## Stoichiometry of Acid-Base Titrations

James Richard Fromm

In an acid-base titration, we slowly add the titrant strong acid or strong base until the equivalence point is reached as indicated in the previous section. The equivalence point is that point at which the number of moles of acid or base added as titrant is exactly equivalent to the number of moles of acid or base present originally in the other solution in accordance with the stoichiometric reaction.

Example. The equivalence point for the titration of 50.00 mL of 0.100 molar HCl with 0.200 molar NaOH could be calculated as follows: 50 mL x 0.1 mol/L = 5.0 mmol HCl. The titration uses the stoichiometric reaction

HCl + NaOH NaCl + H2O,

which could just as accurately be written as

H3O+ + OH- 2H2O.

Since the reaction is a 1:1 reaction, 5.00 mmol of HCl are equivalent to 5.00 mmol NaOH. The volume of NaOH required can be calculated: 5.0 mmol NaOH = 0.2 mol/L x V mL, V = 5.00/0.200 = 25.00 mL NaOH

Example. In the titration of H2SO4, sulfuric acid, the reaction requires 2 moles of NaOH per mole of H2SO4. A complete titration of 50.00 mL of 0.100 molar H2SO4 would therefore require 50.00 mL of 0.200 molar NaOH rather than the 25.00 mL needed for the monoprotic acid HCl in the preceding example.

#### Detecting the Equivalence Point

In acid-base titrations, there is a sharp change in pH at the equivalence point. For example, the stoichiometric chemical reactions in the titration of 2.5 mmol HCl and then 2.5 mmol CH3COOH with 0.1 molar NaOH are:

Na+ + OH- + H3O+ + Cl- H2O + Na+ + Cl-

and

Na+ + OH- + H3O+ + CH3COO- H2O + Na+ + CH3COO-.

The reaction stoichiometry is 1:1 in both cases. The pH change can be detected by a pH meter, an electrochemical device whose discussion we will defer to later sections, or by a chemical indicator. Chemical indicators are acid-base conjugate pairs whose acid form and base form are different in color. A table of useful chemical indicators is given below.

##### Table: Properties of Aqueous Acid-Base Indicators at 25oC
 INDICATOR ACID COLOR pH BASIC COLOR Methyl violet yellow 0-1.6 violet Thymol blue pink 1.2-2.8 yellow Methyl yellow red 2.9-4.0 yellow Brom-phenol blue yellow 3.0-4.7 violet Methyl Orange pink 3.1-4.4 yellow Brom-cresol green yellow 3.8-5.4 blue Methyl red red 4.2-6.2 yellow Litmus red 4.7-8.2 blue Chlorophenol red yellow 4.8-6.4 red Brom-cresol purple yellow 5.2-6.8 purple Bromothymol blue yellow 6.0-7.6 blue Phenol red yellow 6.4-8.0 red Cresol purple yellow 7.4-9.0 purple Thymol blue yellow 8.0-9.6 blue Phenolphthalein colorless 8.0-9.8 pink Thymolphthalein colorless 9.3-10.5 blue Alizarin yellow G colorless 10.1-12.1 yellow Indigo Carmine blue 11.4-13.0 yellow Trinitrobenzene colorless 12.0-14.3 orange

A chemical indicator is a compound which can change color to indicate that the endpoint of a titration has been reached. The color of an indicator changes because it is affected by the concentrations of ions in the solution. An acid-base indicator is an acid-base conjugate pair, a weak acid-weak base system in which the two forms have different colors. This is added, in low concentration so that it exerts essentially no control on the pH of the system. For an indicator, the acid ionization constant Ka = [H3O+][A-]/[HA] is usually written as Ka = [H3O+][In-]/[HIn], where HIn is the acid form of the indicator and In- is the base form of the indicator. Where the ratio [In-]/[HIn] is one, [H3O+] = Ka and pH = pKa. This point is in the color-change region of the indicator, usually at its center. The color-change region of the indicator is usually +/-1 pH unit around pKa. To select a proper indicator, then, requires determination of the pH of the solution at the equivalence point of the titration and selection of an indicator whose pKa is as close to that pH as possible.

Indicators are usually organic structures of some complexity or natural products and, like dyeing materials, are generally known by their trivial names as in the above table. A few indicators, of which thymol blue is an example, are polyprotic acids which can change color more than once as pH is continuously increased. Such indicators can be used at a pH equal to either of their pKa values.