Potentiometric titration curve

The most obvious sensor for an acid-base titration is a pH electrode.For example, Table 9.5 lists values for the pH and volume of titrant obtained during the titration of a weak acid with NaOH. The resulting titration curve, which is called a potentiometric titration curve, is shown in Figure 9.13a. The simplest method for finding the end point is to visually locate the inflection point of the titration curve. This is also the least accurate method, particularly if the titration curve s slope at the equivalence point is small. 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

Dilute solutions of nominally 0.001 M NaOH and HGl are used to demonstrate the effect of an indicator s color transition range on titration error. Potentiometric titration curves are measured, and the indicator s color transition range is noted. Titration errors are calculated using the volume of titrant needed to effect the first color change and for a complete color change. 

Potentiometric titration curves are used to determine the molecular weight and fQ or for weak acid or weak base analytes. The analysis is accomplished using a nonlinear least squares fit to the potentiometric curve. The appropriate master equation can be provided, or its derivation can be left as a challenge. 

The titration of a mixture ofp-nitrophenol (pfQ = 7.0) and m-nitrophenol pK = 8.3) can be followed spectrophotometrically. Neither acid absorbs at a wavelength of 545 nm, but their respective conjugate bases do absorb at this wavelength. The m-nitrophenolate ion has a greater absorbance than an equimolar solution of the p-nitrophenolate ion. Sketch the spectrophotometric titration curve for a 50.00-mL mixture consisting of 0.0500 M p-nitrophenol and 0.0500 M m-nitrophenol with 0.100 M NaOH, and compare the curve with the expected potentiometric titration curves. 

The potentiometric titration curve shown here was recorded on a 0.4300-g sample of a purified amino acid that was dissolved in 50.00 ml of water and titrated with 0.1036 M NaOH. Identify the amino acid from the possibilities listed in the following table. 

Potentiometric titration curves The procedure involves the addition of a salt of a weak acid to the resin and the determination of the pH of the equilibrated solution. Table 9 shows the pK values of the OH groups and dissociation constants of the studied resin. The first ionization occurs at a pH slightly higher than that of sul-... 

Fig. 9. Potentiometric titration curves for branched PAAs obtained by SCVCP of f-BuA with the inimer 1, followed by hydrolysis y=100 (O), 10 (A), 2.5 ( , ) in aqueous solutions. The filled symbols ( ) indicate the region where PAA was insoluble in water. (Reproduced with permission from [31], Copyright 2001 American Chemical Society.)...

The plot of pH against titrant volume added is called a potentiometric titration curve. The latter curve is usually transformed into a Bjerrum plot [8, 24, 27], for better visual indication of overlapping pKiS or for pffjS below 3 or above 10. The actual values of pKa are determined by weighted nonlinear regression analysis [25-27]. 

With a low constant current -1 (see Fig. 3.71) one obtains the same type of curve but its position is slightly higher and the potential falls just beyond the equivalence point (see Fig. 3.72, anodic curve -1). In order to minimize the aforementioned deviations from the equivalence point, I should be taken as low as possible. Now, it will be clear that the zero current line (abscissa) in Fig. 3.71 yields the well known non-faradaic potentiometric titration curve (B B in Fig. 2.22) with the correct equivalence point at 1.107 V this means that, when two electroactive redox systems are involved, there is no real need for constant-current potentiometry, whereas this technique becomes of major advantage... 

Fig. 3.72. Constant current potentiometric titration curves obtained from Fig. 3.71. 

Subsequently, Bos and Dahmen used in m-cresol65 (e = 12.29 at 25° C) a potentiometric titration method combined with conductometry. Essential precautions were the preparation of water-free m-cresol (<0.01% of water), the use of a genuine Bronsted base B, e.g., tetramethylguanidine (TMG), and the application of a glass electrode combined with an Ag-AgCl reference electrode filled with a saturated solution of Me4NCl in m-cresol. The ion product of the self-dissociation of m-cresol, Ks, was determined from the part beyond the equivalence point of the potentiometric titration curve of HBr with TMG comparison with titration curves calculated with various Ka values showed the best fit for Ks = 2 10 19... 

Fig. 4.12. Potentiometric titration curves of benzoic acid in pyridine.

In routine analysis, often a one-dimensional so-called end-point titration can be automatically carried out up to a pre-set pH or potential value and with a previously chosen overall titration velocity in order to avoid overshoot, the inflection point should be sufficiently sharp and the titrant delivery must automatically diminish on the approach to that point in order to maintain equilibrium, and stop in time at the pre-set value. For instance, the Metrohm 526 end-point titrator changes both the dosing pulse length and its velocity by means of a pulse regulator in accordance with the course of the titration curve in fact, the instrument follows the titration two-dimensionally, but finally reports only a one-dimensional result. The Radiometer ETS 822 end-point titration system offers similar possibilities. However, automated titrations mostly represent examples of a two-dimensional so-called eqilibrium titration, where the titration velocity is inversely proportional to the steepness of the potentiometric titration curve hence the first derivative of the curve can usually also be recorded as a more accurate means of determining the inflection... 

