3 Titrimetric and chemical analysis methods
Direct acid/base titrations in the aqueous phase
Titrations of the salts of weak bases in mixed aqueous/non-aqueous media
Indirect titrations in the aqueous phase
Karl Fischer titration (coulometric end-point detection)
Automation of wet chemical methods
Principles
An analyte is chemically reacted with a standard solution of a reagent of precisely known concentration or with a concentration that can be precisely determined. The amount of a standard solution required to completely react with all of the sample is used to estimate the purity of the sample.
Applications
• Provide standard pharmacopoeial methods for the assay of unformulated drugs and excipients and some formulated drugs, e.g. those that lack a strong chromophore.
• Used for standardisations of raw materials and intermediates used in drug synthesis in industry. Suppliers of raw materials may provide these materials at a specified purity which has been assayed titrimetrically to a pharmacopoeial standard.
• Certain specialist titrations, such as the Karl Fischer titration used to estimate water content, are widely used in the pharmaceutical industry.
Advantages
• Capable of a higher degree of precision and accuracy than instrumental methods of analysis, with precisions of ca ± 0.1% being achievable.
• The methods are generally robust.
• Cheap to perform and do not require specialised apparatus.
• They are absolute methods and are not dependent on the calibration of an instrument.
Introduction
Titrimetric methods are still widely used in pharmaceutical analysis because of their robustness, cheapness and capability for high precision. The only requirement of an analytical method that they lack is specificity. This chapter covers the theoretical basis of most of the commonly used methods; the practical aspects of titrations have been covered thoroughly by other textbooks.1,2
Instrumentation and reagents
Glassware
The manufacturers’ tolerances for the volumes of a number of items of glassware are given in Chapter 1. The larger the volume measure the smaller the tolerance percentage is of the nominal volume. Thus, for a Grade A 1 ml pipette the volume is within ± 0.7% of the nominal volume, whereas for the 5 ml pipette the volume is within ± 0.3% of the nominal volume. If greater accuracy than those guaranteed by the tolerances is required, then the glassware has to be calibrated by repeated weighing of the volume of water contained or delivered by the item of glassware. This exercise is also useful for judging how good one’s ability to use a pipette is, since weighing of the volumes of water dispensed correctly several times from the same pipette should give weights that agree closely.
Primary standards and standard solutions
Primary standards are stable chemical compounds that are available in high purity and which can be used to standardise the standard solutions used in titrations. Titrants such as sodium hydroxide or hydrochloric acid cannot be considered as primary standards since their purity is quite variable. So, for instance, sodium hydroxide standard solution may be standardised against potassium hydrogen phthalate, which is available in high purity. The standardised sodium hydroxide solution (secondary standard) may then be used to standardise a standard solution of hydrochloric acid. Table 3.1 lists some commonly used primary standards and their uses.
Table 3.1 Primary standards and their uses
Primary standard | Uses |
Potassium hydrogen phthalate | Standardisation of sodium hydroxide solution |
Potassium hydrogen phthalate | Standardisation of acetous perchloric acid |
Potassium iodate | Standardisation of sodium thiosulphate solution through generation of iodine |
Anhydrous sodium carbonate | Standardisation of hydrochloric acid |
Zinc metal | Standardisation of EDTA solution |
EDTA, Ethylenediamine tetracetic acid.
Direct acid/base titrations in the aqueous phase
Strong acid/strong base titrations
Figure 3.1 shows the titration curve obtained from the titration of a strong acid with a strong base. The pH remains low until just before the equivalence point, when it rises rapidly to a high value. In many titrations a coloured indicator is used, although electrochemical methods of end-point detection are also used. An indicator is a weak acid or base that changes colour between its ionised and un-ionised forms; the useful range for an indicator is 1 pH either side of its pKa value. For example, phenolphthalein (PP) pKa 9.4 (colour changes between pH 8.4 and pH 10.4) undergoes a structural rearrangement as a proton is removed from one of its phenol groups when the pH rises, and this causes the colour change (Fig. 3.2). Methyl orange (MO) pKa 3.7 (colour changes between pH 2.7 and pH 4.7) undergoes a similar pH-dependent structural change. Both these indicators fall within the range of the inflection of the strong acid/strong base titration curve.
There are only a few direct strong acid/strong base titrations carried out in pharmacopoeial assays.
Strong acid/strong base titrations are used in pharmacopoeial assays of: perchloric acid, hydrochloric acid, sulphuric acid and thiamine hydrochloride.
Weak acid/strong base and weak base/strong acid titrations
On addition of a small volume of the strong acid or strong base to a solution of the weak base or weak acid, the pH rises or falls rapidly to about 1 pH unit below or above the pKa value of the acid or base. Often a water-miscible organic solvent such as ethanol is used to dissolve the analyte prior to the addition of the aqueous titrant.
Figure 3.3 shows a plot of pH when 1 M NaOH is added to 25 ml of a 1 M solution of the weak acid aspirin.

