Activity potentiometric titration curves

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. 

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. 

Potentiometric titration curves are obtained by plotting the potential of the indicator electrode (in practice the e.m.f. of the cell) against the volume of the titrant. In acid-base titrations, the pH value is usually plotted instead of the potential. The logarithmic shape of the titration curve is a consequence of the logarithmic dependence of activity or activity ratio of the species participating in the titration reaction according to the Nernst equation ... 

A Nernst equation may be written for every galvanic cell at equilibrium. Therefore the equation is the basis of all thermodynamic applications of potentiometry (i.e. measurement of open-circuit cell potentials by means of a potentiometer or other zero-current device). Cells may be constructed and appropriate Nernst equations written to find, for example, the dissociation constant of water, and many electrolyte activity coefficients and stability and solubilit,v constants. Potentiometric titration curves are also interpieted by means of the appropriate Nernst equation. 

Despite the utility of the additivity rule, without supporting data occasionally it can be difficult to narrow down possible solution structures to one possibility based on EPR data alone. EPR is frequently paired with other techniques, most often po-tentiometry [41,42,44-48], to detect the number of species and to use the additivity rule to give insights into the first coordination sphere donor atoms of the moieties in solution. This information can then be used in the fitting of potentiometric titration curves, which reports on the absolute and relative thermodynamic stabilities of species in solution. EPR spectroscopy is also used as a complementary technique to V NMR [49-51], allowing for characterization of both V(IV) and V(V) complexes in solution. Other techniques include UV-Vis spectroscopy [41,44,46], circular dichroism [48] and neutron activation analysis [52-56]. 

Another important feature of Fig. 18.9 is that in a narrow pH range from 8 to 9, a rapid increase in complexed enzyme activity was observed, whereas the native enzyme activity gradually decreased. In order to understand such abnormal activity on the part of complexed BT, the potentiometric titration curve with NaOH for the acidic groups (COOH and phenolic OH) remaining in the complex was examined. As shown in Fig. 18.10, the titration curve is characterized by two inflection points. Analysis of the titration data using the same method as for evaluating the number of ionizable groups from the values shows that 12... 

In the practice of potentiometric titration there are two aspects to be dealt with first the shape of the titration curve, i.e., its qualitative aspect, and second the titration end-point, i.e., its quantitative aspect. In relation to these aspects, an answer should also be given to the questions of analogy and/or mutual differences between the potentiometric curves of the acid-base, precipitation, complex-formation and redox reactions during titration. Excellent guidance is given by the Nernst equation, while the acid-base titration may serve as a basic model. Further, for convenience we start from the following fairly approximate assumptions (1) as titrations usually take place in dilute (0.1 M) solutions we use ion concentrations in the Nernst equation, etc., instead of ion activities and (2) during titration the volume of the reaction solution is considered to remain constant. 

Among the possible analytical methods for alkalinity determination, Gran-type potentiometric titration [2] combined with a curve-fitting algorithm is considered a suitable method in seawaters because it does not require a priori knowledge of thermodynamic parameters such as activity coefficients and dissociation constants, which must be known when other analytical methods for alkalinity determination are applied [3-6],... 

For multistep complexation reactions and for ligands that are themselves weak acids, extremely involved calculations are necessary for the evaluation of the equilibrium expression from the individual species involved in the competing equilibria. These normally have to be solved by a graphical method or by computer techniques.26,27 Discussion of these calculations at this point is beyond the scope of this book. However, those who are interested will find adequate discussions in the many books on coordination chemistry, chelate chemistry, and the study and evaluation of the stability constants of complex ions.20,21,28-30 The general approach is the same as outlined here namely, that a titration curve is performed in which the concentration or activity of the substituent species is monitored by potentiometric measurement. 

Any titration involves the progressive change of the activities (or concentrations) of the titrated and titrating species and, in principle, can be done potentiometrically. However, for an accurate determination it is necessary that there is a fairly rapid variation in equilibrium potential in the region of the equivalence point. Useful applications are redox, complexation, precipitation, acid-base titrations, etc. From the titration curve it is possible to calculate values of the formal potentials of the titrated and titrating species, as explained below. 

By analogy to pH titration curves of acids and bases, it is customary in precipitation titrations to plot the quantity pM (defined by either — log [M " ] or — log a m ) against titration volume. For certain metals that form reversible electrodes with their ions, the measured electrode potential is a linear function of the logarithm of ion activity, so the titration curve can be realized experimentally in a potentiometric titration. In any case, the curve gives a useful indication of the sharpness of an endpoint break. 