Less complex techniques have been reported to be useful to study the acidic and alkaline treatment processes of biosorbents and the role of carboxyl and carboxylate groups in metal adsorption. Rakhshaee and coworkers101 used potentiometric titration curves to assess the content of such groups in L. minor biomass treated with NaOH and HC1. The results showed an increase (up to 25%) in the adsorption of Hg(II), Cr(III), Cr(VI), and Cu(II) with NaOH-treated biomass as a consequence of an increase of -COO- groups (0.92-2.42 mmol/g). On the contrary, the -COOH groups increase observed (1.50-2.41 mmol/g) due to the acidic treatment led to a decrease in the metal ions uptake (up to 33%) despite activation by the chloride salts. 

Potentiometric titration curves, (a) Normal curve, (b) First derivative curve. 

Figure 16.1 Potentiometric Titration Curves of 25 ml of 0.01 M Sodium Fluoride Vs 0.01 M Lanthanum...

This agreement is considered to be quite good when allowance is made for the fact that these are independently measured runs at concentrations varying by a ratio of 5000 to 1 The 10 ppm run at 120°C is probably in error due to a trace contaminant in the vapor samples observed in the potentiometric titration curve. This problem was not observed at 80°C. 

Abstract Titration of weak bases in non-aqueous solvents can provide valuable information about these weak bases. Some primary amines 1-aminobutane, 1-aminopropane, 2-aminoheptane, aminocyclohexane, 3-amino-l-phenylbutane were titrated with hydrochloric acid in toluene solvent. All the primary amines gave very well-shaped potentiometric titration curves. The same titrations were done with hydrochloric acid in methanol solvent to show the effect of amphiprotic solvent in the titrations with hydrochloric acid. 

Figure 4.3 Potentiometric titration curve obtained by dissolving 200 mg of dishwashing fluid in water and titrating against hexadecylpyridinium chloride solution, employing a zeolite-polydimethylsiloxane (NaY-PDMS) modified electrode (cf. SAQ 4.3). From Matysik, S Matysik, F.-M., Mattusch, J. and Einicke, W.-D., Electroanalysis, 10, 98-102, (1998), Wiley-VCH, 1998. Reproduced by permission of Wiley-VCH.

The potentiometric titration curves of gels, which relate the pH of the exterior solution to the degree of ionization of the gel, resemble the titration curves of monofunctional acids or bases. However, the dissociation constants differ, often by two orders of magnitude, from the expected value for the functional group, and the slope of the curves is not the usual one. Addition of neutral salt changes the picture markedly and brings the curves closer to expectation. In the case of weak or medium... 

The experimental procedures of BET, TGA, and XRD have been described in detail elsewhere [8]. The interlayer d-spacing from XRD pattern is determined by the angle of ((X)l) reflection. For the measurement of ion-exchange capacity, SO mg of sample was suspended with 10 cm of NaCl solution (0.1 N), and the pH values were measured with addition of NaOH solution (0.1 N) to obtain the potentiometric titration curve at rocnn temperature. 

Comparison of the potentiometric titration curves of milk and CCP-free milk shows more reactive organic phosphate groups in the latter, suggesting that CCP is attached to the organic casein phosphate groups, thereby rendering them less active. 

Fig. 3.7 Potentiometric titration curve of a mixture of acids in MIBK [21]. Titrated with 0.2 M Bu4NOH using a glass electrode-Pt electrode system.

Figure 4 Typical potentiometric titration curves for the precipitation of Ni(N03)2 (1), A1(N0 3) 3 (2), and a mixture of Ni(N03) 2 and A1(N03)3(3) using Na2C03 as precipitant. The concentrations used are typical of those used in catalyst preparation...

In the use of potentiometry for the evaluation of stability constants for complex ions, the expressions can become extremely complicated if multiequilibria are present. For a simple one-to-one complex a direct potentiometric titration curve again provides die most satisfactory route to an accurate evaluation of the constant. The curve looks similar to that for an acid-base titration, and the appropriate point to pick is the half-equivalence point. If the complex is extremely stable, then die amount of free metal ion at this point on die dtration curve (ligand titrated with metal ion) is sufficiently low that it can be disregarded. If not, it must be handled in a way similar to the first point on the titration curve for phosphoric acid. Assuming that it is a stable complex, at the first half-equivalence point the concentration of complexed metal ion will be equivalent to that of the free ligand. The potential will give a direct measure of the free metal ion and allow the stability constant for the complex to be evaluated at the half-equivalence point ... 

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. 

Figure 4.2 Potentiometric titration curves (a) experimental titration data (b) first derivative of curve a (c) second derivative of curve a.

Figure 4.3 Dual-polarized electrode potentiometric titration curves (a) titration of Fe(II) by Ce(TV) (b) titration of As(III) by I2.

Potentiometric titration curves of AiSA triblock copolyampholytes in THF/water (2 5 weight/weight) are shown in Fig. 16 for three copolymers possessing identical mole fractions of hydrophobic polystyrene but different amounts of acidic and basic end blocks. 

The potentiometric titration curves of several poly(electrolyte)s, among which PVA and PEI (branched), have been extensively studied by Bloys von Treslong54). He assumes that in the protonation process, the interactions between the various aminic groups present in the macromolecule may result in a charge distribution which, at partial neutralization, is not random. 

Fig. 13.2. Methods for determining the equivalence point of a potentiometric titration curve (including acid-base titrations), (a) First derivative (b) Second derivative (c) Gran plot for titration of a strong acid with a strong base Vx is the initial volume of acid and V the volume of base added.

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