Fig. 3.3 Titration curve for 25 ml of a 1.0 M solution of aspirin (pKa 3.5) titrated with 1.0 M NaOH.
In the case of aspirin, the choice of indicator is restricted by where the inflection in its titration curve lies; PP is suitable as an indicator whereas MO is not.
In the example of the titration of quinine with hydrochloric acid (Fig. 3.4), MO is a suitable indicator because it falls within the inflection of the titration curve whereas PP is not suitable.
Some acids or bases can donate or accept more than one proton, i.e. 1 mole of analyte is equivalent to more than 1 mole of titrant. If the pKa values of any acidic or basic groups differ by more than ca 4, then the compound will have more than one inflection in its titration curve. Sodium carbonate is a salt of carbonic acid and it can accept two protons. The pKa values of carbonate and bicarbonate are sufficiently different (pKa 10.32 and 6.38) for there to be two inflections in the titration curve. The two stages in the titration are:
Which of these indicators could be used in the titration of aspirin and which could be used in the titration of quinine?
In a titration of sodium carbonate, the first inflection is indicated by PP and the whole titration by MO (Fig. 3.5).
A sample containing 25.14 g of neutral salts, glucose and a sodium carbonate/bicarbonate buffer was dissolved in 100 ml of water. A 25 ml aliquot of the resultant solution required 20.35 ml of 0.0987 M HCl when titrated to the PP end-point. A second 25 ml aliquot was titrated to the MO end-point and required 56.75 ml of the acid. Calculate the percentage of Na2CO3 (molecular weight 106) and NaHCO3 (molecular weight 84) in the sample.
How many inflections do the following substances have in their titration curves when titrated with a strong base? Draw the predominant forms of these substances which would exist at pH 14.
Answers: oxalic acid 1, fumaric acid 1, citric acid 1, phenylalanine 2
Weak acid/strong base titration is used in the pharmacopoeial assays of: benzoic acid, citric acid, chlorambucil injection, mustine injection, nicotinic acid tablets and undecanoic acid.
Titrations of the salts of weak bases in mixed aqueous/non-aqueous media
Non-aqueous titrations, which are described below, are still used for the analysis of acids and salts of weak bases. However, in many instances it is simpler to titrate weak bases as their salts in a mixed non-aqueous/aqueous medium using potentiometric end-point detection. The protonated base behaves as a weak acid when titrated with sodium hydroxide.
The advantage of adding a water-miscible solvent such as methanol to the titration is twofold. Firstly, the addition of the organic solvent effectively lowers the pKa value of the base, since the ionised form of the base is less stable in a mixed solvent system where the dielectric constant is lower, and, secondly, the organic solvent keeps the base in solution as it is converted to its free base form during the titration. An example of this can be seen for the titration of lidocaine (lignocaine) hydrochloride in methanol/water mixtures (Fig. 3.6), where the size of the inflection in the titration curve increases when moving from 30% methanol to 70% methanol. This is a very convenient procedure for many organic bases.
Indirect titrations in the aqueous phase
These can be of the strong acid/strong base, weak acid/strong base or weak base/strong acid type. The more common examples are weak acid/strong base.
Estimation of esters by back titration
Excess of sodium hydroxide is added to the ester. The following reaction occurs:
The XSNaOH is back titrated with HCl using PP as an indicator.
This procedure is used in pharmacopoeial assays of: benzyl benzoate, dimethyl phthalate, ethyl oleate, methyl salicylate, cetostearyl alcohol, emulsifying wax, castor oil, arachis oil, cod liver oil and coconut oil.
Saponification value
The assay of fixed oils provides a special case of ester hydrolysis since they are triesters of glycerol. The saponification value for a fixed oil is the number of mg of potassium hydroxide (KOH) equivalent to 1 g of oil. A high value means rancidity, a low value possible adulteration with mineral oil. Almost all edible oils have a saponification value between 188 and 196. Hydrolysis of the fixed oil is carried out with ethanolic KOH.
This procedure is used in the pharmacopoeial assays of: castor oil, cod liver oil, cotton seed oil, almond oil and sesame seed oil.
Acid values are also determined for fixed oils. The acid value for a substance is the number of mg of KOH required to neutralise 1 g of the test substance when it is titrated with 0.1 M ethanolic KOH to a PP end-point. This value is quoted for many fixed oils in order to eliminate rancid oils, which contain large amounts of free fatty acid. Typically acid values for fixed oils are in the range of 1–2.
