Chemistry » Acid-Base Equilibria » Acid-Base Titrations

# Acid-Base Indicators

## Acid-Base Indicators

Certain organic substances change color in dilute solution when the hydronium ion concentration reaches a particular value. For example, phenolphthalein is a colorless substance in any aqueous solution with a hydronium ion concentration greater than 5.0 $$×$$ 10−9M (pH < 8.3). In more basic solutions where the hydronium ion concentration is less than 5.0 $$×$$ 10−9M (pH > 8.3), it is red or pink. Substances such as phenolphthalein, which can be used to determine the pH of a solution, are called acid-base indicators. Acid-base indicators are either weak organic acids or weak organic bases.

The equilibrium in a solution of the acid-base indicator methyl orange, a weak acid, can be represented by an equation in which we use HIn as a simple representation for the complex methyl orange molecule:

$$\begin{array}{ccc}\text{HIn}\left(aq\right)+{\text{H}}_{2}\text{O}\left(l\right)& \phantom{\rule{0.2em}{0ex}}⇌\phantom{\rule{0.2em}{0ex}}& {\text{H}}_{3}{\text{O}}^{\text{+}}\left(aq\right)+{\text{In}}^{\text{−}}\left(aq\right)\\ \phantom{\rule{0.5em}{0ex}}\text{red}\hfill & & \phantom{\rule{5.5em}{0ex}}\text{yellow}\hfill & \end{array}$$

$${K}_{a}=\phantom{\rule{0.2em}{0ex}}\cfrac{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]\left[{\text{In}}^{\text{−}}\right]}{\left[\text{HIn}\right]}\phantom{\rule{0.2em}{0ex}}=4.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}$$

The anion of methyl orange, In, is yellow, and the nonionized form, HIn, is red. When we add acid to a solution of methyl orange, the increased hydronium ion concentration shifts the equilibrium toward the nonionized red form, in accordance with Le Châtelier’s principle. If we add base, we shift the equilibrium towards the yellow form. This behavior is completely analogous to the action of buffers.

An indicator’s color is the visible result of the ratio of the concentrations of the two species In and HIn. If most of the indicator (typically about 60−90% or more) is present as In, then we see the color of the In ion, which would be yellow for methyl orange. If most is present as HIn, then we see the color of the HIn molecule: red for methyl orange. For methyl orange, we can rearrange the equation for Ka and write:

$$\cfrac{\left[{\text{In}}^{\text{−}}\right]}{\left[\text{HIn}\right]}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\cfrac{\left[\text{substance with yellow color}\right]}{\left[\text{substance with red color}\right]}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\cfrac{{K}_{\text{a}}}{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}$$

This shows us how the ratio of $$\cfrac{\left[{\text{In}}^{\text{−}}\right]}{\left[\text{HIn}\right]}$$ varies with the concentration of hydronium ion.

The above expression describing the indicator equilibrium can be rearranged:

$$\cfrac{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}{{K}_{\text{a}}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\cfrac{\left[\text{HIn}\right]}{\left[{\text{In}}^{\text{−}}\right]}$$

$$\text{log}\left(\phantom{\rule{0.2em}{0ex}}\cfrac{\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}{{K}_{\text{a}}}\right)\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}=\text{log}\left(\phantom{\rule{0.2em}{0ex}}\cfrac{\left[\text{HIn}\right]}{\left[{\text{In}}^{\text{−}}\right]}\right)\phantom{\rule{0.2em}{0ex}}$$

$$\text{log}\left(\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]\right)-\text{log}\left({K}_{\text{a}}\right)=\text{−log}\left(\phantom{\rule{0.2em}{0ex}}\cfrac{\left[{\text{In}}^{\text{−}}\right]}{\left[\text{HIn}\right]}\right)\phantom{\rule{0.2em}{0ex}}$$

$$-\text{pH}+\text{p}{K}_{\text{a}}=\text{−log}\left(\phantom{\rule{0.2em}{0ex}}\cfrac{\left[{\text{In}}^{\text{−}}\right]}{\left[\text{HIn}\right]}\right)\phantom{\rule{0.2em}{0ex}}$$

