Titration illustration

For the required limited dispersion in the above pH and pCa determinations, the analytical read-out had to be made within a residence time of only 5 s however, in the gradient flow injection titration illustrated in Fig. 5.16 and 5.17, and explained on pp. 331-332, the residence time increased from about 0.2 to 6 min (Fig. 5.17) or more. 

Figure 12-10 Three regions in an EDTA titration illustrated for reaction of 50.0 mL of 0.050 0 M with 0.050 0 M EDTA, assuming K, = 1.15 x 1016. The concentration of free Mn+ decreases as the titration proceeds.

Figure 11.5.2 Current-potential curves at a platinum electrode during titration of Fe " with Ce at different fractions titrated,/, illustrating the potential attained by this indicator electrode (v5. SCE) at (a) zero current ( ) (b) small applied cathodic current, ic (A) (c) small applied anodic current, ( ). (The magnitudes of the actual applied currents used in a titration would be much smaller than those shown here, which are exaggerated for clarity.)...

Figure 11.5.4 Current-potential curves at a platinum electrode during titration of Fe with Ce at different fractions titrated,/, illustrating the currents attained (d) for an indicator electrode at potential E ( ) ...

The use of Eriochrome Black T as an indicator in the Zn -EDTA titration illustrates a case in which the indicator metal-complex is so stable that the color change occurs after the equivalence point, (log P nin equivalence point). Since log znin changes more rapidly with pH than does pZn (Why ), it is possible to adjust the pH to reduce the difference between them to a reasonably small value. (Table 9.2). 

Figure V-8 illustrates that there can be a pH of zero potential interpreted as the point of zero charge at the shear plane this is called the isoelectric point (iep). Because of specific ion and Stem layer adsorption, the iep is not necessarily the point of zero surface charge (pzc) at the particle surface. An example of this occurs in a recent study of zircon (ZrSi04), where the pzc measured by titration of natural zircon is 5.9 0.1...

Figure Bl.22.1. Reflection-absorption IR spectra (RAIRS) from palladium flat surfaces in the presence of a 1 X 10 Torr 1 1 NO CO mixture at 200 K. Data are shown here for tluee different surfaces, namely, for Pd (100) (bottom) and Pd(l 11) (middle) single crystals and for palladium particles (about 500 A m diameter) deposited on a 100 A diick Si02 film grown on top of a Mo(l 10) single crystal. These experiments illustrate how RAIRS titration experiments can be used for the identification of specific surface sites in supported catalysts. On Pd(lOO) CO and NO each adsorbs on twofold sites, as indicated by their stretching bands at about 1970 and 1670 cm, respectively. On Pd(l 11), on the other hand, the main IR peaks are seen around 1745 for NO (on-top adsorption) and about 1915 for CO (tlueefold coordination). Using those two spectra as references, the data from the supported Pd system can be analysed to obtain estimates of the relative fractions of (100) and (111) planes exposed in the metal particles [26].

The Kad Fischer jack on the back of most pH meters, used to monitor Kad Fischer titrations, suppHes a constant regulated current to the cell, which can consist of two identical (platinum) working electrodes. The voltammograms shown in Figure 9 illustrate the essential features of this technique. The initial potential difference, AH, is small because both redox forms of the sample coexist to depolarize the electrodes. The sample corresponds to the wave on the right-hand (cathodic) side of each figure and is therefore easily oxidized. The titrant is represented by the wave on the left-hand (anodic) side and is therefore easily reduced. Halfway to the end point the potential difference,, remains small, but at the end point the potential difference,... 

