When a buffer solution of sodium acetate and acetic acid is diluted with water, then pH

Options

A. Increases
B. Decreases
C. Unaffected
D. None of these

Answer

To determine how the pH of a buffer solution of sodium acetate and acetic acid changes upon dilution with water, we can follow these steps:

### Step 1: Understand the Components of the Buffer Solution
A buffer solution consists of a weak acid and its conjugate base. In this case, acetic acid (CH₃COOH) is the weak acid and sodium acetate (CH₃COONa) is the conjugate base.

### Step 2: Recall the Henderson-Hasselbalch Equation
The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
Where:
- \(\text{pK}_a\) is the negative logarithm of the acid dissociation constant of acetic acid.
- \([\text{Salt}]\) is the concentration of sodium acetate.
- \([\text{Acid}]\) is the concentration of acetic acid.

### Step 3: Analyze the Effect of Dilution
When the buffer solution is diluted with water, the volume of the solution increases. However, the number of moles of acetic acid and sodium acetate remains constant.

### Step 4: Determine the New Concentrations After Dilution
Let’s assume the initial volume of the buffer solution is \(V\). After dilution, the new volume becomes \(2V\). The concentrations of the acid and salt after dilution will be:
- \([\text{Salt}] = \frac{n_{\text{Salt}}}{2V}\)
- \([\text{Acid}] = \frac{n_{\text{Acid}}}{2V}\)

Where \(n_{\text{Salt}}\) and \(n_{\text{Acid}}\) are the initial number of moles of sodium acetate and acetic acid, respectively.

### Step 5: Substitute into the Henderson-Hasselbalch Equation
Substituting the new concentrations into the Henderson-Hasselbalch equation gives:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{\frac{n_{\text{Salt}}}{2V}}{\frac{n_{\text{Acid}}}{2V}}\right) \]

### Step 6: Simplify the Equation
The \(2V\) terms cancel out:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{n_{\text{Salt}}}{n_{\text{Acid}}}\right) \]

### Step 7: Conclusion
Since the ratio \(\frac{n_{\text{Salt}}}{n_{\text{Acid}}}\) remains unchanged during dilution, the pH of the buffer solution remains constant. Thus, the pH is unaffected by the dilution.

### Final Answer
The pH of the buffer solution of sodium acetate and acetic acid, when diluted with water, remains **unaffected**.

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