Potentiometric titration curve Differential

Potentiometric titration curves normally are represented by a plot of the indicator-electrode potential as a function of volume of titrant, as indicated in Fig. 4.2. However, there are some advantages if the data are plotted as the first derivative of the indicator potential with respect to volume of titrant (or even as the second derivative). Such titration curves also are indicated in Figure 4.2, and illustrate that a more definite endpoint indication is provided by both differential curves than by the integrated form of the titration curve. Furthermore, titration by repetitive constant-volume increments allows the endpoint to be determined without a plot of the titration curve the endpoint coincides with the condition when the differential potentiometric response per volume increment is a maximum. Likewise, the endpoint can be determined by using the second derivative the latter has distinct advantages in that there is some indication of the approach of the endpoint as the second derivative approaches a positive maximum just prior to the equivalence point before passing through zero. Such a second-derivative response is particularly attractive for automated titration systems that stop at the equivalence point. 

Differential potentiometric titration — means the experimental recording of the first derivative of potential over volume of added titrant of a -> potentiometric titration curve. This can be achieved with a -> retarded electrode as developed by - Maclnnes. In a broader sense this term also covers the mathematical derivation of potentiometric titration curves. 

For the determination of phosphoms chemically bound to cellulose, impregnated samples were washed with water with a modulus of 1 200, then dried under reduced pressure at 40 °C. The washed sample (20-100 mg) was suspended in a potassium chloride solution (0.75 g of K.C1 in 25 ml of water), and was titrated potentiometrically with 0.025 N NaOH. The degree of substitution for phosphoric acid esters (mono-, di-and tri-esters) was determined by titration curve differentiation [17],... 

A potentiometric titration curve often has an inflection point at the PZC (Section 2.6.3). This property has been proposed as a method to determine the PZC [673]. The inflection point method gained some popularity after a publication by Zalac and Kallay [670]. Also, the differential potentiometric titration described in [674] is equivalent to the inflection point method. This method is not recommended by the present author as a standalone method to determine the PZC, but a few results obtained by the inflection point method, usually in combination with other methods, are reported in the tables in Chapter 3 (as Inflection in the Methods columns). In [675], the potentiometric titration curve of one sample had two inflections, and the inflection at the lower pH was assumed to be the PZC. The potentiometric titration curves of other samples had one inflection each. Reference [676] reports an inflection point in the titration curve of niobia at pH 8, which is far from the pHg reported in the literature. A few examples of charging curves without an inflection point or with multiple inflection points are discussed in Section 2.6.3. 

This reaction is characterized by a pK value of — 2.04 0.4 and the buffer number equal to (3 — 0.12. The equivalence point of this neutralization step can be detected more sharply using the differential potentiometric titration curve. 

The curves from the direct and reverse potentiometric titration of metavanadate ions with the Lux bases NaOH and Na2C03 are presented in Fig. 1.2.14a. The neutralization process runs in two stages according to the equations (1.2.87) and (1.2.88), to which two small diffuse pO-drops (bends) in the potentiometric curves correspond. Nevertheless, these bends become apparent on the differential potentiometric titration curve, shown in Fig. 1.2.14b. The reverse titration results in two steps of neutralization, also, that confirms the reversibility of the process of the acid-base neutralization of vanadium(V) oxocompounds in molten Nal. Comparison with the corresponding dependencies for the molten equimolar KCl-NaCl... 

Figure 15.16 Relationship between (a) a simple potentiometric titration curve and its (b) first, and (c) second differentials.

In fact, this has already been illustrated in Fig. 3.73 for the differential electrolytic potentiometric titration of Ce(IV) with Fe(II), both being reversible systems. This technique can be usefully applied, for instance, to the aforementioned KF titration of water and its reverse titration (cf., Verhoef and co-workers preference for bipotentiometric detection) in these instances the potentiometric dead-stop end-point titration and the reversed potentiometric dead-stop end-point titration, respectively, yield curves as depicted in Fig. 3.83. 

Direct potentiometric titration with alkali gave rather flat curves without distinct inflection points 26, 44). Villars 26) concluded that no chemical groups of distinct acidities were present. However, very often the potential becomes constant only several hours after the addition of alkali. Therefore, it was attempted in my laboratory 45-47) to differentiate the acid groups by neutralization with bases of different basicities. The samples were agitated for at least 16 hours with 0.06 N solutions of four bases NaHCOs, NajCO., NaOH, and Na ethoxide. The... 

