The Acid Dissociation Constant Ka (OCR A-Level Chemistry A): Revision Notes

The Acid Dissociation Constant Ka

Introduction to strong and weak acids

Understanding how acids behave in water is fundamental to physical chemistry. When we talk about acid strength, we're referring to how readily an acid releases hydrogen ions (protons) in aqueous solution.

Strong acids undergo complete dissociation in water. This means that virtually every acid molecule breaks apart to form ions. Hydrochloric acid is a classic example:

$\text{HCl(aq)} \rightarrow \text{H}^+(aq) + \text{Cl}^-(aq)$

Notice the forward arrow—this reaction goes essentially to completion.

Weak acids, in contrast, only partially dissociate in water. They establish a dynamic equilibrium between the intact acid molecules and the ions formed. Ethanoic acid demonstrates this behaviour:

$\text{CH}_3\text{COOH(aq)} \rightleftharpoons \text{H}^+(aq) + \text{CH}_3\text{COO}^-(aq)$

Most acids you'll encounter at A-Level are weak acids, making it essential to quantify just how weak they are.

What is the acid dissociation constant Ka?

The acid dissociation constant, represented as $K_a$, provides a numerical measure of the extent to which a weak acid dissociates in solution. It's a specialized version of the equilibrium constant $K_c$, adapted specifically for acid-base equilibria.

General form of acid dissociation

For any weak acid (which we can represent generically as HA), the dissociation in water follows this pattern:

$\text{HA(aq)} \rightleftharpoons \text{H}^+(aq) + \text{A}^-(aq)$

Here, HA represents the undissociated acid molecule, and A⁻ represents the conjugate base formed when the acid loses its proton.

The Ka expression

Following the principles of equilibrium constants, we write the $K_a$ expression by placing product concentrations in the numerator and reactant concentrations in the denominator:

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

The square brackets represent equilibrium concentrations measured in mol dm⁻³.

Units of Ka

The units derive from the concentration terms in the expression. Because we have two concentration terms in the numerator and one in the denominator:

$\text{Units} = \frac{(\text{mol dm}^{-3}) \times (\text{mol dm}^{-3})}{(\text{mol dm}^{-3})} = \text{mol dm}^{-3}$

Interpreting Ka values

The magnitude of $K_a$ tells us about acid strength. When Ka is large, the equilibrium position lies further to the right, meaning more dissociation has occurred—indicating a stronger acid. Conversely, a small Ka value reveals that the equilibrium heavily favours the undissociated acid, characterizing a weaker acid.

The pKa scale

Why we need pKa

Working directly with $K_a$ values presents a practical challenge. Weak acids have very small $K_a$ values—often expressed in scientific notation with negative exponents—making them cumbersome to compare. The solution mirrors the approach used for hydrogen ion concentrations: apply a logarithmic scale.

The $\text{pK}_a$ value transforms $K_a$ using a negative logarithm:

$\text{pK}_a = -\log K_a$

This relationship parallels the pH scale, where $\text{pH} = -\log[\text{H}^+]$.

Converting between Ka and pKa

To reverse the calculation and find $K_a$ from $\text{pK}_a$:

$K_a = 10^{-\text{pK}_a}$

These transformations prove invaluable for exam calculations and comparing acid strengths.

Worked example: converting from Ka to pKa

Worked example: converting from pKa to Ka

Advantages of pKa values

The $\text{pK}_a$ scale offers several benefits over raw $K_a$ values. Firstly, $\text{pK}_a$ values typically fall within a manageable range of approximately 0 to 14 for common weak acids, avoiding unwieldy scientific notation. Secondly, comparing relative acid strengths becomes more intuitive—though remember the inverse relationship.

Comparing acid strengths using Ka and pKa

Interpreting the values

Understanding the relationship between these constants and acid strength is crucial:

• Stronger acids have larger Ka values and smaller pKa values
• Weaker acids have smaller Ka values and larger pKa values

Let's examine some specific examples:

Acid	Formula	$K_a$ / mol dm⁻³	$\text{pK}_a$	Relative strength
Nitrous acid	HNO₂	$4.10 \times 10^{-4}$	3.39	Strongest
Methanoic acid	HCOOH	$1.77 \times 10^{-4}$	3.75	↑
Ethanoic acid	CH₃COOH	$1.76 \times 10^{-5}$	4.75	↓
Chloric(I) acid	HClO	$3.00 \times 10^{-8}$	7.53	Weakest

Biological significance

Values of $\text{pK}_a$ prove particularly useful when studying biological systems, where the behaviour of weak acids influences countless processes from enzyme activity to cellular pH regulation. The convenient scale allows biochemists to quickly assess which acids will dominate ionization at physiological pH (around 7.4).

Polybasic weak acids

Dibasic acids: stepwise dissociation

Some acids contain more than one ionizable hydrogen atom. Dibasic acids possess two protons that can dissociate, and this happens in sequential steps, each with its own equilibrium constant.

Sulfurous acid ($\text{H}_2\text{SO}_3$) provides an excellent example. This weak dibasic acid dissociates in two stages:

In the first dissociation step, one proton leaves the molecule, forming the hydrogensulfite ion ($\text{HSO}_3^-$). This occurs relatively easily, with a $\text{pK}_a$ value of 1.92, indicating moderate acid strength.

The second dissociation step removes the remaining proton from $\text{HSO}_3^-$ to form the sulfite ion ($\text{SO}_3^{2-}$). This second ionization is considerably more difficult, as evidenced by the $\text{pK}_a$ of 7.18—substantially larger than the first.

Organic acids in wine

Wine chemistry beautifully illustrates weak acid behaviour in a real-world context. The characteristic tartness of wine derives largely from organic acids naturally present in grapes.

Malic and tartaric acids

These dibasic acids represent the primary acids found in wine grapes:

Both acids contain two carboxyl groups (COOH), which can each donate a proton. When these acids ionize, the hydrogen ions dissociate specifically from the COOH groups, not from the hydroxyl (OH) groups also present in the molecules. This selectivity occurs because the COOH group is far more acidic than the OH group.

The first dissociation of malic acid occurs at the carboxylic acid group:

This initial proton loss has a $\text{pK}_a$ of 3.40, indicating that malic acid is reasonably acidic—though still weak compared to strong mineral acids.

The second carboxylic acid group then dissociates in a separate equilibrium:

Tribasic acids

Citric acid takes this concept further as a tribasic acid containing three carboxylic acid groups:

Citric acid undergoes three successive dissociations, each progressively weaker than the last. You can write equilibrium expressions for each of the three ionization steps, with each having its own distinct $K_a$ and $\text{pK}_a$ value.

Exam tips and common mistakes

Key calculation skills

• Converting between Ka and pKa: Practice these transformations until they become automatic. Remember: $\text{pK}_a = -\log K_a$ and $K_a = 10^{-\text{pK}_a}$
• Unit awareness: $K_a$ always has units of mol dm⁻³, but $\text{pK}_a$ has no units (it's a logarithm)
• Significant figures: Typically give $\text{pK}_a$ values to 2 decimal places and $K_a$ values to 2 significant figures in standard form

Exam technique

• Always write out the dissociation equation before writing the $K_a$ expression
• Check you're using the correct temperature (usually 298 K)
• When comparing acids, clearly state which is stronger and explain using both $K_a$ and $\text{pK}_a$ values
• For polybasic acids, identify which dissociation step you're considering
• Show all working when converting between $K_a$ and $\text{pK}_a$—partial marks are available for method