+I effect), which destabilizes the negative charge.
- **C₆H₅COO⁻**: The phenyl group (C₆H₅) has a +I effect but also has resonance stabilization, making it more stable than the methyl group.
- **CH₃CH₂COO⁻**: The ethyl group (CH₃CH₂) is similar to the methyl group but slightly more destabilizing than the phenyl group due to its larger size and +I effect.

3. **Rank the Stability of the Conjugate Bases:**
- The order of stability based on the effects of the substituents is:
1. **F₃C-COO⁻** (most stable due to −I effect)
2. **C₆H₅COO⁻** (stable due to resonance)
3. **CH₃COO⁻** (less stable due to +I effect)
4. **CH₃CH₂COO⁻** (least stable due to +I effect)

4. **Determine the Order of Acidity:**
- Since the stability of the conjugate base is inversely related to acidity:
- F₃C-COOH > C₆H₅COOH > CH₃COOH > CH₃CH₂COOH

5. **Convert to pKa Values:**
- The order of pKa values will be the reverse of the order of acidity:
- pKa order: CH₃CH₂COOH (highest pKa) > CH₃COOH > C₆H₅COOH > F₃C-COOH (lowest pKa)

### Final Order of pKa Values:
- **Correct order of pKa values**: (iv) > (ii) > (iii) > (i) or 4 > 2 > 3 > 1

### Answer:
The correct order of pKa values is: **4 > 2 > 3 > 1**.