The increasing order of `pK_(a)` for the following phenols is
(A) `2,4` -Dinitrophenol
(B) 4-Nitrophenol
(C) `2,4,5` -Trimethylphenol
(D) Phenol
(E) 3-Chlorophenol

Options

A. (A), (E), (B), (D), (C)
B. (C), (E), (D), (B), (A)
C. (C), (D), (E), (B), (A)
D. (A), (B), (E), (D), (C)

Answer

To determine the increasing order of \( pK_a \) for the given phenols, we need to analyze the acidity of each compound based on the substituents present on the phenolic ring. The acidity of phenols is influenced by the electron-withdrawing or electron-donating effects of the substituents.

### Step-by-Step Solution:

1. **Identify the Structures**:
- (A) 2,4-Dinitrophenol: Contains two nitro groups (-NO2) at positions 2 and 4.
- (B) 4-Nitrophenol: Contains one nitro group at position 4.
- (C) 2,4,5-Trimethylphenol: Contains three methyl groups (-CH3) at positions 2, 4, and 5.
- (D) Phenol: Contains only the hydroxyl group (-OH).
- (E) 3-Chlorophenol: Contains one chloro group (-Cl) at position 3.

2. **Assess the Effects of Substituents**:
- Nitro groups (-NO2) are strong electron-withdrawing groups due to their -M (mesomeric) and -I (inductive) effects, which increase the acidity of phenols.
- Methyl groups (-CH3) are electron-donating groups through their +I effect, which decrease acidity.
- The chloro group (-Cl) has a -I effect but no significant -M effect when in the meta position.

3. **Rank the Acidity**:
- **2,4-Dinitrophenol (A)**: Highest acidity due to two strong -NO2 groups.
- **4-Nitrophenol (B)**: Less acidic than 2,4-Dinitrophenol but more acidic than the others due to one -NO2 group.
- **3-Chlorophenol (E)**: Moderately acidic due to the -Cl group, which has a -I effect.
- **Phenol (D)**: Less acidic than 3-Chlorophenol as it has no electron-withdrawing substituents.
- **2,4,5-Trimethylphenol (C)**: Least acidic due to three -CH3 groups, which decrease acidity.

4. **Order of Acidity (Ka)**:
- The order of acidity from highest to lowest is:
- 2,4-Dinitrophenol (A) > 4-Nitrophenol (B) > 3-Chlorophenol (E) > Phenol (D) > 2,4,5-Trimethylphenol (C)

5. **Convert to pKa Order**:
- Since \( pK_a \) is inversely related to acidity (higher acidity corresponds to lower \( pK_a \)), the increasing order of \( pK_a \) is:
- 2,4,5-Trimethylphenol (C) < Phenol (D) < 3-Chlorophenol (E) < 4-Nitrophenol (B) < 2,4-Dinitrophenol (A)

### Final Answer:
The increasing order of \( pK_a \) for the given phenols is:
**C < D < E < B < A**