pH and pKa

Learning Objective 8.7.A Explain the relationship between the predominant form of a weak acid or base in solution at a given pH and the pKa of the conjugate acid or the pKb of the conjugate base.

Quick Notes

The ratio of acid to base forms of a weak acid/base depends on the pH of the solution and the pK_a of the acid.

If pH < pK_a then more protonated form (HA) exists.
If pH > pK_a then more deprotonated form (A⁻) exists.

Indicators change color around their pKa.
In titrations, indicators should be chosen with a pK_a ≈ pH at equivalence point.

Full Notes

Protonation State and the pH–pK_a Relationship

The protonation state of an acid (HA) refers to whether it is mostly in its protonated form (HA) or its deprotonated form (A⁻).

This can be predicted by comparing pH of the solution to the pK_a of the acid.

AP Chemistry diagram showing relationship of HA and A− concentrations when pH is lower or higher than pKa.

Key Rule:

Relationship	Dominant Species
pH < pK_a	Protonated form (HA)
pH > pK_a	Deprotonated form (A⁻)
pH ≈ pK_a	[HA] ≈ [A⁻] (equal concentrations)

When pH = pK_a, the system is at the half-equivalence point and the solution is buffered.

Worked Example

Q: Which form of acetic acid dominates in a solution at pH = 5.76, given that pK_a = 4.76?

A: Since pH > pK_a, the conjugate base (A⁻) dominates. The solution has more acetate ions (CH₃COO⁻) than acetic acid (CH₃COOH).

Indicators as Weak Acids

Acid–base indicators function through an equilibrium system:

HInd (aq) ⇌ H⁺ (aq) + Ind⁻(aq)

HInd = weak acid form (one colour)
Ind⁻ = conjugate base (different colour)

As pH changes, the position of this equilibrium shifts, causing the colour to change.

In an acidic solution, a higher [H⁺] causes equilibrium to shift left, giving more HInd (acid colour).
In a basic solution, a lower [H⁺] causes equilibrium to shift right, giving more Ind⁻ (base colour).

pK_a and Endpoint

The pK_a of the indicator tells you the pH at which the colour changes.

When solution pH = pK_a, [HInd] = [Ind⁻] — this is the transition point and gives an equal mix of both colours.

In acid-base titrations, indicators are chosen so that the pK_a matches the equivalence point of the titration as closely as possible.

Choosing an Appropriate Indicator

Indicator must change colour close to the equivalence point of a titration. Common examples include:

Phenolphthalein: pH range ~8.3–10.0 (colourless to pink)

AP Chemistry diagram of phenolphthalein indicator showing colourless in acid and pink in alkali with transition at pH above 8.5.

Methyl orange: pH range ~3.1–4.4 (red to yellow)

AP Chemistry diagram of methyl orange indicator showing red in acid and yellow in alkali with transition at pH above 3.5.

Universal Indicator

Universal indicator is a mixture of many indicators, each with different pK_a values.

Because it contains lots of different indicators, it can provide a continuous colour gradient from pH 1 to 14.

We can use it for estimating the pH of a solution however it is not suitable for precise titration endpoints as there is no 'sudden' colour change.

Summary

The balance between acid and conjugate base forms of a weak acid is governed by pH relative to pK_a.
If pH is low, the solution holds onto protons (more HA).
If pH is high, protons are lost (more A⁻).
Indicators work because their structure shifts with pH.
Choosing the correct indicator is essential for accurate titration results.