The terms batch equilibration [653], pH drift method [654], addition method [552], solid addition method [655], powder addition method (cited in [656] after [654]), potentiometric titration [234] ( sic —in the present book, the term potentiometric titration is reserved for a different method, described in Section 2.5), and salt addition [573] ( sic —in the present book, the term salt addition is reserved for a different method, described later in this section) refer to the same method, which is now described. A series of solutions of different pHs is prepared and their pHs are recorded. Then, the powder is added and the final pH is recorded. The addition of a solid induces a shift in the pH in the direction of the PZC. The pH at which the addition of powder does not induce a pH shift is taken to be the PZC. Alternatively, the PZC is determined as the plateau in the pHfln, (pH ,.,., .j) curve. The method assumes that the powder is absolutely pure (free of acid, base, or any other surface-active substance), which is seldom the case. Even with very pure powders, the above method is not recommended for materials that have a PZC at a nearly neutral pH. Namely, the method requires accurate values of the initial pH, which is the pH of an unbuffered solution. The display of a pH meter in unbuffered solutions in the nearly neutral pH range is very unstable, and the readings are not particularly reliable. The problem with pH measurements of solutions is less significant at strongly acidic or strongly basic pHs (see Section 1.10.3). The above method (under different names) became quite popular, and the results are referred to as pH in the Method columns in the tables in Chapter 3. The experimental conditions in the above method (solid-to-liquid ratio, time of equilibration, and nature and concentration of electrolyte) can vary, but little attention has been paid to the possible effects of the experimental conditions on the apparent PZC. The plateau in the pH, , (pH, ,, ) curve for apatite shifted by 2 pH units as the solid-to-liquid ratio increased from 1 500 to 1 100 [653]. Thus, the apparent PZC is a function of the solid-to-liquid ratio. 

Chao and Cheng [76CHA/CHE] studied the determination of a number of anions, single or in mixtures, by a stepwise potentiometric titration with silver nitrate at pH = II. The silver ion activity was measured with a silver ion selective electrode based on silver sulphide. The data were also used to estimate the solubility products of the silver salts formed during a titration. The method is only sketched in the paper but appears to have proceeded along the following course. The potential of incipient precipitation ( prec) was estimated graphically from the shape of the titration curve. p,ec would thus be a measure of the silver ion activity at the nominal and known concentration of the anion in the presence of its silver salt. 

The experimental apparatus for a potentiometric titration can be quite simple only a pH or millivolt meter, a beaker and magnetic stirrer, reference and indicator electrodes, and a burette for titrant delivery are really needed for manual titrations and point-by-point plotting. Automatic titrators are available that can deliver the titrant at a constant rate or in small incremental steps and stop delivery at a preset endpoint. The instrument delivers titrant until the potential difierence between the reference and indicator electrodes reaches a value predetermined by the analyst to be at, or very near, the equivalence point of the reaction. Alternatively, titrant can be delivered beyond the endpoint and the entire titration curve traced. Another approach to automatic potentiometric titration is to measure the amount of titrant required to maintain the indicator electrode at a constant potential. The titration curve is then a plot of volume of standard titrant added versus time, and is very useful, for example, for kinetic studies. The most extensive use of this approach has been in the biochemical area with so-called pH-stats—a combination of pH meter, electrodes, and automatic titrating equipment designed to maintain a constant pH. Many enzymes consume or release protons during an enzymatic reaction therefore, a plot of the volume of standard base (or acid) required to maintain a constant pH is a measure of the enzyme activity, the amount of enzyme present. 

This approach will not be practical for some time to come. The fundamental properties of surfactants (micelle formation, enrichment at interfaces) mean that the activity of a surfactant will usually differ from its absolute concentration (1). Just as serious is the technical problem that current surfactant-selective electrodes suffer from response which varies with their past and recent history they are also sensitive to the concentration of nonsurfactant ions. The result is that quantitative applications use electrodes not in direct measurements relating potential to concentration, but as indicators of the end point of a titration. In this latter application, it is not important that the electrode potential be exactly reproducible, but only that the potential change sharply as the surfactant concentration changes. For the titration of an anionic surfactant with a cationic surfactant, the electrode used for end point detection can be chosen to respond to either surfactant. Because of the drift in electrode potential, titrations must be conducted to an inflection in the titration curve rather than to a specific millivolt value. Details of the potentiometric titration methods can be found earlier in this chapter. The electrodes have also been demonstrated as detectors for flow injection analysis. 

Experimental neutralization curves closely approximate the theoretical curves described in Chapters 14 and 15. Usually, the experimental curves are somewhat displaced from the theoretical curves along the pH axis because concentrations rather than activities are used in their derivation. This displacement has little effect on determining end points, and so potentiometric neutralization titrations are quite useful for analyzing mixtures of acids or polyprotic acids. The same is true of bases. 

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