Titration curves defined

Paramount to the experimental setup is the purpose of the calorimetric titration that is, whether the association constant and stoichiometry along with the standard enthalpy are to be determined or only the latter is the final goal. Such decision dictates the selection of the dimensionless c-value (7), which should lie within a span from 5 to 500 in order to render the titration curve sigmoidal. In this case, the step height between the asymptotic values at 0 and CX3 with respect to the molar ratio axis is read from a nonlinear least-square fit of the experimental data points and represents the standard enthalpy A 77°. The position of the inflection point in the sigmoidal titration curve defines the association stoichiometry, whereas the slope of the curve at this point translates as the association constant, which can be converted into the free energy AG° (1). 

Derivative methods are particularly well suited for locating end points in multi-protic and multicomponent systems, in which the use of separate visual indicators for each end point is impractical. The precision with which the end point may be located also makes derivative methods attractive for the analysis of samples with poorly defined normal titration curves. 

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... 

When the titration curve is symmetrical about the equivalence point the end point, defined by the maximum value of AE/AV, is identical with the true stoichiometrical equivalence point. A symmetrical titration curve is obtained when the indicator electrode is reversible and when in the titration reaction one mole or ion of the titrant reagent reacts with one mole or ion of the substance titrated. Asymmetrical titration curves result when the number of molecules or ions of the reagent and the substance titrated are unequal in the titration reaction, e.g. in the reaction... 

When plotted on a graph of pH vs. volume of NaOH solution, these six points reveal the gross features of the titration curve. Adding additional calculated points helps define the pH curve. On the curve shown here, the red points A-D were calculated using the buffer equation with base/acid ratios of 1/3 and 3/1. Point E was generated from excess hydroxide ion concentration, 2.00 mL beyond the second stoichiometric point. You should verify these additional five calculations. 

In the process of a weak acid or weak base neutralization titration, a mixture of a conjugate acid-base pair exists in the reaction flask in the time period of the experiment leading up to the inflection point. For example, during the titration of acetic acid with sodium hydroxide, a mixture of acetic acid and acetate ion exists in the reaction flask prior to the inflection point. In that portion of the titration curve, the pH of the solution does not change appreciably, even upon the addition of more sodium hydroxide. Thus this solution is a buffer solution, as we defined it at the beginning of this section. 

Table 5.1 gives commonly used examples of conjugate acid-base pair combinations and the pH range for which each is useful. This range corresponds to the pH range defined by the buffer region in the titration curve for each, and the middle of the range corresponds to the midpoint of each titration. 

Define monoprotic acid, polyprotic acid, monobasic base, polybasic base, titration curve, and inflection point. 

It is possible to compare the strengths of weak acids by the values of their acid dissociation constants Ka. Figure 3.1 shows the titration curves for acids (HA or BH+) of different Ka values. The ordinate shows poH, which is defined by paH = -loga(SI I)). paH corresponds to the pH in aqueous solutions (see Section 3.2). The poH of non-aqueous solutions can be measured with a glass pH electrode or some other pH sensors (see Sections 3.2.1 and 6.2). For the mixture of a weak acid A and its conjugate base B, poH can be expressed by the Henderson-Hassel-balch equation ... 

Two methods are commonly used to determine the endpoint of an acidity titration. The potentiometric method titrates to a predetermined pH and the colorimetric method uses an indicator that changes color at a particular pH to determine the endpoint. Other methods define the endpoint as the inflection of a titration curve, i.e., plots of pH value versus milliliter of NaOH used (Sadler and Murphy, 1998 Hand et al., 1993). However, the increased precision... 

Above pH 8 the titration curve shows uptake of a second equivalent of base corresponding to production of (en)Pd(OH)2. This second section of the titration curve is also flattened, owing to break up of oligomers by uptake of a second hydroxide at high pH. Though little reaction occurs directly by this route, we define the second acidity constant in the usual way. 

A typical thermometric enthalpy titration curve is shown in Figure 6. The well defined endpoint provided a convenient method for quantitating sulfidic sulfur. 

The typical plot of titration curves is presented in Fig. 6. By the comparison of H+ or OH- concentration changes, for defined volume of the acid or base, the surface charge can be calculated according to the equation ... 

The distinction between the isoelectric and isoionic states of a protein was first made in a classic paper by S0rensen et at. (1926). Three definitions of the isoionic point were proposed, one of these being the stoichiometrically defined point which we have called the point of zero net proton charge. The other tw o were operational definitions (summarized by Linderstr0m-Lang and Nielsen, 1959). The term isoionic point, as used here, corresponds to one of these two operational definitions, chosen because it always permits calculation of the point of zero net proton charge, which is the only parameter of real interest in the analysis of titration curves. The same choice has been made by Scatchard and Black (1949). 

To change the reference point of a titration curve from an arbitrary reference pH to one of the reference points just defined simply involves a... 

Earlier Johnson and Kahn (1959) had reported that the titration curve of paramyosin has a plateau between pH 3 and pH 5. They concluded that the carboxyl groups were titrated in two distinct steps, one near pH 6 and one below pH 3. This finding would have suggested highly unusual interactions within the molecule. Riddiford and Scheraga (1962) did not find such a plateau in their studies. However, the fact that the protein is in an insoluble state between pH 3.5 and 6.5 suggests that the differences between the two sets of results may depend upon the particular conditions of preparation and handling of the protein, in a manner not yet adequately defined. 

Four types of hydrous antimony oxide (antimonic acid), the amorphous (A-SbA), the glassy (G-SbA), the cubic (C-SbA), and the monoclinic (M-SbA) are known so far [138]. Both the A-SbA and G-SbA affect the selectivity sequence Li" < Na" < K" " < Rb+ < Cs", while the selectivity sequence of C-SbA is unusual with Li" " K+ < Cs < Rb" Na" " for micro amounts in acid media (Fig. 19). The degree of crystallinity of a-ZrP strongly influences its ion-exchange behavior as mentioned earlier. The pH versus base added plots for a-ZrP with different crystallinity are shown in Fig. 13. It is seen that each increase in acid concentration at a fixed reflux time is reflected in the shape of the curves. The titration curves with the most well-defined plateaus were obtained with the most highly crystalline samples [126]. 

Titration curves used in precipitation reactions usually use a concentration-dependent variable called the p function rather than the concentration itself The p function for a species X is defined as follows ... 

The autoprotolysis constant The extent of ionization (4-19) of a pure amphiprotic solvent is measured by the autoprotolysis constant SH> defined as the product Since the autoprotolysis reaction results in the formation of both solvent cations and solvent anions, the autoprotolysis constant is a measure of the differentiating ability of a solvent. If a solvent has a large Ash value, the existence in it of a wide range of strengths of either adds or bases is not possible. In contrast, if the autoprotolysis constant is small, adds and bases of varying strengths show titration curves distinctly different from each other. 

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. 

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