Arrange the following in decreasing order of their acidic character:
(i) `p-CH_(3)O-C_(6)H_(4)OH`,
(ii) `p-NO_(2)-C_(6)H_(4)OH`,
(iii) `C_(6)H_(5)OH`

Answer

To determine the decreasing order of acidic character among the given compounds, we need to analyze the stability of their conjugate bases. The compounds are:

1. **p-CH₃O-C₆H₄OH** (para-methoxyphenol)
2. **p-NO₂-C₆H₄OH** (para-nitrophenol)
3. **C₆H₅OH** (phenol)

### Step 1: Identify the conjugate bases
When phenols lose a proton (H⁺), they form phenoxide ions. We will denote the conjugate bases as follows:

- For **p-CH₃O-C₆H₄OH**, the conjugate base is **p-CH₃O-C₆H₄O⁻**.
- For **p-NO₂-C₆H₄OH**, the conjugate base is **p-NO₂-C₆H₄O⁻**.
- For **C₆H₅OH**, the conjugate base is **C₆H₅O⁻**.

### Step 2: Analyze the effects of substituents on the conjugate bases
- **p-CH₃O-C₆H₄O⁻**: The methoxy group (–OCH₃) is an electron-donating group through resonance (+M effect). This increases electron density on the aromatic ring, which destabilizes the negative charge on the oxygen of the phenoxide ion.

- **p-NO₂-C₆H₄O⁻**: The nitro group (–NO₂) is a strong electron-withdrawing group (-M effect). This stabilizes the negative charge on the oxygen of the phenoxide ion by delocalizing the charge through resonance, making the conjugate base more stable.

- **C₆H₅O⁻**: The phenoxide ion derived from phenol does not have any substituents to stabilize or destabilize the negative charge. Thus, it has intermediate stability.

### Step 3: Compare the stability of the conjugate bases
- The conjugate base of **p-NO₂-C₆H₄OH** is the most stable due to the strong -M effect of the nitro group.
- The conjugate base of **C₆H₅OH** is less stable than that of para-nitrophenol but more stable than that of para-methoxyphenol.
- The conjugate base of **p-CH₃O-C₆H₄OH** is the least stable due to the destabilizing +M effect of the methoxy group.

### Step 4: Determine the order of acidity
Since the stability of the conjugate base is directly related to the acidity of the corresponding acid, we can arrange the compounds in decreasing order of acidity:

1. **p-NO₂-C₆H₄OH** (most acidic)
2. **C₆H₅OH** (intermediate acidity)
3. **p-CH₃O-C₆H₄OH** (least acidic)

### Final Answer
The decreasing order of acidic character is:
**p-NO₂-C₆H₄OH > C₆H₅OH > p-CH₃O-C₆H₄OH**