Question

Find the pH of a solution formed by mixing equal volume of solution of \(0.1\) M sodium propionate and \(0.1\) molar propionic acid.
(Given The dissociation constant of propionic acid is \(1.3\times 10^{-5}\))

• A. \(2.45\)
• B. \(4.89\)
• C. \(5.98\)
• D. \(6.89\)

Hint:

Equal volumes of equal concentrations give salt/acid ratio of 1, so pH = pKa.

Answer 1

The Correct Option is B

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:
\[ \text{pH} = \text{p}K_a + \log\frac{[\text{salt}]}{[\text{acid}]} \]

Step 3: Calculate:
Equal volumes of \(0.1\) M solutions are mixed, so both concentrations drop to \(0.05\) M, and the ratio is \(1\). Then \(\log 1 = 0\) and pH = p\(K_a\).
\[ \text{p}K_a = -\log(1.3\times10^{-5}) = 5 - \log 1.3 = 5 - 0.114 = 4.886 \]
So pH \(\approx 4.89\).

Step 4: Why the other options are wrong:
\(2.45\) is far too acidic for a mixture that holds a large amount of the salt. \(5.98\) and \(6.89\) are too high, because with equal amounts of acid and salt the pH must sit exactly at p\(K_a\).

Final Answer:
The buffer has pH equal to p\(K_a\), about \(4.89\). This is option (B). \[ \boxed{4.89} \]