Detection of the Equivalence Point

The usefulness of the fundamental reaction of direct and indirect lodometries has its roots, at least in part, in the fact that it is accompanied by the disappearance or appearance of the yellow-brown color in the solution due to tri-iodide ions. Tri-iodide ions are their proper indicator. Hence, its equivalence point detection is particularly easy. In some difficult cases, starch may be used. The partitioning of iodine into an organic phase at the equivalence point may also be used. Finally, some internal indicators of intermediary standard potential values such as variamine blue (E° 0.60 V) may also be used. The difficult cases are those in which the tri-iodide coloration is masked by that of the solution. 

The fundamental reaction of lodometries consists of the action of iodine or tri-iodide ions on thiosulfate ions 8203 giving tetrathionate ions 8406 according to the scheme 

Thiosulfate and tetrathionate ions are colorless. The half-equilibrium S40e /S203 obeys the equation 

Thiosulfate ions are a good reducing species. A normal solution of thiosulfate contains one mole per liter since the half-redox reaction involving it exchanges one electron for one 8203 molecule. Let s recall that in thiosulfate ions, one of the sulfur atoms exhibits the -l-IV oxidation state, while the other sulfur exhibits the null value. From another standpoint, we can consider that each sulfur atom exhibits the value -l-II. Likewise, in tetrathionate ions, we can consider that, on average, the oxidation state of each sulfur atom is 2.5. If we consider the stmcture of the tetrathionate ion  

The iodine/thiosulfate reaction can be used only in a slightly acidic medium, that is, in the approximate range 2 pH 5. In a strongly acidic medium (pH 2), thiosulfuric acid, which forms in these conditions, decomposes into sulfurous acid and sulfur according to the reactions 

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Thus pFe2+ changes from 4.3 to 10 between 0.1 per cent before and 0.1 per cent after the stoichiometric end point. These quantities are of importance in connection with the use of indicators for the detection of the equivalence point. 

Procedure (copper in crystallised copper sulphate). Weigh out accurately about 3.1 g of copper sulphate crystals, dissolve in water, and make up to 250 mL in a graduated flask. Shake well. Pipette 50 mL of this solution into a small beaker, add an equal volume of ca AM hydrochloric acid. Pass this solution through a silver reductor at the rate of 25 mL min i, and collect the filtrate in a 500 mL conical flask charged with 20 mL 0.5M iron(III) ammonium sulphate solution (prepared by dissolving the appropriate quantity of the analytical grade iron(III) salt in 0.5M sulphuric acid). Wash the reductor column with six 25 mL portions of 2M hydrochloric acid. Add 1 drop of ferroin indicator or 0.5 mL N-phenylanthranilic acid, and titrate with 0.1 M cerium(IV) sulphate solution. The end point is sharp, and the colour imparted by the Cu2+ ions does not interfere with the detection of the equivalence point. 

Recently, Mazzocchin et al. have studied several titration methods for determining relatively large amounts of technetium. The most precise results have been obtained by coulometric titration of TcO ions With electrogenerated tin (II) according to the procedure suggested by Bard and Lingaiie . The supporting electrolyte consists of 2.5 M sodium bromide, 0.15 M stannic chloride and 0.2 M hydrochloric acid. The titration reaction is very fast and currents up to 40 mA can readily be employed in the detection of the equivalence point. 

Several titration methods were studied for determining Tc(IV) or Tc(VII) in the concentration range of 10 -10 M. Tc(IV) was titrated volumctrically with Ce(TV) using potcntiomctric, biampcrometric, and bipotentiomctric detection of the equivalence point. The most precise results were obtained by coulomctric titration of TcOj... 

A titration in which measurement of the current flowing at a voltammetric indicator electrode is used for detection of the equivalence point is termed an amperometric titration. The current measured is almost always a limiting current which is proportional to concentration, and can be due to the substance titrated, to the titrant itself, to a product of the reaction, or to any two of these—depending on the potential of the electrode and the electrochemical characteristics of the chemical substances involved. The titration curve is a plot of the limiting current, corrected for dilution by the reagent and, if necessary, for any residual current, as a function of the volume of titrant. Ideally, the titration curve consists of two linear segments which intersect at the equivalence point. 

