Question

A buffer solution contains 100ml of 0.01(M) \(\text{CH}_3\text{COOH}\) and 200ml of 0.02(M) \(\text{CH}_3\text{COONa}\). 700ml of water is added subsequently to the buffer solution. The pH before and after dilution are [given, \(\text{p}K_a = 4.74\); \(\log 2 = 0.301\)]

• A. 5.04, 5.04
• B. 5.04, 0.504
• C. 5.04, 1.54
• D. 5.34, 5.34

Hint:

The pH of a buffer solution is determined by the ratio of the conjugate base to the weak acid. Since dilution affects both concentrations equally, the ratio does not change, and the pH remains constant. This is a primary feature of a buffer system.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to calculate the pH of an acidic buffer solution containing acetic acid and sodium acetate both before and after dilution with water.


Step 2: Key Formula or Approach:
For an acidic buffer, the Henderson-Hasselbalch equation is:
\[ \text{pH} = \text{p}K_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
Since both components are in the same volume, the ratio of molar concentrations is equal to the ratio of their millimoles:
\[ \text{pH} = \text{p}K_a + \log\left(\frac{n_{\text{salt}}}{n_{\text{acid}}}\right) \]


Step 3: Detailed Explanation:
Let us calculate the millimoles of acetic acid ($\text{CH}_3\text{COOH}$) and sodium acetate ($\text{CH}_3\text{COONa}$):
- Millimoles of weak acid, $n_{\text{acid}} = 100 \text{ ml} \times 0.01 \text{ M} = 1.0 \text{ mmol}$.
- Millimoles of conjugate base (salt), $n_{\text{salt}} = 200 \text{ ml} \times 0.02 \text{ M} = 4.0 \text{ mmol}$.
Now, calculate the pH before dilution using the Henderson-Hasselbalch equation:
\[ \text{pH}_{\text{before}} = \text{p}K_a + \log\left(\frac{4.0}{1.0}\right) \]
\[ \text{pH}_{\text{before}} = 4.74 + \log(4) \]
\[ \text{pH}_{\text{before}} = 4.74 + 2\log(2) \]
\[ \text{pH}_{\text{before}} = 4.74 + 2(0.301) = 4.74 + 0.602 = 5.342 \approx 5.34 \]
Next, let us consider the effect of adding 700 ml of water (dilution):
- Dilution changes the total volume of the solution, but the number of millimoles of the weak acid ($1.0 \text{ mmol}$) and its conjugate base ($4.0 \text{ mmol}$) remains unchanged.
- Since both concentrations are divided by the same new volume ($1000 \text{ ml}$), the ratio $\frac{[\text{Salt}]}{[\text{Acid}]}$ remains exactly the same.
- Hence, the pH of a buffer solution remains practically unchanged upon dilution.
\[ \text{pH}_{\text{after}} = 5.34 \]
Thus, the pH before and after dilution are 5.34 and 5.34 respectively.


Step 4: Final Answer:
The correct option is (D).