There is also evidence for stable 3,4-adducts from the X-ray analysis of 2-amino-4-ethoxy-3,4-dihydropteridinium bromide, the nucleophilic addition product of 2-aminopteridine hydrobromide and ethanol (69JCS(B)489). The pH values obtained by potentiometric titration of (16) with acid and back-titration with alkali produces a hysteresis loop, indicating an equilibrium between various molecular species such as the anhydrous neutral form and the predominantly hydrated cation. Table 1 illustrates more aspects of this anomaly. 2-Aminop-teridine, paradoxically, is a stronger base than any of its methyl derivatives each dimethyl derivative is a weaker base than either of its parent monomethyl derivatives. Thus the base strengths decrease in the order in which they are expected to increase, with only the 2-amino-4,6,7-trimethylpteridine out of order, being more basic than the 4,7-dimethyl derivative. 

Titrimetric analysis is a classical method for generating concentration-time data, especially in second-order reactions. We illustrate with data on the acetylation of isopropanol (reactant B) by acetic anhydride (reactant A), catalyzed by A-methyl-imidazole. The kinetics were followed by hydrolyzing 5.0-ml samples at known times and titrating with standard base. A blank is carried out with the reagents but no alcohol. The reaction is... 

In Sections 10.11-10.16 it is shown how the change in pH during acid-base titrations may be calculated, and how the titration curves thus obtained can be used (a) to ascertain the most suitable indicator to be used in a given titration, and (b) to determine the titration error. Similar procedures may be carried out for oxidation-reduction titrations. Consider first a simple case which involves only change in ionic charge, and is theoretically independent of the hydrogen-ion concentration. A suitable example, for purposes of illustration, is the titration of 100 mL of 0.1M iron(II) with 0.1M cerium(IV) in the presence of dilute sulphuric acid ... 

Strong acid with a weak base. The titration of a strong acid with a moderately weak base (K sslO-5) may be illustrated by the neutralisation of dilute sulphuric acid by dilute ammonia solution [curves 1 and 3, Fig. 13.2(a)]. The first branch of the graph reflects the disappearance of the hydrogen ions during the neutralisation, but after the end point has been reached the graph becomes almost horizontal, since the excess aqueous ammonia is not appreciably ionised in the presence of ammonium sulphate. 

The principle of coulometric titration. This involves the generation of a titrant by electrolysis and may be illustrated by reference to the titration of iron(II) with electro-generated cerium(IV), A large excess of Ce(III) is added to the solution containing the Fe(II) ion in the presence of, say IM sulphuric acid. Consider what happens at a platinum anode when a solution containing Fe(II) ions alone is electrolysed at constant current. Initially the reaction... 

The procedure may be illustrated by the actual results obtained for the potentiometric titration of 25.0 mL of ca 0.1 M ammonium iron(II) sulphate with standard (0.1095M) cerium(IV) sulphate solution using platinum and saturated calomel electrodes ... 

It was pointed out in Section 6.5 on pH profiles that substrate titrations and certain steady-state mechanisms take the same algebraic form. This ambiguity also prevails when association equilibria can be established. This is illustrated by the reaction17... 

Now consider the overall shape of the pH curve. The slow change in pH about halfway to the stoichiometric point indicates that the solution acts as a buffer in that region (see Fig. 11.3). At the halfwayr point of the titration, [HA] = [A ] and pH = pfCa. In fact, one way to prepare a buffer is to neutralize half the amount of weak acid present with strong base. The flatness of the curve near pH = pKa illustrates very clearly the ability of a buffer solution to stabilize the pH of the solution. Moreover, we can now see how to determine pKa plot the pH curve during a titration, identify the pH halfway to the stoichiometric point, and set pKa equal to that pH (Fig. 11.8). To obtain the pfCh of a weak base, we find pK3 in the same way but go on to use pKa -1- pfq, = pKw. The values recorded in Tables 10.1 and 10.2 were obtained in this way. 

One major drawback of end group analysis is that it rapidly becomes inaccurate as relative molar mass increases. This arises because the percentage of the end groups becomes smaller and smaller, and hence more and more uncertainty attaches to the numerical values of end group content that may be obtained. To illustrate this point, let us consider a polyester with acid end groups being determined by titration. Results for such titrations are shown in Table 6.5. 

