The pH of an acetic acid ` + ` sodium acetate buffer is given by `pH = pK_(a) + log . "[Salt]"/"[Acid]" " where " K_(a)` of acetic acid ` = 1.8 xx 10^(-5)`
If [Salt] = [Acid] ` = 0.1` M, then the pH of the solution would be about

Options

A. 7
B. `4.7`
C. `5.3`
D. `1.4`

Answer

To find the pH of the acetic acid and sodium acetate buffer solution, we can use the Henderson-Hasselbalch equation:

\[ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{Salt}]}{[\text{Acid}]} \right) \]

### Step 1: Calculate pK_a
Given that the \( K_a \) of acetic acid is \( 1.8 \times 10^{-5} \), we can calculate \( pK_a \) using the formula:

\[ \text{pK}_a = -\log(K_a) \]

Substituting the value of \( K_a \):

\[ \text{pK}_a = -\log(1.8 \times 10^{-5}) \]

### Step 2: Calculate pK_a value
Using a calculator:

\[ \text{pK}_a \approx 4.74 \]

### Step 3: Substitute values into the Henderson-Hasselbalch equation
Since the concentrations of salt and acid are both given as \( 0.1 \, M \):

\[ [\text{Salt}] = 0.1 \, M \]
\[ [\text{Acid}] = 0.1 \, M \]

Substituting these values into the Henderson-Hasselbalch equation:

\[ \text{pH} = 4.74 + \log \left( \frac{0.1}{0.1} \right) \]

### Step 4: Simplify the logarithmic term
Since \( \frac{0.1}{0.1} = 1 \):

\[ \log(1) = 0 \]

### Step 5: Final calculation of pH
Thus, the equation simplifies to:

\[ \text{pH} = 4.74 + 0 \]
\[ \text{pH} = 4.74 \]

### Final Answer
The pH of the acetic acid and sodium acetate buffer solution is approximately **4.74**.

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