Question

Calculate the pH of buffer solution containing 0.1M \(\text{CH}_3\text{COOH}\) and 0.1 M \(\text{CH}_3\text{COONa}\) \([K_a = 1.8\times 10^{-5}]\)

• A. \(4.745\)
• B. \(5.741\)
• C. \(2.876\)
• D. \(7.001\)

Hint:

Use the Henderson-Hasselbalch equation; equal acid and salt concentrations give pH = pKa.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A mixture of a weak acid and its salt is an acidic buffer. Its pH follows the Henderson-Hasselbalch equation.

Step 2: Key Formula or Approach
\[ \text{pH}=\text{p}K_a+\log\frac{[\text{salt}]}{[\text{acid}]} \]

Step 3: Find pKa
\[ \text{p}K_a=-\log(1.8\times10^{-5})=5-\log1.8=5-0.2553=4.745 \]

Step 4: Concentration term
The salt and acid are both 0.1 M, so the ratio is 1 and \(\log1=0\).

Step 5: Result
\[ \text{pH}=4.745+0=4.745 \]

Step 6: Why the other options fail
The pH of a buffer made from a weak acid must be close to its pKa, which is near 4.7. Option (D) 7.001 is neutral. Option (C) 2.876 is the pH of a plain 0.1 M acetic acid solution without salt. Option (B) 5.741 would need a salt to acid ratio of 10.

Final Answer:
The buffer has equal acid and salt, so pH equals pKa, which is 4.745, option (A). \[ \boxed{4.745} \]