In one type of titration, a solution of a strong base such as sodium hydroxide is added slowly to a solution that contains an unknown amount of an acid. Each hydroxide ion added to the acid solution accepts one proton from a molecule of acid. As the titration proceeds, fewer and fewer acid molecules remain in the acid solution, but the solution is still acidic. At the stoichiometric point, just enough hydroxide ions have been added to react with every acidic proton present in the acid solution before the titration was started. The hydroxide ions in the next drop of titrant do not react because acid molecules are no longer present in the solution. Before the stoichiometric point, the solution contains excess acid. After the stoichiometric point, the solution contains excess OH". Figure 4-11 shows a titration setup and molecular views illustrating titration of a strong acid by a strong base. 

Example illustrates that the pH at the stoichiometric point in a titration of a weak acid differs from 7.0. 

The effect of the nature of the divalent cation is very pronounced as illustrated in Figure 2 on sample A30. Pectins were found to be much more sensitive to copper than to calcium. A scale of affinity towards divalent cations can be easily obtained this way [18]. This result corroborates what has been measured by pH titration upon addition of increasing amount of cations [28,29], where the order of decreasing selectivity was Pb = Cu Zn > Cd = Ni > Ca. This scale does not follow the size of the radius of the cations but is in agreement with the sequence of complex stability of Irving-Williams [30]. 

In Fig. 2.6, curve I illustrates the displacement titration of CH3COONa with HC1 according to... 

Case C, the titration of a weak acid with a weak base and vice versa, has in fact already been illustrated in Fig. 2.18 by the curves BB and B B are fully valid and for characteristic (3) the initial point is still dependent on the original concentration c however for the further main part of the curve we see a clean symmetry versus the equivalence point, which has become a true inflection point, independent of the concentration and simply determined by the mean value of pKg and pKb, i.e., (p/ia + pKh)/2 or (pifa + pifw - pKa.)/2. It also means that in the simultaneous titration of a polyvalent acid or a series of weak acids of different strength with a strong base and vice versa, (1) the stronger the acid the earlier it is titrated within the series, (2) the initial point and the final end-point of the series are still influenced by the concentration, but (3) the intermediate steps are only determined at the pH of the inflection point by the mean value of the pifas of the subsequent acids and in its steepness by the difference between these pKgs. Therefore, consultation of pKa tables provides the most suitable way of predicting the results of such simultaneous titrations. 

The titration course can be illustrated (see Fig. 2.20) by a pAg curve whose values are obtained from the silver potential EAg = E g + RT/Fln aAg+ or at 25° C EAg = EAg - 0.05916 pAg. As AgN03 as a salt is fully dissociated into ions, the initial point of the curve is determined by the original concentration the later part of the curve up to the titration end-point can be obtained in the same way because the Ag+ concentration undergoes a simple reduction as a consequence of the withdrawal of Ag+ into the AgCl precipitate. At the... 

Most successful is a rotating Pt wire microelectrode as illustrated in Fig. 3.75 as a consequence of the rotation, which should be of a constant speed, the steady state is quickly attained and the diffusion layer thickness appreciably reduced, thus raising the limiting current (proportional to the rotation speed to the 1/3 power above 200 rpm140 and 15-20-fold in comparison with a dme) and as a result considerably improving the sensitivity of the amperometric- titration. 

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. 

Fig. 4.7 shows the titration with perchloric acid of a mixture of piperidine, ethylenediamine and p-toluidine. Fig. 4.8 illustrates the effect of different chain lengths on the titration (with perchloric acid) of diamines in nitrobenzene containing 2.5% (v/v) of methanol once the first amino group of EDA has been protonated, the resulting proton bridge with the lone pair of electrons of the second amino group lowers the basicity of the latter considerably the effect decreases on the introduction of more intermediate CH2 groups until complete disappearance when six are present. 

Mixtures of solvents. Figs. 4.3, 4.4, 4.8, 4.10 and 4.11 have already illustrated that the use of mixed solvents may sometimes have a beneficial effect on the titration result some further practical examples are worth mentioning. 

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