5.6.2 pKa

What is $pKₐ$?

The $pKₐ$ value is a logarithmic measure of an acid's strength, derived from its dissociation constant, $K_a$. It offers a more manageable way to express very small $K_a$ values and is frequently used to determine the pH and behaviour of weak acids in solution.

Relationship between $K_a$ and $pK_a$

The relationship between $K_a$ and $pK_a$ is given by the formula:

$$pK_a = -\log_{10} K_a$$

To find $K_a$ from $pK_a$, use the reverse expression:

$$K_a = 10^{-\text{p}K_a}$$

These expressions allow conversion between $K_a$ and $pK_a$, aiding in calculations and comparisons of acid strength.

Calculating pH of a Weak Acid Using $K_a$ and $pK_a$

The pH of a weak acid can be calculated if the $K_a$ and the initial concentration of the acid ($[\text{HA}]{\text{initial}}$) are known.

For weak acids, we assume that the dissociation is minimal, so

$$[\text{HA}]{\text{initial}} \approx [\text{HA}]_{\text{equilibrium}}$$

Formula to Estimate $\text{[H}^+ \text{]}$

For a weak acid dissociating as:

$$\text{HA} \leftrightharpoons \text{H}^+ + \text{A}^-$$

We use:

$$\text{[H}^+ \text{]} = \sqrt{K_a \times [\text{HA}]_{\text{initial}}}$$

Then, pH can be found using:

$$pH = -\log_{10}[\text{H}^+]$$

Sample Calculations

Special Point: Half-Equivalence in Titration

During the titration of a weak acid, at the half-equivalence point, pH = $pK_a$. This is because the concentrations of $\text{HA}$ and $\text{A}^-$ are equal at this stage, simplifying the $K_a$ expression.