Acid-base Titrations and Their Graphs

During titration we determine the volume of one solution which just reacts with a fixed volume of the other solution.

An acid-base titration is a procedure used in quantitative chemical analysis to determine the concentration of either an acid or a base. Generally, an acid solution of known concentration is taken in a burette and is added to an alkaline solution of unknown concentration taken in a conical flask. The solution that is titrated (the solution with fixed volume) is known as titrand, analyte or titrate while the solution with which titration is performed is called titrant. The titrate is taken in a conical flask while the titrant is taken in a burette.

The end point or the equivalence point reaches when the stoichiometric amount of acid has been added to the alkali solution. At this point all the alkali has been neutralised and the solution contains salt and water only.

From the end point we can find the volume of the base (V b) having molarity Mb required to neutralize a certain volume of the acid (V) of molarity Ma. Now, number of moles in V cm3 of a solution of molarity Misgiven by M x V/1000. For the titrations involving monobasic acid and monoacid base, one mole of base is required to completely C neutralize one mole of the acid.

Therefore , Ma V a / 1000 = Mb V b / 1000   or   Ma V a = M b V b

For titration involving polyacid bases and polybasic acids the above equation takes the form

n a Ma V a = n b Mb V b

where n a is the basicity of the acid while n b is the acidity of the base.

Thus, for the titration of tetraoxosulphate(VI) acid with sodium hydroxide, the equation applicable is

2 Ma V a / Mb V b

Ma V a / Mb V b = 1/2

Similarly, for the titration of barium hydroxide (a diacid base) against hydrochloric acid (a monobasic acid) the equation becomes

Ma V a = 2 Mb V b

or                                             Ma V a / Mb V b = 2/1

The end point is indicated by colour change of the indicator or a sudden rise or fall in pH. The pH of the reaction mixture changes during the course of titration.

A graph of the pH versus the volume (V) of titrating solution (titrant) is known as titration curve.

With the help of titration curves we can choose proper indicator for a particular titration.

Let us assume that a titration is carried out by adding alkali solution to an acid solution. If the variation of pH is plotted against the volume of alkali solution added four different types of titration curves are obtained depending upon whether the acid and base are strong or weak (Fig. 27.2).  Fig. 27.2. Titration curves : (A) strong base with strong acid;

(B) weak base with strong acid;

(C) strong base with weak acid;

(D) weak base with weak ac1d.

It may be noted that at the equivalence point there is a sharp increase in pH except in case of titration of a weak base with a weak acid. A proper acid-base indicator is theone whose pH range falls on the vertical portion of the  titration curve. Such an indicator gives a sharp colour change at the end point.

(i) Titration of Strong Acid against Strong Alkali

The graph (A) in Fig. 27.2 shows how pH changes during the titration of 50 cm3 of 0.1 M HCl with 0.1 M NaOH.

NaOH (aq) + HCl(aq) à NaCl(aq) + H2O(l)

The pH of the 0.1 M solution of HCl in the beginning would be 1. As the alkali is added, the pH changes slowly in the beginning. However, at the equivalence point pH changes rapidly from about 3.5 to 10. It can be shown by simple calculations that pH of the solution is 3.7 when 49.8 cm3 of 0.1 M NaOH solution have been added. The pH suddenly changes to 10 after addition of50.1 cm3 of the NaOH solution. Thus, any indicator having pH range between 3.5 and 10 will identify the equivalence point. This means that anyone of phenolphthalein, methyl orange or bromothymol blue could be used as indicator.

(ii) Titration of Strong Acid against Weak Alkali

The graph (B) in Fig. 27.2 shows how pH changes during titration of 50 cm3 of 0.1 M HCl with 0.1 M NH3

HCl(aq) + NH4OH(aq) à NH4Cl(aq) + H2O(l)

In this case the pH changes rapidly from 3.5 to 7.0 at the equivalence point. Methyl orange, methyl red and bromocresol green are suitable indicators for this type of titration. Phenolphthalein is unsuitable because its pH range lies outside the vertical portion of the curve.

(iii) Titration of Weak Acid against Strong Base

The graph (C) in Fig. 27.2 shows how pH changes during titration of 50 cm3 of 0.1 M CHFOOH with 0.1 M NaOH.

CH3COOH(aq) + NaOH(aq) àCH3COOHa(aq) + H2O

The vertical portion of this titration curve lies between pH 7 and pH 10.6. Phenolphthalein is suitable indicator for this titration. Methyl orange is not suitable for this titration because its pH range (3.2 -4.4) is outside the sharp pH change  (7- 10) at the end point.

(iv) Titration of Weak Acid against Weak Base

The graph (D) in Fig. 27.2 represents the titration curve obtained for titration of 50 cm3 of 0.1 M C3COOH with 0.1 M NH3.

CH3COOH(aq)  + NH4OH(aq) à CH3COONH4(aq) + H2O(l)

For this type of titration there is no sharp increase in pH at the equivalence point. No indicator is suitable for this type of titration.