Edexcel International A Level (IAL) Chemistry (YCH11) - Unit 4 - 14.9 pH of weak acids (Ka, pKa)-Study Notes - New Syllabus

14.9 Calculating pH of a Weak Acid from \( \mathrm{K_a} \) or \( \mathrm{pK_a} \)

The pH of a weak acid cannot be calculated directly from its concentration because it only partially dissociates. Instead, the acid dissociation constant (\( \mathrm{K_a} \)) is used along with appropriate assumptions to simplify the calculation.

Step 1: Write the Equilibrium Expression

\( \mathrm{HA \rightleftharpoons H^+ + A^-} \)

\( \mathrm{K_a = \frac{[H^+][A^-]}{[HA]}} \)

Step 2: Make the Key Assumption

• Weak acids dissociate only slightly.
• Therefore:

\( \mathrm{[HA]_{equilibrium} \approx [HA]_{initial}} \)

This avoids solving quadratic equations.

Step 3: Simplified Expression

Let initial concentration = \( \mathrm{c} \), and \( \mathrm{[H^+] = x} \):

\( \mathrm{K_a = \frac{x^2}{c}} \)

So:

\( \mathrm{x = \sqrt{K_a \times c}} \)

Then:

\( \mathrm{pH = -\log_{10}x} \)

Using \( \mathrm{pK_a} \)

Recall:

\( \mathrm{pK_a = -\log_{10}K_a} \)

From the simplified expression:

\( \mathrm{[H^+] = \sqrt{K_a \cdot c}} \)

Taking logs gives:

\( \mathrm{pH = \frac{1}{2}(pK_a – \log_{10}c)} \)

Key Assumption Condition

• Valid when dissociation is small (typically < 5%).
• i.e. \( \mathrm{K_a \ll c} \).

Key Features

• Weak acids require equilibrium calculations.
• Use approximation to avoid quadratic equations.
• \( \mathrm{[H^+] = \sqrt{K_a c}} \) is the key result.
• Can also use \( \mathrm{pK_a} \) form for quicker calculations.