`pK_(a)` of `CH_(3)COOH` is 4.74 . The pH of 0.01 M `CH_(3)COONa` IS

Options

A. 4.74
B. 8.37
C. 9.48
D. None of these

Explanation

To find the pH of a 0.01 M solution of sodium acetate (CH₃COONa), we will use the relationship between the pH of a salt solution derived from a weak acid and a strong base. Here are the steps to solve the problem:

### Step 1: Identify the components
Sodium acetate (CH₃COONa) is a salt formed from acetic acid (CH₃COOH), a weak acid, and sodium hydroxide (NaOH), a strong base.

### Step 2: Use the formula for pH of a salt solution
The pH of a solution of a salt of a weak acid and a strong base can be calculated using the formula:
\[ \text{pH} = 7 + \frac{1}{2} \text{pK}_a + \log C \]
where:
- \(\text{pK}_a\) is the dissociation constant of the weak acid (acetic acid in this case),
- \(C\) is the concentration of the salt solution.

### Step 3: Substitute the known values
Given:
- \(\text{pK}_a\) of acetic acid (CH₃COOH) = 4.74
- Concentration \(C = 0.01 \, M\)

Now, substitute these values into the formula:
\[ \text{pH} = 7 + \frac{1}{2} \times 4.74 + \log(0.01) \]

### Step 4: Calculate \(\log(0.01)\)
We know that:
\[ \log(0.01) = \log(10^{-2}) = -2 \]

### Step 5: Calculate \(\frac{1}{2} \times 4.74\)
\[ \frac{1}{2} \times 4.74 = 2.37 \]

### Step 6: Combine the values
Now, substitute back into the pH equation:
\[ \text{pH} = 7 + 2.37 - 2 \]
\[ \text{pH} = 7 + 2.37 - 2 = 7 + 0.37 = 8.37 \]

### Final Answer
The pH of the 0.01 M solution of sodium acetate (CH₃COONa) is **8.37**.

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