The pH of a 0.01 M solutions of acetic acid having degree of dissociation 12.5% is

Options

A. 5.623
B. 2.903
C. 3.723
D. 4.509

Explanation

To calculate the pH of a 0.01 M solution of acetic acid with a degree of dissociation of 12.5%, we can follow these steps:

### Step 1: Understand the given data
- Concentration of acetic acid (C) = 0.01 M
- Degree of dissociation (α) = 12.5% = 0.125

### Step 2: Calculate the concentration of dissociated acetic acid
The concentration of dissociated acetic acid (CH₃COOH) can be calculated using the formula:
\[ \text{Concentration of dissociated acetic acid} = C \times \alpha \]
Substituting the values:
\[ \text{Concentration of dissociated acetic acid} = 0.01 \, \text{M} \times 0.125 = 0.00125 \, \text{M} \]

### Step 3: Determine the concentration of H⁺ ions
Since acetic acid (CH₃COOH) dissociates into H⁺ and CH₃COO⁻ ions, the concentration of H⁺ ions will be equal to the concentration of dissociated acetic acid:
\[ [H^+] = 0.00125 \, \text{M} \]

### Step 4: Calculate the pH
The pH can be calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
Substituting the value of [H⁺]:
\[ \text{pH} = -\log(0.00125) \]

### Step 5: Perform the logarithmic calculation
Using a calculator:
\[ \text{pH} = -\log(1.25 \times 10^{-3}) \]
\[ \text{pH} = -(\log(1.25) + \log(10^{-3})) \]
\[ \text{pH} = -\log(1.25) + 3 \]
Using the approximate value of \(\log(1.25) \approx 0.09691\):
\[ \text{pH} \approx -0.09691 + 3 \]
\[ \text{pH} \approx 2.90309 \]

### Final Answer
The pH of the 0.01 M solution of acetic acid with a degree of dissociation of 12.5% is approximately **2.903**.

---