Advantages and Limitations of Radiometric Titrations. Radiometric detection of the equivalence point is a general method that does not depend on the chemical reaction employed. This contrasts with other methods of detection, which depend on specific chemical or physical transitions at the equivalence point. Amperometric titrations are applicable only to electrochemically active systems conductometric titrations apply only to ionic solutions, and so on. In principle, any titration system in which a phase separation can be effected is amenable to radiometric detection, provided there exist suitable radioactive labels. The major limitation of the method is the requirement for phase separation. In precipitation titrations, the phase separation is automatic and the method is well suited to this class of titrations. For other classes of titrations, special phase-separation methods, such as solvent extraction, need to be applied. At the present time, the method suffers from a lack of phase-separation techniques suitable for continuous monitoring of the titration curves. 

On the basis of results obtained the possibility of thorium determination in the presence of five-fold excess of rare earths was stated by means of HMDTA titration and h.f.t. detection of the equivalent point. 

As in any titration, a suitable method of detection of the equivalence point is necessary. In general, it can be said that any of the techniques that are useful in classical volumetric titrimetry are also applicable to coulometric titrations. As noted above, Szebelledy and Somogyi used traditional color-change indicators to determine their end points. 

A large number of metallochromic indicators have been proposed for the detection of the equivalence point for the titration of the rare earths with EDTA and other polydentate ligands. These include Alizarin Red, Arsenazo I, Xylenol Orange, Eriochrome Black T, and Murexide to name only a few. The structure, conditions under which these indicators can be used, possible interferences, and references to the original papers are summarized by Aladjem (1970), p. 287. 

The gradual change near the equivalence point must be ascribed to the fact that the neutralization reaction is too equilibrated. This is the case when the couples HAi/Ai and HA2/A2 are too close to each other on the acidity scale. Reciprocally, when they are suflBciently far from each other, we can expect to achieve an accurate titration. The example of the titration of acetic acid (pATa=4.75) by ammonia pAra(NH4 ) = 9.21] is interesting to consider since it is on the border of satisfactory and nonsatisfactory titrations. Indeed, with 10 mol/L—solutions and with a pH-metric detection of the equivalence point, the titration error is about 0.5%. It is higher than that due to the graduation of the glassware (0.2%). However, it remains acceptable. The lack of precision is higher, by far, when neutralization indicators are used. 

A variation on these titrations consists of adding hydrochloric acid to the hydroalcoholic solution of the solute and then titrating them with a sodium hydroxide solution. The equivalence point is detected by pH-metry. Ephedrine, bupivacaine, de-sipramine, chlorprothixene, and amantadine hydrochlorides are titrated in this way. Using pH-metry is necessary in this variation since we must detect the successive equivalence points with an optimal precision. The first equivalence point corresponds to the end of the neutralization of hydrochloric acid, the second to that of the cation. The addition of hydrochloric acid facilitates the detection of the beginning of the cation neutralization reaction. It can be inferred from all these results that the addition of ethanol to water permits a satisfactory detection of the equivalence point of this kind of products, even of those that exhibit the higher pK values, such as the amantadine hydrochloride (pK = 10.68). This means that the reaction between the base of the titrant couple and the cation is more quantitative in these mixtures than in water. In other words, the couple BH+/B is farther from the couple H20/0H in these mixtures than it is in water. Actually, the titrant is a mixture of the couple H2O/OH- andC2H50H/C2Hs0. ... 

The absolute titration error (by definition due to the false detection of the equivalence point) depends on the difference in formal potentials AE°. The last expression clearly shows that when AE° is very high, the error tends toward zero since the numerator itself tends toward zero and the denominator simultaneously tends toward unity. For example, when AE° = 0.24 V and when the color redox indicator changes for the potential value Ffp = (Fep — 0.01)V, the relative error expressed in percentages is about —0.67%. When AE° = 0.30 V, with the same difference Ffp — Fep, the error decreases to —0.21%. In the case of the titration of Fe + by Ce, the titration error remains about —0.01 V, even if the indicator color changes for a potential value weaker than that at the equivalence point by a difference as great as 0.20 V. This remarkable result must be attributed to the great difference AE° (AF° = 0.76 V). 

The detection of the equivalence point is often achieved by adding some drops of carbon tetrachloride or chloroform to the aqueous solution in the titration vessel. The equivalence point is detected by the disappearance of the purple coloration of the organic phase, which was due to the presence of iodine. (This is further proof of the sequence of reactions given above.) The color of an iodine monochloride is pale yellow. 

Under this heading, titration reactions themselves are not redox ones or, in any case if they are, are not implicated in the detection of the equivalence point. One example is given by the method sometimes called nitritometry evoked in connection with the indirect iodometry. Nitrous acid in excess appearing once the equivalence point is reached during the titration of aromatic primary amines is detected by the formation of bromine. Bromide ions, added in the medium before the beginning of the titration, are indeed oxidized by nitrous acid in excess. The titration reaction itself is... 

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