The following data were obtained for a sample of cod liver oil:
Weight of oil taken for analysis = 2.398 g
Ethanolic KOH (molecular weight 56.1) used in determination = 0.986 M
Amount of ethanolic KOH used for hydrolysis and in blank titration = 25 ml
Amount of 0.470 M HCl required to neutralise excess KOH = 35.2 ml
Amount of 0.470 M HCl required in the titration of blank = 52.3 ml
Calculation
Amount of KOH used initially = 52.3 × 0.47 = 24.6 mmole
Amount of HCl required to neutralise excess KOH = 35.20 × 0.470 = 16.5 mmole
Amount of KOH used in hydrolysis = 24.6 – 16.5 = 8.1 mmole × molecular weight = mg
Amount of KOH used in the hydrolysis = 8.1 × 56.1 = 454.0 mg
Amount of KOH/g of fixed oil used in the hydrolysis = 454/2.398 = 189.3 mg
Calculate the saponification value of a sample of castor oil from the following data:
• Weight of oil taken for analysis = 2.535 g
• Ethanolic KOH used in the hydrolysis = 1.03 M
• Amount of KOH used in hydrolysis = 25 ml
• Amount of 0.514 M HCl required to neutralise excess KOH = 34.2 ml
• Amount of 0.514 M HCl required in the titration of blank = 50.2 ml.
Estimation of alcohols and hydroxyl values by reaction with acetic anhydride (AA)
Alcohols can be determined by reaction with excess acetic anhydride (AA) (Fig. 3.7). This is a useful titrimetric method because the alcohol group is difficult to estimate by any other means.
The excess AA and acetic acid may be back titrated with NaOH using PP as an indicator.
In a related assay, a hydroxyl value is determined for a fixed oil. A 1:3 mixture of AA in pyridine is used in the determination; the pyridine is present as a catalyst. The hydroxyl value may be defined as:
The number of mg of KOH required to neutralise a blank titration of the reagents – the number of mg KOH required to neutralise excess AA + acetic acid after reaction with 1 g of the test substance.
The following data were obtained for a sample of castor oil:
Weight of castor oil taken for analysis = 1.648 g
Volume of acetic anhydride used for the reaction = 5 ml
Molarity of ethanolic KOH used to neutralise the excess AA + acetic acid = 0.505 M
Volume of ethanolic KOH required to titrate 5 ml of reagent = 53.5 ml
Volume of ethanolic KOH required to neutralise excess AA + acetic acid after reaction with the castor oil = 44.6 ml.
Number of mmoles of KOH used in the blank titration = 53.5 × 0.505 = 27.0
Number of mg of KOH used in the titration of the blank = 27.0 × 56.1 = 1515
Number of mmoles of KOH used in titration of AA + acetic acid = 44.6 × 0.505 = 22.5
Number of mg KOH used in titration of excess AA + acetic acid = 22.5 × 56.1 = 1262
To be completely accurate, the acid value for the fixed oil should be added to the hydroxyl value, since any free acid in the oil will titrate along with the excess reagents, giving a small overestimate. The acid value for castor oil is about 2.0, giving a hydroxyl value for the above sample of 156.
Reaction with acetic anhydride is used in pharmacopoeial assays of benzyl alcohol and dienestrol, and determination of hydroxyl values of castor oil, cetosteryl alcohol and cetomacrogol.
Non-aqueous titrations
Theory
Non-aqueous titration is the most common titrimetric procedure used in pharmacopoeial assays and serves a double purpose, as it is suitable for the titration of very weak acids and bases and provides a solvent in which organic compounds are soluble. The most commonly used procedure is the titration of organic bases with perchloric acid in acetic acid. These assays sometimes take some perfecting in terms of being able to judge the end-point precisely.
The theory is, very briefly, as follows: water behaves as both a weak acid and a weak base; thus, in an aqueous environment, it can compete effectively with very weak acids and bases with regard to proton donation and acceptance, as shown in Figure 3.8.
The effect of this is that the inflection in the titration curves for very weak acids and very weak bases is small, because they approach the pH limits in water of 14 and 0 respectively, thus making end-point detection more difficult. A general rule is that bases with pKa < 7 or acids with pKa > 7 cannot be determined accurately in aqueous solution. Various organic solvents may be used to replace water since they compete less effectively with the analyte for proton donation or acceptance.
Non-aqueous titration of weak bases
Acetic acid is a very weak proton acceptor and thus does not compete effectively with weak bases for protons. Only very strong acids will protonate acetic acid appreciably according to the equation shown below:
Perchloric acid is the strongest of the common acids in acetic acid solution, and the titration medium usually used for non-aqueous titration of bases is perchloric acid in acetic acid. Addition of acetic anhydride, which hydrolyses to acetic acid, is used to remove water from aqueous perchloric acid. Weak bases compete very effectively with acetic acid for protons. Oracet blue, quinalidine red and crystal violet (very weak bases) are used as indicators in this type of titration. A typical analysis is shown in Figure 3.9 for L-3,4-dihydroxyphenylalanine (LDOPA).
When the base is in the form of a salt of a weak acid, removal of an anionic counter ion prior to titration is not necessary, e.g. for salts of bases with weak acids such as tartrate, acetate or succinate. However, when a base is in the form of a chloride or bromide salt, the counter ion has to be removed prior to titration. This is achieved by the addition of mercuric acetate; the liberated acetate is then titrated with acetous perchloric acid. This is illustrated in Figure 3.10 for the example of phenylephrine HCl.

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