Titration Curves, Types

In the overview to this chapter we noted that the experimentally determined end point should coincide with the titration s equivalence point. For an acid-base titration, the equivalence point is characterized by a pH level that is a function of the acid-base strengths and concentrations of the analyte and titrant. The pH at the end point, however, may or may not correspond to the pH at the equivalence point. To understand the relationship between end points and equivalence points we must know how the pH changes during a titration. In this section we will learn how to construct titration curves for several important types of acid-base titrations. Our... 

It was noted that the content of functional groups on the surface of studied A1,03 was 0,92-10 mol/g of acid character for (I), FOS-IO mol/g of basic character for (II). The total content of the groups of both types was 1,70-lO mol/g for (III). The absence of appreciable point deviations from a flat area of titration curves in all cases proves simultaneously charges neutralization character on the same adsoi ption centers and non-depending on their density. The isoelectric points of oxide surfaces have been detenuined from titration curves and have been confirmed by drift method. 

The various relationships concerning the interconversion between un-ionised and ionised or different resonant forms of indicators referred to in Section 10.7 apply equally well to those indicators used for non-aqueous titrations. However, in this type of titration the colour change exhibited by an indicator at the end point is not always the same for different titrations as it depends upon the nature of the titrand to which it has been added. The colour corresponding to the correct end point may be established by carrying out a potentiometric titration while simultaneously observing the colour change of the indicator. The appropriate colour corresponds to the inflexion point of the titration curve (see Section 15.18). 

To measure the e.m.f. the electrode system must be connected to a potentiometer or to an electronic voltmeter if the indicator electrode is a membrane electrode (e.g. a glass electrode), then a simple potentiometer is unsuitable and either a pH meter or a selective-ion meter must be employed the meter readings may give directly the varying pH (or pM) values as titration proceeds, or the meter may be used in the millivoltmeter mode, so that e.m.f. values are recorded. Used as a millivoltmeter, such meters can be used with almost any electrode assembly to record the results of many different types of potentiometric titrations, and in many cases the instruments have provision for connection to a recorder so that a continuous record of the titration results can be obtained, i.e. a titration curve is produced. 

Figure 2-4. Titration curve for an acid of the type HA. The heavy dot in the center of the curve indicates the p/fg 5.0.

Final remarks on end-point detection. In addition to our remarks above on the types of titration curves and the Henderson equation or more extended relationships, we can state that in Gran s method activity coefficients are taken into account however, these were assumed to be constant, which is incorrect, and therefore the addition of an ISA (ion strength adjuster) must be recommended (for errors of the Gran method see ref.66). 

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... 

Figure 12 [115] shows a series of complex formation titration curves, each of which represents a metal ion-ligand reaction that has an overall equilibrium constant of 1020. Curve A is associated with a reaction in which Mz+ with a coordination number of 4 reacts with a tetradentate ligand to form an ML type complex. Curve B relates to a reaction in which Mz+ reacts with bidentate ligands in two steps, first to give ML complexes, and finally close to 100% ML2 complexes in the final stages of the titration. The formation constant for the first step is 1012, and for the second 108. Curve C refers to a unidentate ligand that forms a series of complexes, ML, ML2. .. as the titration proceeds, until ultimately virtually 100% of Mz+ is in the ML4 complex form. The successive formation constants are 108 for ML, 106 for ML2, 104 for ML3, and 102 for ML4 complexes. 

To obtain information on the coupling of the various intermediates one has to analyze the relationship between the corresponding titration curves. Scheme 3.4-3 shows typical steady-state curves for the (1) stepwise twofold association of ligand L with metal complex M, (2) association of L with two metal complexes M and N at equilibrium and (3) association of L to two metal complexes M and N being not at equilibrium (kinetically separated). From these three types of coupling most of the partial maps can be easily interpreted. 

In [LJ-control maps the substitution of one ligand by another one results in a change of the range of existence of the manifold intermediates. This change can be expressed by the ligand-property imluced shift of the titration curves identified by the relative position of their inflection points Lq s on the log (lL o/[Ni)Q) scale. These characteristic shifts provide information on the thermodynamic selectivity governed by the association processes only. This type of analysis is designated by . 

Recently, Ta2Os- and Si3N4-type pH-ISFETs have been used in non-aqueous systems, by preparing them to be solvent-resistant [17]. In various polar non-aqueous solvents, they responded with Nernstian or near-Nernstian slopes and much faster than the glass electrode. The titration curves in Fig. 6.5 demonstrate the fast (almost instantaneous) response of the Si3N4-ISFET and the slow response of the glass electrode. Some applications of pH-ISFETs are discussed in Section 6.3.1. 

