How Do Acid-Base Indicators Work and Why Do They Change Color at a Specific pH? (HL)

Acid-base indicators are weak acids whose acid and conjugate-base forms have different colors. They do not usually change color at one exact pH; they change across a transition range centered approximately on the indicator’s $\mathrm{p}K_a$.

An indicator can be represented as $\mathrm{HIn}$, with its differently colored conjugate base represented as $\mathrm{In^-}$:

$$\mathrm{HIn(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + In^-(aq)}$$

The equilibrium position depends on the hydrogen ion concentration and therefore the pH. Adding acid increases $[\mathrm{H_3O^+}]$, shifting the equilibrium left and increasing the proportion of $\mathrm{HIn}$. Adding alkali removes $\mathrm{H_3O^+}$, shifting it right and increasing the proportion of .

For the indicator equilibrium,

$$K_a=\frac{[\mathrm{H_3O^+}][\mathrm{In^-}]}{[\mathrm{HIn}]}$$

Rearranging gives:

$$\mathrm{pH}=\mathrm{p}K_a+\log\left(\frac{[\mathrm{In^-}]}{[\mathrm{HIn}]}\right)$$

At pH equal to pKa, the logarithmic term is zero, so the two forms have equal concentrations. One pH unit below pKa, the ratio of base form to acid form is 0.1, while one pH unit above pKa, it is 10. This hundredfold change in ratio across two pH units explains why the visual transition is narrow but not instantaneous.

The molecular structures of HIn and In− absorb different wavelengths of visible light because proton transfer changes their electron delocalization. The color seen is the light not absorbed by the predominant form. Since only a few drops are added, the indicator should not significantly alter the solution pH.

The eye normally detects a clear change as the ratio $[\mathrm{In^-}]:[\mathrm{HIn}]$ moves from about $1:10$ to $10:1$. Therefore, the transition range is approximately to .

A common misconception is that an indicator changes instantly at the equivalence point. Instead, its end point occurs within its transition range. For an IB HL titration question, select an indicator whose transition range overlaps the steep pH change around the equivalence point, and explain the color change using equilibrium and the relative concentrations of $\mathrm{HIn}$ and $\mathrm{In^-}$.