Question

At \(298K\), a certain buffer solution contains equal concentrations of \(X^-\) and \(HX\). If \(K_b\) for \(X^-\) is \(10^{-10}\), what is the pH of this buffer solution?

• A. \(4\)
• B. \(6\)
• C. \(2\)
• D. \(10\)

Hint:

For a buffer having equal acid and salt concentrations, \(pH=pK_a\).

Answer 1

The Correct Option is A

Step 1: Understand the buffer.
The solution contains: \[ HX \] and: \[ X^- \] This is an acidic buffer made of weak acid \(HX\) and its conjugate base \(X^-\).

Step 2: Use relation between \(K_a\) and \(K_b\).
For conjugate acid-base pair: \[ K_a\times K_b=K_w \] At \(298K\): \[ K_w=10^{-14} \] Given: \[ K_b=10^{-10} \] Therefore: \[ K_a=\frac{10^{-14}}{10^{-10}} \] \[ K_a=10^{-4} \]

Step 3: Find \(pK_a\).
\[ pK_a=-\log K_a \] \[ pK_a=-\log(10^{-4}) \] \[ pK_a=4 \]

Step 4: Use Henderson-Hasselbalch equation.
For acidic buffer: \[ pH=pK_a+\log\frac{[X^-]}{[HX]} \] Given: \[ [X^-]=[HX] \] So: \[ \frac{[X^-]}{[HX]}=1 \] \[ \log1=0 \] Therefore: \[ pH=pK_a \] \[ pH=4 \]