The pH window is very wide in solvents that are weak both in acidity and basicity. The widths of the pH window are well over 30 in such solvents, compared to about 14 in water (Table 6.6). The usefulness of these expanded pH regions is discussed in Section 3.2.2. In particular, potentiometric acid-base titrations in such solvents are highly useful in practical chemical analyses as well as physicochemical studies [22]. Acid-base titrations in lion-aqueous solvents were popular until the 1980s, but now most have been replaced by chromatographic methods. However, the pH-ISFETs are promising to realize simple, rapid and miniature-scale acid-base titrations in lion-aqueous solvents. For example, by use of an Si3N4-type pH-ISFET, we can get an almost complete titration curve in less than 20 s in a solution containing several different acids [17d]. 

For each type of titration in this chapter, our goal is to construct a graph showing how the pH changes as titrant is added. If you can do this, then you understand what is happening during the titration, and you will be able to interpret an experimental titration curve. 

Every titration curve involves the same four categories, but exactly which of the nine types of calculation you use will depend on whether (a) the acid is added to the base, or vice versa (b) the acid is strong or weak and (c) the base is strong or weak. 

Some method of signaling is required to indicate when the amount of titrant generated is equivalent to the amount of unknown present, and all of the endpoint detection methods used in volumetric titrimetry are, in principle, applicable to coulometric titrations. A list that covers most of the published coulo-metric titration procedures is given in Table 25.2. It is beyond our scope here to describe any of these in detail because each of these methods is a subject for discussion in its own right. Discussions of the equations for a number of types of titration curves are found in texts by Lingane [15], Butler [16], and Laitinen and Harris [17]. 

We can calculate pH titration curves using the principles of aqueous solution equilibria. To understand why titration curves have certain characteristic shapes, let s calculate these curves for four important types of titration (1) strong acid-strong base, (2) weak acid-strong base, (3) weak base-strong acid, and (4) polyprotic acid-strong base. For convenience, we ll express amounts of solute in millimoles (mmol) and solution volumes in milliliters (mL). Molar concentration can thus be expressed in mmol/mL, a unit that is equivalent to mol/L ... 

The pH at the half-way point on full titration curves of the Fig. 3 type, or on the similar curves approaching the plateau in Fig. 8, gives a simple indication of the p-K Sj) in favourable cases. For compounds of either Case I or Case II type, the pH at the half-way point is log o [k2T 0/(l + 6iT0)], which is only the same as p.K(Si) if t 0 = t0 and k1T0 1. Apart from the complication of the lifetime ratio, the half-way point on an emission titration curve can only be expected to correspond to the excited state pK-value if equilibrium is achieved in the protolytic reaction i.e. k1 and k2 must be large compared with the rates of the decay processes, which sum to 1/t0 and 1/tq respectively, whence r0 > 1 and k 2T 0 > 1. [The 1 in the denominator, or numerator, of equations like (25), (26), (27), or (29) always takes care of the extent to which failure to achieve equilibrium is important.]... 

Linear titration curve — A type of -> titration curve in which a variable that is directly proportional to the concentration of the titrand and/or -> titrant, and/or a product of their chemical reaction is plotted as a function of the volume of titrant added. Thus, a linear titration curve generally consists of two linear segments that have to be extrapolated to intersect at a point that is associated with the equivalence point. The measurements are performed below and above the zone of the equivalence point and preferably away from this last point where nonlinear behavior is commonly found [i]. Linear titration curves are typical for - amperometric titrations, and - conductometric titrations, whereas - poten-tiometrc titrations yield nonlinear curves (- logarithmic titration curve). 

Titration curve — A plot of a variable or function, usually linearly or logarithmically related to the concentration (- activity) of the analyte, versus the volume of - titrant added or the degree of titration. Two kinds of titration curves are commonly found, the first type is called -> linear titration curve while the second one is denominated logarithmic titration curve. These curves are helpful in judging the feasibility of a - titration and in selecting the proper indicator [i]. 

Potentiometric titration denotes a change in the pH of any given clay or soil suspension as a function of base or acid added. Generally, three types of potentiometric titration curves are produced (Fig, 3.36). The first type, represented by Figure 3.36a, shows a common crossover point for all three potentiometric curves, representing three different concentrations of an indifferent electrolyte (i.e, NaN03). The crossover point of the titrations is known as the point of zero salt effect (PZSE). The intercept of the dotted line with the titration lines is known as the pH of zero titration (PZT). For a pure oxide,... 

The second type of potentiometric titration curves are shown in Figures 3.36b and c. Figure 3.36b shows that the crossover point of the same colloid system as in Figure... 

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