Another specialized form of potentiometric endpoint detection is the use of dual-polarized electrodes, which consists of two metal pieces of electrode material, usually platinum, through which is imposed a small constant current, usually 2-10 /xA. The scheme of the electric circuit for this kind of titration is presented in Figure 4.1b. The differential potential created by the imposition of the ament is a function of the redox couples present in the titration solution. Examples of the resultant titration curve for three different systems are illustrated in Figure 4.3. In the case of two reversible couples, such as the titration of iron(II) with cerium(IV), curve a results in which there is little potential difference after initiation of the titration up to the equivalence point. Hie titration of arsenic(III) with iodine is representative of an irreversible couple that is titrated with a reversible system. Hence, prior to the equivalence point a large potential difference exists because the passage of current requires decomposition of the solvent for the cathode reaction (Figure 4.3b). Past the equivalence point the potential difference drops to zero because of the presence of both iodine and iodide ion. In contrast, when a reversible couple is titrated with an irreversible couple, the initial potential difference is equal to zero and the large potential difference appears after the equivalence point is reached. 

By differentiating the titration curve twice and then equating the second derivative to zero, it can be shown that for a symmetrical titration curve ( i = the point of maximum slope theoretically coincides with the equivalence point. This conclusion is the basis for potentiometric end-point detection methods. On the other hand, if 2> the titration curve is asymmetrical in the vicinity of the equivalence point, and there is a small titration error if the end point is taken as the inflection point In practice the error from this source is usually insignificant compared with such errors as inexact stoichiometry, slowness of titration reaction, and slowness of attainment of electrode equilibria. 

In all potentiometric titrations, both slope and height of the pH variation determine the detectable limit of the amount and strength of functional groups. In differential curves, this is expressed by the height and sharpness of the peaks in proximity of the equivalence points. In particular, in the titration of weak acids or bases, such as the surface functional groups of carbon, at halfway to the inflection point the concentration is almost equal to the functional groups to be titrated. For example, for a base -C-OH ... 

For an acid titrated halfway to its equivalent point, pH = pKa. For mixtures of acids and bases, and hence for carbons having functional groups of different acid or basic strength, this holds true as well. For weak acid and base groups, the effect of water dissociation is significant around pH = 7. Therefore, a simple potentiometric titration can give information about the dissociation constants and neutralization equivalence of the carbon. In several cases these indications can be sufficient to determine the nature of the functional groups and provide a comprehensive description of the behavior of carbon in terms of acidity and basicity. A differential plot of the titration curve can be considered in the same way as a conventional absorption spectrum of the sample. Acidity or basicity constants are then calculated at half-titration, as pH = pKw — pKb for a base and pH = pKa for an acid. 

Computerized method provides convenient and accurate determination of the ionization constant in aqueous solution and of the apparent ionization constant in the presence of octanol. From these parameters, partition coefficients and apparent partition coefficients are easily calculated and agree with data reported using the shaker technique or HPLC. The curve-fitting method has been applied to the differential titration technique in which the solvent curve is subtracted from the solution curve before calculations are begun. This method has been applied to the potentiometric titration of aqueous solutions of the salts of bases with very low solubility in water. 

Valik19 made differential potentiometric titrations of aspartic acid, one series of results being given in curve (c) of Fig. 6. The volume of solution of alkali necessary to titrate tlie second acid dissociation for which the ionization constant is 2.5 X 10"10 should be exactly equal to that for the first unless there is a difference between the potentiometric and stoichiometric end points. Within the rather large limit of error, this was found to be true, but the end point could not be located with accuracy due to the flatness of the curve, as shown above. Differences between the stoichiometric and potentiometric end points are predicted for titrations of weak acids or weak bases. Such a difference increases the weaker the acid or base, but the difficulty of locating the end point also increases. It may be safely concluded that within the accuracy to which the potentiometric end point of a titration can be established it is identical with the stoichiometric end point. 

The sequence of some points from the initial section of the potentiometric curve (namely, points 1 -4) is characterized by a monotonous pP eo decrease from 6.06 to 5.12, whereas the pA Meo values remain practically constant. This section of the titration curve corresponds to a sharp e.m.f. decrease at low initial concentrations of the titrant (see Fig. 3.6.3, the titration and differential titration curves). From the above-said it is seen that the PbO solution is unsaturated and the concentration constant of PbO can be estimated from the data of this section (points 2-4) as pXpb0 = 3.29 0.04. 

Fig. 3.6.3. The dependence of E vs initial molality of base-titrant 2NaOH (m -) at the potentiometric titration of Pb2+ (0.051 mol kg-1) in the molten KC1 — NaCl equimolar mixture at 700 °C (1), and the corresponding differential titration curve (2). The points in the titration curve are numbered according to the data in Table 3.6.1.

Grunwald s differential titration method can also give results of high precision provided the slope of the titration curve at the equivalence point is not too large. The results of Ritchie and Heffley s study of the ionisation of some picolinium ions by this method are given in Appendix 3.5.3. A direct, rather than differential, potentiometric titration had to be used for derivatives of bicyclo[2.2.2]octane-l-carboxylic acid these results are given in Appendix 3.5.4. 

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