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# AcidBase: Indicators

### Skills to develop

• Explain color changes of indicators.
• Determine the acidic dissociation constants Ka or Kai of indicators.

# Indicators

Why is the color all mixed up? To be fixed!

Indicators are substances whose solutions change color due to changes in pH. These are called acid-base indicators. They are usually weak acids or bases, but their conjugate base or acid forms have different colors due to differences in their absorption spectra.

Indicators are complicate organic weak acids or bases with complicated structures. For simplicity, we represent a general indicator by the formula HIn, and its ionization in a solution by the equilibrium,

HIn = H+ + In-, and define the equilibrium constant as Kai,
```        [H+][In-]
Kai = ----------.
[HIn]
```
Which can be rearranged to give
```    [In-]     Kai
------- = -----
[HIn]     [H+]
```
When [H+] is greater than 10 Kai, In- color dominates, whereas color due to HIn dominates if [H+] < Kai / 10. The above equation indicates that the color change is the most sensitive when [H+] = Kai in numerical value.

We define pKai = - log(Kai), and the pKai value is also the pH value at which the color of the indicator is most sensitive to pH changes.

Taking the negative log of Kai gives,

```                           [In-]
-log Kai = -log[H+] - log------
[HIn]
or
[In-]
pH = pKai + log-----
[HIn]
```
This is a very important formula, and its derivation is very simple. Start from the definition of the equilibrium constant K, you can easily derive it. Note that pH = pKai when [In-] = [HIn]. In other words, when the pH is the same as pKai, there are equal amounts of acid and base forms. When the two forms have equal concentration, the color change is most noticeable.

Colors of substances make the world a wonderful place. Because of the colors and structures, flowers, plants, animals, and minerals show their unique characters.

Many indicators are extracted from plants. For example, red cabbage juice and tea pigments show different colors when the pH is different. The color of tea darkens in a basic solution, but the color becomes lighter when lemon juice is put into a tea. Red cabbage juice turns blue in a basic solution, but it shows a distinct red color in an acidic solution.