The pH values of 0.1 M solution of HCl, CH3COOH, NH4Cl and CH3COONa will have the order :

Options

A. `HCl lt CH_(3)COOH lt NH_(4)Cl lt CH_(3)COONa`
B. `CH_(3)COONa lt NH_(4)Cl lt CH_(3)COOH lt HCl`
C. `NH_(4)Cl lt CH_(3)COONa lt CH_(3)COOH lt HCl`
D. All will have same of pH value

Explanation

To determine the order of pH values for the given solutions (0.1 M HCl, CH3COOH, NH4Cl, and CH3COONa), we need to analyze the nature of each solution based on the strength of the acids and bases involved.

### Step-by-Step Solution:

1. **Identify the Solutions:**
- HCl: Strong acid
- CH3COOH (Acetic acid): Weak acid
- NH4Cl (Ammonium chloride): Salt of a weak base (NH3) and strong acid (HCl)
- CH3COONa (Sodium acetate): Salt of a weak acid (CH3COOH) and strong base (NaOH)

2. **Determine the pH of HCl:**
- HCl is a strong acid and completely dissociates in solution. Therefore, the concentration of H⁺ ions will be equal to the concentration of HCl.
- For 0.1 M HCl, [H⁺] = 0.1 M.
- pH = -log[H⁺] = -log(0.1) = 1.

3. **Determine the pH of CH3COOH:**
- Acetic acid is a weak acid and does not completely dissociate. The dissociation can be represented as:
\[ CH3COOH \rightleftharpoons H^+ + CH3COO^- \]
- The pH will be higher than that of HCl. For a weak acid, we can use the formula:
\[ \text{pH} = \frac{1}{2} \left( pK_a - \log C \right) \]
- The pK_a of acetic acid is approximately 4.76. Thus, for 0.1 M acetic acid:
\[ \text{pH} \approx \frac{1}{2} (4.76 - \log(0.1)) \approx \frac{1}{2} (4.76 + 1) \approx 2.88. \]

4. **Determine the pH of NH4Cl:**
- NH4Cl is a salt that produces NH4⁺ ions in solution, which can hydrolyze to produce H⁺ ions:
\[ NH4^+ + H2O \rightleftharpoons NH3 + H3O^+ \]
- Since NH4⁺ is the conjugate acid of the weak base NH3, the solution will be slightly acidic. The pH will be higher than that of acetic acid but lower than 7.
- The pH for 0.1 M NH4Cl can be approximated to be around 5.1.

5. **Determine the pH of CH3COONa:**
- CH3COONa produces CH3COO⁻ ions, which can hydrolyze to produce OH⁻ ions:
\[ CH3COO^- + H2O \rightleftharpoons CH3COOH + OH^- \]
- This makes the solution basic. The pH will be higher than 7. For 0.1 M CH3COONa, the pH can be estimated to be around 9.2.

6. **Order the pH Values:**
- Based on the analysis:
- HCl: pH ≈ 1 (lowest)
- CH3COOH: pH ≈ 2.88
- NH4Cl: pH ≈ 5.1
- CH3COONa: pH ≈ 9.2 (highest)
- Thus, the order of pH values from lowest to highest is:
\[ \text{HCl} < \text{CH3COOH} < \text{NH4Cl} < \text{CH3COONa} \]

### Final Answer:
The order of pH values for the solutions is:
**HCl < CH3COOH < NH4Cl < CH3COONa**