pH of a 0.01 M solution `(K_(a)=6.6xx10^(-4))`

Options

A. 7.6
B. 8
C. 2.6
D. 5

Explanation

To calculate the pH of a 0.01 M solution with a given \( K_a = 6.6 \times 10^{-4} \), we can follow these steps:

### Step 1: Identify the given values
- Concentration of the solution, \( C = 0.01 \, M \)
- Acid dissociation constant, \( K_a = 6.6 \times 10^{-4} \)

### Step 2: Calculate the degree of dissociation (\( \alpha \))
The degree of dissociation can be calculated using the formula:
\[ \alpha = \sqrt{\frac{K_a}{C}} \]
Substituting the values:
\[ \alpha = \sqrt{\frac{6.6 \times 10^{-4}}{0.01}} = \sqrt{0.066} \approx 0.257 \]

### Step 3: Calculate the concentration of \( H^+ \) ions
The concentration of \( H^+ \) ions can be calculated using the formula:
\[ [H^+] = C \cdot \alpha \]
Substituting the values:
\[ [H^+] = 0.01 \cdot 0.257 = 2.57 \times 10^{-3} \, M \]

### Step 4: Calculate the pH
The pH can be calculated using the formula:
\[ pH = -\log[H^+] \]
Substituting the concentration of \( H^+ \):
\[ pH = -\log(2.57 \times 10^{-3}) \approx 3 - \log(2.57) \approx 3 - 0.41 \approx 2.60 \]

### Final Answer
The pH of the 0.01 M solution is approximately **2.60**.

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