$$\text{pH}=\text{p}K\text{a}+\text{log}\left(\phantom{\rule{0.2em}{0ex}}\cfrac{\left[{\text{In}}^{\text{−}}\right]}{\left[\text{HIn}\right]}\right)\phantom{\rule{0.4em}{0ex}}\text{or}\phantom{\rule{0.3em}{0ex}}\text{pH}=\text{p}{K}_{\text{a}}+\text{log}\left(\phantom{\rule{0.2em}{0ex}}\cfrac{\left[\text{base}\right]}{\left[\text{acid}\right]}\right)\phantom{\rule{0.2em}{0ex}}$$

The last formula is the same as the Henderson-Hasselbalch equation, which can be used to describe the equilibrium of indicators.

When [H3O+] has the same numerical value as Ka, the ratio of [In] to [HIn] is equal to 1, meaning that 50% of the indicator is present in the red form (HIn) and 50% is in the yellow ionic form (In), and the solution appears orange in color. When the hydronium ion concentration increases to 8 $$×$$ 10−4M (a pH of 3.1), the solution turns red. No change in color is visible for any further increase in the hydronium ion concentration (decrease in pH). At a hydronium ion concentration of 4 $$×$$ 10−5M (a pH of 4.4), most of the indicator is in the yellow ionic form, and a further decrease in the hydronium ion concentration (increase in pH) does not produce a visible color change. The pH range between 3.1 (red) and 4.4 (yellow) is the color-change interval of methyl orange; the pronounced color change takes place between these pH values.

There are many different acid-base indicators that cover a wide range of pH values and can be used to determine the approximate pH of an unknown solution by a process of elimination. Universal indicators and pH paper contain a mixture of indicators and exhibit different colors at different pHs. The figure below presents several indicators, their colors, and their color-change intervals.

This chart illustrates the ranges of color change for several acid-base indicators.

Titration curves help us pick an indicator that will provide a sharp color change at the equivalence point. The best selection would be an indicator that has a color change interval that brackets the pH at the equivalence point of the titration.

Color change pH intervals for three different acid-base indicators are shown in the figure below. Since the phenolphthalein color change interval occurs within the near-vertical portions of both titrations curves, this indicator may be used to signal the end point in both strong and weak acid titrations.

The graph shows a titration curve for the titration of 25.00 mL of 0.100 M CH3CO2H (weak acid) with 0.100 M NaOH (strong base) and the titration curve for the titration of HCl (strong acid) with NaOH (strong base). The pH ranges for the color change of phenolphthalein, litmus, and methyl orange are indicated by the shaded areas.

Litmus is a suitable indicator for the HCl titration because its color change brackets the equivalence point. However, we should not use litmus for the CH3CO2H titration because the pH is within the color-change interval of litmus when only about 12 mL of NaOH has been added, and it does not leave the range until 25 mL has been added. The color change would be very gradual, taking place during the addition of 13 mL of NaOH, making litmus useless as an indicator of the equivalence point.

We could use methyl orange for the HCl titration, but it would not give very accurate results: (1) It completes its color change slightly before the equivalence point is reached (but very close to it, so this is not too serious); (2) it changes color, as the figure above shows, during the addition of nearly 0.5 mL of NaOH, which is not so sharp a color change as that of litmus or phenolphthalein; and (3) it goes from yellow to orange to red, making detection of a precise endpoint much more challenging than the colorless to pink change of phenolphthalein.

The figure above shows us that methyl orange would be completely useless as an indicator for the CH3CO2H titration. Its color change begins after about 1 mL of NaOH has been added and ends when about 8 mL has been added. The color change is completed long before the equivalence point (which occurs when 25.0 mL of NaOH has been added) is reached and hence provides no indication of the equivalence point.

We base our choice of indicator on a calculated pH, the pH at the equivalence point. At the equivalence point, equimolar amounts of acid and base have been mixed, and the calculation becomes that of the pH of a solution of the salt resulting from the titration.