Reactivity 3.1.14 — Acid–base indicators and their equilibrium expressions

Acid–base indicators are typically weak acids (or weak bases) whose conjugate acid–base pairs exhibit different colours. The colour observed in a solution depends on the pH, which affects the relative concentrations of the acid (HIn) and its conjugate base (In⁻).

 Key Interpretation Point
The colour change of an indicator occurs at a pH value approximately equal to its pKa. This point is called the end point and reflects when the ratio \([ \text{In}^- ] / [ \text{HIn} ] \approx 1\), i.e., both acid and conjugate base are present in nearly equal amounts.

Equilibrium Expression for a Weak Acid Indicator

Consider a weak acid indicator represented by HIn, where HIn (acid form) has one colour and In⁻ (conjugate base) has a different colour:

\(\text{HIn (aq)} \rightleftharpoons \text{H}^+ (aq) + \text{In}^- (aq)\)

At equilibrium, the acid dissociation constant \( K_a \) is:

\(K_a = \frac{[\text{H}^+][\text{In}^-]}{[\text{HIn}]}\)

Taking the negative logarithm of both sides:

\(\text{pH} = \text{pKa} + \log\left(\frac{[\text{In}^-]}{[\text{HIn}]}\right)\)

This is the Henderson–Hasselbalch equation. It shows how the ratio of the conjugate base to the acid form controls the pH and therefore the observed colour of the solution.

 Colour Change Mechanism

Nature and Role of Acid–Base Indicators

Acid–base indicators are typically weak acids, represented by the general formula \( \text{HInd} \). These substances establish an equilibrium in aqueous solution as follows:

\( \text{HInd (aq)} \rightleftharpoons \text{H}^+ (aq) + \text{Ind}^- (aq) \)

The acid form \( \text{HInd} \) and its conjugate base \( \text{Ind}^- \) are typically different in colour. As the pH of the solution changes, the position of this equilibrium shifts, causing a visible colour change. This colour change occurs over a narrow pH range and is centered around the pKa of the indicator.

At:

• \( \text{pH} < \text{p}K_a \): The equilibrium lies to the left → more \( \text{HInd} \) → colour of the acid form.
• \( \text{pH} > \text{p}K_a \): The equilibrium lies to the right → more \( \text{Ind}^- \) → colour of the base form.
• \( \text{pH} = \text{p}K_a \): Equal amounts of both forms → intermediate colour (usually a blend or midpoint).

Explanation Using Equilibrium Concepts

Let us write the equilibrium law for the dissociation of the indicator:

\( K_a = \dfrac{[\text{H}^+][\text{Ind}^-]}{[\text{HInd}]} \)

Rewriting in terms of logarithms:

\( \text{pH} = \text{p}K_a + \log \left( \dfrac{[\text{Ind}^-]}{[\text{HInd}]} \right) \)

This is the Henderson–Hasselbalch equation, which shows that the ratio of the conjugate base to the acid form determines the pH – and consequently, the colour seen. The observable colour change usually spans about two pH units: from \( \text{p}K_a – 1 \) to \( \text{p}K_a + 1 \).

Examples of Common Indicators

Universal Indicator

Unlike individual indicators, universal indicator is a complex mixture of several acid–base indicators. This allows it to provide a continuous range of colour changes over a wide pH span, typically from pH 1 to 14. It does not function as a single equilibrium system but combines the colour transitions of multiple indicators to create a gradient of hues that corresponds to specific pH values.

This makes the universal indicator useful for estimating the pH of a solution across a broad range, although it is not precise enough to determine equivalence points in titration due to its gradual and composite colour transitions.

Key Point:

An ideal indicator for titration changes colour sharply at a pH that matches the equivalence point of the titration curve.