Indicators may be considered as weak acids or weak bases that act like buffers and also exhibit color changes as their degree of dissociation varies with pH. For example, methyl red shows its full alkaline color, yellow, at a pH of about 6 and its full acid color, red, at about pH 4.
Dissociation and Equilibrium of pH Indicators
The dissociation of an acid indicator is given in simplified form as,
$$ \underset{\underset{(Acid\;color)}{Acid_1}}{HIn}+\underset{Base_2}{H_2O} ⇌\underset{Acid_2}{H_3O^+}+\underset{\underset{(Alkaline\;color)}{Base_1}}{In^-} $$
The equilibrium expression is
$$ \frac{[H_3O^+][In^-]}{[HIn]}=K_{In} $$
HIn is the un-ionized form of the indicator, which gives the acid color, and In– is the ionized form, which produces the basic color. KIn is referred to as the indicator constant.
If an acid is added to a solution of the indicator, the hydrogen ion concentration on the right-hand side of equation increases, and the ionization is repressed by the common ion effect. The indicator is then predominantly in the form of HIn, showing the acid color.
If a base is added, the [H3O+] concentration is reduced by the reaction of the acid with the base. As a result, reaction proceeds to the right, yielding more ionized indicator (In–), and the basic color predominates.Thus, the color of an indicator is a function of the pH of the solution.
The equilibrium expression can be treated in a manner similar to that for a buffer consisting of a weak acid and its salt or conjugate base. Hence
$$ [H_3O^+]=K_{In}\frac{[HIn]}{[In^-]} $$
And because [HIn] represents the acid color of the indicator and the conjugate base [In–] represents the basic color, these terms can be replaced by the concentration expressions [Acid] and [Base]. The formula for pH will then be:
$$ pH=pK_{In}+log(\frac{[Base]}{[Acid]}) $$
Just as a buffer shows its greatest efficiency when pH = pKa, an indicator exhibits its middle tint when [Base]/[Acid] = 1 and pH = pKIn.
The most efficient indicator range, corresponding to the effective buffer interval, is about 2 pH units, that is, pKIn ± 1.
The reason for the width of this color range can be explained as follows: it is known from experience that one cannot discern a change from the acid color to the salt or conjugate base color until the ratio of [Base] to [Acid] is about 1 to 10. That is, there must be at least one part of the basic color to ten parts of the acid color before the eye can detect a change in color from acid to alkaline.
The pH value at which this change is perceived is given by the equation:
$$ pH=pK_{In}+log\frac{1}{10}=pK_{In}-1 $$
Conversely, the eye cannot discern a change from the alkaline to the acid color until the ratio of [Base] to [Acid] is about 10 to 1, or
$$ pH=pK_{In}+log\frac{10}{1}=pK_{In}+1 $$
Therefore, when base is added to a solution of a buffer in its acid form, the eye first visualizes a change in color at pKIn−1, and the color ceases to change any further at pKIn+1. The effective range of the indicator between its full acid and full basic color can thus be expressed as
$$ pH=pK_{In}±1 $$
Chemical indicators are typically compounds with chromophores that can be detected in the visible range and change color in response to a solution’s pH. Most chemicals used as indicators respond only to a narrow pH range. Several indicators can be combined to yield so-called universal indicators just as buffers can be mixed to cover a wide pH range. A universal indicator is a pH indicator that displays different colors as the pH transitions from pH 1 to 12. A typical universal indicator will display a color range from red to purple.
Reference:
- Sinko, P. (2011). Martin’s Physical Pharmacy and Pharmaceutical Sciences. Baltimore, : Lippincott Williams & Wilkins, a Wolters Kluwer business.